Abstract

The growth and remodelling of soft tissues plays a significant role in many physiological applications, particularly in understanding and managing many diseases. A commonly used approach for soft tissue growth and remodelling is volumetric growth theory, introduced in the framework of finite elasticity. In such an approach, the total deformation gradient tensor is decomposed so that the elastic and growth tensors can be studied separately. A critical element in this approach is to determine the growth tensor and its evolution with time. Most existing volumetric growth theories define the growth tensor in the reference (natural) configuration, which does not reflect the continuous adaptation processes of soft tissues under the current configuration. In a few studies where growth from a loaded configuration was considered, simplifying assumptions, such as compatible deformation or geometric symmetries, were introduced. In this work, we propose a new volumetric growth law that depends on fields evaluated in the current configuration, which is residually stressed and loaded, without any geometrical restrictions. We illustrate our idea using a simplified left ventricle model, which admits inhomogeneous growth in the current configuration. We compare the residual stress distribution of our approach with the traditional volumetric growth theory, that assumes growth occurring from the natural reference configuration. We show that the proposed framework leads to qualitative agreements with experimental measurements. Furthermore, using a cylindrical model, we find an incompatibility index that explains the differences between the two approaches in more depth. We also demonstrate that results from both approaches reach the same steady solution published previously at the limit of a saturated growth. Although we used a left ventricle model as an example, our theory is applicable in modelling the volumetric growth of general soft tissues.

Highlights

  • The interactions between living organs and the bio-environment play essential roles in regulating pathological or physiological growth

  • We propose a new framework of volumetric growth evaluated in the current configuration, which is thermodynamically consistent, and without releasing the residual stress or imposing geometrical and deformational restrictions

  • We show that the total cumulative growth from the reference configuration, the expression of which is prescribed in previous volumetric growth theories, can be derived based on this new framework

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Summary

Introduction

The interactions between living organs and the bio-environment play essential roles in regulating pathological or physiological growth. It has been experimentally demonstrated that environmental factors, such as the chemical, mechanical or genetic stimulus, could induce growth and remodelling (G&R) processes in living organs. Living organs can re-shape themselves, reset their constituents’ growth (or turnover) rates, and develop volumetric and mass changes to adapt to pathological or physiological changes in the bioenvironment. Mature organs are expected to stay in a relatively stable living state and serve as fully functional; pathologically, the dynamic impact of bio-environmental changes will induce a quick remodelling process to renovate the functional tissue. An embryo heart can continuously and instinctively develop its heart structure due to genetic factors, and tumours may grow independently of mechanical factors (Volokh 2006). A mature heart seems to grow along the direction of principal tensile stress due to mechanical factors (Taber and Eggers 1996). One is known as eccentric hypertrophy in response to chronic

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