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Mechanobiology of soft skeletal tissue differentiation—a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications

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Abstract

The material properties of multipotent mesenchymal tissue change dramatically during the differentiation process associated with skeletal regeneration. Using a mechanobiological tissue differentiation concept, and homogeneous and isotropic simplifications of a fiber-reinforced poroelastic model of soft skeletal tissues, we have developed a mathematical approach for describing time-dependent material property changes during the formation of cartilage, fibrocartilage, and fibrous tissue under various loading histories. In this approach, intermittently imposed fluid pressure and tensile strain regulate proteoglycan synthesis and collagen fibrillogenesis, assembly, cross-linking, and alignment to cause changes in tissue permeability (k), compressive aggregate modulus (H A), and tensile elastic modulus (E). In our isotropic model, k represents the permeability in the least permeable direction (perpendicular to the fibers) and E represents the tensile elastic modulus in the stiffest direction (parallel to the fibers). Cyclic fluid pressure causes an increase in proteoglycan synthesis, resulting in a decrease in k and increase in H A caused by the hydrophilic nature and large size of the aggregating proteoglycans. It further causes a slight increase in E owing to the stiffness added by newly synthesized type II collagen. Tensile strain increases the density, size, alignment, and cross-linking of collagen fibers thereby increasing E while also decreasing k as a result of an increased flow path length. The Poisson's ratio of the solid matrix, ν s, is assumed to remain constant (near zero) for all soft tissues. Implementing a computer algorithm based on these concepts, we simulate progressive changes in material properties for differentiating tissues. Beginning with initial values of E=0.05 MPa, H A=0 MPa, and k=1×10–13 m4/Ns for multipotent mesenchymal tissue, we predict final values of E=11 MPa, H A=1 MPa, and k=4.8×10–15 m4/Ns for articular cartilage, E=339 MPa, H A=1 MPa, and k=9.5×10–16 m4/Ns for fibrocartilage, and E=1,000 MPa, H A=0 MPa, and k=7.5×10–16 m4/Ns for fibrous tissue. These final values are consistent with the values reported by other investigators and the time-dependent acquisition of these values is consistent with current knowledge of the differentiation process.

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Acknowledgements

We would like to thank Jay Henderson, Sandra Shefelbine, and Dr. R. Lane Smith for their helpful suggestions. Support for this work was provided by VA Merit Review project A501–4RA.

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Authors and Affiliations

  1. Biomechanical Engineering Division, Mechanical Engineering Department, Stanford University, Stanford, CA, 94305, USA

    E. G. Loboa, T. A. L. Wren, G. S. Beaupré & D. R. Carter

  2. Rehabilitation R&D Center, VA Palo Alto Health Care System, 3801 Miranda Avenue/153, Palo Alto, CA, 94304-1200, USA

    E. G. Loboa, T. A. L. Wren, G. S. Beaupré & D. R. Carter

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  1. E. G. Loboa
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  2. T. A. L. Wren
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  3. G. S. Beaupré
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Correspondence to E. G. Loboa.

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Loboa, E.G., Wren, T.A.L., Beaupré, G.S. et al. Mechanobiology of soft skeletal tissue differentiation—a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications. Biomech Model Mechanobiol 2, 83–96 (2003). https://doi.org/10.1007/s10237-003-0030-7

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