Thread 1. Computational Methods in Biomechanics and Mechanobiology

5323 Th, 11:45-12:00 (P42) A mechanobiological model of periprosthetic tissue healing P. Swider 1 , D. Ambard 1 , J.E. Bechtold 2, K. S~balle 3. 1Biomechanics Laboratory EA 3697, Toulouse, France, 2Midwest Orthopaedic Research Foundation, Minneapolis, MN, USA, 3University Hospital of Aarhus, Aarhus, Denmark

Conditions influencing bone growth around implants include the surgical tech- nique and coupled mechanical and biochemical factors [1]. In our previous in-vivo studies with a canine implant, we have identified that low performances were generally associated with a low mineralization or a heterogeneous distribution of bony structure in the new-formed surrounding tissue [2]. We hypothesized that associating biological concept of cell migration to convection- diffusion into porous media might help to predict the heterogeneity of mineral density in the healing process of periprosthetic tissue in the early post- operative period. Modelling in cellular biology and mechanics of reactive porous media were coupled. The multiphasic model involved a solid phase (extracellular osseous matrix), an extracellular fluid phase, an osteoblastic phase with active mi- gration, a nd a growth factor phase. The non-linear coupled convection- diffusion equations was solved involving mechanical strain variable in time. Predicted models were compared to ex-vivo histomorphometric data and the results were satisfying. A sensitivity analysis was implemented to gain a better understanding of mechanobiological phenomena. The increase of the initial periprosthetic gap and initial growth factor con- centration would favour the homogenous bone healing within the gap. This was in agreement with in-vivo results when allologous growth factors sources were used. The haptotaxic migration was unfavourable to the homogenous healing and the chemotatic migration was favourable to the bone formation at the implant surface and homogenous healing. These conflicting effects could explain oscillations observed in the in-vivo periprosthetic consolidation. The mechanical strain in loaded implants increased the heterogeneity of the periprosthetic tissue healing.

References [1] Puleo DA, et al. Osteoblast responses to orthopedic implant materials in vitro.

J Biomed Mater Res. 1991 Jun; 25(6): 711-23. [2] Vestermark et al. Mechanical interface conditions affect morphology and cellular

activity of sclerotic bone rims forming around experimental loaded implants. J Orthop Res. 2004 May; 22(3): 647-52.

5749 Th, 12:00-12:15 (P42) Simulations predicting bone remodelling and interfacial tissue formation in uncemented hip replacements P.T. Scannell, P.J. Prendergast. Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Ireland

The influence of stem stiffness on bone remodelling patterns and interface stresses [1] shows that stiffer stems cause more proximal bone resorption than those of a lower stiffness; however, proximal interface stresses were found to be highest for the low stiffness stems. It is widely accepted that bone remodelling is influenced by both strain and microdamage. We hypothesize that combining these two stimuli, both bone remodelling and interface remodelling/repair can be simultaneously predicted. The mechanoregulation equation is based on that proposed in [2] and [3], whereby strain-based remodelling is only allowed when the accumulated damage is below a certain critical value; once that value has been exceeded damage-driven resorption takes over. By varying the elastic modulus, the influence stem stiffness has on bone remodelling patterns and periprosthetic damage accumulation was predicted. Flexible stems exhibit very little proximal bone resorption due to stress shield- ing whereas stiffer stems are predicted to incur significant resorption. However, at the proximal stern/bone interface, where interface stresses tend to be higher in flexible stems than in stiff stems, high interfacial stresses caused damage- induced bone resorption as a repair mechanism. Hence, these flexible stems inhibit bone ingrowth to the proximal HA coated portion of the stem, due to excessive interface damage and micro-motion, leading to fibrous tissue formation. In the stiffer stems distal load transfer has a similar effect where excessive distal tip motion due to damage accumulation and resorption at the interface leads to implant loosening. Therefore this model allows simultaneous prediction of both bone resorption and interfacial resorption due to damage. The model could be used to optimize hip prosthesis design.

References [1] Weinans H., et al. J. Orthop. Res. 1992; 10(6): 845-53. [2] Prendergast P.J. Meccanica 2002; 37: 317-334. [3] McNamara L.M., Prendergast P.J. Eur. J. Morphol. 2005; 42(1/2): 99-109.

T1.9 Computational Bone Mechanobiology $413

4355 Th, 14:00-14:15 (P45) Three-dimensional bone adaptation - A hierarchical model P.G. Coelho 1, P.R. Fernandes 2, J.B. Cardoso 1, J.M. Guedes 2, H.C. Rodrigues 2. 1DEMI, FC T/UNL, Caparica, Portugal, 21DMEC-IS T, Lisbea, Portugal

Mathematical models for bone functional adaptation usually compute the change on bone apparent density for every point depending on a mechanical stimulus. Some of these models consider bone as an isotropic structural material, which is a shortcoming on the treatment of trabecular bone, since it disregards orientation in the remodelling equations. To overcome this, there are models that couple material density and orientation into a single model. An approach to obtain such coupling is to model bone assuming it as a cellular material with an orthotropic microstructure and identifying remodelling with a material optimization process [1]. To avoid any a priori assumption of material symmetries, Rodrigues et al. [2] presented a global-local hierarchical approach in which a global model of an entire bone supplies strain and density information to a series of local models of microstructure at each material point of the global model. In the actual work, a three-dimensional hierarchical model for bone remod- elling is presented. The natural process of bone adaptation is mathematically described for two levels of the bone structure: the macroscopic level where the bone apparent density is determined and a microscopic level where the trabecular structure is defined by its mechanical properties. The law of bone remodelling is obtained assuming that bone adapts to functional demands in order to satisfy a multi-criteria for structural stiffness and metabolic cost of bone formation. Results for two-dimensional and three-dimensional examples are presented where the distribution of density as well as the anisotropic properties of internal trabecular architecture is achieved. The three-dimensional examples show the requirement for biologic regulators in the model, such as the control of porosity. It is discussed the application of the three-dimensional hierarchical model to the design of bone scaffolds used for tissue regeneration.

References [1] P. Fernandes et al. Comp. Meth. Biomech and Biomed Eng 1999; 2: 125-138. [2] H. Rodrigues et al. In: IUTAM Symposium on Synthesis in Bio Solid Mechanics.

1999, Kluwer, pp. 221-233.

6529 Th, 14:15-14:30 (P45) A FE algorithm for spine growth and growth modulation P. BLichler, A. Lindberg, S. Olsen. MEM Research Center, University of Bern, Switzerland

Scoliosis is a debilitating condition involving excessive twisting and bending of the spinal column during growth. Young patients, mainly girls in their early teens, suffering from this condition must go through highly invasive spine surgery which has the sole aim of fusing the spine. This treatment may prevent the deformity from developing, but it also greatly limits motion and halts natural growth. Many basic questions remain to be addressed in this area. It has been shown that growth is load modulated, but the relationship between load, growth and scoliosis progression is not clear. For example, it is difficult to predict the consequences of initial mechanical instability on the scoliotic progression. For this reasons, the goal of the present study is to provide a better understanding of the scoliosis progression and correction The initial conditions leading to a scoliotic spine are not known. However, the evolution of the curvature is thought to be primarily biomechanical. The onset of the initial deformation results in an asymmetric loading on the vertebras, which in turn provokes an asymmetric growth of the vertebral bone causing a progression of the deformity. This mechanical modulation of the growth is known as the Heuter-Volkman principle. High loads inhibit bone growth while diminished loads hasten growth. A finite element algorithm describing the vertebra growth including its modu- lation was developed and implemented in a commercial finite element code. This method is able to solve simultaneously the bone growth and the bone stress alteration due to this growth. The proposed algorithm was used to evaluate different scoliosis correction techniques on idealized spine models. Bone growth limitation as well as spine stiffening was observed for current fusion techniques. This tool may be used to further evaluate novel correction techniques as well as test hypotheses of scoliosis progression.

4856 Th, 14:30-14:45 (P45) Optimisation of scaffold porosity using a stochastic model for cell proliferation and migration in mechanobiological simulations D.P. Byrne, P.J. Prendergast, D.J. Kelly. Centre for Bioengineering, Department of Mechanical Engineering, Trinity College Dublin, Ireland

Numerical techniques are a valuable tool used for the assessment of bone scaffold mechanical properties, and can contribute to an optimised scaffold