Reduced order model for patient specific fluid transient simulation of blood flow in aortic cross

Abstract

Cardiovascular diseases are one of the major causes of death and continue to increase globally. Even though coronary artery diseases and strokes are the main causes (Mendis et al. 2011), large arteries are also subject to a lot of pathologies like aneurysms or aortic dissections and depict a high risk of mortality. Over the past decades, due to the numerous progress in computing time, models of large arteries have been developed to help our understanding of the physics induced by the pathologies. 3D patient-specific fluid simulations can provide clinicians relevant data like the velocity of the blood, pressure or wall shear stress (WSS) of large arteries in a non-invasive way (Zhu et al. 2018) for the evaluation and diagnostic of the diseases or surgical and treatment planning (Canchi et al. 2015; Alimohammadi et al. 2015). The main drawback of 3D computational fluid simulation is the high computational cost. It is difficult to integrate those kinds of techniques in the medical workflow since they are highly time consuming. Dynamic Reduced Order models (ROM) based on neural networks can be used to replace 3D transient fluid simulation. This technic allows to obtain real time results. In this paper, we present a patient specific ROM computed from fluid simulations of blood flow in a healthy aortic cross. Several 3D transient fluid simulation using different set of boundary conditions were computed. From the results, we computed dynamic ROM returning 3D results for any set of boundary conditions. 2.1 3D Geometry of the aorta The 3D geometry of the aorta was manually extracted from CT-scan data. The data set consisted of 246 slices of 512*512 pixels, with an effective slice thickness of 1.25mm. The 3D geometry includes the end of the ascending aorta, the beginning of the brachiocephalic artery, the left subclavian artery, the left carotid and the descending aorta. 2.2 Transient fluid simulation of the aorta The aorta was meshed with polyhedral elements and 8 prism layers on the wall. The final mesh has 193 037 cells and 534 160 nodes. A mesh sensitivity test was carried out. We considered the blood to be an incompressible Newtonian fluid with a density of 1056 kg/m3 and a viscosity of 0.0035 kg/m-s. The aorta wall is supposed to be rigid. We set the turbulence model to Scale Adaptative Simulation. 3 seconds were simulated with a constant time step of 0.001 second to have at least 3 cardiac cycles. Mass flow profiles were applied at the inlet and pressure profiles were applied at the outlets. Several fluid simulations were computed to generate learning and validation data for the construction of the reduced order model. We generated 15 set of boundary conditions covering a high range of variation. The heart rate varies between 50 and 120, pressure between 3000 and 19 000 Pascal and mass flow rate between-0.27 and 1 m3.s-1. The 15 corresponding fluid simulations were computed and for each case the WSS, the pressure at the wall and the velocity fields were saved every 10 time steps. 2.3 Computation of the ROM The dynamic ROM corresponds to an identification of the nonlinear differential equations which relates solver inputs to solver outputs computed using neural networks. This model has already demonstrated good results on vascular constriction models (Feher 2018). The ROM can only learn 1D outputs. To compute the value of the pressure at the wall, the WSS and the velocity fields, the different 3D outputs were decomposed in modes with a singular value decomposition. The ROM then resulted from the learning of the different modes in function of the boundary conditions. The computations were all performed on 64-bit 16 core (Intel ® Xeon ® 3.10GHz) machine with 64.0 GB shared memory. On average, each simulation took 17h.