An improved analytical method to estimate three-dimensional residual stresses of the aorta

•Load-free condition in the residually-stressed state was properly incorporated.•Residual deformations in agreement with experiment.•Opening angles of each layer of the aorta incorporated as variables.•Patterns of residual stress and in vivo stress distribution was renewed.•Influence of the residual stress on the aortic compliance was quantified. Residual stress plays a fundamental role in maintaining the homeostatic state of the aortic wall. Since residual stress was discovered via the opening angle experiment, a large body of literature has been dedicated to this topic of research. However, current analytical approaches estimating the residual stress of the aorta still suffer from a number of limitations. In this study, we improved the current approaches by addressing the following limitations: 1) the variations in the residual deformations are not incorporated, 2) the load-free condition along the axis of the aorta is not properly accounted for, and 3) the obtained axial residual stretch of the media mismatches with the experimental data. In our newly-proposed analytical method, the load-free condition was imposed at the end cross-section of the residually-stressed aorta. The solution procedure was also modified to ensure that the experimentally measured residual stretches were properly specified. Moreover, the opening angles of the media and the adventitia were incorporated as variables so that their influences on the residual stress field can be investigated. Compared with other methods, this method resulted in a similar pattern of residual stress distribution in the intima and adventitia. In the media, however, this method showed that the residual stresses were tensile in both circumferential and axial directions, in contrast to other methods with the pattern of half compressive and half tensile in the circumferential direction and totally compressive in the axial direction. The axial residual stretch of the media, the opening angle of the media and the opening angle of the adventitia had significant influence on the residual stress and in vivo stress distribution. The inter-layer in vivo stress difference was evaluated to support future finite element simulation of residual stress using the tissue growth method. Moreover, the influence of the residual stress on the pressure–radius response was quantified, and the residual stress led to more than 360% increase in distensibility. The proposed method alleviated some limitations of previous analytical m