Numerical framework for patient‐specific computational modelling of vascular tissue

Accurate determination of the biomechanical implications of vascular surgeries or pathologies on patients requires developing patient-specific models of the organ or vessel under consideration. In this regard, combining the development of advanced constitutive laws that mimic the behaviour of the vascular tissue with advanced computer analysis and medical imaging techniques provides a powerful tool for modelling vascular tissues on a patient-specific basis. A framework for developing patient-specific models of blood vessel geometries obtained from medical imaging techniques is presented. The multiplicative decomposition of the deformation gradient tensor is intensively combined with the finite element method in order to account for the residual stress present on those geometries. In addition, an algorithm to compensate the mismatching effect of the load on the medical images is also discussed. Hence, a residually stressed and geometrically consistent model of the patient is obtained. The general framework is demonstrated in a realistic geometry of a carotid bifurcation. The example presented in this work shows that the incorporation of the residual stress dramatically affects the circumferential stress field, homogenizing the distribution and reducing the stress gradient. It also demonstrates that not accounting for the residual stress on a patient-specific geometry can lead to a completely different deformed configurations. Copyright © 2009 John Wiley & Sons, Ltd.