Mechanical Modeling And Numerical Quantification Of The Three-Dimensional Residual Stress Of Aorta

The aortic wall is an important component of the circulatory system,and it is also the human organ that harbors serious pathologies,such as aneurysms and dissections.Accurate in vivo stress analysis is crucial in evaluating the rupture potential of the aortic aneurysm,predicting the initiation and propagation of the aortic dissection.Residual stress in the aorta directly affects the accuracy of in vivo stress analysis.The residual stress is found to be layer-specific,three-dimensional,as well as subject-specific.However,the existing mechanical models can not reflect these features.Therefore,it is a significant scientific task to establish an accurate mechanical model of the residual stress of the aorta.This study focuses on the mechanical modelling of three-dimensional residual stress and in vivo stress analysis of the aorta.The work includes the following aspects:Firstly,an analytical model within the scope of the nonlinear elasticity was proposed to recover the residual stress.As the residual deformation varies among different subjects,the opening angle and lateral bending angle were modelled as parameters.The deformation feature of the intima,media and adventitia can be described with the residual deformation gradients.The axisymmetric governing equation can be solved with proper boundary conditions.Three-dimensional residual stress distribution and the in vivo stress distribution of the aortic wall were computed.Although the value of the residual stress is small,it reduces the inter-layer and intralayer stress homogeneity of the in vivo stress.The residual deformations,such as the residual stretch of the media,the opening angle of the intima,media and adventitia,influence the residual stress and the in vivo stress of the aorta.The residual stress also changes the mechanical behavior of the aorta,for instance,improve the compliance of the aorta during the inflation test.Secondly,an experimental approach of the residual stress,including the opening angle experiment,lateral bending angle experiment and the biaxial mechanical test,were redesigned and carried out.The new experiment flowchart and procedure aim to obtain the residual deformation parameters and material parameters of the same subject simultaneously.The detailed processes were(1)cut the aorta into rings,strips and squares,cut the rings and strips to obtain the opening angles and lateral bend angles of the aorta;(2)divide the aorta into media and adventitia layer to obtain the opening angle and lateral bending angle;(3)do the biaxial tests with the standard 7 protocols and fit the material parameters of the aorta,media and adventitia.The aorta,media and adventitia have different opening angle and lateral bending angle,indicating that the residual stress is layer-specific and three-dimensional.The material parameter of the aorta,media and adventitia were different,implying that the heterogeneity of the aorta wall.The residual stress should be modelled into media and adventitia separately.The residual stress and in vivo stress of the abdominal aorta were computed based on the experimental data,which lay the foundation for the numerical model.Thirdly,a numerical method was proposed to recover the residual stress field of the aorta.According to the feature of stress distribution on the in vivo state,the numerical implementation based on the anisotropic volume growth method was carried out.The incompatible deformation derived by the stress was assumed to be the source of residual stress.A new growth evolution function was established to capture the interlayer and intra-layer stress homogeneity.The commercial software ABAQUS with user-defined subroutine UMAT was utilized to conduct the numerical simulation.The in vivo stress and the residual stress were same as the analytical ones,which validated the accuracy of the growth method.The virtual opening angles and lateral bending angles of the media and adventitia were simulated.Compared with the experiments,the errors of the virtual opening angle and lateral bending angle were all within 5%.The residual stress and in vivo stress of a patient aorta was recovered by the numerical method,which provides a pathway for the in vivo patient-specific quantitative modelling.Finally,the influence of the three-dimensional residual stress on the in vivo stress was studied,and the applications of the numerical method were explored.Including:(1).Compared with the three-dimensional subject-specific residual stress,the errors of two-dimensional and non-subject-specific residual stress were shown.The results verified the accuracy and applicability of the three-dimensional subject-specific residual stress modelling.(2).The aortic dissection model was established considering the residual stress.By varying the material and geometry parameters,the initial tear of the young and old human subjects was simulated by element deletion.The results showed that the residual stress help to protect the aorta from excessive damage and propagation.For the young subject,the initial tear has little impact,while for the old subject the dissected aorta will propagate or rupture on the extremely higher pressure.(3).The intimal buckling of the dissected aorta was simulated by deleting the elements within the media layer.The results showed the compressed intima will compress the true lumen with the increase of the dissection angle.The numerical results agreed well with the experiments.In summary,the analytical and numerical modelling methods are of great significance for the analysis of the three-dimensional residual stress,in vivo stress and other mechanical behavior of the aorta.The new experimental protocol is the supplement and improvement of the traditional opening angle experiment.The numerical model provides a pathway for patient-specific modelling.The numerical results contribute to the understanding of the mechanism of the formation and expansion of aortic dissection considering the residual stress,which can provide support for the diagnosis and treatment of some related vascular diseases.