Numerical Simulation of Blood Flows in Patient-specific Abdominal Aorta with Primary Organs

A study on the ultimate mechanical properties of middle-aged and elderly human aorta based on uniaxial tensile test

Background

The mechanical properties of the aorta are particularly important in clinical medicine and forensic science, serving as basic data for further exploration of aortic disease or injury mechanisms.

Objective

To study the influence of various factors (age, gender, test direction, anatomical location, and pathological characteristics) on the mechanical properties and thickness of the aorta.

Methods

In this study, a total of 24 aortas (age range: 54-88 years old) were collected, one hundred and seventy-four dog-bone-shaped samples were made, and then the uniaxial tensile test was run, finally, pathological grouping was performed through histological staining.

Results

Atherosclerotic plaques were mainly distributed near the openings of blood vessel branches. The distribution was most severe in the abdominal aorta, followed by the aortic arch. Aortic atherosclerosis was a more severe trend in the male group. In the comparison of thickness, there were no significant differences in age (over 50 years) and test direction, the average thickness of the aorta was greater in the male group than the female group and decreased progressively from the ascending aorta to the abdominal aorta. Comparing the mechanical parameters, various parameters are mainly negatively correlated with age, especially in the circumferential ascending aorta (εp "Y = -0.01402*X + 1.762, R2 = 0.6882", εt "Y = -0.01062*X + 1.250, R2 = 0.6772"); the parameters of males in the healthy group were larger, while the parameters of females were larger in atherosclerosis group; the aorta has anisotropy, the parameters in the circumferential direction were greater than those in the axial direction; the parameters of the ascending aorta were the largest in the circumferential direction, the ultimate stress [σp "1.69 (1.08,2.32)"] and ultimate elastic modulus [E2"8.28 (6.67,10.25)"] of the abdominal aorta were significantly larger in the axial direction; In the circumferential direction, the stress [σp "2.2 (1.31,3.98)", σt "0.13 (0.09,0.31)"] and ultimate elastic modulus (E2 "14.10 ± 7.21") of adaptive intimal thickening were greater than those of other groups, the strain (εp "0.82 ± 0.17", εt "0.53 ± 0.14") of pathological intimal thickening was the largest in the pathological group.

Conclusion

The present study systematically analyzed the influence of age, sex, test direction, anatomical site, and pathological characteristics on the biomechanical properties of the aorta, described the distribution of aortic atherosclerosis, and illustrated the characteristics of aortic thickness changes. At the same time, new insights into the grouping of pathological features were presented.

An aneurysm-specific preconditioning technique for the acceleration of Newton-Krylov method with application in the simulation of blood flows

In this paper, we develop an algorithm to simulate blood flows in aneurysmal arteries and focus on the construction of robust and efficient multilevel preconditioners to speed up the convergence of both linear and nonlinear solvers. The work is motivated by the observation that in the local aneurysmal region, the flow is often quite complicated with one or more vortices, but in the healthy section of the artery, the principal component of blood flows along the centerline of the artery. Based on this observation, we introduce a novel two-level additive Schwarz method with a mixed-dimensional coarse preconditioner. The key components of the preconditioner include (1) a three-dimensional coarse preconditioner covering the aneurysm; (2) a one-dimensional coarse preconditioner covering the central line of the healthy section of the artery; (3) a collection of three-dimensional overlapping subdomain preconditioners covering the fine meshes of the entire artery; (4) extension/restriction operators constructed by radial basis functions. The blood flow is modeled by the unsteady incompressible Navier-Stokes equations with resistance outflow boundary conditions discretized by a stabilized finite element method on fully unstructured meshes and the second-order backward differentiation formula in time. The resulting large nonlinear algebraic systems are solved by a Newton-Krylov algorithm accelerated by the new preconditioner in two ways: (1) the initial guess of Newton is obtained by solving a linear system defined by the coarse preconditioner; (2) the Krylov solver of the Jacobian system is preconditioned by the new preconditioner. Numerical experiments indicate that the proposed preconditioner is highly effective and robust for complex flows in a patient-specific artery with aneurysm, and it significantly reduces the numbers of linear and nonlinear iterations.