Inverse elastostatic stress analysis for biological structures

Mechanical factors such as stresses play a critical role in the development, growth, remodeling and damage of biological tissues. Given the importance of stress, a major task of biomechanical analysis is to estimate the stress distribution in a living organ. Although the principles and methodologies for mechanical stress analysis have been long established, the application in living biological systems presents new challenges due to mostly the lack of information. For examples, the issue of not knowing the initial stress-free configuration in the current practice of patient-specific analysis arises since the input geometry derived from medical images may correspond to a deformed state. The stress analysis in such cases gives rise to an inverse elastostatic problem for which the deformed state is given and the initial configuration and stress are sought.;This work is a comprehensive development of computational methods for inverse elastostatics and investigation of its biomechanical applications. The work consists of three parts. The first part focuses on developing finite element formulations for the inverse elastostatic method. Targeting the biological soft tissues that are generally incompressible and fibrous anisotropic, the inverse formulations are provided for general 3D continua and thin-walled structures modeled as shells and membranes.;The second part presents several important biomechanical applications in vascular biomechanics. Stress analysis with the inverse elastostatic method suits naturally to pressurized vascular organs, which evaluates the structural integrity and sometimes even provides information on the pathological condition of vascular organs. In addition, it is demonstrated the inverse method can be used to predict the residual stress which is known to present in most vascular organs.;The third part of the work is to evaluate the sensitivity of stress solution to material model. This is an important ingredient of this study because patient-specific material properties are difficult to obtain. It will be shown the stress distribution in thin-walled structures is insensitive to material properties to a great extent. This offers a possible way of determining stresses accurately without knowing the true elastic material behavior.;In summary, the present inverse elastostatic method provides a new paradigm of stress analysis for biological structures.