An engineering tool to estimate eigenstresses in three-dimensional patient-specific arteries

In this contribution we propose an engineering based approach to incorporate eigenstress distributions in arteries. Eigenstresses are known for a variety of biological tissues. In the case of arterial walls the so called opening angle experiment is frequently used to characterize the residual strains/stresses. Assuming that the transmural stress distribution of suitable stress measures should be smooth, a residual stress tensor is directly estimated from the Cauchy stresses. These stress measures are constructed in such a way that the basic biophysiological characteristics, like the fiber orientations which are taken into account by suitable structural tensors, are adequately respected. In order to achieve reasonable eigenstress distributions in the arteries the local stress measures should approach spatial-sector averaged values. These ideas are imbedded in an algorithm to update the residual stress tensor incrementally. An ideal tube and degenerated patient-specific arteries from medical imaging are used to demonstrate the performance of the proposed procedure and to estimate the opening angle.