Open Access

ARTICLE

Biological Growth and Remodeling: A Uniaxial Example with Possible Application to Tendons and Ligaments

I. J. Rao¹, J.D. Humphrey², K.R. Rajagopal³

1 Dept. of Mechanical Engineering, New Jersey Institute of Technology, Newark, NJ 07102
2 Corresponding Author, Biomedical Engineering 233 Zachry Engineering Center Texas A&M University, College Station, TX 77843-3120 jhumphrey@tamu.edu
3 Mechanical Egineering Texas A&M University, College Station, TX 77843

Computer Modeling in Engineering & Sciences 2003, 4(3&4), 439-456. https://doi.org/10.3970/cmes.2003.004.439

Abstract

Recent discoveries in molecular and cell biology reveal that many cell types sense and respond (via altered gene expression) to changes in their mechanical environment. Such mechanotransduction mechanisms are responsible for many changes in structure and function, including the growth and remodeling process. To understand better, and ultimately to use (e.g., in tissue engineering), biological growth and remodeling, there is a need for mathematical models that have predictive and not just descriptive capability. In contrast to prior models based on reaction-diffusion equations or the concept of volumetric growth, we examine here a newly proposed constrained mixture model for growth and remodeling. Specifically, we use this new model to present illustrative computations in a representative, transversely-isotropic soft tissue subjected to homogeneous deformations under uniaxial loading. Consequences of various assumptions for the kinetics of mass production and removal are discussed, as are open problems in this important area of biomechanics.

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