Pointwise identification of elastic properties in nonlinear heterogeneous membranes, and application to soft tissues

Identifying the elastic properties of heterogeneous materials has long been a very challenging problem both theoretically and experimentally. When it comes to biological tissues, this task is even more difficult since biological tissues generally exhibit substantial anisotropic behavior. Moreover, identification is often required to be performed in the service condition of living human tissues and organs, i.e., in vivo. Presently, a method capable of performing such tasks is lacking.

The primary goal of this study is to fill this gap by developing a novel experimental method, termed as pointwise identification method (PWIM), for delineating the elastic properties in nonlinear heterogeneous membranes. Fundamentally, the method hinges on a unique feature of membrane equilibrium problems, that is, wall stress can be determined from equilibrium consideration alone (static determinacy). Thanks to the static determinacy, membrane wall stress can be computed numerically by using finite element inverse elastostatics method (FEIEM), and depends minimally on the constitutive model.

In PWIM, an inflation test is conducted for the target membrane with a series of tracking markers, and a series of deformed configurations are recorded by using appropriate motion tracking techniques. Subsequently, the pointwise stress distribution in each deformed configuration can be acquired independently by applying FEIEM, whereas the corresponding strain distribution can be determined from the deformation relative to the reference configuration which contains implicitly the elastic properties of the material. Consequently, the elastic properties at every material point can be extracted by fitting an appropriate constitutive model to the pointwise stress-strain data pairs.

In this work, we have validated the method for nonlinear isotropic and anisotropic materials through numerical simulations on a patient-specific cerebral aneurysm model, developed an experimental system and validated the method experimentally by conducting an inflation test on a rubber balloon, and conducted a test on a rabbit urinary bladder. The situation of the global stress-free configuration being unknown was considered numerically by employing a concept of local stress-free configuration. In this regard, the method holds the promise of identifying in vivo the elastic properties of membrane-like living organs, e.g., cerebral aneurysms, using medical images upon the availability of powerful image registration techniques.