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Introduction

Introduction. Mechanical loads on cartilage -> chondrocytes expression Chondrocyte response to mechanical stimuli usually studied in vitro / in situ Need to study chondrocyte mechano-responsiveness in OA tissue. Structure and composition. Low friction Small fiber diameter

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Introduction

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  1. Introduction Mechanical loads on cartilage -> chondrocytes expression Chondrocyte response to mechanical stimuli usually studied in vitro/in situ Need tostudychondrocytemechano-responsiveness in OA tissue

  2. Structure and composition Low friction Small fiber diameter Small cells, high density Strong PG/collXlinks

  3. Structure and composition Thicker fiber diameter About isotropic Spherical cells Highest PG content

  4. Structure and composition Thick fibers High PG content Low water content

  5. Structure and composition Chondrocyte stiffness: ~103 lower than ECM but deformations are similar • Filtering mechanism • ECM strain 6-8%: cell strains are independent and larger • 8-14%: cell strains are smaller Modeling: Chondrocyte deformations depend on tissue BCs.

  6. Mechanical properties of AC Viscous, porous, multiphasic, anisotropic, depth-dependent Viscoelasticity: Flow dependent / independent Interstitial fluid: Darcy’s law Compressive properties: PGs Tensile properties: collagen fibers Shear properties small shear strains: collagen fibers high shear strains: fluid (swelling pressure)

  7. Cartilage swelling - Swelling pressure material constants hard to determine experim. FEM: swelling P incorporated to Darcy’s law - - Poroelastic pressure Swelling pressure - Total fluid stress - - Donnan osmotic pressure (ions)

  8. Friction in cartilage Fluid film lubrication Mixture lubrication Boundary lubrication Low relative velocity (~static): rather boundary lubrication Dynamic mode / high loads: rather fluid film lubrication

  9. AC modeling – tissue level Linear elastic single phase AC, rigid non-def SB simplisticmechanicalmodels, static / quasi-staticloading Poroelastic / biphasicmodels Biphasic: solidandfluidphases are (near) incompressible =poroelasticforincompressiblematerials Equations for solid and fluid phase (solve for displacement fields) internal stresses = external mech. forces (fluid stress, swelling P) BCs: unconfined zero PP / confined zero flux Robust model but does not take into account depth-dependent properties

  10. Biphasic modellimitations and assumptions Geometric nonlinearity >10% strains - problem with commercial codes Fiber-reinforced models: material non-lin., but not geometric non-lin. Under large def: better use viscous, hyperelastic model for solid phase non-linear linear non-linear in displacement field Time and storage expensive Hyperelastic models: strain energy density function to derive stress/strain relationship [M]: mass lumping -> diagonalize matrix enables real-time local mesh refinement

  11. Energy lost in AC tissue Energy dissipation • IF viscosity • ECM, collagen, GAGs, chondrocytesviscoelasticity • Drag forcesbetweenfluid / solidphases Assumption: no energy dissipation other that resulting from interactions btn phases (not valid for confined compression, viscoelastic behavior in tension) Fast-rate BC in AC tissue modeling Lack of inertial forces in the biphasic codes: pb with time varying load deformation behavior

  12. Chondrocyte modeling – cell level Role of PCM and PCC Micro vs. macro cell is biphasic, embedded in infinite matrix Cell mechanics: Role of cytoskeleton – tensegrity models (complicated loading) Continuum model – fluid / viscoelastic or solid / viscoelastic and elastic microtubules microfilaments Intermediate filaments

  13. Multiscale modeling of AC Problem: 104DoF per spatial dimension -> use parallel computing -> develop large-scale solution w/o small-scale details Authors suggest coupling micro/macro scales (Lagrange multipliers): Elastic potential of whole system = f(micro and macro-displacements) Run units in parallel Conventional FEM for each unit

  14. Conclusions AC is heterogenous Be wary of limitations using commercial codes large deformations missing inertial force (pb w/ fast-rate loading) fluid phase modeled with zero viscosity 7 orders of magnitude for stiffness in cell components BCs: different in harvested tissue and in joint OA diagnosis: need for a better model of cell deformation, related mechanical loading to chondrocyte signaling (Ca2+)

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