Table 1.
Material Properties, Applied Mechanical Stimuli, and Resulting Findings From Selected Mechanoregulation Studies
| Authors | Application | Material Properties | Stimuli | Outcome |
|---|---|---|---|---|
| Huiskes et al.55 | Tissue differentiation | Bone: E = 4590, k = 3.7e−13; fibrous tissue (initial cond.): E = 2, k = 1.0e−14 | Fluid/solid velocity, shear strain | Tissue differentiation sequences in agreement with those found experimentally |
| Lacroix and Prendergast56 | Tissue differentiation | Granulation tissue: E = 0.2, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; fibrous tissue: E = 2, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; cartilage: E = 10, k = 5e−15, ν = 0.167, S bm = 3400, F bm = 2300, n = 0.8; marrow: E = 2, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; immature bone: E = 1000, k = 1e−13, ν = 0.3, S bm = 13920, F bm = 2300, n = 0.8; mature bone: E = 6000, k = 3.7e−13, ν = 0.3, S bm = 13920, F bm = 2300, n = 0.8; cortical bone: E = 20,000, k = 1e−17, ν = 0.3, S bm = 13920, F bm = 2300, n = 0.04 | Fluid/solid velocity, shear strain | Cell diffusion rate is a key parameter for healing speed |
| Geris et al.57 | Tissue differentiation | Granulation tissue: E = 1, ν = 0.17, k = 1e−14; cartilage: E = 10, ν = 0.17, k = 5e−15; bone: E = 1000, ν = 0.3, k = 1e−13 | Fluid/solid velocity, shear strain | Successful prediction of tissue differentiation in a rabbit bone chamber |
| Heegaard et al.58 | Joint morphogenesis | Cartilage: E = 1.0, ν = 0.4; tendons: E L = 3.0, E T = 0.1, ν L = ν T = 0.2, G = 1.0 | Hydrostatic stress | Prediction of congruent surfaces within the joint region |
| Shefelbine and Carter59 | Growth front progression | Newly formed bone: E = 500, ν = 0.2; cartilage: G = 2, ν = 0.49 | Hydrostatic stress, octahedral shear | Successful prediction of normal and abnormal loadings on growth front progression |
| Isaksson et al.60 | Bone regeneration | Cortical bone: E = 15,750, k = 1e−17, ν = 0.325, S bm = 17,660, F bm = 2300, n = 0.04; marrow: E = 2, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; granulation tissue: E = 1, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; fibrous tissue: E = 2, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; cartilage: E = 10, k = 5e−15, ν = 0.167, S bm = 3400, F bm = 2300, n = 0.8; immature bone: E = 1000, k = 1e−13, ν = 0.325, S bm = 17660, F bm = 2300, n = 0.8; mature bone: E = 6000, k = 3.7e−13, ν = 0.325, S bm = 17660, F bm = 2300, n = 0.8 | Fluid/solid velocity, shear strain | Prediction of spatial and temporal tissue distributions observed in distraction osteogenesis experiments |
| Garcia‐Aznar et al.61 | Tissue growth/differentiation | Periosteum (initial cond.): E = 35.3, ν = 0.048; endosteum (initial cond.): E = 35.3, ν = 0.048; gap: E = 8.2, ν = 0.048 | Second invariant of the deviatoric strain tensor | Correct prediction of callus size in the presence of interfragmentary movements |
| Giorgi et al.62 | Joint morphogenesis | Cartilage: E = 1.1, ν = 0.49; synovial capsule: E = 0.287 kPa, ν = 0.4 | Hydrostatic stress | Prediction of interlocking surfaces for hinge and ball and socket joints |
| Giorgi et al.63 | Hip Joint morphogenesis | Cartilage: E = 1.1, ν = 0.49 | Hydrostatic stress | Importance of movements to maintain acetabular depth and femoral head sphericity |
| Isaksson et al.64 | Cell and tissue differentiation | Cortical bone: E = 15,750, k = 1e−17, ν = 0.325, S bm = 17,660, F bm = 2300, n = 0.04; marrow: E = 2, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; granulation tissue: E = 1, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; fibrous tissue: E = 2, k = 1e−14, ν = 0.167, S bm = 2300, F bm = 2300, n = 0.8; cartilage: E = 10, k = 5e−15, ν = 0.167, S bm = 3400, F bm = 2300, n = 0.8; immature bone: E = 1000, k = 1e−13, ν = 0.325, S bm = 17,660, F bm = 2300, n = 0.8; mature bone: E = 6000, k = 3.7e−13, ν = 0.325, S bm = 17,660, F bm = 2300, n = 0.8 | Fluid/solid velocity, shear strain | Spatial and temporal predictions of fibrous tissue, cartilage, and bone. Correctly describe fracture healing and disrupted healing |
| Pérez and Prendergast65 | Cell and tissue differentiation | Granulation tissue: E = 0.2, k = 1e−14, ν = 0.167, S bm = 2300, D = 0.8; fibrous tissue: E = 2, k = 1e−14, ν = 0.167, S bm = 2300, D = 0.1; cartilage: E = 10, k = 0.5e−14, ν = 0.3, S bm = 3700, D = 0.05; immature bone: E = 1000, k = 0.1e−14, ν = 0.3, S bm = 13,940, D = 0.01; cortical bone: E = 17,000, k = 0.001e−14, ν = 0.3, S bm = 13,920 | Fluid/solid velocity, shear strain | Qualitative agreement with experimental data on bone tissue distribution at the bone–implant interface |
| Burke and Kelly66 | Cell differentiation | Granulation tissue: E = 0.2, k = 1e−11, ν = 0.167, μ = 1e−9, n = 0.8; fibrous tissue: E = 2, k = 1e−11, ν = 0.167, μ = 1e−9, n = 0.8; cartilage: E = 10, k = 5e−15, ν = 0.167, μ = 1e−9, n = 0.8; marrow: E = 2, k = 1e−14, ν = 0.167, μ = 1e−9, n = 0.8; immature bone: E = 1000, k = 1e−13, ν = 0.3, μ = 1e−9, n = 0.8; mature bone: E = 6000, k = 3.7e−13, ν = 0.3, μ = 1e−9, n = 0.8; cortical bone: E = 20,000, k = 1e−17, ν = 0.3, μ = 1e−9, n = 0.04 | Substrate stiffness, oxygen tension | Good agreement with results in fracture repair experiments |
E is Young's modulus (MPa), k is permeability (m4/N s), G is shear modulus (MPa), μ is fluid dynamic viscosity (N s/m2), S bm is solid bulk modulus (MPa), F bm is fluid bulk modulus (MPa), D is diffusion coefficient (mm2/iter), n is porosity, and υ is Poisson's ratio.