## 3 Results
### Numerical Modelling Augmentation
#### 3.7.2 Novel Numerical Techniques  
Despite the capabilities of numerical modelling to predict the behaviour of complex biomechanical systems, their implementation in clinical practice is still very limited, with few examples of success. Possible reasons for this fact are presented and discussed below. Here, we present works aiming at the development of numerical models using innovative computational techniques (e.g., SPH, ML, ROM) and exploring new methods to improve the efficiency of FEM modelling. Regarding FEM modelling improvements, in our research, we found efforts in developing novel and more realistic BC, more robust methods to model the aortic wall and develop new meshing processes. Starting with BC-related works, [PERSON] et al. (2018) developed an equation that modelled the cardiac output towards the ascending aorta. The numerical results presented close agreement with in vivo data after calibration. [PERSON] et al. (2018) created a simplistic mathematical model aiming to recreate the coupling between the left ventricle and the ascending aorta by recreating the dynamics of the AV. [PERSON] and [PERSON] (2018) applied optimisation algorithms to estimate inlet and outlet BC. The proposedapproach provides a systematic strategy to improve the model predictions regarding clinically relevant haemodynamic data. The method provided physiological flow patterns with reduction in 4D flow MRI measurement noise and outperformed regular CFD simulations. [PERSON] et al. [114] proposed a novel outlet BC for compliant arteries. This BC consisted of the addition of a tube composed of porous media at the outlets. This condition aimed to recreate the reflection of pulse waves promoted by the downstream vasculatures and presented higher computational efficiency than (1D-3D) models. [PERSON] et al. [29] developed an ML tool trained with CSM data to estimate the zero-pressure geometries of patient-specific aortas. Aortic reference configurations are important to accurately represent the complex stress state of deformed aortas. [PERSON] et al. [35] used second-harmonic imaging microscopy data to assist a new micromechanical model with patient-specific data of collagen fibre orientation, to better predict the mechanical response of the aortic wall. They postulated that the developed methodology can capture the overall response of soft tissue by resorting to fewer constitutive parameters. They also found increased stiffness for larger strains (J-shaped curve) and poor approximations for the supra-physiological loading range. [PERSON] et al. [55] presented an ML tool surrogate of traditional wall constitutive models. This tool was trained with data from 63 ATAA human samples and outperformed well-recognised models such as the Holzapfel-Gasser-Ogden model. On meshing-related topics, [PERSON] et al. [115], [PERSON] et al. [43] and [PERSON] et al. [32] explored the application and generation of structured grids on patient-specific aortic models. [PERSON] et al. [61] compared the results of RPIM and FEM models of AAA. The results of both approaches were very similar. However, the meshing process in RPIM is less complex, which constitutes an advantage to the approach. [PERSON] et al. [31] presented a mesh morphing technique to assist and facilitate the meshing process for FEM simulations. [PERSON] et al. [30] developed a new method to assist the construction of both solid and lumen domains for FSI analysis, using SimVascular. The opportunity to independently choose the element size and the introduction of prestress methods contributed to a reduction in computational effort. Regarding the development of new techniques, there were several examples of works focusing on developing and improving previously developed ROM. In 1992, we found the first reference to these applications. In this work, [PERSON] [18] developed a 1D model of the aorta and AV. At the inlet, a pressure evolution over time was applied to mimic the cardiac pulse. At the outlet, the flow was calculated using a resistance BC.