Computational Modeling and Simulation Examples in Bioengineering. Группа авторов

Computational Modeling and Simulation Examples in Bioengineering - Группа авторов


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that ILT reduced AAA wall stress, progressive AAA growth was not related to the diameter but AAA volume and relative ILT volume, and that higher wall stress was related to AAA growth only when ILT was not included in the simulations.

      By using an inverse optimization method, Zeinali and Baek [103] created a computational framework toward patient‐specific AAA modeling. Namely, using a 3D geometry from medical images, they identified initial material parameters for healthy aorta to satisfy homeostatic condition and then created different computational shapes and considered multiple spatiotemporal forms of elastin degradation and stress‐mediated collagen turnover. The results exhibited the importance of the role of elastin damage extent, geometric complexity of an enlarged AAA, and sensitivity of stress‐mediated collagen turnover on the wall stress distribution and the rate of expansion. Also, the study showed that the distributions of stress and local expansion initially correspond to the extent of elastin damage, but change because of stress‐mediated tissue growth and remodeling dependent on the aneurysm shape. The specificity of their study lies in the fact that the authors did not use AAA patient‐specific model, but medical images of a healthy subject. On the other hand, they suggest that in spite of the model used for the present study, their computational framework could be used in a patient‐specific modeling to predict AAA shape and mechanical properties if improved in the domain of boundary conditions, description of aortic tissue, growth and remodeling, and the development of inverse scheme using AAA patients' longitudinal images.

      Meaningful limitation of the study is mirrored in the fact that authors assumed a rigid wall which may alter the results since ILT tissue can deform during a cardiac cycle and consequently influence the fluid dynamics and the distribution of chemicals.

      Blood flow in aorta has a time‐dependent 3D flow, so the time‐dependent and full three‐dimensional Navier–Stokes equations were solved. The laminar flow condition appropriate for this type of analysis [107] was used. The finite element code was validated using the analytical solution for shear stress and velocities through the curved tube [108]. A penalty formulation will be used [109]. The incremental–iterative form of the equations for time step and equilibrium iteration “i” is:

      (1.1)Start 2 By 2 Matrix 1st Row 1st Column StartFraction 1 Over normal upper Delta t EndFraction bold upper M Subscript bold v Baseline plus Superscript t normal upper Delta t Baseline bold upper K Baseline Subscript bold v v Superscript left-parenthesis i minus 1 right-parenthesis Baseline plus Superscript t normal upper Delta t Baseline bold upper K Baseline Subscript mu bold v Superscript left-parenthesis i minus 1 right-parenthesis Baseline plus Superscript t normal upper Delta t Baseline bold upper J Baseline Subscript bold v v Superscript left-parenthesis i minus 1 right-parenthesis Baseline 2nd Column bold upper K Subscript bold v p Baseline 2nd Row 1st Column bold upper <hr><noindex><a href=Скачать книгу