Thread 1. Computational Methods in Biomechanics and Mechanobiology T1.9 Computational Bone Mechanobiology $411

of BMU morphology. We developed computational simulations to examine remodelling theories for complex BMU forms observed in secondary bone. One idealized model and two geometrically accurate (single and branched canal forms) generated from three-dimensional ~tCT data were analyzed. Models were subjected to differing magnitudes of axial compressive loads. Upon loading, fluid flowed from the bone matrix into the low-pressure resorption space. Consistent with previous models, the idealized form had reduced longitudinal normal strain directly in front of the cutting cone where osteoclasts are activated and increased strain behind the cutting cone where osteoclasts are inhibited. The geometrically accurate single canal model also displayed decreased strain in front of the cutting cone, although strain behind the cone increased minimally, relative to the idealized case. Similarly, the geometrically accurate branched model demonstrated strain reduction in front of both cutting cones and minimally increased strain behind the cones. Branched morphology also displayed significant strain reduction above the fork in the canal, where it divided into two resorption spaces. If strain plays a central role in remodelling, inter-branch strain shielding suggested that the region between resorption spaces would also be prone to osteoclastic activity, eliminating the branched structure. Therefore, strain and related fluid flow may not explain complex canal geometries. Further investigation is required to elucidate alternative mechanisms involved in cortical bone remodelling.

References [1] Parfitt J. Cell. Biochem. 1994; 55: 273-286. [2] Burger et al. J. Biomech. 2003; 36: 1453-1459. [3] Smit and Burger J. Bone Miner. Res. 2000; 15: 301-307. [4] Smit et al. J. Bone Miner. Res. 2002; 17: 2021-2029.

5519 Th, 08:30-08:45 (P39) Impact of age-dependent cortical bone rarefaction on tissue f luid pressure: Implications for mechanotransduction D.M.L. Cooper 1 , G.C. Goulet 2, C.D.L. Thomas 3, J.G. Clement 3, D. Coombe 4, R.F. Zernicke 2,5 . 1Department of Orthopaedics, University of British Columbia, Vancouver, Canada, 2 Schulich School of Engineering, University of Calgary, Calgary, Canada, 3School of Dental Science, University of Melbourne, Melbourne, Australia, 4Computer Modeling Group, Ltd., Calgary, Canada, 5Faculties of Medicine and Kinesiology, University of Calgary, Calgary, Canada

Load induced fluid flow may play a pivotal role in bone mechanotransduction. Modeling has demonstrated the significance of osteonal canals as routes for fluid pressure relaxation, but existing models are limited to idealized and implicitly static canal geometries. We hypothesized that age-dependent cortical bone rarefaction, which occurs through an increase in both the number and size of osteonal canals, would, under equal strain conditions, result in decreased intracortical fluid pressure. To test that hypothesis, 2D micro-CT images from three human female femoral midshaft specimens were integrated into the STARS (Computer Modeling Group, Ltd., Calgary, AB, Canada) mechan- ics/fluid flow simulator. The specimens, aged 22, 65, and 87 years, exhibited porosities of 3.9%, 14.4%, and 44.7%, respectively. A dual porosity model was developed to account for fluid flow at the levels of the osteonal and the lacuno-canalicular networks. Under uniaxial compression (200 ~t~), the 65 and 87 year old specimens, respectively, exhibited 50% and 78% reductions in mean fluid pressure relative to the younger specimen. Localized fluid pressure was proportional to the distance to the nearest osteonal canal, indicating that inter-canal spacing, was the primary factor affecting fluid flow at that level. If fluid flow plays a central role in the regulation of bone modeling and remodeling, then these results indicated that the concomitant microstructural changes associated with these processes, in turn, may affect fluid flow. Further investigation is required to determine the significance of this potential feedback mechanism. For example, age dependent loss of bone may be an adaptive response to decreased loading, resulting in the maintenance of strain and fluid pressure magnitudes. Alternatively, that relation may be strictly detrimental, inhibiting mechantransduction and accelerating bone loss.

4953 Th, 08:45-09:00 (P39) Simulation of the effect of alternating resting-loading periods in bone remodelling P. Fornells, J.M. Garcia-Aznar, M. Doblare. Group ef Structural Mechanics and Materials Modelling, Aragon Institute of Engineering Research (13A), University of Zaragoza, Zaragoza (Spain)

Bone remodelling models usually consider a mechanical stimulus related with strain or strain rate. However, several authors suggest that the stimulus is shear stress induced to osteocytes by canalicular fluid flow [1]. Nevertheless, it is quite difficult to directly measure fluid flow velocities and shear stresses within the lacuno-canalicular system. Therefore, computational poroelastic models at the microstructural level can be used in order to estimate these quantities [2]. Recently, Srinivasan et al. [3] performed experiments on rats showing that

inserting a resting period between load cycles can induce a significant increase in bone formation. The aim of this paper is to investigate if a continuum double- porosity approach can explain this fact. The finite element model of a rat tibia studied by Srinivasan et al. [3] has been developed. Alternating resting- loading periods have been considered to simulate the experiments. The fluid flow distribution is analyzed, correlating it with the zones of bone formation observed in the laboratory, in order to test the initial hypothesis.

References [1] Cowin SC. Mechanosensation and fluid transport in living bone. J Musculoskel

Neuron Interact 2002; 2(3): 256-260. [2] Steck R, Niederer P, Knothe Tate ML. A Finite Element analysis for the prediction

of load-induced fluid flow and mechanochemical transduction in bone. J Theor Biol 2003; 220: 249-259.

[3] Srinivasan S, Agans SC, King KA, Moy NY, Poliachik SL, Gross TS. Enabling bone formation in the aged skeleton via rest-inserted mechanical loading. Bone 2003; 33: 946-955.

7304 Th, 09:00-09:15 (P39) Modeling and simulation of trabecular surface remodeling considering morphological characteristics of osteocyte network T. Adachi, N. Sato, M. Tanaka, M. Hojo. Department of Mechanica/ Engineering and Science, Kyoto University, Kyoto, Japan

Functional adaptation by remodeling in cancellous bone is accomplished by complex coupled osteoclastic resorption and osteoblastic formation on trabecular surface at cellular level under the influence of local mechanical environment. This adaptive process at the microscopic level leads to spatial and temporal regulation of the trabecular structure as a load-bearing construct to meet its functional demands to the macroscopic mechanical environment. Osteocyte embedded in bone matrix is recognized as a candidate to play an important role in the mechanosensory system. The osteocytes in the lacuna connect to each other via cell processes in canaliculi, and are believed to sense the mechanical stimulus such as shear stress due to interstitial fluid flow in the lacuno-canalicular system. This study aimed to investigate the relationship between morphological characteristics of the lacuno-canalicular system and mechanical signals at the cellular level on the trabecular surface on which osteoclastic and osteoblastic cells exist to remodel its surface. A rate equation of trabecular surface remodeling was proposed considering morphological characteristics of the lacuno-canalicular system. The characteristics of the system were quantitatively evaluated for trabeculae in cancellous bone excised from a swine femur, and were taken into account in the rate equation as the anisotropic sensitivity to the macroscopic pressure gradient that causes the interstitial fluid flow. A computational simulation of trabecular remodeling was conducted for a single trabecula under uniaxial compressive loading, in which the Level Set method was introduced to express smooth surface movement due to the remodeling, combining with the voxel FEM for mechanical analysis. The trabecula changed its shape by remodeling to align along the loading direction, that implies the functional adaptation to the applied mechanical loading. In addition, the simulation revealed that the anisotropy of the network system was one of the important parameters that affect the trabecular surface remodeling.

4613 Th, 09:15-09:30 (P39) Mathematical modeling of bone regeneration including the angiogenic process L. Geris, J. Vander Sloten, H. Van Oosterwyck. Division of Biomechanics and Engineering Design, Katholieke Universiteit Leuven, Leuven, Belgium

Nowadays, a number of mechanoregulatory and biological models are avail- able that simulate bone regeneration during fracture healing, to help identifying possible regeneration pathways. These models use various mechanical and biological stimuli triggering and guiding the healing process. Angiogenesis is often missing in these models, although good vascular regeneration is imper- ative for successful bone regeneration. Furthermore, an adequate description of cell migration is absent in most of these models. A novel mathematical model for the simulation and prediction of bone regen- eration is currently under evaluation. The model is capable of simulating bone regeneration through both intramembraneous and endochondral ossification. Angiogenesis has been added as one of the key events in the regeneration process. This constitutes the addition of an endothelial cell type, a vascular growth factor and a variable representing the vascular tissue density. The models' constituting cell types are mesenchymal stem cells, fibroblasts, chon- drocytes, osteoblasts and endothelial cells. Cellular actions such as migration, proliferation, differentiation and matrix production are described by the model's equations. These actions are coordinated by the concentrations of osteogenic, chondrogenic and vascular growth factors and by the cell and matrix densities. An elaborate description of migration for different cell types, including chemo- taxis and haptotaxis, has been added to the corresponding equations. The mathematical model is implemented in a custom finite volumes code, especially developed for biological applications, taking into account the mod-