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This work deals with the prediction of the mechanical response of a section of a human common carotid artery (CCA). The arterial residual stress state is accounted for using the thermomechanical analogy (TMA) approach, which is applied in this work to model the mechanical response of a two-layered arterial structure. The starting point to model the arterial residual stress state is normally the cut-open section, which is in the case of patient-specific artery not known. With TMA approach, however, instead of using the arterial zero-stress cut-open configuration to predict the arterial residual stress state, a thermomechanical model of the CCA is considered with its zero-stress geometry defined based on the actual CCA in vivo configuration. The approximation to the CCA residual stress state is then obtained by exposing the auxiliary CCA model to a volumetric deformation, enforced via adequate thermal dilatations. The approach is validated on a circular arterial model and by predicting the CCA cut-open zero-stress state.

In this work, the residual stress state of a human common carotid artery is predicted using the so-called thermomechanical analogy approach. The purpose of the approach is to enable consistent mapping of residual stresses and the respective configuration from a circular arterial segment to a patient-specific arterial geometry. This is achieved by applying proper volumetric dilatations to the actual arterial stress-free in vivo geometry, which makes use of the analogy that states that the bending stresses can be obtained on an equivalent manner by applying proper thermal dilatations. The common carotid artery data are obtained in vivo from a healthy 28-year-old man using non-invasive methods. The predicted residual stresses of the common carotid artery are in good quantitative agreement with the data from prior work in this field. The approach is validated by predicting the common carotid artery zero-stress state configuration, where a sector-like (cut-open) state is obtained. With this approach, it is thus possible to predict the residual stresses as well as the configuration of patient-specific arterial geometry without the need to model its cut-open zero-stress configuration.

It is shown that Onsager’s principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is argued, in the case of stationary processes, that this extremum is a maximum rather than a minimum.