Bio–chemo–mechanical modeling of growing biological tissues: Finite element method. (January 2019) - Yin, Si-Fan; Xue, Shi-Lei; Li, Bo; Feng, Xi-Qiao
Abstract: Deciphering the bio–chemo–mechanical mechanisms in tissue growth and deformation helps understand the morphogenesis of organs and organisms under physiological and pathological conditions. In this paper, we present a finite element method that can account for the interplay of volumetric growth, chemical transport, and mechanical deformation in soft tissues, such as tumors. The poroelastic theory and the volumetric growth model are combined to capture the essential growth and deformation traits of biological tissues. This method can not only simulate the bio–chemo–mechanical coupling processes in growing tissues, but also track their morphological instabilities and evolutions. The deformation and instability of interacting blood vessels in a growing tumor are considered as an example. The mechanisms underpinning the collapse of blood vessels observed in vascular solid tumors are revealed. This work holds promise for applications in the diagnosis and therapy of diseases such as cancer. Graphical abstract: Highlights: Finite element method for simulating the volumetric growth of biological tissue. Theory of bio–chemo–mechanical coupling poroelasticity for soft tissues. Instability and morphological evolution of blood vessels in a growing solid tumor.