Modeling initial strain distribution in soft tissues with application to arteries

Abstract

A general theory for computing and identifying the stress field in a residually stressed tissue is presented in this paper. The theory is based on the assumption that a stress free state is obtained by letting each point deform independently of its adjacent points. This local unloading represents an initial strain, and can be described by a tangent map. When experimental data is at hand in a specific situation, the initial strain field may be identified by stating a nonlinear minimization problem where this data is fitted to its corresponding model response. To illustrate the potential of such a method for identifying initial strain fields, the application to an in vivo pressure-radius measurement for a human aorta is presented. The result shows that the initial strain is inconsistent with the strain obtained with the opening-angle-method. This indicates that the opening-angle-method has a too restrictive residual strain parameterization, in this case.