## 3 Results
### Computational Techniques to Model Diseased Aortas  
Regarding the utilised numerical methods, our analysis revealed the usage of 12 different techniques. These and their relative frequency are depicted in Figure 4. The vast majority of the reviewed works resorted to the FEM and Finite Volume Method (FVM), which are grid-based methods to solve partial differential equations and allow the calculation of CSM [34; 35; 36], CFD [31; 37; 38] and FSI [21; 39; 40] simulations. FEM solves the differential equation by diving the analysed systems into finite elements and their predominance can be supported by several aspects. The main reasons are the wide implementation in computational platforms, the ability to handle complex geometries and, as of today, it represents the preferred choice to perform CSM simulations. Moreover, it was reported the use of FEM in CFD simulations (Garlekin Method) [41; 42]. FVM integrates, over finite volumes, the system governing equations and, using the divergence theorem, converts these volume integrals into surface integrals. Therefore, the physical properties of interest can be assessed as flux on the cell's surface, which is meant to improve convergence. This fact explains the recurrent choice of FVM to develop CFD simulations. As shown in Figure 3, the top five reported platforms (Abaqus, ANSYS, SimVascular, MatLab, OpenFOAM) all primarily resort to FEM and FVM techniques to develop the available modules. Figure 4: Relative frequency (values presented in percentage) of the identified numerical approaches. \(n=115\) articles. Figure 3: (a) Studied anatomical regions. (b) Selected software to perform the numerical modelling. Several other grid-based methods were reported. Finite Difference Method (FDM), similarly to FEM and FVM, also aims to solve partial differential equations, in this case by approximation to finite differences [19; 43; 44]. Extended Finite Element Method (XFEM) combines the formulations of generalised FEM and the Partition of Unity method and is mainly used in situations where grid refinement is not enough to achieve convergence. This feature is highly desirable in crack propagation simulations and coincidentally was used only in one work [45] to study the progression of AD. Regularised Lattice Boltzman Method (RLBM) and Virtual Flux Method (VFM) were the only Cartesian grid methods depicted in our summary [46]. The latter virtually calculate fluxes to impose pressure conditions on body surfaces, being able to reproduce their motion, and the former represents a set of methods for CFD simulations. These techniques were combined by [PERSON] and [PERSON] [46] to model the AV leaflet motion (VFM) and the transvalvular flow (RLBM). The second most used technique was the Reduced Order Model (ROM). Combining the works that resorted to 0D (4) [47; 48], 1D (6) [49; 50] and 2D (1) [51] models to recreate the haemodynamics of diseased and healthy aortas resulted in a total of 12 reports. ROM techniques are useful to overcome computational complexity-related problems by reducing the model degrees of freedom. In comparison with FEM or FVM simulations, which can easily take days or even weeks to conclude, these techniques allow for accurate computations in a few minutes or even seconds of incomplete characterisations of flow fields and WSS distributions. The 0D models, also known as electric analogues, are often used in in silico simulations of the cardiovascular system as Boundary Condition (BC) that recreates the compliance and resistance of arterial blood flow. The 1D models are mainly used to study Pulse Wave Velocity (PWV), which is an important metric to assess aortic stiffness, as recommended in clinical guidelines [2]. These models have been applied in FSI simulations to estimate the haemodynamics [52; 53]. The 2D models are nowadays less utilised as 3D simulation has become more accessible due to improvements in computer processing and the availability of 3D solvers.