Modelling of Residual Stresses of Blood Vessels



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University of Cape Town

The diagnosis of vascular diseases can be achieved with a suitably determined circum­ferential stress at arterial walls. The stress distribution over arterial walls in blood vessels is affected by residual stresses and stresses due to blood pressure. However, residual stresses are still not reliably determined. For this reason, a suitable incorporation of these stresses is required in order to establish the wall stress as a reliable diagnostic indicator. Thus this study aims to model residual stresses by incorporating them into the wall stress distribution, and to investigate the effect that parameters defining the study constitutive model have on the stress distribution. The constitutive model makes use of the Cosserat fibre continuum in order to account for mechanics of arterial walls. It was developed for cardiac tissues by Skatulla et al. (2014), but it can also be used for a preliminary investigation on arterial tissues as these two types of tissues exhibit comparable mechanics. Residual stresses are incorporated by using three problem definitions, which are derived from the opening angle method, into a three dimensional two-layer artery con­sisting of the media and adventitia. The first problem incorporates residual stresses that are locked within individual load-free layers. The second problem continues the first problem by incorporating residual stresses acting at the interface surface between arterial layers, and then determine the artery wall stress distribution under blood pressure. The third problem determines the wall stress in the stress-free artery under blood pressure. On the other hand, the effect of parameters defining the constitutive model is investi­gated by varying the size of parameters in these problems. However, the second problem is not analysed in this study because it requires an analysis implementation that could not be achieved within the study timeline. Similarly, model parameters of problems are not calibrated to available experimental data. There­fore, this study only provides qualitative results. The investigation results on the incorporation of residual stresses into the stress distribution are found to be inconclusive as they provide contradictory results. The char­acteristic scaling parameters are found to influence the magnitude and gradient of the stress distribution. However, these results are not conclusive to clearly define the influ­ence. Thus it is recommended that further research be conducted in order to gain con­clusive results.