Computational Modeling and Simulation Examples in Bioengineering. Группа авторов

      Here, ΔU⁽ⁱ⁾ are the nodal displacement increments for the iteration “i,” and the system matrix , the force vector , and the vector of internal forces ^{n + 1}F^{int(i − 1)} correspond to the previous iteration.

      We described the material nonlinearity of blood vessels which is used in further applications. The geometrically linear part of the stiffness matrix, , and nodal force vector, ^{n + 1}F^{int(i − 1)}, are defined:

      (1.10)

      Here, the consistent tangent constitutive matrix of tissue and the stresses at the end of time step ^{n + 1}σ^{(i − 1)} depend on the material model used.

      1.7.4 FSI Interaction

      In many models of cardiovascular examples where deformation of blood vessel walls was taken into account, we can implement the loose coupling approach for the FSI [113–116]. The overall algorithm consists of the following steps:

      1 For the current geometry of the blood vessel, determine blood flow (with Arbitrary Lagrangian–Eulerian (ALE) formulation). The boundary conditions for the fluid are wall velocities at the common blood–blood vessel surface.

      2 Calculate the loads, which act on the walls from fluid domain (blood).

      3 Determine deformation of the walls taking the current loads from the fluid domain (blood).

      4 Check for the overall convergence which includes fluid and solid domain. If convergence is reached, go to the next time step. Otherwise go to step (1).

      5 Update blood domain geometry and velocities at the common solid–fluid boundary for the new calculation of the fluid domain. In case of large wall displacements, update the finite element mesh for the fluid domain. Go to step (1).

The shear stress and drag force distribution have been presented in Figures 1.2 and 1.3 for two different patients for proximal and distal AAA.

Figure 1.2 (a) Shear stress distribution. (b) Drag force distribution.

Figure 1.3 (a) Shear stress distribution. (b) Drag force distribution.

1.8 Data Mining and Future Clinical Decision Support System

      Together with CFD simulation, there are numerous statistics‐based machine learning methods that can be used to give more accurate and faster conclusions for clinicians [117].

Kolachalama et al. [118] proposed a DM technique that accounted for the geometric variability in patients for predicting cardiovascular flows. A Bayesian network‐based algorithm was used to understand the influence of key parameters through a sensitivity analysis. Martufi et al. [119] investigated a geometrical characterization of the wall thickness distribution in AAA. They were able to train a model to differentiate the wall thicknesses in ruptured and un‐ruptured AAA. Shum et al. [120] developed a model from 66 ruptured data sets and 10 non‐ruptured data sets and their geometric indices and wall thickness variations. The results of this study showed that, in addition to maximum diameter, sac length, sac height, volume, surface area, bulge height, and ILT volume were all highly correlated with rupture status. In this study, the overall classification accuracy was 86.6%. It used a decision tree algorithm that is one of the possible machine learning methods that can be used for large data sets requiring a decision output.

      Filipovic et al. [121] combined DM techniques and CFD for the estimation of the wall shear stresses in AAA under prescribed geometry changes. They performed large‐scale CFD runs for creating machine learning data on the Grid infrastructure and their results showed that DM models provide good prediction of the shear stress at the AAA in comparison with full CFD model results on real patient data.

      The abovementioned studies have been limited by the use of geometric parameters and, in particular, the maximum diameter of lumen alone as factors contributing to the rupture of an AAA. But other parameters such as patient history and comorbidities and presence of stents or other geometric parameters such as the aneurysm neck angles, tortuosity, and genetics factors [122–126] should be included. Despite the fact that state‐of‐the‐art FEM approaches represent powerful tool for estimation of AAA, their application in clinical practice remains limited due to several reasons. Firstly, every patient has specific and complex anatomy and it is not possible to create a general or parametric human model. Moreover, accuracy of simulations depends on the considered level of details, meaning that increasing required computation time and power will be necessary for obtaining precise results. As a consequence, performing patient‐specific simulation may take a few hours (if patient scans are available in the first place). This makes current FEM approaches inadequate for urgent situations such as alerting patient in case of AAA rupture.

      In order to avoid described limitations, the patient‐specific DSS could be proposed. The main idea is to perform patient‐specific forward simulations in advance. AAA of different types (sizes and positions) will be simulated and calculated stress analysis will be used for training of intelligent model. But, in order to perform forward FEM simulations patient geometry is required. For this reason, during the registration into our system, in local workstation (user hospital), patient or his/her medical institution will be asked to provide us patients' medical scans (CT or MRI for example), if there are any. However, it is assumed