Computational Biomechanics of Soft Biological Tissues: Arterial Walls, Hearts Walls, and Ligaments

Abstract

Computational biomechanics of soft biological tissue is increasing our ability to address multi‐disciplinary problems of academic, industrial, and clinical importance. This chapter reviews parts of our current knowledge of the biomechanics of soft biological tissue such as the arterial wall, the heart wall with the heart valves, and the ligament, as well as some of the available computational methods used to analyze them. The inherent complexities of the biological microstructure and functions of the respective soft tissue are partly reviewed briefly, research effort related to the constitutive modeling is catalogued, and a representative constitutive model for each considered soft tissue is discussed in more detail. An account of residual stresses and biological processes such as growth and remodeling is provided. Finally, a few three‐dimensional finite element models, which attempt to explain the integrated function of the respective soft tissue in terms of geometry, structure, and material properties are emphasized.

On the thermodynamic consistency of Quasi-Linear Viscoelastic models for soft solids

“…We should be aware of the limitations of the QLV model, which is known to hardly capture the discrepancy between creep and relaxation time scales [18] and which in general does not exhibit straindependent relaxation effects. Moreover, QLV may only be valid at moderate deformations [11].…”

“…This expression leads to high computational costs as it requires the storage of the whole deformation history [9]. This drawback can be avoided by approximating G as an exponential series [17,18] 1 of the form…”

“…A popular and simple model of the integral type is Fung's quasi-linear viscoelasticity (QLV) [12,13] sor and the elastic stress response. Originating in biomechanics, Fung's QLV has been successfully employed in related applications, with the development of associated experimental techniques [14,15,16] and dedicated computational methods [17,18]. It has also been employed to model polymers and rubbers [19,20].…”

“…The computation of the instantaneous QLV stress by means of the convolution product requires the storage of the whole strain history, since the constitutive law is non-local in time. In computational applications, this can be avoided by expanding the relaxation tensor as a Prony series, leading to the natural definition of memory variables [17,18]. Suitable memory variables account for the deformation history in a time-local fashion [21], allowing efficient evaluation of the mechanical response.…”

Microindentation of fresh soft biological tissue: A rapid tissue sectioning and mounting protocol

“…3D biomimetic models are powerful tools in better understanding disease processes. Data from experimental mechanical testing of fresh biological tissues are used to inform these 3D biomimetic models allowing researchers to better simulate in vivo conditions for a more robust understanding of the tissue extracellular matrix (ECM) [1][2][3]. While macroscale mechanical testing is useful for obtaining the bulk mechanical properties of biological tissue, this type of testing cannot capture the regional mechanical differences that occur in the ECM microenvironment [4][5][6][7].…”