Computational Modeling and Simulation Examples in Bioengineering. Группа авторов

For future clinical DSS, we suggest the following scenario: new user has already performed medical scanning (CT or MRI) and these data are uploaded to the central server (or they are available over institution existing connection). In that case, we will generate 3D patient‐specific FEM model by using image‐based modeling software developed on the server. It is important to mention that, for the project purposes, accurate reconstructions will be necessary only for torso and aorta. We will reconstruct only aorta (by using statistical shape models) and torso interface (by using level set and marching cubes algorithms) because they are needed for setting FEM boundary conditions and because, on the other hand, accurate reconstruction of all organs represents time‐consuming and computationally expensive problem with current medical imaging methods. In this way, highly accurate geometry, materials, and boundary conditions could be obtained for every patient (Figure 1.4).

Figure 1.4 Description of clinical decision support system for AAA disease.

1.9 Conclusions

      In the first part of this paper, literature survey on AAA biomechanics is reported including several aspects from experimental test, constitutive model, and ILT. Further, we presented our FE models, aimed at simulating and enhancing the computational study of the aneurismatic pathology. The combination of fluid and nonlinear structure modeling can give better understanding of the flow, pressure distribution, wall shear stress quantification, and effect of material properties and geometrical parameters. Computational methods have made patient‐specific analyses possible, a feature essential for understanding the progression of AAA in a particular patient. Finally, future clinical DSS is suggested by using DM approach. The main aim is to run predictive FSI model in order to estimate the risk of rupture and to use patient‐specific wall properties with calcium, tissue disease, and thrombus to overcome multiple level of uncertainties.

      During the last two decades, significant efforts have been made in order to define a computational model which includes biomechanical and biological approach, but still a lot of clinical studies are necessary in order to make these computational studies real in everyday clinical practice.

      Exercise 1.1 Modeling of Blood Flow Within the AAA

      The shape of AAA is very important. The severity of AAA is commonly estimated in clinical practice by considering the AAA maximal diameter. However, from the mechanical point of view, the hemodynamic effects and the mechanical stresses within the AAA tissue certainly are important in the process of the AAA rupture. Bulge diameter alone may not be a sufficient criterion for determination of rupture risk; therefore, an insight into the hemodynamic effects and the stress–strain quantification and distribution within the vessel wall are of great significance even in medical practice.

      Generation of the Finite Element Model

A simplified geometry of an aneurism is shown in Figure 1.5. With the on‐web software, the 3D finite element model for the blood flow domain can be parametrically generated. A transition smoothness between the surfaces is achieved by using Bezier's curves. Also, the results can be displayed with a user‐friendly menu in a way suitable for an insight into medical aspects of the blood flow conditions. A detailed description of the software use is given on the web (within Tutorial of each example), while the description of geometric parameters is given in the caption of Figure 1.5.

Figure 1.5 Geometrical parameters of AAA: “Length” is the parameter which defines the total horizontal projection of the generated aneurysm model; “A” is the height of the arc of central line; “Aorta diameter” is the abdominal aorta diameter; “B” is the radius from the central line to the inner wall of the aneurysm; “C” is the radius from the central line to the outer wall of the aneurysm; “Aneurysm length” is an average length of the AAA.

      Boundary Conditions

      At the inflow aorta cross‐section, a fully developed parabolic flow is assumed, determined by a selected volume flux. The normal stress and tangential stress are set to be equal to zero (stress‐free condition) or they are prescribed at the outlet cross‐section.

It is assumed that the entering flow is pulsatile, with a typical waveform shown in Figure 1.6 [127]. As described in the software menu, the waveform can be changed.

Figure 1.6 A typical in‐flow waveform at the aorta entry. Q is the volumetric in‐flux and t/T is the relative time with respect to the cycle period T.

      Results

      Results for two examples of the symmetric AAA are given here: (i) case with rigid walls and (ii) AAA with deformable walls. Results not shown here and solutions for other model parameters can be obtained using Software on the web.

      Modeling of AAA Assuming Rigid Walls

      We analyze an aneurism at the straight aorta domain, where aorta proximal and distal to the AAA bulge is idealized as straight rigid tube and branching arteries are excluded. The model has ratio D/d = 2.75 and geometry generated according to Figure 1.5 (D and d are diameters of the bulge and aorta, respectively). The data are: blood density is ρ = 1.05 g/cm³; kinematic viscosity (Newtonian fluid) ν = 0.035 cm²/s, d = 12.7 mm. The inflow velocity is defined by the flux function given in Figure 1.6. The FE mesh consisted of approximately 8000 3D 8‐node brick elements.

The results for the velocity and pressure at peak systole t/T = 0.16 are shown in Figure 1.7. The velocity disturbance in the region of the aneurism is notable. Also, the region of maximum pressure is located inside AAA.

Figure 1.7 Velocity field (left panel) and pressure distribution (right panel) for peak systole t/T = 0.16 of AAA for the model with D/d = 2/75, d = 12.7 mm.

      Modeling AAA with Deformable Walls

Here, an aneurysm of the straight aorta with deformable walls is modeled according to the FSI algorithm. Blood flow is calculated using 2112 eight‐node 3D elements, and 264 four‐node shell elements used to model the aorta wall, with the wall thickness δ = 0.2