Age-dependent mathematical models of ligaments and tendons

Abstract

Understanding the internal structure and the underlying physical mechanisms governing the mechanical properties of ligaments and tendons, particularly the elastic modulus, across different stages of life is critical for enhancing tissue strength during growth, maturation, and aging. This knowledge is essential not only for preventing tissue failure in older adults but also for advancing the development of biomaterials that can substitute or augment ligament and tendon function across all age groups. Despite the significance of this area, a comprehensive, mechanistic understanding of the relationship between structural changes and mechanical properties over time remains largely unexplored. To date, there is a lack of detailed studies that elucidate the physical mechanisms involved in these age-related changes. The absence of such mechanistic insights highlights a significant gap in the literature, necessitating further investigation. Therefore, this research delves into the age-dependent structural and mechanical property changes in ligaments and tendons, emphasizing both growth and mature phases. Utilizing a comprehensive approach, we have developed new mathematical models that directly correlate the growth of collagen in fibrils with the increasing elastic modulus in the fibers of ligaments and tendons over time. By integrating experimental data from mouse tail tendons in published work and conducting simulations, we have observed that the cross-sectional area of collagen in fibrils and the elastic modulus of a collagen fiber increase rapidly during the growth phase and stabilize during the mature phase. Our proposed models effectively describe the trends in collagen growth and the elastic modulus of fibers in ligaments and tendons over different ages, exhibiting consistency with experimental data. Through detailed analysis, we elucidate the mechanistic relationship between collagen growth and the elastic modulus of fibers as they age. This comprehensive approach significantly enhances our understanding of the age-related structural and mechanical property changes in connective tissues, providing a robust framework for future investigations.