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Download Bone remodeling simulation models Bone density and shape adapt
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Bone density and shape adapt to loading Turkey Ulna experiments (Rubin et al) Sheep ulnar osteotomy (McNamara) Bone remodeling simulation models Bert van Rietbergen • Bone is deposited in regions of high loading • Load-dependent response • Only dynamic loading results in bone apposition Bone remodeling But... • Generally accepted that ostecytes are mechanosensors and regulate the remodeling process because they: • How is this process regulated? • • • • are sensitive to mechanical load are sensitive to fluid flow are the most abundant cell type in bone can regulate OCl and OBl activity Frost: mechanostat theory • How can this process leads to mechanically ‘optimized’ structures? • H How can cells ll att the th scale l off 10 microns i produce d 'optimal' structures at a scale 100-1000 times larger? Bone remodeling theory Cowin et al., “Theory of Adaptive Elasticity” (1974) Carter et al., Huiskes et al., Beaupre et al., ..... o e adapts its ts mass ass to mechanical ec a ca demands de a ds Bone Bone mass Sref mechanical signal: S Frost, 1960 'lazy zone' 1 Mechanical signal S ? Mechanostat theory something that can be measured by osteocytes • Stress/strain parameters • peak/average strain • strain-rate • Can it explain bone shape adaptation? • strain energy density U or U/ • ‘energy stress’ 2 EU • von Mises stress • Physiological loading • • • • accumulated microdamage fluid flow cell wall shear stress ..... Analysis of stress/strain distribution: FE-method Simulation of bone remodeling process bone geometry t=t+t Update Geometry FE-model Change in bone mass dM A S Sref dt ? mechanical signal: S Brown et al., 1990 Simulation of bone remodeling process: Turkey ulna Martinez and Cerrolaza, 2005 Beaupre et al., 1990, Huiskes et al., 1991 Simulation of bone remodeling process: Bone straightening Roberts and Hart, 2005 2 Mechanostat theory Simulation of bone remodeling process Stiffness distribution • Can it explain bone shape adaptation? • Can it explain bone density distribution? t=t+t Update Stiffness E=c Change in bone mass d A S S ref dt mechanical signal: S Beaupre et al., 1990, Huiskes et al., 1991 Wolff's law can explain density distribution Bone remodeling simulation models • as a pre-clinical tool to evaluate implants initial density final Weinans et al., 1995 Application: prediction of adverse bone resorption Bone loss around implants: result of "Stress shielding" 3 Simulation of bone remodeling process Bone remodeling simulation: cemented stems Stiffness distribution t=t+t Change in bone Stiffness E=c Change in bone mass d A S S ref dt mechanical signal: S Beaupre et al., 1990, Huiskes et al., 1991 Weinans et al, 1992 Bone remodeling simulation: uncemented stems Weinans et al, 1992 Effect of stem fixation and material on normal stress Weinans et al, 1992 3D Simulation of bone remodeling process site specific remodeling required Stiffness distribution Site-specific vs. non-site specific • Non-site specific Sref= constant • Site specific: t=t+t • Sref= dependent on the location • Usually large 'lazy zone' required Change in bone Stiffness E=c Change in bone mass d A S S ref dt Bone mass Sref mechanical signal: S mechanical signal: S reference signal: Sref 'lazy zone' 4 Bone remodeling / interface stress analysis as a pre-clinical tool Bone remodeling simulation: 3D g/cm-3 MPa -2.0 0 gcm-3 0.0 0.0 2.0 1.8 1.8 pre-remodeling post-remodeling Remodeling simulation validation Comparison with DEXA pre-remodeling post-remodeling Normal stresses pre-remodeling post-remodeling Shear stresses Mechanostat theory • Can it explain bone shape adaptation? • Can it also explain bone density distribution? • Can it explain bone morphology? Kerner et al. 1999 Predicted density not smooth Weinans et al., J.Biomech, 1992 "Plate model" Weinans et al., J.Biomech, 1992 5 "Plate model" Problem • Results will be mesh dependent • Solution: decouple biology from FE-mesh . . . . . . . . . . . . Weinans et al., J.Biomech, 1992 Spatial decay osteocyte stimulus Simulation of bone morphogenesis 1 f f (d ) e 2 d D 2 mm d 80x80 elements Mullender and Huiskes, JOR, 1995 Simulation of bone morphogenesis Mullender and Huiskes, JOR, 1995 Simulation morphogenesis 2 Mpa external stress, cycling at 1.0 Hz (1.5 mm) Mullender and Huiskes, JOR, 1995 3 Ruimerman et al, J of Biomechanics, 2005 6 Simulation of adaptation Tanck et al, Bone 28, 2001 Computer Simulation Ruimerman et al, J of Biomechanics, 2005 Ruimerman et al, J of Biomechanics, 2005 Mechanostat theory • • • • Can it explain bone shape adaptation? Can it also explain bone density distribution? Can it explain bone morphology? Can it explain remodeling at the tissue level • osteoblasts and osteoclasts always go together Hypothesis: Strain as the coupling factor in remodeling Quiescence Resorption cavity Mechanically regulated formation Development trabecular BMU Quiescence stress LC Ocy Oc e-Ob Ob elevated strain Huiskes et al., Nature, 2000 n-Ocy recruitment stimulus 3x3 mm2 7 Development trabecular BMU Development trabecular BMU Eriksen, Endocr. Rev. 1986 Can the theory also explain remodeling in cortical bone? Development cortical BMU Haversian system Osteon 2x2 mm2 Development cortical BMU 30 degrees rotated load no load 2x2 mm2 8 A unified theory for osteonal and hemiosteonal remodeling Clinical application • Major problem: physiological loading conditions are not know ? van Oers et al., Bone, 2008 Other hypotheses Mechanostat theory • • • • This afternoon Can it explain bone shape adaptation? Can it also explain bone density distribution? Can it explain bone morphology? Can it explain remodeling at the tissue level • Use a matlab code to simulate bone remodeling 9
