review article design, materials, and mechanobiology of...

Review ArticleDesign Materials and Mechanobiology of BiodegradableScaffolds for Bone Tissue Engineering

Marco A Velasco1 Carlos A Narvaacuteez-Tovar12 and Diego A Garzoacuten-Alvarado2

1Studies and Applications in Mechanical Engineering Research Group (GEAMEC) Universidad Santo Tomas Bogota Colombia2Biomimetics Laboratory and Numerical Methods and Modeling Research Group (GNUM) Instituto de Biotecnologıa (IBUN)Universidad Nacional de Colombia Bogota Colombia

Correspondence should be addressed to Marco A Velasco marcovelascousantotomaseduco

Received 4 November 2014 Accepted 27 January 2015

Academic Editor Xuejun Wen

Copyright copy 2015 Marco A Velasco et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A review about design manufacture and mechanobiology of biodegradable scaffolds for bone tissue engineering is givenFirst fundamental aspects about bone tissue engineering and considerations related to scaffold design are established Secondissues related to scaffold biomaterials and manufacturing processes are discussed Finally mechanobiology of bone tissue andcomputational models developed for simulating how bone healing occurs inside a scaffold are described

1 Introduction

Bones are rigid organs that consist of osseous tissue bonemarrow endosteum periosteum cartilage nerves and vas-cular channels constituting the skeleton of vertebrate animalsOsseous tissue which fulfills mechanical functions is formedby connective tissue cells such as osteocytes osteoblasts andosteoclasts [1 2] in an extracellular matrix composed mainlyof minerals proteins and water The bone composition andconfiguration will vary according to factors such as theanatomical location supported load age and gender of theindividual and the possible diseases that he or she couldsuffer [3 4] In regard to bone composition mineral phaseis between 60 and 70wt and water between 5 and 10wtwhile the remaining portion is an organic matrix of collagenand other proteins

The mineral phase of bone is essentially a calcium phos-phate called hydroxyapatite presented in the form ofnanocrystals with sizes between 25 and 50 nm in length [5]Variations in the chemical composition of hydroxyapatitemodify its physical properties specially its solubility [6] Onthe other hand its biochemical properties mainly dependon the organic phase of the extracellular matrix of boneApproximately 90 of the organic phase is formed by type I

collagenThe remainder consists of proteins lipids and othermacromolecules such as growth factors cytokines oste-onectin osteopontin osteocalcin osteoinductive proteinssialoproteins proteoglycans phosphoproteins and phospho-lipids [7ndash9] Mineral and organic phases determine themechanical properties of bone as a composite

According to its structure osseous tissue may be cancel-lous (trabecular) or cortical (lamellar) Cancellous bone is anetwork of interconnected porosities ranging between 50to 90 of void space with a solid portion which is formedof struts and plates that can adopt different configurations Itis located at the epiphysis of long bones and the interior ofcuboid bones Cortical tissue is located at the bone surfaceand it has a homogeneous and compact macrostructure It isfound mainly at the bone diaphysis and its thickness variesaccording to the bone anatomical location Cortical boneconsists of structural and functional units called osteons orHaversian systems Osteons are arranged along the boneInside the osteons there are small spaces or lacunae whereosteocytes are housed Osteons contains tiny channels orcanaliculi to provide nutrient and oxygen to the cells Alongthe center of the osteons there is a central channel with vesselsand nerves

Hindawi Publishing CorporationBioMed Research InternationalVolume 2015 Article ID 729076 21 pageshttpdxdoiorg1011552015729076

2 BioMed Research International

Table 1 Mechanical properties of bone From Bandyopadyay-Ghosh [39] and Knudson [40]

Property Cortical bone Cancellous boneTensile strength (MPa) 50ndash150 10ndash100Compressive strength (MPa) 130ndash230 2ndash12Youngrsquos modulus (GPa) 7ndash30 002ndash05Strain to failure () 1ndash3 5ndash7Shear strength (MPa) 53ndash70Shear modulus (GPa) 3

Bones have mechanical synthetic and metabolic func-tions The mechanical functions are protection of internalorgans body support and interaction with muscles and ten-dons to generate body movement [5] The synthetic functionis conducted by the bone marrow where both bone andblood cells are synthesized in a process called hematopoiesis[10] Metabolic functions are related to act as a reservoir ofcalcium phosphorus growth factors and fat [11] Besidesbone tissue helps to regulate pH level of blood releasingalkaline salts [12]

Referring to mechanical function bones are the struc-tural elements of the human body Skeletal system supportsloads due to the different activities of an individual as holdingthings walking pushing and so forth These loads inducetensile compressive or shear stresses on the bone tissueMore complex stresses such as those caused by bendingor twisting of bone can be decomposed into the threebasic aforementioned stresses To study these stresses bonemechanical properties such as elasticity modulus compres-sive and tensile strength are important These propertiesare highly dependent on the position of the bone and thecondition of the individual Besides mechanical propertiesof bone vary depending on the load orientation with respectto the orientation of the tissue (anisotropy) and the speed towhich the load is applied (viscoelasticity) [3 13] Reference[14] provides a good source of data andmodels of mechanicalproperties for different types of human bones Some impor-tant mechanical properties are described in Table 1

Another important physical property of osseous tissue ispermeability that describes the porosity and interconnectivityof tissue Permeability is estimated between 0003ndash11 times10minus6m4Nsdots for trabecular bone in humans and 09ndash78 times10minus11m4Nsdots in cortical bone for canine and bovine animals[15] A detailed explanation of permeability in bone can befound in [16 17]

Bone tissuemay suffer various diseases that can be causedby excessive load or hormonal deficiencies among otherreasons [18 19] Bone tissue as an engineering material canfail becausemechanical loads originate stresses over the limitsa healthy bone can bear or because themechanical propertiesof bone are decreased by various pathologiesmaking the boneweak and prone to be damaged Some of the diseases of bonetissue are as follows

(i) Fracture it is partial or total loss of bone continuity Itis caused by traumas by mechanical loads that exceedthe allowable stresses of the bone There may be

associated factors to the extent that allowable stressesare conditioned by other diseases that affect bonedensity They can be classified considering the type oftrauma fracture shape and the location and directionof the load [20]

(ii) Osteogenesis imperfecta it is bone embrittlement dueto deficiencies in the collagen matrix [21]

(iii) Osteoporosis it is loss of bone minerals by hormonaldeficiencies [22]

(iv) Osteomalacia or rickets it is loss of bone mineralcaused by nutritional deficiencies [23]

(v) Osteomyelitis it is bone infection caused by bacteria[24 25]

(vi) Cancer primary ormetastatic type causes progressivedamage of bone tissue and its functions [26]

Asmentioned above those diseases affectmultiple demo-graphic groups according their socioeconomic conditionsFor example in developed countries the life expectancy ofthe population has increased considerably causing a rise inosteoporosis cases [27]

2 Bone Tissue Engineering

Tissue engineering combines the use of cells engineeringmaterials and physicochemical factors to improve or replacethe biological functions of damaged tissues or organs Ituses the principles and methods of engineering biology andbiochemistry for understanding the structure and function ofnormal and pathological mammalian tissues and for devel-oping biological substitutes in order to restore maintain orimprove its function [28] A wide area of interest for tissueengineering is the development of scaffolds that contributeto bone regeneration processes [29] This development couldfollow some or all of the stages listed below [30]

(1) scaffold fabrication(2) growth factor placement in the scaffold or damaged

area(3) seeding of an osteoblast population into the scaffold

in a static culture (petri dish)(4) growth of premature tissue in a dynamic environment

(spinner flask)(5) growth of mature tissue in a physiologic environment

(bioreactor)(6) surgical transplantation of the scaffold(7) tissue-engineered transplant assimilationremodel-

ing

The number and the way that previous stages are com-bined give complexity to the bone regeneration processesin tissue engineering For scaffold fabrication factors likesize mass porosity surfacevolume ratio form surfaceshape and chemistry of the element to be manufacturedand composition structure molecular weight andmolecularorientation of the biomaterial must be considered For stages

BioMed Research International 3

that occur in in vitro environments variables like culturemedium pH fluid flow mechanical stimuli temperatureorigin of cells number of cells mobility of the cells and cellactivity affect the growth of new tissue Finally defect sitespecies gender age inflammatory process immunologicalprocess mechanical stimuli biochemical stimuli enzymesand vascularization determine the bone regeneration pro-cesses in in vitro environments [15]

21 Socioeconomic Considerations In 2007 it was calculatedthat the whole area of tissue engineering consists of 50companies employing 3000 equivalent full-time positions[31] In 2010 the number of companies related to regenerativemedicines was increased significantly to 391 but only asmall portion of these has a commercial product [32] About500000 bone grafts are performed each year in the UnitedStates [33] This quantity is close to the estimation thatbetween 5 and 10 of the 6 million fractures that occurredin North America present delays or consolidation problemsin the healing process [34]

Scaffolds implants biomaterials cell based therapiesand growth factors are usually considered as bone graftssubstitutes in bone tissue engineering Diverse analyses showdifferent market sizes and their growth rates depending ofwhat it is denominated as bone graft substitute the globalbone graft substitute market was valued at $19 billion in 2010and it is forecast to reach $33 billion in 2017 [35] Anothersource states that the market for orthopedic biomaterialsin the United States was almost $34 billion in 2012 [36]Another study affirms that 1 g of bone graft substitute costsapproximately 100 USD and the volume of materials isestimated close to 10 tons per year in 2010 [37]The Europeanmarket for bone graft substitute products for spinal fusionwas valued at USD 177 million in 2010 and its growth rateis projected close to 17 per year reaching an estimatedvalue of $461 million in 2016 [38] The global bone graftsubstitute market consists of eight different segments [36]orthopedic bone graft substitute growth factors stem cellscell therapies orthopedic hyaluronic acid viscosupplementa-tion orthopedic tendon graft orthopedic cartilage repair andspinal machined bone allograft Growth factors represent thelargest segment close to 40 of the market The segmentsrelated to synthetic materials represent only about 15 of themarket but their growth rate is the largest (close to 15 peryear) [37]

The cost of replacing organs was estimated in 8 ofthe worldwide cost of health in 2009 [41] The high cost oftissue engineering is associated not only with research anddevelopment but also with the regulations governing humanhealthcare products [42] Besides some reasons for the sizeand growth rates of the bone tissue engineering marketsare an aging but more active population the increase ofoverweight issues in population the increased interest ofindividuals in their own healthcare the improvement ofpublic health systems around the world and the developmentof orthopedic procedures for people of all ages [43]

22 Growth Factors Growth factors are substances likecytokines or hormones which act as biochemical signals

capable of triggering cellular processes like growth prolifer-ation or differentiation among others The most consideredgrowth factors in bone tissue engineering are listed below

(i) Bone morphogenetic proteins (BMPs) BMPs are afamily of cytokines that stimulates the proliferationof chondrocytes and osteoblasts and increases extra-cellular matrix production BMPs induce the differ-entiation of mesenchymal stem cells into osteoblastsBMPs allow not only skeletal tissue formation duringembryogenesis growth and adulthood but also bonehealing process In newbornsrsquo skeletons BMPs can befound in the collagen fibers of the bone matrix andalso in cells located in the periosteum and the bonemarrow After a fracture BMPs growth factors diffusefrom bone matrix and activate osteoprogenitor cellswhich in turn produce more BMPs [44] The BMP2 BMP 4 and BMP 7 are the only growth factors thatcan singly provoke bone formation in in vitro culturesand at in vivo heterotopic sites BMPs 1ndash3 increasethe production of collagen type I and osteocalcinin in vitro osteoblasts like cells and improve theformation of mineralized bone nodules from bonemarrow mesenchymal stem cells [45] BMPs are themost representative bone graft substitute of growthfactors segment due to their therapeutic possibilities[31 41 46] Studies of the combined application ofBMPs and porous scaffolds indicate that these growthfactors promote growth of new bone tissue insidethese structures [47ndash51]

(ii) Fibroblast growth factors (FGFs) FGFs stimulatethe proliferation of mesenchymal cells osteoblastsand chondrocytes FGFs enhance growth of differenttissues due to their angiogenic properties FGF-2 orbFGF is the most studied cytokine of this family forbone regeneration applications [51 52]

(iii) Insulin-like growth factors (IGFs) IGFs promote theproliferation of osteoblasts and chondrocytes andinduce matrix secretion from both cell types [51]IGFs stimulate collagen synthesis and mineralizationof bone tissue [53]

(iv) Platelet-derived growth factors (PDGFs) PDGFsincrease the proliferation of chondrocytes and oste-oblasts However depending on their concentrationslevels they have also been implicated in bone resorp-tion [51] PDGFs act as chemotactic and mitogenicfactor for osteoblasts and other cells [54]

(v) Transforming growth factors-120573 (TGFs-120573) TGFs-120573cause the differentiation of mesenchymal cells intochondrocytes and may also induce chondrocyte andosteoblast proliferation [55] Like PDGFs they havebeen seen to increase bone resorption at certain con-centrations playing a role in coupling bone formationand resorption activities [51]

23 Scaffolds Scaffolds are fundamental devices for theregeneration of lost or damaged tissues and they have becomean important tool in tissue engineering [56]Their functions


from themechanical point of view consist of bearing externalloads and giving shape to the tissue that is regeneratedon it [57ndash59] From the biological point of view thosestructures support the development of extracellular matrixand cell colonization In addition scaffolds should allowtransit of nutrient substances from the surrounding tissueor the culture media and waste disposal coming from thetissue being formed Therefore scaffold stiffness mechanicalresistance and permeability are important properties Anadditional scaffoldsrsquo desirable feature may be a controlleddegradation after they are implanted in order to get void spacewhere new tissue can grow

The mechanical properties and degradation of the scaf-fold depend on the material properties and the porositygeometry of its structure meanwhile permeability dependson its structure The mechanical properties of the scaffoldmust be similar to the properties of the replaced bone tissuein order to prevent stress shielding Finally the degradationrate must be as close as possible to the tissue growth rate tomaintain stable properties in the tissue-scaffold compoundduring the regeneration process

231 Design Considerations A bioactive scaffold reacts in acontrolled manner with its environment in order to stim-ulate specific biological responses where it is placed Thedevelopment of scaffolds to promote cellular growth insidethem has been one of the fundamental goals of bone tissueengineering [30 60 61]The biomechanical processes of boneregeneration are complex so the requirements for scaffolddesign are diverse [12 62ndash68] Some of the most importantdesign considerations are listed below

(i) Biofunctionality it is ability of the scaffold tomeet thefunctional requirements for which it was designedrestoring the functions of the replaced tissue

(ii) Biocompatibility it is ability to support normal cel-lular activity including molecular signaling systemswithout eliciting or evoking local or systemic adverseeffects to the host Among the undesirable effects thatmust be eliminated minimized or controlled uponscaffold implantation in the body are cytotoxicitygenotoxicity immunogenicity mutagenicity throm-bogenicity and swelling For example inflammationshould be avoided because it can decrease the regen-eration rate and promote tissue rejection

(iii) Bioresorbability or biodegradability it is ability todegrade with time in in vitro or in vivo environmentspreferably at a controlled resorption rate in order tocreate space for new tissue to grow In other words itis expected that as long as cells proliferate void spacein the scaffold increases and degradation rate of thematerial should match growth rate due to healing orregeneration process It is related with biocompatibil-ity because degradation products should be nontoxicand must be able to get metabolized and eliminatedfrom the body For example the degradation behaviorof the scaffolds should vary based on applicationssuch as 9months ormore for scaffolds in spinal fusion

or 3ndash6 months for scaffolds in craniomaxillofacialapplications [69]

(iv) Mechanical properties mechanical properties such aselastic modulus tensile strength fracture toughnessfatigue and elongation percentage should be as closeas possible to the replaced tissue (mechanical com-patibility) in order to prevent bone loss osteopeniaor ldquostress shieldingrdquo effect associated with the useof bone grafts They are related to bioresorbabilitybecause the variation in mechanical properties dueto degradation process should be compatible withbone regeneration process A scaffold must haveenough mechanical strength to retain its structure inorder to comply with its mechanical function after itsimplantation in the case of hard load-bearing tissuesas bone The large variation in mechanical propertiesas seen in Table 1 makes it difficult to design an ldquoidealbone scaffoldrdquo

(v) Pore size and porosity a three-dimensional designaffects the spatial distribution and location of cellsnutrients and oxygen thus affecting the viability ofthe new formed tissue Porous scaffolds facilitate themigration and proliferation of cells providing anappropriate microenvironment for cell proliferationand differentiation and allowing the mass transferof nutrients oxygen and waste metabolic productswithin the structure Scaffolds should have a largeinternal surface area due to overall porosity and poresize The surface to volume ratio of porous scaffoldsdepends on the size of the pores A large surface areaallows cell adhesion and proliferation whereas a largepore volume is required to contain and later deliver acell population sufficient for healing or regenerationprocess Mass transfer and cell migration will beinhibited if pores are not connected even if the overallporosity is high Unfortunately an increase in poros-ity causes a decrease of mechanical properties such ascompressive strength and increases the complexity forscaffold manufacturing On the other hand osseoustissues typically have arranged on curved surfacestherefore tomimic this biomorphic pattern pores areintended to have curved cross sections [12]

Comprehensive lists of terms related to tissue engineeringand biomaterial are available in [70 71] With regard to bonescaffolds there are some specific features like the following

(i) Osteoconductivity it is ability to allow the bone cellsto adhere proliferate and form extracellular matrixon its surface and pores [69] This property is relatedto the biodegradability because the scaffold materialmust be reabsorbed to make space for the maturetissue that it initially helped to support Besidesscaffolds act as amold of the desired anatomical form

(ii) Osteoinductivity it is ability to induce new bone for-mation through biomolecular or mechanical stimulirecruiting progenitor cells and allowing differentia-tion in a controlled phenotype or particular lineages[72]


(iii) Osteogenicity it is ability to act as osteoblasts or mes-enchymal cells (capable of deriving in an osteoblasticlineage) reservoir because these cells can form andmineralize the extracellular matrix of new osseoustissue

(iv) Osteointegrity it is ability to form strong bonds withsurrounding osseous tissue allowing material conti-nuity and proper transfer load

Finally additional functions for bone scaffolds could beas follows [73ndash75]

(i) acting as carrier of drugs (ie antibiotics andor anti-inflammatories) growth factors or cultured cells

(ii) radiolucency ability to differentiate radiographicallywith respect to the tissue where it was implanted

(iii) formability ability to be shaped by a manufacturingprocess in order to obtain the necessary internal andexternal geometry

(iv) sterilizability ability to ride out and facilitate a pro-cess of microbial destruction after being manufac-tured and before being used

(v) stability on storage (shelf life) ability to preservethe physical chemical and dimensional propertieswithin the estimated storage period between manu-facture and its use

The conflicting nature of the above desired characteristicswas described byKarageorgiou andKaplan [76]who reportedthat higher porosities induce greater bone ingrowth butlower mechanical stiffness and strength Therefore scaffoldporosity must lie within a critical range small enough tomaintain the mechanical integrity of the scaffold and largeenough to provide optimal bioactivity [63]

232 Design Scales The design and fabrication of scaffoldsfor bone regeneration applications attempt to obtain andcontrol architecture at different levels due to external formand internal structure tomeet the clinical requirements spec-ified in the previous section The architecture has differentproperties and characteristics depending on the dimensionsof an element of the scaffold Three basic scales refer todifferent features and processes

The macro-mesoscale describes the geometry measuredin millimeters Among its features are the following [77ndash82]

(i) scaffold external shape (appropriated to the site whereit will be implanted)

(ii) mechanical properties(iii) density(iv) porosity as a percentage of volume of the scaffold is

empty

Themicroscale describes features in the order ofmicrom-eters as

(i) pore size(ii) interconnectivity of pores and tortuosity(iii) degradability

The features in nanometers include factors such as(i) surface topology of the pores(ii) surface physical chemistry

233 Porosity Design Pore size and porosity are impor-tant geometric properties in scaffolds for bone regenerationbecause they affect the phenotype and the amount of tissuesthat grow on the construct As mentioned before inter-connected pores are necessary for bone tissue regenerationbecause they allow migration and proliferation of osteoblastsandmesenchymal cells besides vascularization It is observedthat even a biomaterial like hydroxyapatite must have aporous structure in order to promote bone growth in vivo[83] or a high porosity to allow cell seeding in vitro [84]Scaffolds implanted in vivo with pore sizes close to 100120583mallow chondrogenesis but scaffoldswith pores close to 350120583mpromote osteogenesis [85] Although intensive research hasbeen developed in both experimental and computationalmodeling there are no final conclusions about the optimalporosity and pore size of a scaffold for bone regenerationFor example the porosity range is between 50 and 90 forscaffolds that are not subjected to mechanical loads [86]meanwhile the recommended size of the pores varies between150 and 600120583m [87] from 400 to 1200120583m [88] and 350 120583mor above [76] The variety of conclusions may be due to thecomplexity of the process of bone regeneration which ismultivariable and multiobjective [89]

Considering this and the emergence of solid-free formmanufacturing methods to fabricate scaffolds [90] that allowcontrolling geometry characteristics better than other con-ventional methods like salt leaching there is an increasinginterest in porosity design Giannitelli et al showed an exten-sive review of the design techniques used to create porousstructures in the scaffolds noting that these geometries canbe obtained in three ways [67] periodic structures non-periodic structures and optimization techniques Periodicporous structures can be based on CAD systems for solidand surface modeling such as constructive solid geometry(CSG) using primitives like cubes cylinders and spheresto represent the pores [91ndash97] and boundary representation(B-Rep) supported on facets and vertices [98] In the lastyears there is research about the use of implicit surfaces liketriply periodic minimal surfaces [99ndash104] and space-fillingcurves like Hilbert curves [105] Meanwhile nonperiodicstructures have been developed based on image of bonesurfaces [77] trabecular bone portions [106 107] or scaffolds[108] and stochastic methods and Voronoi diagrams [109]The disadvantage of periodic and nonperiodic structures isthe necessity of trial and error methods to determine if theyare suitable for a particular purpose [110 111] In contrastoptimization methods [112] using finite element methodsobtaining porous structures considering different objectivesas mechanical properties and permeability [59 60 113ndash115]

3 Biomaterials for Bone Tissue Engineering

A number of definitions have been developed for theterm ldquobiomaterialsrdquo One definition is ldquomaterial exploited in


contact with living tissues organisms or microorganismsrdquo[71] Another definition is as follows ldquoa biomaterial is asubstance that has been engineered to take a form whichalone or as part of a complex system is used to direct bycontrol of interactions with components of living systemsthe course of any therapeutic or diagnostic procedure inhuman or veterinarymedicinerdquo [116] In general biomaterialsare intended to interface with biological systems to evaluatetreat augment or replace any tissue organ or function of thebody and are now used in a number of different applicationsthroughout the body The major difference of biomaterialsfrom other classes of materials is their ability to remain in abiological environment without damaging the surroundingsand without being damaged in that process

Naturally derived materials ceramics polymers andcomposites can be used as biomaterials Natural biomaterialscan be the bone from the same individual (autografts) fromindividuals of the same species (allografts) or from differentspecies (xenografts)On the other hand ceramicmaterials arebased on calcium phosphates and bioglassesThey have goodosteoinductive properties but low mechanical propertiesand difficulties in forming process Polymers such as thosederived from polyglycolic acid (PGA) and polylactic acid(PLA) have easy formability good mechanical propertiesand biodegradability which may vary according to theirmolecular weight but low osteoinductive capacity For theirpart ceramic-polymer composite materials allow obtaininga biodegradable material with good mechanical strengthosteoinductive osteoconductive and conformability proper-ties combining the properties of each material family Herewe mention some of them

31 Grafts A biomaterial commonly used for bone regener-ation is osseous tissue taken from the same individual (Auto-grafts) Autografts are considered the ldquogold standardrdquo becausethey are osteoinductive osteoconductive and osteogenicThis material is normally taken from a site that is notunder mechanical load such as the iliac crest Autograftscontain cells and growth factors that support the processof bone regeneration and do not exhibit risk of rejectionand disease transmission [117] Some drawbacks of autograftsare the necessity of additional surgeries possible infectionsmorbidity of the bone pain and its limited availabilityDepending on the source of the osseous tissue there mayalso be allografts (tissue from individuals of the same species)or xenografts (tissue from individual of different species)Allografts presented benefits as ready availability and easyhandling but require treatments such as freeze drying irra-diation and washing with acid among others to preventrejection by the receptor and remove any possible infectionsfrom the tissue to be implanted these processes can affecttheir mechanical and biological properties Xenografts thatusually come from cows and coral [118] could be osteoin-ductive and osteoconductive and with low cost with highavailability but have the disadvantages of immune responseand risk of transmission of animal diseases [119]

32 Ceramics Ceramic materials are a group of inorganicoxides and salts used in bone tissue engineering because of

their similarity to the mineral component of bone in the caseof calcium phosphate or because of their capacity of strengthbonding to osseous tissues in the case of bioglasses [117]Some ceramic materials used in bone regeneration are listedbelow

Calcium Phosphates Calcium phosphates are a family ofmin-erals composed of calcium ions (Ca2+) orthophosphates(PO4

3minus) metaphosphates or pyrophosphates (P2

O7

4minus) andsometimes hydrogen or hydroxide ions The most commoncalcium phosphates for tissue engineering are hydroxyap-atite (HA) calcium sulphate hemihydrate (CSH) gypsumcalcium sulphate dehydrate (CSD) calcium carbonate dical-cium phosphate (DCP) octacalcium phosphate (OCP) 120573-tricalcium phosphate (120573-TCP) biphasic calcium phosphate(BCP) and 120573-calcium pyrophosphate (120573-CPP) [37] Com-mercially available calcium phosphates proceed from naturalor synthetic sources and are processed in many physicalforms like particles blocks cements and coatings on metalimplants or composites with polymers

The most common calcium phosphate for bone tissueregeneration is hydroxyapatite (HA) which is a crystallinecalcium phosphate (Ca

10

(PO4)6

(OH)2

) present in bonesDepending on its source it can be natural or synthetizedfor example it can be produced from calcium carbonateand monoammonium phosphate at ambient pressure [120]or from natural sources like cattle or coral [121] SomeHA presentations exhibit a very similar bone structure withosteoconductive characteristics allowing connective tissuesurrounding and start the regeneration process

Calcium phosphates are bioactive materials because oftheir ability to form bone apatite like material or carbonatehydroxyapatite on their surfaces They have the ability topromote cellular function and expression besides the capacityof forming a strong bind between bone and biomaterialinterface In addition calcium phosphates biomaterials pro-cessed in porous forms are capable of binding and collectinggrowth factors and become osteoinductive biomaterials [122123] In addition calcium phosphates are materials thatallow adhesion of osteoblasts and promotemesenchymal cellsmigration Related to degradation tricalcium phosphatesare capable of tunable bioresorption rate [124] Differentcalcium phosphates can be used simultaneously to improvethe scaffold performance [125]

Calcium phosphates applications in bone regenerationinclude their use as a scaffold in periodontal treatmenthealing of bone defects fracture treatment total joint replace-ment orthopedics craniomaxillofacial reconstruction andspinal surgery Moreover calcium phosphates are widelyapplied as a coatingmaterial to provide strength to polymericscaffolds or to enhance the bioactivity onmetal surfaces [121]

Bioglasses Bioglasses are a family of bioactive glasses com-pound of SiO

2

Na2

OCaO and P2

O5

in variable proportionsThere are several types of bioactive glasses conventionalsilicates such as bioglass 45S5 phosphate-based glasses andborate-based glasses A hydroxycarbonate apatite (HCA)layer is formed on the surface of the glass following initialglass dissolution HCA is similar to bone mineral and


interacts with collagen to bind the bioglass with the hosttissueOsteoinductivity in bioglasses is related to the action ofdissolution products of these biomaterials on osteoprogenitorcells stimulating new bone growth Besides the HCA layerprovides a surface capable of enhancing osteogenic cellattachment and proliferation As calcium phosphates theHCA layer adsorbs protein and growth factors to promotenew bone formation An advantage of bioglasses abovecalcium phosphates is their faster degradation rate [126]

Bioglasses are used in bone regeneration like periodontalpocket elimination alveolar ridge augmentation maxillo-facial reconstruction spinal surgery and otorhinolaryngo-logical reconstruction [127 128] They can be processedand manufactured to generate a range of three-dimensionalscaffolds with different porosities and surface characteristics[117]

33 Polymers In tissue engineering biopolymers are syn-thetic organic materials which are biocompatible withhumans They may be of natural or synthetic origin Amongthe natural polymers used for tissue regeneration are thosematerials inspired by the extracellular matrix like collagen[129] Among the synthetic polymers used for bone tissueregeneration are polylactic acid (PLA) polyglycolic acid(PGA) and copolymers of PLA-PGA (PLGA) Properties ofsome polymers and copolymers biomaterials are listed inTable 2 A detailed list of commercial polymeric scaffoldsrsquoproducts can be found in [130 131]

Collagen collagen is the main component of connectivetissue in mammals Collagen type I is present in the form ofelongated fibrils in bone and is the most abundant in natureandmost considered for biomedical applications It possessesgood biocompatibility and low antigenicity Collagen has theability of crosslinking thereforemechanical and degradationproperties can be tailored [129] Collagen type I has Youngrsquosmodulus of 5 plusmn 2GPa for dry fibrils and from 02 to 05GPafor fibrils immersed in phosphate-buffered saline (PBS) [132]

Poly(120572-ester)s poly(120572-ester)s are thermoplastic polymerswith hydrolytically labile aliphatic ester bonds in their chainsPoly(120572-ester)s can be developed from a variety of monomersusing ring opening and condensation polymerization routeschanging the monomeric units Bioprocess methods can beused to develop some poly(120572-ester)s [133]The poly(120572-ester)sare biodegradable nontoxic and biocompatible Amongpoly(120572-ester)s the most extensively investigated polymersare the poly(120572-hydroxy acid)s which include poly(glycolicacid) and poly(lactic acid) The most extensively studiedmonomers for aliphatic polyester synthesis for biomedicalapplications are lactide glycolide and caprolactone [134]Poly(120572-ester)s mainly are degraded by hydrolysis bulk ero-sion The polymeric matrices degrade over their all crosssection and have erosion kinetics that usually are nonlinearwith discontinuities [135]

Polyglycolide (PGA) is a highly crystalline polymer (45ndash55 crystallinity) therefore it exhibits a high tensilemoduluswith very low degradation rate due to organic solvents Thefirst biodegradable synthetic suture that was approved by theFDA in 1969 was based on polyglycolide [136] Nonwovenpolyglycolide scaffolds have been widely used as matrices

for tissue regeneration due to their excellent degradabilitygood initial mechanical properties and cell viability Highmechanical properties of PGA are due to its high crystallinitySelf-reinforced forms of PGA showhigher stiffness than otherdegradable polymeric systems used clinically and exhibit anelasticity modulus of approximately 125 GPa Polyglycolidedegrades by nonspecific scissions of the ester chain PGAloses its strength in 1-2 months when hydrolyzed and lossesmass within 6ndash12 months In the body PGA degradationproduct is glycine which can be excreted in the urine orconverted into carbon dioxide and water via the citric acidcycle [137] Due to its good initial mechanical propertiespolyglycolide has been investigated as bone internal fixationdevices (Biofixs) However the high rates of degradation andacidic degradation products limit the clinical applications ofPGATherefore copolymers containing PGA units are beingdeveloped to overcome those disadvantages

Polylactide (PLA) is a chiral molecule and exists intwo optically active forms L-lactide and D-lactide Theirpolymerization forms a semicrystalline polymer and PLAbehaves as crystalline or amorphous depending of thesestereoisomers The polymerization of racemic (dl)-lactideand mesolactide results in the formation of amorphouspolymers [138 139] The molar mass of the polymer as wellas the degree of crystallinity has a significant influence on themechanical properties [140]

Poly-L-lactide (PLLA) is a low rate degradation polymercompared to PGA and has good tensile strength and highYoungrsquos modulus (48GPa approx) therefore it is usefulfor load-bearing applications such as orthopedic fixationdevices [134] It has been reported that high molecularweight PLLA can take between 2 and 56 years for totalresorption in vivo [144] On the other hand semicrystallinePLA is selected to the amorphous polymer when bettermechanical properties are necessary Semicrystalline PLAhasan approximate tensile modulus of 35 GPa tensile strengthof 50MPa flexural modulus of 5GPa flexural strength of100MPa and an elongation at break of about 4 [145]

Poly(lactide-co-glycolide) (PLG) both L- and DL-lactides have been used for copolymerization with glycolidemonomers in order to obtain different degradation ratesPLG degradation rates depend on a variety of parametersincluding the LAGA ratio molecular weight and the shapeand structure of the matrix For example 5050 poly(DL-lactide-co-glycolide) degrades in approximately 1-2 months7525 PLG in 4-5 months and 8515 copolymers in 5-6months [146] The popularity of these copolymers can beattributed to the FDA approval for use in humans and theirgood processability [134]

Polycaprolactone (PCL) PCL is semicrystalline polyesterobtained by the ring opening polymerization of monomericunits of ldquo120576-caprolactonerdquo PCL presents hydrolytic degrada-tion due to the presence of hydrolytically labile aliphatic esterbonds however the rate of degradation of homopolymer israther slow (2-3 years) with respect to polymers like PLAPCL has low tensile strength (approximately 23MPa) andhigh elongation at breakage (gt700) [134] It can be used inconjunction to other materials for load-bearing applications[147]


Table 2 Mechanical properties of typical polymers and copolymers for tissue engineering From Maurus and Kaeding Wu et al andMiddleton and Tipton [131 137 141]

Materials Compressivetensilestrength (MPa)

Youngrsquosmodulus(GPa)

Elongation()

Meltingpoint (∘C)

Glass-transitiontemp (∘C)

Loss ofstrength(months)

Loss of mass(months)

PLLA poly(L-lactide) 28ndash2300 48 5ndash10 175 60ndash65 6 24ndash68PDLLApoly(DL-lactide) 29ndash150 19 3ndash10 165ndash180 40ndash69 1-2 12ndash16

PGApoly(glycolide) 350ndash920 125 15ndash20 200 35ndash40 1-2 6ndash12

8515 DLPLGpoly(DL-lactide-co-glycolide) 50ndash55 5-6

7525 DLPLGpoly(DL-lactide-co-glycolide) 414ndash552 20 3ndash10 Amorphous 50ndash55 1-2 4-5



PCL poly(120576-caprolactone) 23 04 300ndash500 57 50ndash60 9ndash12 gt24

34 Biocomposites The literature review shows in recentyears a trend in the development of scaffolds made ofceramicpolymer composites [142] This is because ceramicslike calcium phosphates have excellent osteoinductive prop-erties but low degradability low mechanical strength anddifficulty in forming processes for controlling the physicaland geometrical characteristics required from the scaffoldFurthermore polymers such as PLA exhibit poor osteoin-ductivity but better mechanical properties and degradabilityrates besides that they can be formed by various manufac-turing processes that allow better control of their geometriccharacteristics Composites of collagen type I and calciumphosphates are widely used in bone tissue engineering dueto the similarity to natural bone and capacity of enhancingosteoblast differentiation and accelerating osteogenesis [143148 149] The development of ceramic-polymer compositesallows biodegradable materials with good mechanical andbiological properties as seen in Tables 3 and 4

35 Biomaterial Degradation In the case of scaffolds madeof biodegradable polymers many resorption mechanismsare identified depending of the material type [37] In thosemodels water molecules diffuse into the polymer and breakthe link into polymer molecules This phenomena cause amolecular weight decrease besides a decrease of elasticitymodulus After a certain threshold of molecular weight thepolymer is considered completely degraded [57 135] A moreelaborate model is proposed by Chen et al [78] includingautocatalysis Han proposed a model that includes the effectof crystallization [160] On the other hand ceramics such ascalcium phosphates and hydroxyapatite degrade by dissolu-tion and osteoclasts effect as modeled in [161] (Table 5)

36 Scaffold Fabrication Techniques Various manufactur-ing methods have been used to achieve certain properties

at different scales These methods are classified into con-ventional and additive manufacturing methods Conven-tionalmethods are solvent castingparticulate leaching phaseinversionparticulate leaching fiber meshingbonding meltmolding gas foaming membrane lamination hydrocarbontemplating freeze drying emulsion freeze drying solutioncasting and ceramic sintering These methods use physic-ochemical phenomena to ensure internal structures witha variable pore size between 100 and 500 microns withporosities up to 90 [15] They have the disadvantage thatinternal structure consists of randomly arranged trabeculaeand physical properties as permeability vary and are difficultto control In recent years methods of additive manufac-turing also called rapid prototyping (RP) or solid free-formmodeling (SFF) have beenused for scaffold fabrication Someof these methods are fused deposition modeling (FDM)three-dimensional printing or plotting (3DP) selective lasersintering (SLS) and stereolithography (SLA) These methodsachieve large scaffolds with oriented structures but fail toobtain high porositywith small poresDetailed lists of specificmaterials processing methods and properties obtained aregiven in [15 130] On the other hand an alternative to solidbone scaffolds is injectable bone cements [162 163] Theseare mainly used in the fixation of prostheses and filling bonecavities and kyphoplasty treatments [164]

4 Mechanobiology of Bone Tissue

Mechanobiology studies show howmechanical stimuli influ-ence the shape and structure of tissues of living beingsin particular muscle tendon cartilage and bone tissues[165] Mechanical and biochemical stimuli influence prolif-eration differentiation and cell functions [166] Thereforemechanobiologywould be useful to suggest clinical and tissueengineering strategies to control osseous tissue behavior


Table 3 Porous biocomposites used for bone tissue engineering From Chen et al [142] and Wahl and Czernuszka [143]

Biocomposite Percentage ofceramic (wt) Porosity () Pore size (120583m) Strength

(MPa)Modulus(MPa)

Ultimatestrain ()

Amorphous CaP PLGA 28 to 75 75 gt100 65120573-TCP Chitosan-gelatin 10 to 70 322 to 355 032 to 088 394 to 1088

HA

PLLA 50 85 to 96 100 times 300 039 10 to 14PLGA 60 to 75 81 to 91 800 to 1800 007 to 022 2 to 75PLGA 30 to 40 110 to 150 337 to 1459

Collagen Variable sim0 sim0 34ndash60 044ndash282PLG 75 43 89 042 51

Bioglass PLLA 20 to 50 77 to 80

Approximately 100(macro)

approximately 10(micro)

15 to 39 137 to 260 11 to 137

PLG 01 to 1 50 to 300

PDLLA 5 to 29 94Approximately 100(macro) 10 to 50

(micro)007 to 008 065 to 12 721 to 133

Phosphate glass AW PLA-PDLLA 40 93 to 97 98 to 154 0017 to 0020 0075 to 012PDLLA 20 to 40 855 to 952

Bioglass PGS 90 gt90 300 to 500 04 to 10

Table 4 Properties of bone graft substitutes Adapted fromMa and Elisseeff [150] and Brown et al [151]

Property Allograft Polymers Ceramics Composites Cell based therapies Growth factorsBiocompatibility Yes Yes Yes Yes Yes YesOsteoconductivity Yes Yes Yes Yes No NoOsteoinductivity Yes No No Yes No YesOsteogenicity Yes No No No Yes NoOsteointegrity Yes No Yes Yes Yes NoMechanical match No Yes Yes Yes No No

Bone tissue is formed by a process called osteogenesis[167] In this process cells capable of producing tissue interactwith chemotactic factors to form bone Firstly osteoblastssecrete substances to form osteoid tissue or immature bonea nonmineral matrix compound of collagen [168] and gly-cosaminoglycans Subsequently the matrix mineralizationoccurs by deposition of hydroxyapatite [169 170] Duringthis process some osteoblasts become trapped in the newlyformed bone and become osteocytes surrounded by osteonsOsteocytesmaintain the extracellularmatrix and it is hypoth-esized that they act as a network sensingmechanical stimulusthat activates the bone remodeling units (BMUs) formed byosteoblasts and osteoclasts

Once the bone is formed it can be remodeled or regen-erated by mechanical and biochemical stimulus Remodelingprocess took place in old bone when tissue is replaced bynew one in order to support changing loads or to replacebone with microdamage A turnover rate of 100 per yearin the first year of life 10 per year in late childhood [12]and near 5 per year in adult life [171ndash173] is estimatedRegeneration allows the creation of new tissue when aninjury or lack of continuity occurs for example in caseof fracture [174ndash176] Both processes are carried out by

BMUs [177ndash180] in which osteoclasts resorb deterioratedbone matrix and osteoblasts deposit new bone Sometimesthose processes present disorders like in Pagetrsquos disease [181]The processes of remodeling and regeneration are still understudy because of the large number of physical and biologicalfactors creating complexity in their interactions [13] Forexample it is hypothesized that osteocytes by piezoelectricphenomena respond to mechanical deformations or stressesand send signals to osteoblasts and osteoclasts so they engageand conform BMUs to perform the resorption or depositionof new bone [2]

Remodeling and regeneration require actions at differ-ent scales The mechanosensitivemechanoresponsive pro-cess starts in nanoscale or molecular level activating genesand signals in cells [182 183] and it continues with amechanotransduction process at cell level in nano-microscaleactivating electrical chemical or biochemical activity forexample ion channels or integrins the differentiation ofmesenchymal cells into bone cells (osteocytes osteoblastsand osteoclasts) and the interactions of those cells in thebone deposition and resorption processes [184] Finally in amacroscale stimuli determine the mechanical properties ofbone tissue bone shape and magnitude of the loads they can


Table 5 Resorption mechanisms for biomaterials for scaffolds used in bone regeneration From Bohner [37]lowast

Material type Material Degradation mechanism

Bioglass Generally very limited degradationthrough partial dissolution

Plaster of Paris(= calcium sulphate hemihydrate CSH)Gypsum

Dissolution

Ceramic

Dicalcium phosphate dehydrate(= calcium sulphate dihydrate CSD)

Dissolution andor conversion into anapatite

Calcium carbonate Dissolution or cell-mediated dependingon the mineral phase

Dicalcium phosphate (DCP)Octacalcium phosphate (OCP)120573-Tricalcium phosphate (120573-TCP)Biphasic calcium phosphate (BCP)Precipitated hydroxyapatite crystals120573-Calcium pyrophosphate (120573-CPP120573-Ca2P2O7)

Cell-mediated

Sintered hydroxyapatite Practically no degradation

MetalMagnesium (alloy) CorrosionIron (alloy) CorrosionTantalum titanium Practically no degradation

Polymer

Polylactides polyglycolidesPolycaprolactone Hydrolysis

CelluloseHyaluronanFibrinCollagenChitosan

Transport to lymph nodesHyaluronidasePlasminCollagenaseLysozyme

lowastReprinted fromMaterials Today with permission from Elsevier [37]

support One example of adaptation of shape and structureof bone due to mechanical loads is described in Wolff rsquos law[185ndash187] It states that bone adapts its internal and externalform depending on the forces applied on it [188]

From the clinical point of view mechanobiology isstudied using in vivo and in vitro models These methodscan be expensive time-consuming and difficult to controland in some cases with ethical drawbacks An alternativeto these models are computational methods or in silicoexperiments Computational mechanobiology studies theeffect of mechanical stimuli in the differentiation growthadaptation and maintenance of tissues establishing quali-tative and quantitative rules between the different variablesinvolved in these processes In computational mechanobi-ology numerical methods generally finite element methodFEM are used to solve systems of equations describing therelationships between the variables and parameters of thephenomena studiedWhereas some variables and parametersof these processes may not be measurable trial and errormethods are applied [189 190]

41 Mechanical Stimuli Variables A first task in computa-tional mechanobiology is to determine which mechanicalstimulus will serve as input variable The mechanical stimuli

that monitor the cells and the means they used to mea-sure that signal are still debated [191ndash196] Signals can beessentially volumetric deformation component (change insize) and a deviatoric deformation component (change inshape) Several researchers have proposed various types ofmechanical signals Frost proposed a minimum stress valuein the osseous tissue to trigger a bone apposition process[197] and later he changed the stress signal by a deformationsignal [198 199] Carter et al propose the principal strainand hydrostatic stress as mechanical signal [200] Claes andHeigele use the principal strain and the hydrostatic porepressure to study the fracture healing process [201] Lacroixand Prendergast use the deviatoric strain and fluid velocityto study tissue differentiation in fracture healing [202] andHuiskes et al studied strain energy density or SED to predictbone remodeling [203] The output variables help to describethe differentiation process (how many and which cell linesare produced) proliferation (which is the rate of growth)and adaptation and maintenance of tissues (position andmechanical properties of formed tissues)

42 Regeneration and Remodeling of Bone Tissues The studyof the bone regeneration process may consider tissue dif-ferentiation depending on the type and magnitude of themechanical stimulusThere are four basicmechanoregulatory


Deformation (strain)

Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)

Fibrous tissueFibrocartilage

Cartilage Bone

Principal tensile strain ()

Hydrostatic pressure (MPa)

(b)

minus20minus15minus10

0

101520

minus04 minus03 minus02 minus01 0 01 02 03 04000000000000000000000

minus0minus0minus0minus0minusminus0minus0minus0minus0minus0minusminusminus0minusminusminus0minusminus0111111111111 000000000000000000000000000000 0101010100101010010100101000000Intramembranous

ossificationminus0minus0minus0minus0minus0minus00minus00minus00minus000000000000 444444444444444 minus0minus0minus00minus0minus0minus0minus0minus0minus0minus0minus0minusminus0minus0minus033333333333333 minus0minus0minus0minus0minus0minus0000minus00minus000minus000000000000 22222222222222Endochondral

ossification

Hydrostatic pressure

(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10

0 2 4 6 8 10 12Tissue distortional strain ()

Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)

Figure 1 Graphic representation of mechanoregulatory models proposed by (a) Pauwels [204] (b) Carter et al [200] (c) Claes and Heigele[201] and (d) Prendergast [205] Adapted from Geris et al [34] with permission from the Royal Society

models of bone tissue differentiation Pauwels postulatedthat high strains led to the formation of fibrous tissuewhile higher pressures led to cartilage tissue [204] LaterCarter et al proposed a model where the type of tissuedepends on the direction and magnitude of the stress Forexample the osseous tissue is possible where stresses anddeformations have low magnitudes due to tension [200]Claes and Heigele [201] developed a model that unlike theprevious two qualitative models proposes ranges of valuesin which different types of tissues are obtained For exampleosseous tissue is generated by intramembranous ossificationif the stress is plusmn015MPa and the strain is less than plusmn5Finally Lacroix and Prendegrast propose a model wheretissues are not considered as a single material but as solidphase biphasic poroelastic materials In this model high fluidvelocity values and deviatoric strains cause fibrous tissue[205] Those models are represented in Figure 1

Another line of research involves bone remodeling Thisprocess includes the adaptation of the properties of thetissue that supports the mechanical loads This line of workdeveloped by Fyhrie and Carter [206] has been exten-sively used in computational models Here bone tissue isconsidered as a continuous system with variable apparentdensity (120588)This apparent density is expressed in terms of thestress (120590) to which the material is subjected This is definedby the expression It is considered that the bone tissue is

a continuous system with variable apparent density 120588 Thisapparent density is expressed in terms of the stress 120590 to whichthe material is subjected This is defined by the expression

120588 = 119860120590120572

(1)

where 119860 and 120572 are constants Considering 120572 = 05 it followsthat

1205902

= 2119864119880 (2)

where119864 is the elastic modulus and119880 is the strain energy den-sity With regard to the elastic modulus 119864 experimentationleads to the relationship

119864 = 1198881205883

(3)

For example one form of this equation that considers theviscoelastic behavior of the material is

119864axial = 119862 120576006

1205883

(4)

where119862 is a constant that considers values of elastic modulusand density of reference while 120576 is the rate of deformation

Therefore considering that bone remodeling is an opti-mization problem follows that the strain energy and bonedensity are related by

120588 = 1198881015840

119880 (5)


43 Other Processes Besides bone regeneration and boneremodeling due to mechanical stimulus another processesmust be considered in bone tissue engineering Sengers etal [207] in an extended review analyze the processes listedbelow

(i) Proliferation it is growth of cell population due tomitosis Exponential or logistic law is usually consid-ered here [153 155]

(ii) Nutrient transport and consumption they are nutri-ent concentrations gradients due to cell popula-tion location and generation and disposal of wastesubstances Regarding the interaction of nutrientavailability and cell proliferation reaction diffusionequations is employed as seen in [153 155]

(iii) Senescence it is decrease of cell population due toapoptosis [184 208]

(iv) Motility it is cells movement and adhesion through-out their environment due to taxis Although in boneremodeling and regeneration process it is usuallyconsidered that osteoblasts are not migrating cellsmodels as random walk or diffusion sometimes areapplied Random walk is a stochastic process thatconsists of a series of discrete steps of specific lengthA random variable determines the step length andwalk direction [63 209] Diffusion processes are usedto predict osteoblast movement [210] or Darcyrsquos lawto model movement in porous media [154]

(v) Differentiation stem cells turn into other more spe-cialized cell types Regarding bone regenerationmes-enchymal cells turn into fibroblast chondrocytes andosteoblasts not only due to mechanical signal asmentioned above but also due to chemical factors

(vi) Extracellular matrix changes cells like osteoblastsproduce matrix components (ie collagen andhydroxyapatite) and matrix degradation may occurby the action of osteoclasts

(vii) Cell to cell interactions cells can communicate witheach other in order to trigger processes For exampleosteocytes act as receptors of mechanical or chemicalsignals and dispose the formation of BMUs

44TheMechanostatTheory Frost suggests that bone changemust be considered in two phases the internal phase wherethe bone tissue changes its density and so its mechanicalproperties and the external one where there are changes dueto the deposition or removal of osseous tissue on the bonesurface [197] In both cases the remodeling process is activedepending on the value of the mechanical stimulus It canbe seen that in a range of mechanical stimuli remodeling isinactive [203]

For external remodeling the rate at which a bone isdeposited or removed is given by

119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption

Strain energy density (U)

Un

2s

Rate of bonechange

Figure 2 Rate of bone change as a function of the strain energydensity (119880) From Frost [197]

where 119883 is the thickness of the formed layer 119880 is thestrain energy density (SED) 119880

119899

is a reference value and 119862119909

is proportionality constant Similarly Youngrsquos modulus 119864change due to the mechanical stimulus is

119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)

Therefore the description of external remodeling process(Figure 2) is given by

119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)

Meanwhile the elasticity modulus change for internalremodeling is expressed as

119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Stiffness increase)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Stiffness decrease)

(9)

This type of response model to mechanical stimulationis widely used in bone remodeling and bone regenerationsimulations

45 Adaptive Remodeling with Variable Loading ConditionsA drawback of the models previously discussed is that theydo not propose how to consider the effect of variable loadsJacobs et al [211] suggest a model that considers the effect as

120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)


where 119899 is the number of load cases considered 119899119894

is thenumber of times that the load is applied per day and 120590

119887

is theaverage cyclic stress On the other hand the work of Carteret al [212] contributes to bone remodeling models weightingthe effect of various loads The expression for the mechanicalstimulus 119878 is

119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894

is the mechanical stimulus for the 119894th load case 119899 isthe total number of load cases and 120588 is the apparent densityWeinans et al [213] used this stimulus to establish the changein bone bulk density by

119889120588

119889119905

= 119861 (119878 minus 119896) (12)

where 119878 is the stimulus with 119861 and 119896 as constants

46 BioinspiredModels In contrast to previousmodels Mul-lender and Huiskes [214 215] model the action of osteoblastsand osteoclasts separately It is considered that the process ofbone remodeling in a location 119909 at time 119905 is given by

119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)

The variables 119898cl and 119898bl represent the adsorbed materialby osteoclasts and deposited material by osteoblasts respec-tively

The second term represents the material appositionwhich is given by

119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)

where 119875(119909 119905) is the stimulus received by the osteoblast fromthe osteocyte 119896 is a reference value for the stimulus and120591 is a constant of proportionality It should be noted herethat the stimulus is not the value of the strain energy densityat the point considered it is the weighted summation ofsignals sent by osteocytes in the neighborhood around thatpoint Ruimerman et al [216] applied this model to simulatebone adaptation under the influence of changes in the loadorientation

47 Mathematical Modeling of Bone Regeneration on Scaf-folds Considering the foregoing there are two differentand complex processes first scaffold degradation whichdecreases its volume and mechanical properties secondtissue regeneration that increases stiffness and mechanicalresistance of new bone Therefore experimental [217ndash225]and computational models are required to show the systemevolution over time and to help to identify the optimal initialproperties of the scaffold when it is implanted [78 79 108 111114 226ndash235]

Computer simulations allow analyzing scaffold propertiesand their effect on growth rate and mechanical behaviorof the tissue Those models vary as different properties

assumptions domains and solving approaches are consid-ered From the geometric point of view the most studiedproperty is porosity [63 236 237] The development ofadditivemanufacturingmethods has generated interest in theeffect of the shape and size of the scaffold pores In thosestudies a representative volume element (RVE) instead of thewhole model of the scaffold is studied [57 78] Simulationscan be developed for different processes at different scalesAt a nanoscale level the mechanisms of cell adhesion to thewalls can be studied [80 81] In the microscale the effectof the shape and size of the pores can be considered [5778] and at the macroscale the mechanical behavior of thescaffold [77 79 238] Finally the use of homogenization andmultiscale methods has allowed the researching of variousphenomena influencing the process of bone regeneration[111 239 240] like substances transport [241 242] Someexamples of computational mechanobiological models forfracture healing and bone regeneration on porous scaffoldsare listed in Table 6

5 Discussion

The global bone graft substitutes market is actually growingmainly due to the population needs and the improvement ofthe health services In this context design and manufactureof biodegradable scaffolds are one of the major researchand development interests in tissue engineering This papergives a review about the scaffold design considerationsand requirements the biomaterials that can be selected fora biodegradable scaffold and their related manufacturingprocesses

During the scaffold design process there are many con-siderations to be made biofunctionality biocompatibilitybiodegradability mechanical properties and porosity areamong the most important ones Designing a biodegradablescaffold is a complex process in three ways First thereare contradictions between the design parameters whichmust be solved for example high porosity versus highmechanical stiffness Second the scaffold must be designedusing patient-specific parameter values in order to satisfyits functional requirements thus it is necessary to estimateindividual porosity pore size and mechanical properties ofthe affected tissue Third the scaffold has to be designedas easy as possible to manufacture therefore design formanufacturability concepts must be taken into account

This review discussedmany biomaterials and theirmanu-facturing processes for biodegradable scaffold fabrication butlimited work has been done in order to obtain biomaterialswith patient-specific degradation rate One of the futurechallenges in bone tissue engineering is to design and tomanufacture biodegradable scaffolds with a homogeneousgrowth rate over their entire volume using pore size gradientsor specific distributions of embedded growth factors Thisrequires manufacturing processes with higher resolution andbiofabrication capabilities

The mechanobiological computational models of thebone regeneration and remodeling processes can assist thedesign of biodegradable scaffolds because they can help to


Table 6 Computational mechanobiological models for fracture healing and bone regeneration on scaffolds

Modeled phenomena Input variable Output variables Material Cellsconsidered Reference

Fluid motion of a bonesubstitute applied to thehigh tibial osteotomy withthree different wedge sizes

Fluid-induced shear stress

Elastic modulus Poissonrsquosratio porosity andpermeability values thatoptimize the internal fluidmotion

Not specified Not specified [152]

Cell growthIn vitro versus in silico Local oxygen tension Cell density PLGA Preosteoblast [153]

Cell differentiation andproliferation onbiodegradable scaffold

Shear strain and fluidicvelocity

Cell differentiationCell growthMechanical properties

PLGA

Mesenchymalcells

OsteoblastOsteoclast

ChondrocyteFibroblast

[58]

Cell growth on porousscaffolds Cell density Cell density

Pressure Not specified Not specified [154]

Cell growth anddistribution Cell density Cell density and

distribution Not specified Not specified [155]


Porosity Youngrsquos modulusand dissolution rateShear strain and fluidicvelocity

Cell differentiation PLGA

Mesenchymalcells



[63]


Scaffold stiffness porosityresorption kinetics poresize and preseeding

Cell growthScaffold mass lossPermeabilityPorosity

Polymer Not specified [156]

Mechanical behavior anddrug delivery

Stress loads according todifferent position invivo

Drug releaseStress Hydroxyapatite Not specified [157]

Cell growth anddifferentiationover implantporous surface

Force Cell differentiation Not specified

Mesenchymalcells



[158]

Proliferation andhypertrophy ofchondrocytes in the growthplate

Stress Cell proliferation Not specified Chondrocyte [159]

understand the effect of scaffold properties on bone ingrowththerefore their results can be used to optimize the scaffoldstructure in order to meet patient-specific mechanical andpore characteristics A disadvantage of these models is thatthey involve many parameters whose values have to beestimated with in vitro or in vivo experimentation It isnecessary to rationalize the number of model parameterswithout loss of reliability of the numerical results

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is kindly supported by Universidad Santo TomasFODEIN Fund Code 056-2014

References

[1] J E Aubin and J M Heersche ldquoBone cell biology osteoblastsosteocytes and osteoclastsrdquo in Pediatric Bone Elsevier 2002

[2] J B Lian and G S Stein ldquoThe cells of bonerdquo Proteins 2006[3] S Cowin Bone Mechanics Handbook CRC press LLC New

York NY USA 2001[4] O Fricke Z Sumnik B Tutlewski A Stabrey T Remer and E

Schoenau ldquoLocal body composition is associated with gender


differences of bone development at the forearm in pubertyrdquoHormone Research vol 70 no 2 pp 105ndash111 2008

[5] S Weiner and H D Wagner ldquoThe material bone structure-mechanical function relationsrdquo Annual Review of MaterialsScience vol 28 no 1 pp 271ndash298 1998

[6] L C Chow ldquoSolubility of calcium phosphatesrdquo Monographs inOral Science vol 18 pp 94ndash111 2001

[7] M Wendel Y Sommarin and D Heinegard ldquoBone matrixproteins isolation and characterization of a novel cell- bindingkeratan sulfate proteoglycan (osteoadherin) from bovine bonerdquoJournal of Cell Biology vol 141 no 3 pp 839ndash847 1998

[8] C M Gundberg ldquoMatrix proteinsrdquo Osteoporosis Internationalvol 14 supplement 5 pp S37ndashS42 2003

[9] P G Robey N S Fedarko T E Hefferan et al ldquoStructure andmolecular regulation of bone matrix proteinsrdquo Journal of BoneandMineral Research vol 8 supplement 2 pp S483ndashS487 1993

[10] S J Morrison and D T Scadden ldquoThe bone marrow niche forhaematopoietic stem cellsrdquo Nature vol 505 no 7483 pp 327ndash334 2014

[11] J F Raposo L G Sobrinho and H G Ferreira ldquoA minimalmathematical model of calcium homeostasisrdquo Journal of Clini-cal Endocrinology andMetabolism vol 87 no 9 pp 4330ndash43402002

[12] F Barrere T Mahmood K Degroot and C VanblitterswijkldquoAdvanced biomaterials for skeletal tissue regeneration instruc-tive and smart functionsrdquoMaterials Science and Engineering RReports vol 59 no 1ndash6 pp 38ndash71 2008

[13] M Pawlikowski M Klasztorny and K Skalski ldquoStudies onconstitutive equation that models bone tissuerdquo Acta of Bioengi-neering and BiomechanicsWrocław University of Technologyvol 10 no 4 pp 39ndash47 2008

[14] B Helgason E Perilli E Schileo F Taddei S Brynjolfsson andM Viceconti ldquoMathematical relationships between bone den-sity and mechanical properties a literature reviewrdquo ClinicalBiomechanics vol 23 no 2 pp 135ndash146 2008

[15] U Meyer T Meyer J Handschel and H P Wiesmann Fund-amentals of Tissue Engineering and Regenerative MedicineSpringer Berlin Germany 2009

[16] M A Meyers P-Y Chen A Y-M Lin and Y Seki ldquoBiologicalmaterials structure and mechanical propertiesrdquo Progress inMaterials Science vol 53 no 1 pp 1ndash206 2008

[17] MDoblare JM Garcıa andM J Gomez ldquoModelling bone tis-sue fracture and healing a reviewrdquo Engineering FractureMecha-nics vol 71 no 13-14 pp 1809ndash1840 2004

[18] K Piper and G Valentine ldquoBone pathologyrdquoMethods in Mole-cular Biology vol 915 pp 51ndash88 2012

[19] N Peel ldquoBone remodelling and disorders of bone metabolismrdquoSurgery vol 27 no 2 pp 70ndash74 2009

[20] J L Marsh T F Slongo J Agel et al ldquoFracture and dislocationclassification compendiummdash2007 Orthopaedic Trauma Asso-ciation Classification Database and Outcomes CommitteerdquoJournal of Orthopaedic Trauma vol 21 no 10 supplement ppS1ndashS133 2007

[21] F Rauch and F H Glorieux ldquoOsteogenesis imperfectardquo TheLancet vol 363 no 9418 pp 1377ndash1385 2004

[22] P Meunier Osteoporosis Diagnosis and Management Taylor ampFrancis London UK 1998

[23] J A Eisman ldquo6 Osteomalaciardquo Baillierersquos Clinical Endocrinologyand Metabolism vol 2 no 1 pp 125ndash155 1988

[24] P J Carek L M Dickerson and J L Sack ldquoDiagnosis andmanagement of osteomyelitisrdquo American Family Physician vol63 no 12 pp 2413ndash2420 2001

[25] H A Mousa ldquoBone infectionrdquo The Eastern MediterraneanHealth Journal vol 9 no 1-2 pp 208ndash214 2003

[26] J A Buckwalter and E A Brandser ldquoMetastatic disease of theskeletonrdquo The American Family Physician vol 55 no 5 pp1761ndash1768 1997

[27] J A Buckwalter J D Heckman and D P Petrie ldquoAging of thenorth American population new challenges for orthopaedicsrdquoJournal of Bone and Joint SurgerymdashSeries A vol 85 no 4 pp748ndash758 2003

[28] R Lanza R Langer and J Vacanti Principles of Tissue Engineer-ing Academic Press New York NY USA 3rd edition 2007

[29] J Hollinger T A Einhorn B Doll and C Sfeir Bone TissueEngineering CRC Press 2004

[30] D W Hutmacher ldquoScaffolds in tissue engineering bone andcartilagerdquo Biomaterials vol 21 no 24 pp 2529ndash2543 2000

[31] M J Lysaght A Jaklenec and E Deweerd ldquoGreat expecta-tions private sector activity in tissue engineering regenerativemedicine and stem cell therapeuticsrdquo Tissue EngineeringmdashPartA vol 14 no 2 pp 305ndash315 2008

[32] G Lewis ldquoRegenerative medicine at a global level current pat-terns and global trendsrdquo inTheGlobal Dynamics of RegenerativeMedicine A Social Science Critique A Webster Ed p 248Palgrave Macmillan 2013

[33] A Greenwald S Boden R Barrack et al ldquoThe evolving role ofbone-graft substitutesrdquo in Proceedings of the American Academyof Orthopaedic Surgeons 77th Annual Meeting p 6 2010

[34] L Geris J V Sloten and H van Oosterwyck ldquoIn silico biologyof bone modelling and remodelling Regenerationrdquo Philosoph-ical Transactions of the Royal Society A Mathematical Physicaland Engineering Sciences vol 367 no 1895 pp 2031ndash2053 2009

[35] Global Data Bone Graft SubstitutesmdashGlobal Pipeline AnalysisCompetitive Landscape and Market Forecast to 2017 GlobalData London UK 2011

[36] iData Research US Orthopedic Biomaterials Market iDataResearch Dallas Tex USA 2013

[37] M Bohner ldquoResorbable biomaterials as bone graft substitutesrdquoMaterials Today vol 13 no 1-2 pp 24ndash30 2010

[38] Medtech InsightElsevier Business Intelligence ldquoEuropeanmarkets for bone graft substitute products for spinal fusionrdquoTech Rep A329 Life Science Intelligence Huntington BeachCalif USA 2011

[39] S Bandyopadyay-Ghosh ldquoBone as a collagen-hydroxyapatitecomposite and its repairrdquo Trends in Biomaterials and ArtificialOrgans vol 22 no 2 pp 116ndash124 2008

[40] D Knudson Fundamentals of Biomechanics Springer BostonMass USA 2007

[41] E S Place N D Evans and M M Stevens ldquoComplexity inbiomaterials for tissue engineeringrdquoNatureMaterials vol 8 no6 pp 457ndash470 2009

[42] A-K Bock E Rodriguez-Cerezo B Husing B Buhrlen andM Nusser ldquoHuman tissue-engineered products potentialsocio-economic impacts of a new European regulatory frame-work for authorisation supervision and vigilancerdquo Tech RepEUR 21838 EN Joint Research Center Karlsruhe Germany2005

[43] Knowledge Enterprises The Worldwide Orthopedic Marketmdash2005-2006 Knowledge Enterprises Chagrin Falls Ohio USA2006


[44] C A Kirker-Head ldquoPotential applications and delivery strate-gies for bonemorphogenetic proteinsrdquoAdvanced Drug DeliveryReviews vol 43 no 1 pp 65ndash92 2000

[45] L Grgurevic B Macek MMercep et al ldquoBonemorphogeneticprotein (BMP)1ndash3 enhances bone repairrdquo Biochemical andBiophysical Research Communications vol 408 no 1 pp 25ndash312011

[46] N Sykaras and L A Opperman ldquoBonemorphogenetic proteins(BMPs) how do they function and what can they offer theclinicianrdquo Journal of Oral Science vol 45 no 2 pp 57ndash73 2003

[47] J W Lee K S Kang S H Lee J-Y Kim B-K Lee and D-WCho ldquoBone regeneration using a microstereolithography-produced customized poly(propylene fumarate)diethylfumarate photopolymer 3D scaffold incorporating BMP-2loaded PLGA microspheresrdquo Biomaterials vol 32 no 3 pp744ndash752 2011

[48] Z Chen D Li B Lu Y Tang M Sun and S Xu ldquoFabricationof osteo-structure analogous scaffolds via fused depositionmodelingrdquo Scripta Materialia vol 52 no 2 pp 157ndash161 2005

[49] J-Y Lee J-E Choo Y-S Choi et al ldquoOsteoblastic differenti-ation of human bone marrow stromal cells in self-assembledBMP-2 receptor-binding peptide-amphiphilesrdquo Biomaterialsvol 30 no 21 pp 3532ndash3541 2009

[50] S C-N Chang H Chuang Y-R Chen et al ldquoCranial repairusing BMP-2 gene engineered bone marrow stromal cellsrdquoJournal of Surgical Research vol 119 no 1 pp 85ndash91 2004

[51] Y Bai G Yin Z Huang et al ldquoLocalized delivery of growth fac-tors for angiogenesis and bone formation in tissue engineeringrdquoInternational Immunopharmacology vol 16 no 2 pp 214ndash2232013

[52] V I Sikavitsas J S Temenoff and A G Mikos ldquoBiomaterialsand bone mechanotransductionrdquo Biomaterials vol 22 no 19pp 2581ndash2593 2001

[53] T L McCarthy M Centrella and E Canalis ldquoInsulin-likegrowth factor (IGF) and bonerdquo Connective Tissue Research vol20 no 1ndash4 pp 277ndash282 1989

[54] D Kaigler G Avila L Wisner-Lynch et al ldquoPlatelet-derivedgrowth factor applications in periodontal and peri-implantbone regenerationrdquo Expert Opinion on Biological Therapy vol11 no 3 pp 375ndash385 2011

[55] M Bosetti F BoccafoschiM Leigheb andM F Cannas ldquoEffectof different growth factors on human osteoblasts activities apossible application in bone regeneration for tissue engineer-ingrdquo Biomolecular Engineering vol 24 no 6 pp 613ndash618 2007

[56] Y Ikada ldquoChallenges in tissue engineeringrdquo Interface vol 3 no10 pp 589ndash601 2006

[57] T Adachi Y Osako M Tanaka M Hojo and S J HollisterldquoFramework for optimal design of porous scaffold microstruc-ture by computational simulation of bone regenerationrdquoBioma-terials vol 27 no 21 pp 3964ndash3972 2006

[58] Y Chen S Zhou and Q Li ldquoMicrostructure design ofbiodegradable scaffold and its effect on tissue regenerationrdquoBiomaterials vol 32 no 22 pp 5003ndash5014 2011

[59] S J Hollister R D Maddox and J M Taboas ldquoOptimal designand fabrication of scaffolds to mimic tissue properties andsatisfy biological constraintsrdquo Biomaterials vol 23 no 20 pp4095ndash4103 2002

[60] S J Hollister ldquoPorous scaffold design for tissue engineeringrdquoNature Materials vol 4 no 7 pp 518ndash524 2005

[61] M Schicker H Seitz I Drosse S Seitz and W MutschlerldquoBiomaterials as scaffold for bone tissue engineeringrdquo EuropeanJournal of Trauma vol 32 no 2 pp 114ndash124 2006

[62] A W Lloyd ldquoInterfacial bioengineering to enhance surfacebiocompatibilityrdquo Medical Device Technology vol 13 no 1 pp18ndash21 2002

[63] D P Byrne D Lacroix J A Planell D J Kelly and P JPrendergast ldquoSimulation of tissue differentiation in a scaffoldas a function of porosity Youngrsquos modulus and dissolution rateapplication ofmechanobiologicalmodels in tissue engineeringrdquoBiomaterials vol 28 no 36 pp 5544ndash5554 2007

[64] A Kolk J Handschel W Drescher et al ldquoCurrent trends andfuture perspectives of bone substitute materialsmdashfrom spaceholders to innovative biomaterialsrdquo Journal of Cranio-Maxi-llofacial Surgery vol 40 no 8 pp 706ndash718 2012

[65] S Rajagopalan and R A Robb ldquoSchwarz meets Schwanndesign and fabrication of biomorphic and durataxic tissueengineering scaffoldsrdquoMedical Image Analysis vol 10 no 5 pp693ndash712 2006

[66] M Vert ldquoPolymeric biomaterials strategies of the past vsstrategies of the futurerdquo Progress in Polymer Science vol 32 no8-9 pp 755ndash761 2007

[67] S M Giannitelli D Accoto M Trombetta and A RainerldquoCurrent trends in the design of scaffolds for computer-aidedtissue engineeringrdquo Acta Biomaterialia vol 10 no 2 pp 580ndash594 2014

[68] C Estrada A C Paz and L E Lopez ldquoIngenierıa de tejido oseoconsideraciones basicasrdquo Revista EIA vol 5 pp 93ndash100 2006

[69] S Bose M Roy and A Bandyopadhyay ldquoRecent advances inbone tissue engineering scaffoldsrdquo Trends in Biotechnology vol30 no 10 pp 546ndash554 2012

[70] S Ramakrishna J Mayer E Wintermantel and K W LeongldquoBiomedical applications of polymer-composite materials areviewrdquo Composites Science and Technology vol 61 no 9 pp1189ndash1224 2001

[71] M Vert Y Doi K-H Hellwich et al ldquoTerminology for biore-lated polymers and applications (IUPAC recommendations2012)rdquo Pure and Applied Chemistry vol 84 no 2 pp 377ndash4102012

[72] F Edalat H Bae SManoucheri J M Cha and A Khademhos-seini ldquoEngineering approaches toward deconstructing andcontrolling the stem cell environmentrdquo Annals of BiomedicalEngineering vol 40 no 6 pp 1301ndash1315 2012

[73] T Garg O Singh S Arora and R Murthy ldquoScaffold a novelcarrier for cell and drug deliveryrdquo Critical Reviews inTherapeu-tic Drug Carrier Systems vol 29 no 1 pp 1ndash63 2012

[74] D Logeart-Avramoglou F Anagnostou R Bizios andH PetiteldquoEngineering bone challenges andobstaclesrdquo Journal of Cellularand Molecular Medicine vol 9 no 1 pp 72ndash84 2005

[75] J M Taboas R D Maddox P H Krebsbach and S J HollisterldquoIndirect solid free form fabrication of local and global porousbiomimetic and composite 3D polymer-ceramic scaffoldsrdquoBiomaterials vol 24 no 1 pp 181ndash194 2003

[76] V Karageorgiou and D Kaplan ldquoPorosity of 3D biomaterialscaffolds and osteogenesisrdquo Biomaterials vol 26 no 27 pp5474ndash5491 2005

[77] W Sun B Starly J Nam and A Darling ldquoBio-CAD modelingand its applications in computer-aided tissue engineeringrdquoComputer-Aided Design vol 37 no 11 pp 1097ndash1114 2005

[78] Y Chen S Zhou and Q Li ldquoMathematical modeling ofdegradation for bulk-erosive polymers applications in tissueengineering scaffolds and drug delivery systemsrdquo Acta Bioma-terialia vol 7 no 3 pp 1140ndash1149 2011


[79] R Voronov S VanGordon V I Sikavitsas and D V Papavas-siliou ldquoComputational modeling of flow-induced shear stresseswithin 3D salt-leached porous scaffolds imaged via micro-CTrdquoJournal of Biomechanics vol 43 no 7 pp 1279ndash1286 2010

[80] W A Comisar N H Kazmers D J Mooney and J JLinderman ldquoEngineering RGD nanopatterned hydrogels tocontrol preosteoblast behavior a combined computational andexperimental approachrdquo Biomaterials vol 28 no 30 pp 4409ndash4417 2007

[81] V J Chen L A Smith and P X Ma ldquoBone regeneration oncomputer-designed nano-fibrous scaffoldsrdquo Biomaterials vol27 no 21 pp 3973ndash3979 2006

[82] S Zhang D M Marini W Hwang and S Santoso ldquoDesignof nanostructured biological materials through self-assembly ofpeptides and proteinsrdquo Current Opinion in Chemical Biologyvol 6 no 6 pp 865ndash871 2002

[83] Y Kuboki H Takita D Kobayashi et al ldquoBMP-induced osteo-genesis on the surface of hydroxyapatite with geometricallyfeasible and nonfeasible structures topology of osteogenesisrdquoJournal of Biomedical Materials Research vol 39 no 2 pp 190ndash199 1998

[84] M Frohlich W L Grayson L Q Wan D Marolt M Drobnicand G Vunjak-Novakovic ldquoTissue engineered bone graftsbiological requirements tissue culture and clinical relevancerdquoCurrent StemCell ResearchampTherapy vol 3 no 4 pp 254ndash2642008

[85] S F Hulbert F A Young R S Mathews J J Klawitter C DTalbert and F H Stelling ldquoPotential of ceramic materials aspermanently implantable skeletal prosthesesrdquo Journal of Bio-medical Materials Research vol 4 no 3 pp 433ndash456 1970

[86] K Whang K E Healy D R Elenz and et al ldquoEngineeringbone regeneration with bioabsorbable scaffolds with novelmicroarchitecturerdquo Tissue Engineering vol 5 no 1 pp 35ndash511999

[87] C N Cornell ldquoOsteoconductive materials and their role assubstitutes for autogenous bone graftsrdquo Orthopedic Clinics ofNorth America vol 30 no 4 pp 591ndash598 1999

[88] S J Hollister C Y Lin E Saito et al ldquoEngineering craniofacialscaffoldsrdquo Orthodontics and Craniofacial Research vol 8 no 3pp 162ndash173 2005

[89] M Bohner Y Loosli G Baroud and D Lacroix ldquoDecipheringthe link between architecture and biological response of a bonegraft substituterdquo Acta Biomaterialia vol 7 no 2 pp 478ndash4842011

[90] S Bose S Vahabzadeh and A Bandyopadhyay ldquoBone tissueengineering using 3D printingrdquoMaterials Today vol 16 no 12pp 496ndash504 2013

[91] X Li D Li B Lu L Wang and Z Wang ldquoFabrication andevaluation of calcium phosphate cement scaffold with con-trolled internal channel architecture and complex shaperdquo Pro-ceedings of the Institution of Mechanical Engineers Part HJournal of Engineering in Medicine vol 221 no 8 pp 951ndash9582007

[92] L Liulan H Qingxi H Xianxu and X Gaochun ldquoDesign andfabrication of bone tissue engineering scaffolds via rapid pro-totyping and CADrdquo Journal of Rare Earths vol 25 no 2 pp379ndash383 2007

[93] J Guo Q X Hu Y Yao Q Lu Y W Yu and Y Qian ldquoA porenetwork model based method for tissue engineering scaffolddesignrdquo in Proceedings of the International Conference onBiomedical Engineering and Computer Science (ICBECS rsquo10) pp1ndash4 April 2010

[94] Q Lian D-C Li Y-P Tang and Y-R Zhang ldquoComputermodeling approach for a novel internal architecture of artificialbonerdquo Computer-Aided Design vol 38 no 5 pp 507ndash514 2006

[95] L Jongpaiboonkit J W Halloran and S J Hollister ldquoInternalstructure evaluation of three-dimensional calcium phosphatebone scaffolds a micro-computed tomographic studyrdquo Journalof the American Ceramic Society vol 89 no 10 pp 3176ndash31812006

[96] A Armillotta and R Pelzer ldquoModeling of porous structures forrapid prototyping of tissue engineering scaffoldsrdquo InternationalJournal of Advanced Manufacturing Technology vol 39 no 5-6pp 501ndash511 2008

[97] C Zhongzhong F Xilan and J Zhiqiang ldquoStructural designand optimization of interior scaffolds in artificial bonerdquo inProceedings of the 1st International Conference on Bioinformaticsand Biomedical Engineering (CBBE rsquo07) pp 330ndash333 July 2007

[98] C M Cheah C K Chua K F Leong and S W Chua ldquoDev-elopment of a tissue engineering scaffold structure libraryfor rapid prototyping Part 1 investigation and classificationrdquoInternational Journal of Advanced Manufacturing Technologyvol 21 no 4 pp 291ndash301 2003

[99] A L Olivares E Marsal J A Planell and D Lacroix ldquoFiniteelement study of scaffold architecture design and culture con-ditions for tissue engineeringrdquo Biomaterials vol 30 no 30 pp6142ndash6149 2009

[100] F P W Melchels A M C Barradas C A van Blitterswijk J deBoer J Feijen and DW Grijpma ldquoEffects of the architecture oftissue engineering scaffolds on cell seeding and culturingrdquo ActaBiomaterialia vol 6 no 11 pp 4208ndash4217 2010

[101] F P W Melchels K Bertoldi R Gabbrielli A H Velders JFeijen andDWGrijpma ldquoMathematically defined tissue engi-neering scaffold architectures prepared by stereolithographyrdquoBiomaterials vol 31 no 27 pp 6909ndash6916 2010

[102] S C Kapfer S T Hyde K Mecke C H Arns and G ESchroder-Turk ldquoMinimal surface scaffold designs for tissueengineeringrdquo Biomaterials vol 32 no 29 pp 6875ndash6882 2011

[103] D Yoo ldquoNew paradigms in internal architecture design andfreeform fabrication of tissue engineering porous scaffoldsrdquoMedical Engineering and Physics vol 34 no 6 pp 762ndash7762012

[104] A Pasko O Fryazinov T Vilbrandt P-A Fayolle and VAdzhiev ldquoProcedural function-based modelling of volumetricmicrostructuresrdquo Graphical Models vol 73 no 5 pp 165ndash1812011

[105] P Pandithevan and G Saravana Kumar ldquoPersonalised bonetissue engineering scaffold with controlled architecture usingfractal tool paths in layered manufacturingrdquo Virtual and Physi-cal Prototyping vol 4 no 3 pp 165ndash180 2009

[106] B S Bucklen W A Wettergreen E Yuksel and M A KLiebschner ldquoBone-derived CAD library for assembly of scaf-folds in computer-aided tissue engineeringrdquo Virtual and Physi-cal Prototyping vol 3 no 1 pp 13ndash23 2008

[107] G H van Lenthe H Hagenmuller M Bohner S J HollisterL Meinel and R Muller ldquoNondestructive micro-computedtomography for biological imaging and quantification ofscaffold-bone interaction in vivordquo Biomaterials vol 28 no 15pp 2479ndash2490 2007

[108] Z Hu B Notarberardino M Baker et al ldquoOn modeling bio-scaffolds structural and fluid transport characterization basedon 3-D imaging datardquo Tsinghua Science and Technology vol 14supplement 1 pp 20ndash23 2009


[109] X Y Kou and S T Tan ldquoA simple and effective geometric rep-resentation for irregular porous structure modelingrdquo ComputerAided Design vol 42 no 10 pp 930ndash941 2010

[110] Z Fang B Starly and W Sun ldquoComputer-aided character-ization for effective mechanical properties of porous tissuescaffoldsrdquo CAD Computer Aided Design vol 37 no 1 pp 65ndash72 2005

[111] R J Shipley G W Jones R J Dyson et al ldquoDesign criteriafor a printed tissue engineering construct a mathematicalhomogenization approachrdquo Journal of Theoretical Biology vol259 no 3 pp 489ndash502 2009

[112] S Cowin ldquoRemarks on optimization and the prediction of boneadaptation to altered loadingrdquo New York Cent Biomed Eng2003

[113] C Y Lin N Kikuchi and S J Hollister ldquoA novel method forbiomaterial scaffold internal architecture design to match boneelastic properties with desired porosityrdquo Journal of Biomechan-ics vol 37 no 5 pp 623ndash636 2004

[114] S J Hollister and C Y Lin ldquoComputational design of tissueengineering scaffoldsrdquo Computer Methods in AppliedMechanicsand Engineering vol 196 no 31-32 pp 2991ndash2998 2007

[115] H D A Almeida and P J da Silva Bartolo ldquoVirtual topologicaloptimisation of scaffolds for rapid prototypingrdquo Medical Engi-neering and Physics vol 32 no 7 pp 775ndash782 2010

[116] D F Williams ldquoOn the nature of biomaterialsrdquo Biomaterialsvol 30 no 30 pp 5897ndash5909 2009

[117] M M Stevens ldquoBiomaterials for bone tissue engineeringrdquoMaterials Today vol 11 no 5 pp 18ndash25 2008

[118] A S AlGhamdi O Shibly and S G Ciancio ldquoOsseous graftingpart II xenografts and alloplasts for periodontal regenerationmdasha literature reviewrdquo Journal of the International Academy ofPeriodontology vol 12 no 2 pp 39ndash44 2010

[119] A Oryan S Alidadi A Moshiri and N Maffulli ldquoBoneregenerative medicine classic options novel strategies andfuture directionsrdquo Journal of Orthopaedic Surgery and Researchvol 9 no 1 article 18 2014

[120] C Verwilghen M Chkir S Rio A Nzihou P Sharrock andG Depelsenaire ldquoConvenient conversion of calcium carbonateto hydroxyapatite at ambient pressurerdquo Materials Science andEngineering C vol 29 no 3 pp 771ndash773 2009

[121] T Guda M Appleford S Oh and J L Ong ldquoA cellular pers-pective to bioceramic scaffolds for bone tissue engineering thestate of the artrdquo Current Topics in Medicinal Chemistry vol 8no 4 pp 290ndash299 2008

[122] R Z LeGeros ldquoProperties of osteoconductive biomaterials cal-cium phosphatesrdquo Clinical Orthopaedics and Related Researchno 395 pp 81ndash98 2002

[123] S Samavedi A R Whittington and A S Goldstein ldquoCalciumphosphate ceramics in bone tissue engineering a review ofproperties and their influence on cell behaviorrdquo Acta Biomate-rialia vol 9 no 9 pp 8037ndash8045 2013

[124] J R Porter T T Ruckh and K C Popat ldquoBone tissue eng-ineering a review in bone biomimetics and drug delivery strate-giesrdquo Biotechnology Progress vol 25 no 6 pp 1539ndash1560 2009

[125] L Tzvetanov S Nikolaeva I Michailov and P Tivchev ldquoBoneand ceramic interaction in the bone union processrdquo Ultrastruc-tural Pathology vol 26 no 3 pp 171ndash175 2002

[126] A Ravaglioli A Krajewski G Baldi F Tateo L Peruzzo andA Piancastelli ldquoGlass-ceramic scaffolds for tissue engineeringrdquoAdvances in Applied Ceramics vol 107 no 5 pp 268ndash273 2008

[127] L L Hench N Roki and M B Fenn ldquoBioactive glasses imp-ortance of structure and properties in bone regenerationrdquo Jour-nal of Molecular Structure vol 1073 pp 24ndash30 2014

[128] J R Jones ldquoReview of bioactive glass From Hench to hybridsrdquoActa Biomaterialia vol 9 no 1 pp 4457ndash4486 2013

[129] J F Mano G A Silva H S Azevedo et al ldquoNatural originbiodegradable systems in tissue engineering and regenerativemedicine present status and some moving trendsrdquo Journal ofthe Royal Society Interface vol 4 no 17 pp 999ndash1030 2007

[130] B Dhandayuthapani Y Yoshida T Maekawa and D S KumarldquoPolymeric scaffolds in tissue engineering application a reviewrdquoInternational Journal of Polymer Science vol 2011 Article ID290602 19 pages 2011

[131] J C Middleton and A J Tipton ldquoSynthetic biodegradablepolymers as orthopedic devicesrdquo Biomaterials vol 21 no 23pp 2335ndash2346 2000

[132] L Yang K O van der Werf C F C Fitie M L Bennink P JDijkstra and J Feijen ldquoMechanical properties of native andcross-linked type I collagen fibrilsrdquo Biophysical Journal vol 94no 6 pp 2204ndash2211 2008

[133] M Okada ldquoChemical syntheses of biodegradable polymersrdquoProgress in Polymer Science vol 27 no 1 pp 87ndash133 2002

[134] L S Nair and C T Laurencin ldquoBiodegradable polymers as bio-materialsrdquo Progress in Polymer Science (Oxford) vol 32 no 8-9pp 762ndash798 2007

[135] A Gopferich ldquoPolymer bulk erosionrdquoMacromolecules vol 30no 9 pp 2598ndash2604 1997

[136] E J Frazza and E E Schmitt ldquoA new absorbable suturerdquo Journalof Biomedical Materials Research vol 5 no 2 pp 43ndash58 1971

[137] P B Maurus and C C Kaeding ldquoBioabsorbable implant mate-rial reviewrdquoOperative Techniques in Sports Medicine vol 12 no3 pp 158ndash160 2004

[138] G-X Chen H-S Kim E-S Kim and J-S Yoon ldquoSynthesisof high-molecular-weight poly(L-lactic acid) through the directcondensation polymerization of l-lactic acid in bulk staterdquoEuropean Polymer Journal vol 42 no 2 pp 468ndash472 2006

[139] M Savioli Lopes A L Jardini and R Maciel Filho ldquoPoly(lactic acid) production for tissue engineering applicationsrdquo inProceedings of the 20th International Congress of Chemical andProcess Engineering (CHISA rsquo12) pp 1402ndash1413 August 2012

[140] G Perego G D Cella and C Bastioli ldquoEffect of molecularweight and crystallinity on poly(lactic acid)mechanical proper-tiesrdquo Journal of Applied Polymer Science vol 59 no 1 pp 37ndash431996

[141] S Wu X Liu KW K Yeung C Liu and X Yang ldquoBiomimeticporous scaffolds for bone tissue engineeringrdquoMaterials Scienceand Engineering R Reports vol 80 no 1 pp 1ndash36 2014

[142] Q Chen C Zhu and G AThouas ldquoProgress and challenges inbiomaterials used for bone tissue engineering bioactive glassesand elastomeric compositesrdquo Progress in Biomaterials vol 1 no1 article 2 2012

[143] D A Wahl and J T Czernuszka ldquoCollagen-hydroxyapatitecomposites for hard tissue repairrdquo European Cells andMaterialsvol 11 pp 43ndash56 2006

[144] J E Bergsma F R Rozema R R M Bos G Boering W Cde Bruijn and A J Pennings ldquoIn vivo degradation and bio-compatibility study of in vitro pre-degraded as-polymerizedpolyactide particlesrdquo Biomaterials vol 16 no 4 pp 267ndash2741995

[145] S Jacobsen and H G Fritz ldquoPlasticizing polylactidemdashthe effectof different plasticizers on the mechanical propertiesrdquo PolymerEngineering and Science vol 39 no 7 pp 1303ndash1310 1999


[146] P Gunatillake R Mayadunne and R Adhikari ldquoRecent devel-opments in biodegradable synthetic polymersrdquo BiotechnologyAnnual Review vol 12 pp 301ndash347 2006

[147] H Chim D W Hutmacher A M Chou et al ldquoA comparativeanalysis of scaffold material modifications for load-bearingapplications in bone tissue engineeringrdquo International Journalof Oral and Maxillofacial Surgery vol 35 no 10 pp 928ndash9342006

[148] C Du F Z Cui Q L Feng X D Zhu and K de Groot ldquoTissueresponse to nano-hydroxyapatitecollagen composite implantsinmarrow cavityrdquo Journal of Biomedical Materials Research vol42 no 4 pp 540ndash548 1998

[149] W Zhang S S Liao and F Z Cui ldquoHierarchical self-assemblyof nano-fibrils in mineralized collagenrdquo Chemistry of Materialsvol 15 no 16 pp 3221ndash3226 2003

[150] P X Ma and J Elisseeff Scaffolding in Tissue Engineering CRCPress New York NY USA 2006

[151] J L Brown S G Kumbar and C T Laurencin ldquoBone tissueengineeringrdquo in Biomaterials Science B Ratner A S HoffmanF J Schoen and J E Lemons Eds pp 1194ndash1214 ElsevierOxford UK 3rd edition 2013

[152] D P Pioletti ldquoBiomechanical considerations can serve asdesign rules in the development of bone tissue engineeringscaffoldrdquo Computer Methods in Biomechanics and BiomedicalEngineering vol 12 supplement 1 pp 17ndash18 2009

[153] J C Y Dunn W-Y Chan V Cristini et al ldquoAnalysis of cellgrowth in three-dimensional scaffoldsrdquo Tissue Engineering vol12 no 4 pp 705ndash716 2006

[154] D J Wilson J R King and H M Byrne ldquoModelling scaffoldoccupation by a growing nutrient-rich tissuerdquo MathematicalModels and Methods in Applied Sciences vol 17 pp 1721ndash17502007

[155] D Jeong A Yun and J Kim ldquoMathematical model and numer-ical simulation of the cell growth in scaffoldsrdquoBiomechanics andModeling in Mechanobiology vol 11 no 5 pp 677ndash688 2012

[156] J A Sanz-Herrera J M Garcia-Aznar and M DoblareldquoA mathematical model for bone tissue regeneration insidea specific type of scaffoldrdquo Biomechanics and Modeling inMechanobiology vol 7 no 5 pp 355ndash366 2008

[157] F Galbusera L Bertolazzi R Balossino and G DubinildquoCombined computational study of mechanical behaviour anddrug delivery from a porous hydroxyapatite-based bone graftrdquoBiomechanics and Modeling in Mechanobiology vol 8 no 3 pp209ndash216 2009

[158] X Liu and G L Niebur ldquoBone ingrowth into a porous coatedimplant predicted by a mechano-regulatory tissue differentia-tion algorithmrdquo Biomechanics andModeling inMechanobiologyvol 7 no 4 pp 335ndash344 2008

[159] C A Narvaez-Tovar and D A Garzon-Alvarado ldquoComputa-tional modeling of the mechanical modulation of the growthplate by sustained loadingrdquo Theoretical Biology and MedicalModelling vol 9 no 1 article 41 2012

[160] XHan and J Pan ldquoAmodel for simultaneous crystallisation andbiodegradation of biodegradable polymersrdquo Biomaterials vol30 no 3 pp 423ndash430 2009

[161] J A Sanz-Herrera and A R Boccaccini ldquoModelling bioactivityand degradation of bioactive glass based tissue engineeringscaffoldsrdquo International Journal of Solids and Structures vol 48no 2 pp 257ndash268 2011

[162] M P Ginebra T Traykova and J A Planell ldquoCalcium phos-phate cements as bone drug delivery systems a reviewrdquo Journalof Controlled Release vol 113 no 2 pp 102ndash110 2006

[163] M Ginebra F Gil and J Planell ldquoAcrylic bone cementsrdquo inIntegrated Biomaterials Science R Barbucci Ed pp 569ndash588Kluwer AcademyPlenum 1st edition 2002

[164] S M Kenny andM Buggy ldquoBone cements and fillers a reviewrdquoJournal of Materials Science Materials in Medicine vol 14 no11 pp 923ndash938 2003

[165] R Huiskes and M C H van der Meulen ldquoWhy mechanobiol-ogyrdquo Journal of Biomechanics vol 35 no 4 pp 401ndash414 2002

[166] D J Kelly and P J Prendergast ldquoMechano-regulation of stemcell differentiation and tissue regeneration in osteochondraldefectsrdquo Journal of Biomechanics vol 38 no 7 pp 1413ndash14222005

[167] R G Bacabac and M G Mullender ldquoMechanobiology of bonetissuerdquo Pathologie Biologie vol 53 no 10 pp 576ndash580 2005

[168] R P Gehron ldquoThe biochemistry of bonerdquo EndocrinologyMetabolism Clinics of North America vol 18 no 4 p 858 1989

[169] H Colfen ldquoBiomineralization a crystal-clear viewrdquo NatureMaterials vol 9 no 12 pp 960ndash961 2010

[170] M J Olszta X Cheng S S Jee et al ldquoBone structure and for-mation a new perspectiverdquo Materials Science and EngineeringR Reports vol 58 no 3ndash5 pp 77ndash116 2007

[171] L G Raisz ldquoBone biology bone structure and remodelingrdquoBone Disease of Organ Transplantation pp 31ndash45 2005

[172] LMMcNamara and P J Prendergast ldquoBone remodelling algo-rithms incorporating both strain and microdamage stimulirdquoJournal of Biomechanics vol 40 no 6 pp 1381ndash1391 2007

[173] R Baron ldquoAnatomy and ultrastructure of bonemdashhistogenesisgrowth and remodelingrdquo in Diseases of Bone and MineralMetabolism 2006

[174] C C Ko M J Somerman and K A An ldquoMotion and boneregenerationrdquo in Engineering of Functional Skeletal Tissues FBronner M Farach and A Mikos Eds pp 110ndash127 SpringerBerlin Germany 2007

[175] L Geris J vander Sloten and H van Oosterwyck ldquoMathemat-ical modeling of bone regeneration including the angiogenicprocessrdquo Journal of Biomechanics vol 39 supplement 1 ppS411ndashS412 2006

[176] P V Giannoudis T A Einhorn and D Marsh ldquoFracturehealing the diamond conceptrdquo Injury vol 38 supplement 4pp S3ndashS6 2007

[177] N A Sims and J H Gooi ldquoBone remodeling multiple cellularinteractions required for coupling of bone formation andresorptionrdquo Seminars in Cell amp Developmental Biology vol 19no 5 pp 444ndash451 2008

[178] A M Parfitt ldquoModeling and remodeling how bone cells worktogetherrdquo Vitamin D vol 1 pp 497ndash513 2005

[179] P Pivonka J Zimak D W Smith et al ldquoModel structure andcontrol of bone remodeling a theoretical studyrdquo Bone vol 43no 2 pp 249ndash263 2008

[180] G R Mundy ldquoCellular and molecular regulation of boneturnoverrdquo Bone vol 24 supplement 5 pp 35Sndash38S 1999

[181] H Tsurukami ldquoDisorder of bone quality in Pagetrsquos diseaserdquoClinical Calcium vol 15 no 6 pp 1000ndash1006 2005

[182] S Nomura and T Takano-Yamamoto ldquoMolecular events causedby mechanical stress in bonerdquoMatrix Biology vol 19 no 2 pp91ndash96 2000

[183] T Adachi Y Aonuma S-I Ito et al ldquoOsteocyte calcium sig-naling response to bone matrix deformationrdquo Journal of Biome-chanics vol 42 no 15 pp 2507ndash2512 2009


[184] V Lemaire F L Tobin L D Greller C R Cho and L J SuvaldquoModeling the interactions between osteoblast and osteoclastactivities in bone remodelingrdquo Journal of Theoretical Biologyvol 229 no 3 pp 293ndash309 2004

[185] C H Turner ldquoFunctional determinants of bone structurebeyond Wolff rsquos law of bone transformationrdquo Bone vol 13 no6 pp 403ndash409 1992

[186] J G Skedros and S L Baucom ldquoMathematical analysis oftrabecular lsquotrajectoriesrsquo in apparent trajectorial structures theunfortunate historical emphasis on the human proximal femurrdquoJournal of Theoretical Biology vol 244 no 1 pp 15ndash45 2007

[187] R E Guldberg C S Gemmiti Y Kolambkar and B PorterldquoPhysical stress as a factor in tissue growth and remodelingrdquoin Principles of Regenerative Medicine pp 512ndash535 AcademicPress San Diego Calif USA 2008

[188] F Forriol ldquoBone response to mechanical demand under phys-iological conditionsrdquo Revista Espanola de Cirugıa Ortopedica yTraumatologıa vol 45 no 3 pp 258ndash265 2001

[189] A Boccaccio A Ballini C Pappalettere D Tullo S Cantoreand A Desiate ldquoFinite element method (FEM) mechanobi-ology and biomimetic scaffolds in bone tissue engineeringrdquoInternational Journal of Biological Sciences vol 7 no 1 pp 112ndash132 2011

[190] M C H Van der Meulen and R Huiskes ldquoWhy mechanobiol-ogyrdquo Journal of Biomechanics vol 35 no 4 pp 401ndash414 2002

[191] D E Ingber ldquoCellular mechanotransduction putting all thepieces together againrdquoTheFASEB Journal vol 20 no 7 pp 811ndash827 2006

[192] H IsakssonWWilson C C vanDonkelaar R Huiskes and KIto ldquoComparison of biophysical stimuli formechano-regulationof tissue differentiation during fracture healingrdquo Journal ofBiomechanics vol 39 no 8 pp 1507ndash1516 2006

[193] S Weinbaum S C Cowin and Y Zeng ldquoA model for theexcitation of osteocytes by mechanical loading-induced bonefluid shear stressesrdquo Journal of Biomechanics vol 27 no 3 pp339ndash360 1994

[194] J P Stains and R Civitelli ldquoCell-to-cell interactions in bonerdquoBiochemical and Biophysical Research Communications vol 328no 3 pp 721ndash727 2005

[195] C PHuang XMChen andZQChen ldquoOsteocyte the impre-sario in the electrical stimulation for bone fracture healingrdquoMedical Hypotheses vol 70 no 2 pp 287ndash290 2008

[196] E H Burger and J Klein-Nulend ldquoMechanotransduction inbonemdashrole of the lacuno-canalicular networkrdquo FASEB Journalvol 13 no 8 pp S101ndashS112 1999

[197] H Frost The Laws of Bone Structure Charles Thomas Spring-field Ill USA 1964

[198] H M Frost ldquoFunctional determinants of bone structurebeyond Wolff rsquos law of bone transformationrdquo The AngleOrthodontist vol 64 no 3 pp 175ndash188 1994

[199] H M Frost ldquoVital biomechanics proposed general conceptsfor skeletal adaptations to mechanical usagerdquo Calcified TissueInternational vol 42 no 3 pp 145ndash156 1988

[200] D R Carter G S Beaupre N J Giori and J A Helms ldquoMecha-nobiology of skeletal regenerationrdquo Clinical Orthopaedics andRelated Research no 355 supplement pp S41ndashS55 1998

[201] L E Claes and C A Heigele ldquoMagnitudes of local stress andstrain along bony surfaces predict the course and type offracture healingrdquo Journal of Biomechanics vol 32 no 3 pp 255ndash266 1999

[202] D Lacroix and P J Prendergast ldquoA mechano-regulation modelfor tissue differentiation during fracture healing analysis of gapsize and loadingrdquo Journal of Biomechanics vol 35 no 9 pp1163ndash1171 2002

[203] R Huiskes H Weinans H J Grootenboer M Dalstra BFudala and T J Slooff ldquoAdaptive bone-remodeling theoryapplied to prosthetic-design analysisrdquo Journal of Biomechanicsvol 20 no 11-12 pp 1135ndash1150 1987

[204] F Pauwels ldquoA new theory on the influence of mechanicalstimuli on the differentiation of supporting tissue The tenthcontribution to the functional anatomy and causal morphologyof the supporting structurerdquo Zeitschrift fur Anatomie undEntwicklungsgeschichte vol 121 pp 478ndash515 1960

[205] P J Prendergast ldquoFinite element models in tissue mechanicsand orthopaedic implant designrdquo Clinical Biomechanics vol 12no 6 pp 343ndash366 1997

[206] D P Fyhrie and D R Carter ldquoA unifying principle relatingstress to trabecular bone morphologyrdquo Journal of OrthopaedicResearch vol 4 no 3 pp 304ndash317 1986

[207] B G SengersM Taylor C P Please and RO COreffo ldquoCom-putational modelling of cell spreading and tissue regenerationin porous scaffoldsrdquo Biomaterials vol 28 no 10 pp 1926ndash19402007

[208] M Kassem L Ankersen E F Eriksen B F C Clark and SI S Rattan ldquoDemonstration of cellular aging and senescencein serially passaged long-term cultures of human trabecularosteoblastsrdquoOsteoporosis International vol 7 no 6 pp 514ndash5241997

[209] M A Perez and P J Prendergast ldquoRandom-walk models of celldispersal included in mechanobiological simulations of tissuedifferentiationrdquo Journal of Biomechanics vol 40 no 10 pp2244ndash2253 2007

[210] A Roshan-Ghias A Vogel L Rakotomanana andD P PiolettildquoPrediction of spatio-temporal bone formation in scaffold bydiffusion equationrdquo Biomaterials vol 32 no 29 pp 7006ndash70122011

[211] C R Jacobs J C Simo G S Beaupre and D R CartertldquoAdaptive bone remodeling incorporating simultaneous densityand anisotropy considerationsrdquo Journal of Biomechanics vol 30no 6 pp 603ndash613 1997

[212] D R Carter T E Orr and D P Fyhrie ldquoRelationships betweenloading history and femoral cancellous bone architecturerdquoJournal of Biomechanics vol 22 no 3 pp 231ndash244 1989

[213] H Weinans R Huiskes and H J Grootenboer ldquoThe behaviorof adaptive bone-remodeling simulation modelsrdquo Journal ofBiomechanics vol 25 no 12 pp 1425ndash1441 1992

[214] M G Mullender and R Huiskes ldquoOsteocytes and bone liningcells which are the best candidates for mechano-sensors incancellous bonerdquo Bone vol 20 no 6 pp 527ndash532 1997

[215] R Huiskes R Rulmerman G H van Lenthe and J D JanssenldquoEffects of mechanical forces onmaintenance and adaptation ofform in trabecular bonerdquo Nature vol 405 no 6787 pp 704ndash706 2000

[216] R Ruimerman P Hilbers B van Rietbergen and R HuiskesldquoA theoretical framework for strain-related trabecular bonemaintenance and adaptationrdquo Journal of Biomechanics vol 38no 4 pp 931ndash941 2005

[217] Y Cao G Mitchell A Messina et al ldquoThe influence of archi-tecture on degradation and tissue ingrowth into three-dimensional poly(lactic-co-glycolic acid) scaffolds in vitro andin vivordquo Biomaterials vol 27 no 14 pp 2854ndash2864 2006


[218] M W Laschke A Strohe C Scheuer et al ldquoIn vivo biocom-patibility and vascularization of biodegradable porous poly-urethane scaffolds for tissue engineeringrdquo Acta Biomaterialiavol 5 no 6 pp 1991ndash2001 2009

[219] A A Deschamps A A vanApeldoorn H Hayen et al ldquoIn vivoand in vitro degradation of poly(ether ester) block copolymersbased on poly(ethylene glycol) and poly(butylene terephtha-late)rdquo Biomaterials vol 25 no 2 pp 247ndash258 2004

[220] H Tsuji and K Ikarashi ldquoIn vitro hydrolysis of poly(L-lactide)crystalline residues as extended-chain crystallites Part I Long-termhydrolysis in phosphate-buffered solution at 37∘CrdquoBioma-terials vol 25 no 24 pp 5449ndash5455 2004

[221] C J Kirkpatrick K Peters M I Hermanns et al ldquoIn vitromethodologies to evaluate biocompatibility status quo andperspectiverdquo ITBM-RBM vol 26 no 3 pp 192ndash199 2005

[222] B Vailhe D Vittet and J-J Feige ldquoIn vitro models of vasculo-genesis and angiogenesisrdquo Laboratory Investigation vol 81 no4 pp 439ndash452 2001

[223] H Kim R P Camata S Chowdhury and Y K Vohra ldquoIn vitrodissolution and mechanical behavior of c-axis preferentiallyoriented hydroxyapatite thin films fabricated by pulsed laserdepositionrdquo Acta Biomaterialia vol 6 no 8 pp 3234ndash32412010

[224] P Buma W Schreurs and N Verdonschot ldquoSkeletal tissueengineeringmdashfrom in vitro studies to large animal modelsrdquoBiomaterials vol 25 no 9 pp 1487ndash1495 2004

[225] Y Kang Y Yao G Yin et al ldquoA study on the in vitro deg-radation properties of poly(l-lactic acid)120573-tricalcuim phos-phate(PLLA120573-TCP) scaffold under dynamic loadingrdquoMedicalEngineering and Physics vol 31 no 5 pp 589ndash594 2009

[226] C A Chung T-H Lin S-D Chen and H-I Huang ldquoHybridcellular automatonmodeling of nutrient modulated cell growthin tissue engineering constructsrdquo Journal of Theoretical Biologyvol 262 no 2 pp 267ndash278 2010

[227] J-T Schantz A Brandwood D W Hutmacher H L Khorand K Bittner ldquoOsteogenic differentiation of mesenchymalprogenitor cells in computer designed fibrin-polymer-ceramicscaffolds manufactured by fused deposition modelingrdquo Journalof Materials Science Materials in Medicine vol 16 no 9 pp807ndash819 2005

[228] J Pierre B David K Oudina H Petite C Ribreau and COddou ldquoModeling of large bone implant culture in a perfusionbioreactorrdquo Journal of Biomechanics vol 39 supplement 1 pS220 2006

[229] P Miranda A Pajares and F Guiberteau ldquoFinite elementmodeling as a tool for predicting the fracture behavior of robo-cast scaffoldsrdquo Acta Biomaterialia vol 4 no 6 pp 1715ndash17242008

[230] SVKomarova ldquoBone remodeling in health anddisease lessonsfrommathematical modelingrdquoAnnals of the New York Academyof Sciences vol 1068 no 1 pp 557ndash559 2006

[231] J A Sanz-Herrera and E Reina-Romo ldquoCell-biomaterialmechanical interaction in the framework of tissue engineeringinsights computational modeling and perspectivesrdquo Interna-tional Journal ofMolecular Sciences vol 12 no 11 pp 8217ndash82442011

[232] J A Sanz-Herrera J M Garcıa-Aznar and M Doblare ldquoOnscaffold designing for bone regeneration a computationalmultiscale approachrdquo Acta Biomaterialia vol 5 no 1 pp 219ndash229 2009

[233] H Kang C-Y Lin and S J Hollister ldquoTopology optimizationof three dimensional tissue engineering scaffold architectures

for prescribed bulk modulus and diffusivityrdquo Structural andMultidisciplinaryOptimization vol 42 no 4 pp 633ndash644 2010

[234] D Lacroix J A Planell and P J Prendergast ldquoComputer-aideddesign and finite-elementmodelling of biomaterial scaffolds forbone tissue engineeringrdquo Philosophical Transactions of the RoyalSociety A Mathematical Physical and Engineering Sciences vol367 no 1895 pp 1993ndash2009 2009

[235] J A Sanz-Herrera J M Garcıa-Aznar and M Doblare ldquoAmathematical approach to bone tissue engineeringrdquo Philosoph-ical Transactions of the Royal Society of London Series AMathematical Physical and Engineering Sciences vol 367 no1895 pp 2055ndash2078 2009

[236] D P Byrne P J Prendergast and D J Kelly ldquoOptimisation ofscaffold porosity using a stochastic model for cell proliferationand migration in mechanobiological simulationsrdquo Journal ofBiomechanics vol 39 supplement 1 pp S413ndashS414 2006

[237] P Swider M Conroy A Pedrono et al ldquoUse of high-resolutionMRI for investigation of fluid flow and global permeability in amaterial with interconnected porosityrdquo Journal of Biomechanicsvol 40 no 9 pp 2112ndash2118 2007

[238] K Karunratanakul J Schrooten and H van OosterwyckldquoFinite element modelling of a unilateral fixator for bone recon-struction Importance of contact settingsrdquoMedical Engineeringand Physics vol 32 no 5 pp 461ndash467 2010

[239] J A Sanz-Herrera JM Garcıa-Aznar andMDoblare ldquoMicro-macro numerical modelling of bone regeneration in tissueengineeringrdquo Computer Methods in Applied Mechanics andEngineering vol 197 no 33-40 pp 3092ndash3107 2008

[240] K S Chan W Liang W L Francis and D P Nicolella ldquoAmultiscale modeling approach to scaffold design and propertypredictionrdquo Journal of the Mechanical Behavior of BiomedicalMaterials vol 3 no 8 pp 584ndash593 2010

[241] H Ye D B Das J T Triffitt and Z Cui ldquoModelling nutrienttransport in hollow fibre membrane bioreactors for growingthree-dimensional bone tissuerdquo Journal of Membrane Sciencevol 272 no 1-2 pp 169ndash178 2006

[242] T S Karande J L Ong and C M Agrawal ldquoDiffusion inmusculoskeletal tissue engineering scaffolds design issuesrelated to porosity permeability architecture and nutrientmixingrdquo Annals of Biomedical Engineering vol 32 no 12 pp1728ndash1743 2004

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


Table 1 Mechanical properties of bone From Bandyopadyay-Ghosh [39] and Knudson [40]

Property Cortical bone Cancellous boneTensile strength (MPa) 50ndash150 10ndash100Compressive strength (MPa) 130ndash230 2ndash12Youngrsquos modulus (GPa) 7ndash30 002ndash05Strain to failure () 1ndash3 5ndash7Shear strength (MPa) 53ndash70Shear modulus (GPa) 3

Bones have mechanical synthetic and metabolic func-tions The mechanical functions are protection of internalorgans body support and interaction with muscles and ten-dons to generate body movement [5] The synthetic functionis conducted by the bone marrow where both bone andblood cells are synthesized in a process called hematopoiesis[10] Metabolic functions are related to act as a reservoir ofcalcium phosphorus growth factors and fat [11] Besidesbone tissue helps to regulate pH level of blood releasingalkaline salts [12]

Referring to mechanical function bones are the struc-tural elements of the human body Skeletal system supportsloads due to the different activities of an individual as holdingthings walking pushing and so forth These loads inducetensile compressive or shear stresses on the bone tissueMore complex stresses such as those caused by bendingor twisting of bone can be decomposed into the threebasic aforementioned stresses To study these stresses bonemechanical properties such as elasticity modulus compres-sive and tensile strength are important These propertiesare highly dependent on the position of the bone and thecondition of the individual Besides mechanical propertiesof bone vary depending on the load orientation with respectto the orientation of the tissue (anisotropy) and the speed towhich the load is applied (viscoelasticity) [3 13] Reference[14] provides a good source of data andmodels of mechanicalproperties for different types of human bones Some impor-tant mechanical properties are described in Table 1

Another important physical property of osseous tissue ispermeability that describes the porosity and interconnectivityof tissue Permeability is estimated between 0003ndash11 times10minus6m4Nsdots for trabecular bone in humans and 09ndash78 times10minus11m4Nsdots in cortical bone for canine and bovine animals[15] A detailed explanation of permeability in bone can befound in [16 17]

Bone tissuemay suffer various diseases that can be causedby excessive load or hormonal deficiencies among otherreasons [18 19] Bone tissue as an engineering material canfail becausemechanical loads originate stresses over the limitsa healthy bone can bear or because themechanical propertiesof bone are decreased by various pathologiesmaking the boneweak and prone to be damaged Some of the diseases of bonetissue are as follows

(i) Fracture it is partial or total loss of bone continuity Itis caused by traumas by mechanical loads that exceedthe allowable stresses of the bone There may be

associated factors to the extent that allowable stressesare conditioned by other diseases that affect bonedensity They can be classified considering the type oftrauma fracture shape and the location and directionof the load [20]

(ii) Osteogenesis imperfecta it is bone embrittlement dueto deficiencies in the collagen matrix [21]

(iii) Osteoporosis it is loss of bone minerals by hormonaldeficiencies [22]

(iv) Osteomalacia or rickets it is loss of bone mineralcaused by nutritional deficiencies [23]

(v) Osteomyelitis it is bone infection caused by bacteria[24 25]

(vi) Cancer primary ormetastatic type causes progressivedamage of bone tissue and its functions [26]

Asmentioned above those diseases affectmultiple demo-graphic groups according their socioeconomic conditionsFor example in developed countries the life expectancy ofthe population has increased considerably causing a rise inosteoporosis cases [27]

2 Bone Tissue Engineering

Tissue engineering combines the use of cells engineeringmaterials and physicochemical factors to improve or replacethe biological functions of damaged tissues or organs Ituses the principles and methods of engineering biology andbiochemistry for understanding the structure and function ofnormal and pathological mammalian tissues and for devel-oping biological substitutes in order to restore maintain orimprove its function [28] A wide area of interest for tissueengineering is the development of scaffolds that contributeto bone regeneration processes [29] This development couldfollow some or all of the stages listed below [30]

(1) scaffold fabrication(2) growth factor placement in the scaffold or damaged

area(3) seeding of an osteoblast population into the scaffold

in a static culture (petri dish)(4) growth of premature tissue in a dynamic environment

(spinner flask)(5) growth of mature tissue in a physiologic environment

(bioreactor)(6) surgical transplantation of the scaffold(7) tissue-engineered transplant assimilationremodel-

ing

The number and the way that previous stages are com-bined give complexity to the bone regeneration processesin tissue engineering For scaffold fabrication factors likesize mass porosity surfacevolume ratio form surfaceshape and chemistry of the element to be manufacturedand composition structure molecular weight andmolecularorientation of the biomaterial must be considered For stages









































empty
















O7



10

(PO4)6

(OH)2





2

Na2

OCaO and P2

O5


















Elongation()

Meltingpoint (∘C)




















(MPa)Modulus(MPa)

Ultimatestrain ()


HA






15 to 39 137 to 260 11 to 137

PLG 01 to 1 50 to 300


(micro)007 to 008 065 to 12 721 to 133














Dissolution

Ceramic





Cell-mediated



Polymer












Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)


Cartilage Bone



(b)


0

101520




ossification


(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10


Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)





120588 = 119860120590120572

(1)


1205902

= 2119864119880 (2)


119864 = 1198881205883

(3)


119864axial = 119862 120576006

1205883

(4)



120588 = 1198881015840

119880 (5)












119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
























































empty
















O7



10

(PO4)6

(OH)2





2

Na2

OCaO and P2

O5


















Elongation()

Meltingpoint (∘C)




















(MPa)Modulus(MPa)

Ultimatestrain ()


HA






15 to 39 137 to 260 11 to 137

PLG 01 to 1 50 to 300


(micro)007 to 008 065 to 12 721 to 133














Dissolution

Ceramic





Cell-mediated



Polymer












Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)


Cartilage Bone



(b)


0

101520




ossification


(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10


Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)





120588 = 119860120590120572

(1)


1205902

= 2119864119880 (2)


119864 = 1198881205883

(3)


119864axial = 119862 120576006

1205883

(4)



120588 = 1198881015840

119880 (5)












119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
























O7



10

(PO4)6

(OH)2





2

Na2

OCaO and P2

O5


















Elongation()

Meltingpoint (∘C)




















(MPa)Modulus(MPa)

Ultimatestrain ()


HA






15 to 39 137 to 260 11 to 137

PLG 01 to 1 50 to 300


(micro)007 to 008 065 to 12 721 to 133














Dissolution

Ceramic





Cell-mediated



Polymer












Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)


Cartilage Bone



(b)


0

101520




ossification


(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10


Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)





120588 = 119860120590120572

(1)


1205902

= 2119864119880 (2)


119864 = 1198881205883

(3)


119864axial = 119862 120576006

1205883

(4)



120588 = 1198881015840

119880 (5)












119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
































Elongation()

Meltingpoint (∘C)




















(MPa)Modulus(MPa)

Ultimatestrain ()


HA






15 to 39 137 to 260 11 to 137

PLG 01 to 1 50 to 300


(micro)007 to 008 065 to 12 721 to 133














Dissolution

Ceramic





Cell-mediated



Polymer












Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)


Cartilage Bone



(b)


0

101520




ossification


(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10


Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)





120588 = 119860120590120572

(1)


1205902

= 2119864119880 (2)


119864 = 1198881205883

(3)


119864axial = 119862 120576006

1205883

(4)



120588 = 1198881015840

119880 (5)












119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















(MPa)Modulus(MPa)

Ultimatestrain ()


HA






15 to 39 137 to 260 11 to 137

PLG 01 to 1 50 to 300


(micro)007 to 008 065 to 12 721 to 133














Dissolution

Ceramic





Cell-mediated



Polymer












Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)


Cartilage Bone



(b)


0

101520




ossification


(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10


Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)





120588 = 119860120590120572

(1)


1205902

= 2119864119880 (2)


119864 = 1198881205883

(3)


119864axial = 119862 120576006

1205883

(4)



120588 = 1198881015840

119880 (5)












119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















Dissolution

Ceramic





Cell-mediated



Polymer












Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)


Cartilage Bone



(b)


0

101520




ossification


(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10


Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)





120588 = 119860120590120572

(1)


1205902

= 2119864119880 (2)


119864 = 1198881205883

(3)


119864axial = 119862 120576006

1205883

(4)



120588 = 1198881015840

119880 (5)












119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















Hyaline cartilage

Fibrocartilage

Fibrousconnective

tissue

Lamellarbone

Mese

nchy

me

Com

pres

sion

(hyd

rost

atic

pre

ssur

e)

(a)


Cartilage Bone



(b)


0

101520




ossification


(MPa)

Strain()

TensionCompression

minus5

5

(c)

0123456789

10


Fibrous tissue

Cartilage

Bone

Flui

d flo

w (120583

ms

)

(d)





120588 = 119860120590120572

(1)


1205902

= 2119864119880 (2)


119864 = 1198881205883

(3)


119864axial = 119862 120576006

1205883

(4)



120588 = 1198881015840

119880 (5)












119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



























119889119883

119889119905

= 119862119909

(119880 minus 119880119899

) (6)

Bone formation

Bone resorption


Un

2s

Rate of bonechange



119899



119889119864

119889119905

= 119862119864

(119880 minus 119880119899

) (7)


119889119883

119889119905

= 119862119909

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone formation)

0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119883

119889119905

= 119862119909

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899

(Bone resorption)

(8)


119889119864

119889119905

= 119862119864

(119880 minus (1 + 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


0 for (1 minus 119904)119880119899

gt 119880 gt (1 minus 119904)119880119899

(Lazy zone)

119889119864

119889119905

= 119862119864

(119880 minus (1 minus 119904)119880119899

)

for 119880 gt (1 + 119904)119880119899


(9)



120595119887

= (

119899

sum

119894=1

119899119894

120590119887

)

1119898

(10)




119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















119887


119878 =

1

119899

1

120588

119899

sum

119894=1

119880119894

(11)

where119880119894


119889120588

119889119905

= 119861 (119878 minus 119896) (12)



119889119898tot119889119905

=

119889119898cl (119909 119905)

119889119905

+

119889119898bl (119909 119905)

119889119905

(13)



119889119898bl (119909 119905)

119889119905

= 120591 (119875 (119909 119905) minus 119896) (14)





5 Discussion
















PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



























PLGA

Mesenchymalcells



[58]








Mesenchymalcells



[63]










Mesenchymalcells



[158]






Acknowledgment


References

































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of












































































































































































































































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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