The Study On Mechanical Properties Of Thoracic Aorta And Optimization Of Constitutive Models For Numerical Simulation

Part ⅠEstablishment of programs for testing mechanical properties of thoracic aortaObjective:We established a series of testing programs to clarify viscoelastic properties of the thoracic aorta, and look for methods to calculate stress-strain, elastic modulus and compliance for different types of the thoracic aorta so as to provide conditions for later development of constitutive models and numerical simulation.Method:Specimens of the porcine thoracic aorta were collected for circumferential tensile breaking and bursting tests of the sheet of thoracic aorta, compliance and biaxial tensile tests of the tubular specimen, respectively. Raw data of the tests were subjected to statistical analysis and calculated with related formula to obtain biomechanical indicators that represented the degree of elasticity and hardening of thoracic aorta.Result:The contraction ratio of thoracic aortic length was about 20%in vivo and in vitro conditions. Under precondition, positive correlations were found between pressure and diameter as well as between tension and displacement, but the hysteresis loop appeared. In the circumferential tensile breaking test of the sheet sample, the initial modulus was 0.529±0.145N/mm2. In the bursting test, the average bursting strength was 9.329±2.112N, and the average bursting displacement was 8.038±1.282mm. Static and dynamic compliance testing of tubular specimen:when the pressure sections were 50-90mmHg,80-120mmHg and 110-150mmHg, static compliance was 23.895±4.094%/100mmHg, 20.847±5.085%/100mmHg and 17.062±3.525%/100mmHg, respectively; and dynamic compliance was 17.215±2.787%/100mmHg,11.126±2.329% /100mmHg and 4.615±1.490%/100mmHg, respectively. The static and dynamic compliance values showed a descending order across the pressure sections within the groups; the value of static compliance between the two groups was greater than that of dynamic compliance, and their differences were statistically significant. Tubular biaxial tensile testing of specimens:the circumferential and axial stress of each sample increased with strain; the same sample under different stress ratios showed a same stress-strain curve slope but different circumferential and axial stress-strain curve slopes; under a same stress ratio, different samples showed different stress-strain curves slopes, at the same time, and the circumferential and axial stress-strain curve slopes were also different.Conclusion:After they were installed, the porcine thoracic aortic specimens should be tested when the contraction had been balanced. Hysteresis loop reflected the viscoelastic properties of the sample. The circumferential tensile breaking tests of sheet samples produced the initial modulus, and the bursting tests defined the bursting strength and displacement of specimen. They provide the basis for a comparison of mechanical properties between different groups’specimens. Compliance of tubular specimen reflected the level of vascular sclerosis and characterized the degree of arterial elasticity expansion; biaxial tensile tests verified aortic anisotropy. They offer a possibility for numerical simulation, establishment and optimization of constitutive models of thoracic aorta.Part ⅡMechanical test of thoracic aorta in different populationsObjective:By measuring and comparing mechanical indexes of thoracic aorta in different populations, we aimed to learn about the difference of mechanical properties of thoracic aorta so as to provide biomechanical data support for exploring the cause of thoracic aortic diseases. The study was hoped to facilitate the analysis of injury mechanism of thoracic aorta and guide clinical treatment and research and improvement of endoscopic materials.Methods:The mechanics of specimens of three groups of human aorta, including normal aorta and aortic aneurysm and aortic dissection, were measured through a circumferential tensile breaking test so as to build the stress-strain relation of displacement and load, calculate the initial modulus of each specimen, and compare each group’s initial modulus. A bursting test was conducted to measure the thickness, bursting strength and displacement of the specimens of the three groups. The relationship between thickness, displacement and bursting strength was established, and bursting strength and displacement of the three groups’ specimens were compared and analyzed.Results:The three groups’ initial modulus gradually increased, with 0.305N/mm2, 0.568N/mm2 and 0.680N/mm2 for normal aorta, aortic aneurysms and aortic dissection, respectively. After removing the effects of thickness, analysis of covariance revealed a significant difference between the three groups (F=112.55, P=0.000). Post-hoc pairwise comparisons with the Bonferroni method showed significance differences between normal aorta and aortic aneurysm, between normal aorta and aortic dissection, as well as between aortic aneurysm and aortic dissection (Ps<0.05). The three specimens’average bursting strength was 10.121±2.543N,6.116±3.008N and 5.461±2.224N, respectively; and their average displacement was 9.791±1.927mm,5.498±1.223mm and 4.605±1.534mm, respectively. There was a pattern of gradual reduction of breaking strength and displacement across the three groups. Analysis of covariance of bursting strength, controlling for the effects of different thicknesses, showed a significant difference between the three groups (F= 6.485, P=0.010). A significance difference between the groups also surfaced for displacement (F=13.641, P=0.001).Conclusion:The tissue elasticity and the ability to resist damage to vascular wall against local vertical force reduced from normal human thoracic aorta to aortic aneurysm and to aortic dissection. The parameters are essential to solid mechanics analysis. They are in line with pathological anatomy of the human thoracic aorta. The testing and evaluation results have great significance for biomechanical modeling and numerical simulation for damage of the human thoracic aortic stent to the vascular wall. the thickness, bursting strength and displacement of the specimens of the three groups. The relationship between thickness, displacement and bursting strength was established, and bursting strength and displacement of the three groups’ specimens were compared and analyzed.Part ⅢEstablishment and optimization of constitutive models of thoracic aortaObjective:We established a constitutive model of the isotropy of thoracic aorta to achieve the derivation of biomechanical properties from the sheet sample to the tubular sample. And though establishment of an anisotropic constitutive model of thoracic aorta, we optimized constitutive material constants and provided basic conditions for numerical simulation.Methods:Based on the stress-strain curves of circumferential tensile breaking testing of a porcine thoracic aortic sheet sample, with repeated fitting and comparisons, we determined the appropriate constitutive equations and built an isotropic constitutive model. We verified the rationality and feasibility of the isotropic constitutive model with stress-strain curves from static compliance testing of a tubular specimen. We established a model on the basis of actual measured geometric parameters of porcine thoracic aorta. Based on actual load of biaxial tensile testing of tubular specimens and Holzapfel-Gasser-Ogden constitutive equation that represents anisotropy, we obtained simular stress-strain curves with circumferential and axial stress ratios of 1.5:1,2:1 and 3:1, respectively. Stress-strain curves from circumferential and axial simulation and that of biaxial tensile testing of tubular specimen were compared through repeated iterations to determine the optimum material constant and fiber orientation angle.Results:After repeated fitting and evaluation, reduced polynomial (order= 4) was the best constitutive equation for establishing an isotropic model. With pressure points in 0-200mmHg, the diameter values of specimens through model fitting and actual values measured through static compliance testing were not statistically significant; and the stress-strain curves also matched well. At the same circumferential and axial stress ratio, the results of circumferential diameter change and axial elongation did not show any significant difference between model simulation and actual tubular specimen measurement; and the stress-strain curve also well matched. The optimized material constant and fiber orientation angle were respectively C10-3.82Kpa, D-OKpa, K1-996.6, K2-524.6, k-0.226 and γ-48.6°.Conclusion:The isotropic constitutive model of tubular specimens’biomechanics derived from a sheet sample is reasonable and feasible. The anisotropic constitutive model combined with Holzapfel-Gasser-Ogden constitutive equation not only reflects the anisotropy of the thoracic aorta, but also helps obtain optimized material constant and fiber orientation angle.Part IVNumerical Simulation of Human Descending Thoracic Aorta and Endoprosthesis on the Basis of Computed Tomography Angiogram and Constitutive Model ConstantObjective:We aimed to make a preliminary analysis of the interaction between the aorta and endoprosthesis through numerical simulation.Methods:The thin layer computed tomography angiogram of a normal thoracic aorta was acquired in a patient with chest pain. A three-dimensional numerical model of the aorta was constructed by use of the Mimics software. With consideration of the constant of a constitutive model about blood vessel and stent, we used the Abaqus software to construct a finite element model of the aorta and load the model of a stent into that of the aorta in the plug-in manner. The contacting analysis and computation were realized through the finite element method, and the related mechanical indicators and maps were generated.Results:In the proximal segment of the descending thoracic aorta, the interceptions of three cross-sections were acquired from the proximal to the distal end. Some changes were observed in the respective perimeter and cross-sectional area. Before the endoprosthesis was assembled, the perimeter was 72.406mm, 69.571mm and 65.381mm at the 3 cross-sections, respectively. They were elevated to 77.468mm,75.931mm and 71.013mm, respectively, after the endoprosthesis was assembled. The growth rate was 6.99%,9.14% and 8.61%, respectively. Similarly, the cross-sectional area increased from 410.690mm2, 379.788mm2 and 337.648 mm2 to 469.697mm2,453.749mm2 and 399.111mm2, respectively. The growth rate was 14.37%,19.47% and 18.20%, respectively. The stress in the vicinity of both ends of the endoprosthesis was relatively concentrated and unevenly distributed, and the largest stress was detected at the proximal end of the stent at the greater curve.Conclusions:It is feasible to conduct a numerical simulation of the aorta and endoprosthesis using the data of the computed tomography angiogram and the constant of constitutive model about blood vessel and stent. The preliminary results appear to be consistent with the clinical phenomena and reasoning.