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A mathematical model approach of bone regeneration using scaffolds
$412
Journal o f Biomechanics 2006, Vol. 39 (Suppl 1)
els' requirements on mass conservation and non-negativity of the variables. This model is capable of simulating normal fracture healing. Considering the presence of the angiogenic process we expect that we will also be able to address pathological situations due to impaired vascularisation.
Oral Presentations [3] Shimko DA, Shimko VF, Sander EA, Dickson KF, Nauman EA. Effect of porosity on the fluid flow characterisation and mechanical properties of tantalum scaffolds. J Biomed Mater Res B: Appl Biomater 2005; 73(B): 315-324. 5927
6933 Th, 09:30-09:45 (P39) The perichondrium determines the mineralization front in long bones R.C.C. van Donkelaar, S.W. Witvoet-Braam, R. Huiskes. Dept Biomedical
Engineering, Eindhoven University of Technology, Eindhoven, Netherlands Introduction: Mineralization of fetal bones starts by hypertrophy in the center of the anlage, followed by local mineral formation. The mineralized area grows laterally before extending proximally and distally [1]. PTHrP and Ihh highly regulate chondrocyte hypertrophy and proliferation. Ihh, expressed in the early hypertrophic zone, stimulates proliferation and PTHrP expression by cells from the periarticular perichondrium. PTHrP prevents cells from becoming hypertrophic and reduces hypertrophy rate [2]. We hypothesize that the typical early mineralization pattern is the consequence of regulation by this PTHrPIhh control-loop and the distances between cells which express signals and receptor-cells. To study the hypothesis we evaluate the effects of different locations of PTHrP-expression on the mineralization pattern in an embryonic anlage, using the finite element method. Method: To study spatial effects we extended our 1D-model of PTHrP-, Ihh-, and VEGF-regulated bone development [3] to 2D. Simulations contain perichondrium, resting, proliferative, early hypertrophic, hypertrophic and mineralized zones. PTHrP, Ihh and VEGF are expressed in the perichondrium, early and late hypertrophic zones, respectively. Ihh and VEGF expression depend on the number of early or late hypertrophic cells. PTHrP expression is Ihh-dependent. Proliferative cells start hypertrophy when reaching a critical PTHrP-value. Hypertrophic cells mineralize upon high VEGF concentrations. Simulations start with an early anlage containing resting and proliferative cells only, and covered with PTHrP-expressing perichondrium at varying locations. Bone development is controlled by PTHrP, Ihh and VEGF only. Result: The Ihh-PTHrP feedback loop is able to control early bone development. By initiating hypertrophy, PTHrP drives mineralization. Differences in mineralization patterns between simulations come to the account of differences in PTHrP distributions. These are determined by the locations of PTHrP expression, i.e. by the geometry of the perichondrium. References
[1] Tanck E, Blankevoort L, et al. JOR 2000; 18: 613~19. [2] Kronenberg HM. Nature 2003; 423: 332-336. [3] Brouwers JEM, van Donkelaar CC, et al. J Biomech, in press. 4587 Th, 11:00-11:15 (P42) A mathematical model approach o f bone regeneration using scaffolds J.A. Sanz, J.M. Garcia-Aznar, M. Doblar6. Aragon Institute of Engineering
Research (13A), University of Zaragoza, Zaragoza, Spain Bone and cartilage regeneration during healing is one of the most critical part in trauma process. It depends on many factors as biological (cell migration, proliferation, differentiation) and mechanical effects (fluid flow, strain energy, mechanical stresses) among others. In order to accelerate and improve the regeneration process, scaffolds are introduced inside the defect keeping them in contact with biological tissue. This contact is influenced by the nature of the scaffold, that is, if reabsorbable or not, grafted or non-grafted and also of its composition. In this work, the vascularisation process of the scaffold at the earlier stage of implantation is modelled. After the invasion of blood vessels, the remodelling model presented in [1] is used in connection with a poroelastic analysis to determine the most appropriate mechanical stimulus able to predict the bone growth within the scaffold. As application, the condyle part of a rabbit (cancellous and cortical bone) implanted with a 7 mm diameter non-reabsorbable scaffold in a lateral incision, is numerically analysed with the previously described approach. The evolution with time of the microstructure of the scaffold produces different mechanical properties and permeability. These have been taken from [3] as a function of porosity (since it varies with time due to the new bone formation). Then, the overall behaviour of the macroscopic scaffold is considered to be anisotropic as consequence of tissue growth over the volume of the scaffold. In order to compare and validate the model presented, results are compared with numerical curves of bone growth inside scaffolds fitted experimentally by Pothuaud et al. [2]. References
[1] Garcia-Aznar JM, Rueberg T, Doblare M. A bone remodelling model coupling microdamage growth and repair by 3D BMU-activiy. Biomechan Model Mechanobiol 2005; 4(2-3): 147-167. [2] Pothuaud L, Fricain JC, Pallu S, Bareille R, Renard M, Durrieu MC, Dard M, Vernizeau M, Amed6e J. Mathematical modelling of the distribution of newly formed bone in bone tissue engineering. Biomaterials 2005; 26: 6788~799.
Th, 11 : 15-11:30 (P42)
Numerical simulation o f bone ingrowth after total knee arthroplasty
L.G. Gruionu, EL. Rinderu. University ef Craieva, Romania Bone-implant interface failure leading to loosening of the prosthetic components in total knee arthroplasty is due to bone resorption and concentrated overloading and depends on the surrounding bone tissue quality, the implant design and the implantation technique. Understanding the bone growth process is essential for a successful design of the knee prosthesis. The objective of this study is to develop a computational model capable to simulate the bone formation process at the bone-implant interface under the loading conditions similar to normal walking. The three-dimensional finite elements model of a human joint after total knee arthroplasty was developed. Geometry of the bones and prosthesis was acquired from a patient derived from images obtained non-invasively in the clinic. Joint kinematics data was acquired using a motion analysis system based on video recorded images of the patient. A finite elements analysis was initially performed to determine the loading condition of the knee during normal walking. Using a sub-structuring approach, bone growth phenomenon was simulated for several small regions at the bone-implant interface. A computational module was developed including an iterative procedure that predicts the bone ingrowth over time by updating the material properties of the elements, together with the changes in the boneimplant interface conditions. The numerical model uses a global optimization criterion with a shear strain formulation to detect where bone ingrowth exists and adapts to the local mechanical environment. The results of the simulation were founded in good agreement with the bone ingrowth process observed on patient recovering images. This computational model is important for the design of knee prosthetics regarding an optimum shape for best ingrowth surface size and location. 6733
Th, 11:30-11:45 (P42)
Press-fit and the AIIoclassic stem: FE predictions vs. clinical evidence
M.J. Schmitz 1, R. Howald 2, M. Froehlich 2, E. Siggelkow 2, D. Hertig 2, S.E. Clift 1. 1Department of Mechanical Engineering, University of Bath, UK,
2Zimmer GmbH, Winterthur, Switzerland The uncemented AIIoclassic hip stem (Zimmer GmbH) has results which compare well with the best modern cemented THA results in the Swedish hip registry [1]. Immediate post operative stability is secured using a standard press-fit technique. How much of this press-fit persists in the clinical situation and what long-term role it has is unknown. This study explored the influence of press-fit on a computational bone remodelling simulation. FE models of a cadaveric femur were created in a similar manner to a previously validated method, where CT scan data was used to create the geometry and bone density distribution [2]. Two cases were investigated for the implanted AIIoclassic; with and without press-fit. An arbitrary radial pressfit of 0.1 mm was used. Friction was included (~t =0.4). Muscle forces were based on peak gait loading [3]. The bone remodelling simulation adapted material properties over time. The local change in strain energy density from the physiological level was used to control the bone remodelling, in a similar manner to previous investigations [4]. The simulation results without press-fit showed significant bone loss over almost the entire length of the stem. With press-fit, bone loss was confined to the more proximal regions and there were also increases in bone density around the distal stem. The results with press-fit were in good agreement with recent clinical evidence [5], where DEXA scans of stable implants showed a limited reduction in proximal bone density and an increase in distal bone density. This implies that the press-fit may play a role in the long-term clinical success of the implant. Therefore, the effect of press-fit should be considered in remodelling simulations, where appropriate. References
[1] [2] [3] [4] [5]
Delaunay and Kapandji. JBJS 2001; 83(B): 408. Taylor et al. J Biomech 2002; 35: 767. Duda et al. J Biomech 1998; 31: 841. Schmitz et al. Proc Inst Mech Eng [H] 2004; 218: 417. Brodner et al. JBJS 2004; 86(B): 20.
Journal o f Biomechanics 2006, Vol. 39 (Suppl 1)
els' requirements on mass conservation and non-negativity of the variables. This model is capable of simulating normal fracture healing. Considering the presence of the angiogenic process we expect that we will also be able to address pathological situations due to impaired vascularisation.
Oral Presentations [3] Shimko DA, Shimko VF, Sander EA, Dickson KF, Nauman EA. Effect of porosity on the fluid flow characterisation and mechanical properties of tantalum scaffolds. J Biomed Mater Res B: Appl Biomater 2005; 73(B): 315-324. 5927
6933 Th, 09:30-09:45 (P39) The perichondrium determines the mineralization front in long bones R.C.C. van Donkelaar, S.W. Witvoet-Braam, R. Huiskes. Dept Biomedical
Engineering, Eindhoven University of Technology, Eindhoven, Netherlands Introduction: Mineralization of fetal bones starts by hypertrophy in the center of the anlage, followed by local mineral formation. The mineralized area grows laterally before extending proximally and distally [1]. PTHrP and Ihh highly regulate chondrocyte hypertrophy and proliferation. Ihh, expressed in the early hypertrophic zone, stimulates proliferation and PTHrP expression by cells from the periarticular perichondrium. PTHrP prevents cells from becoming hypertrophic and reduces hypertrophy rate [2]. We hypothesize that the typical early mineralization pattern is the consequence of regulation by this PTHrPIhh control-loop and the distances between cells which express signals and receptor-cells. To study the hypothesis we evaluate the effects of different locations of PTHrP-expression on the mineralization pattern in an embryonic anlage, using the finite element method. Method: To study spatial effects we extended our 1D-model of PTHrP-, Ihh-, and VEGF-regulated bone development [3] to 2D. Simulations contain perichondrium, resting, proliferative, early hypertrophic, hypertrophic and mineralized zones. PTHrP, Ihh and VEGF are expressed in the perichondrium, early and late hypertrophic zones, respectively. Ihh and VEGF expression depend on the number of early or late hypertrophic cells. PTHrP expression is Ihh-dependent. Proliferative cells start hypertrophy when reaching a critical PTHrP-value. Hypertrophic cells mineralize upon high VEGF concentrations. Simulations start with an early anlage containing resting and proliferative cells only, and covered with PTHrP-expressing perichondrium at varying locations. Bone development is controlled by PTHrP, Ihh and VEGF only. Result: The Ihh-PTHrP feedback loop is able to control early bone development. By initiating hypertrophy, PTHrP drives mineralization. Differences in mineralization patterns between simulations come to the account of differences in PTHrP distributions. These are determined by the locations of PTHrP expression, i.e. by the geometry of the perichondrium. References
[1] Tanck E, Blankevoort L, et al. JOR 2000; 18: 613~19. [2] Kronenberg HM. Nature 2003; 423: 332-336. [3] Brouwers JEM, van Donkelaar CC, et al. J Biomech, in press. 4587 Th, 11:00-11:15 (P42) A mathematical model approach o f bone regeneration using scaffolds J.A. Sanz, J.M. Garcia-Aznar, M. Doblar6. Aragon Institute of Engineering
Research (13A), University of Zaragoza, Zaragoza, Spain Bone and cartilage regeneration during healing is one of the most critical part in trauma process. It depends on many factors as biological (cell migration, proliferation, differentiation) and mechanical effects (fluid flow, strain energy, mechanical stresses) among others. In order to accelerate and improve the regeneration process, scaffolds are introduced inside the defect keeping them in contact with biological tissue. This contact is influenced by the nature of the scaffold, that is, if reabsorbable or not, grafted or non-grafted and also of its composition. In this work, the vascularisation process of the scaffold at the earlier stage of implantation is modelled. After the invasion of blood vessels, the remodelling model presented in [1] is used in connection with a poroelastic analysis to determine the most appropriate mechanical stimulus able to predict the bone growth within the scaffold. As application, the condyle part of a rabbit (cancellous and cortical bone) implanted with a 7 mm diameter non-reabsorbable scaffold in a lateral incision, is numerically analysed with the previously described approach. The evolution with time of the microstructure of the scaffold produces different mechanical properties and permeability. These have been taken from [3] as a function of porosity (since it varies with time due to the new bone formation). Then, the overall behaviour of the macroscopic scaffold is considered to be anisotropic as consequence of tissue growth over the volume of the scaffold. In order to compare and validate the model presented, results are compared with numerical curves of bone growth inside scaffolds fitted experimentally by Pothuaud et al. [2]. References
[1] Garcia-Aznar JM, Rueberg T, Doblare M. A bone remodelling model coupling microdamage growth and repair by 3D BMU-activiy. Biomechan Model Mechanobiol 2005; 4(2-3): 147-167. [2] Pothuaud L, Fricain JC, Pallu S, Bareille R, Renard M, Durrieu MC, Dard M, Vernizeau M, Amed6e J. Mathematical modelling of the distribution of newly formed bone in bone tissue engineering. Biomaterials 2005; 26: 6788~799.
Th, 11 : 15-11:30 (P42)
Numerical simulation o f bone ingrowth after total knee arthroplasty
L.G. Gruionu, EL. Rinderu. University ef Craieva, Romania Bone-implant interface failure leading to loosening of the prosthetic components in total knee arthroplasty is due to bone resorption and concentrated overloading and depends on the surrounding bone tissue quality, the implant design and the implantation technique. Understanding the bone growth process is essential for a successful design of the knee prosthesis. The objective of this study is to develop a computational model capable to simulate the bone formation process at the bone-implant interface under the loading conditions similar to normal walking. The three-dimensional finite elements model of a human joint after total knee arthroplasty was developed. Geometry of the bones and prosthesis was acquired from a patient derived from images obtained non-invasively in the clinic. Joint kinematics data was acquired using a motion analysis system based on video recorded images of the patient. A finite elements analysis was initially performed to determine the loading condition of the knee during normal walking. Using a sub-structuring approach, bone growth phenomenon was simulated for several small regions at the bone-implant interface. A computational module was developed including an iterative procedure that predicts the bone ingrowth over time by updating the material properties of the elements, together with the changes in the boneimplant interface conditions. The numerical model uses a global optimization criterion with a shear strain formulation to detect where bone ingrowth exists and adapts to the local mechanical environment. The results of the simulation were founded in good agreement with the bone ingrowth process observed on patient recovering images. This computational model is important for the design of knee prosthetics regarding an optimum shape for best ingrowth surface size and location. 6733
Th, 11:30-11:45 (P42)
Press-fit and the AIIoclassic stem: FE predictions vs. clinical evidence
M.J. Schmitz 1, R. Howald 2, M. Froehlich 2, E. Siggelkow 2, D. Hertig 2, S.E. Clift 1. 1Department of Mechanical Engineering, University of Bath, UK,
2Zimmer GmbH, Winterthur, Switzerland The uncemented AIIoclassic hip stem (Zimmer GmbH) has results which compare well with the best modern cemented THA results in the Swedish hip registry [1]. Immediate post operative stability is secured using a standard press-fit technique. How much of this press-fit persists in the clinical situation and what long-term role it has is unknown. This study explored the influence of press-fit on a computational bone remodelling simulation. FE models of a cadaveric femur were created in a similar manner to a previously validated method, where CT scan data was used to create the geometry and bone density distribution [2]. Two cases were investigated for the implanted AIIoclassic; with and without press-fit. An arbitrary radial pressfit of 0.1 mm was used. Friction was included (~t =0.4). Muscle forces were based on peak gait loading [3]. The bone remodelling simulation adapted material properties over time. The local change in strain energy density from the physiological level was used to control the bone remodelling, in a similar manner to previous investigations [4]. The simulation results without press-fit showed significant bone loss over almost the entire length of the stem. With press-fit, bone loss was confined to the more proximal regions and there were also increases in bone density around the distal stem. The results with press-fit were in good agreement with recent clinical evidence [5], where DEXA scans of stable implants showed a limited reduction in proximal bone density and an increase in distal bone density. This implies that the press-fit may play a role in the long-term clinical success of the implant. Therefore, the effect of press-fit should be considered in remodelling simulations, where appropriate. References
[1] [2] [3] [4] [5]
Delaunay and Kapandji. JBJS 2001; 83(B): 408. Taylor et al. J Biomech 2002; 35: 767. Duda et al. J Biomech 1998; 31: 841. Schmitz et al. Proc Inst Mech Eng [H] 2004; 218: 417. Brodner et al. JBJS 2004; 86(B): 20.