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

Biomech Model Mechanobiol. 2003 Nov;2(2):83-96. doi: 10.1007/s10237-003-0030-7. Epub 2003 Jul 17.

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, nu(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 x 10(-13) m(4)/Ns for multipotent mesenchymal tissue, we predict final values of E=11 MPa, H(A)=1 MPa, and k=4.8 x 10(-15) m(4)/Ns for articular cartilage, E=339 MPa, H(A)=1 MPa, and k=9.5 x 10(-16) m(4)/Ns for fibrocartilage, and E=1,000 MPa, H(A)=0 MPa, and k=7.5 x 10(-16) m(4)/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.

Publication types

  • Evaluation Study
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Anisotropy
  • Bone and Bones / cytology
  • Bone and Bones / physiology*
  • Cartilage / cytology
  • Cartilage / physiology*
  • Cell Differentiation / physiology*
  • Cell Division / physiology
  • Computer Simulation
  • Connective Tissue / physiology*
  • Connective Tissue / ultrastructure
  • Elasticity
  • Mechanotransduction, Cellular / physiology*
  • Mesenchymal Stem Cells / cytology
  • Mesenchymal Stem Cells / physiology*
  • Models, Biological*
  • Osteogenesis / physiology*
  • Porosity