Pointwise identification for thin shell structures and verification using realistic cerebral aneurysms

Identification of material properties for elastic materials is important in mechanics, material sciences, mechanical engineering and biomedical engineering. Although the principle and techniques have been long established, the application in living biology still faces challenges. The biological materials are in general nonlinear, anisotropic, heterogeneous, and subject-specific. The difficulty is compounded sometimes by the requirement of non-destructiveness in medical applications. Recently, the pointwise identification method (PWIM) was proposed to address some of the needs of soft tissue characterization. PWIM is a non-invasive identification method, designed for thin materials; it can sharply characterize arbitrary heterogeneous property distributions.

The primary goal of this thesis is to extend the pointwise identification method , originally developed for membranes which by default is of convex shape in pressurized states, to thin structures of arbitrary geometry. This work consists of four parts. The first part investigates the insensitivity of stress solution to material parameters in thin shell structures. This is an important first step, because PWIM hinges on the static determinacy property of the equilibrium problem of membranes. Before introducing the shell element into PWIM, it is necessary to test to what extent the assumption of static determinacy remains reasonable. It is shown that saccular structure which bending stress is small compared to in-plane stress, can still be treated as a statically determined structure.

The second part focuses on developing finite element formulations of forward and inverse shell methods for a hyperelastic material model specifically proposed for cerebral aneuryms tissues. This is a preparatory step for the core development.

The third part is the development of pointwise identification method for thin shell structures. Methods for stress solution, strain acquisition, and parameter regression will be discussed in detail. The entire process is demonstrated using an example of a geometrically realistic model of aneurysm.

The fourth part is testing the applicability on geometrically realistic cerebral aneurysms. Six models were selected in the study; the emphasis is placed on cerebral aneurysm with concave or saddle surface region for which the use of shell theory is a must. The identification results of all six human cerebral aneurysms successfully demonstrate that the shell PWIM can be applied to realistic cerebral aneurysms. Four types of heterogeneous property distributions are considered in the study. It is found that the method can accurately back out the property distributions in all cases. Fiber directions can also be accurately estimated. The robustness of the method at the presentence of numerical noise is also investigated. It is shown that the shell PWIM still works when small perturbations exist in displacements.