Section: New Results

Numerical methods for fluid mechanics and application to blood flows

Participants : Grégory Arbia, Jean-Frédéric Gerbeau, Sébastien Martin, Saverio Smaldone, Marc Thiriet, Irène Vignon-Clementel.

• In [18] , a procedure for modeling the heart valves is presented. Instead of modeling complete leaflet motion, leaflets are modeled in open and closed configurations. This method enables significant computational savings compared to complete fluid-structure interaction and contact modeling, while maintaining realistic three-dimensional velocity and pressure distributions near the valve, which is not possible from lumped parameter modeling. To illustrate the versatility of the model, realistic and patient-specific simulations are presented, as well as comparison with complete fluid-structure interaction simulation.

• [37] paves the way for a complete patient-specific fluid-structure vascular modeling in which all types of available measurements could be used to estimate uncertain parameters of biophysical and clinical relevance. We propose a complete methodological chain for the identification of the parameters involved in a model for external tissue support of blood vessels, using patient image data. We demonstrate the use of this framework in a realistic application case involving hemodynamics in the thoracic aorta. The estimation of the boundary support parameters proves successful, in particular in that direct modeling simulations based on the estimated parameters are more accurate than with a previous manual expert calibration.

• In [27] we study the image-based blood flow in the first generation of the pulmonary arterial tree. This patient-specific study is aimed at assessing effects of lung deformation and vascular resistance on the pulmonary blood flow, especially during the acute phase of a pneumothorax and after recovery. Arterial geometry was extracted up to the fifth generation from computed tomography images, and reconstructed. An unsteady laminar flow with a given set of resistances at outlets was modeled. Adaptation is set to match perfusion to ventilation.

• In [44] , [36] we study the reciprocal effect of blood circulation and high-intensity focused ultrasound on the temperature field in the liver. High-intensity focused ultrasound (HIFU) is used as a thermal ablation process to eliminate tumors in different body's organs. Blood flow has a cooling effect. Conversely, ultrasounds are responsible for acoustic streaming. A three-dimensional acoustics-thermal-fluid coupling model is carried out to compute the temperature field a given hepatic cancerous region.

• The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for 3D simulations can provide valuable global dynamic information, particularly for patient specific simulations. In [30] , we have developed and tested a numerical method to couple a 3D Navier-Stokes finite-element formulation and a reduced model of the rest of the circulation, keeping the coupling robust but modular. For Neumann boundaries, implicit, semi-implicit, and explicit quasi-Newton formulations are compared within the time-implicit coupling scheme. The requirements for coupling Dirichlet boundary conditions are also discussed and compared to that of the Neumann coupled boundaries. Both these works were key for applications where blood flows in different directions during the cardiac cycle and where coupling with the rest of the circulation is instrumental (see the shunt optimization application [29] ).

• Boundary conditions in patient-specific blood flow simulations is key because pressure and flow within the modeled domain are driven by the interplay between the local 3D hemodynamics and the rest of the circulation. However, these boundary conditions are rarely the measured variables. In [45] , we showed how one can go from patient-specific clinical data (MRI and catheterization) to simulation input parameters, including modeling assumptions and the impact of both on simulation results. We explained how Windkessel models and more involved LPN can be calibrated.

  In [34] , we developed two multi-scale models, each including the 3D model of the surgical junction constructed from MRI, and a closed-loop LPN derived from pre-operative data obtained from two patients prior to Stage 2 Fontan palliation of single ventricle congenital heart disease. "Virtual" surgeries were performed and a corresponding multi-scale simulation predicted the patient's post-operative hemodynamic conditions, tested under different physiological conditions. The impact of the surgical junction geometry on the global circulation was contrasted with variations of key physiological parameters.

• In [19] , a similar 3D multiscale model was used but for the Stage 3 Fontan palliation. Several studies have been done to optimize the geometry of the surgical connection, to minimizing energy losses and improving surgical outcomes, but usually without taking into account respiration or exercise. A respiration model that modulates the extravascular pressures in the thoracic and abdominal cavities was implemented. Results showed that the preoperative model is able to realistically capture cardiac and respiratory oscillations compared to the venous Doppler velocity tracings. Three virtual surgical alternatives were coupled to the LPN and then investigated under rest and exercise conditions.

• In [29] , such a 3D-closed loop LPN model was integrated with an automated derivative-free optimization algorithm in an idealized systemic-to-pulmonary shunt anatomy (Stage 1 Fontan palliation). The goal was to optimize shunt geometries. Clinicians selected three objective functions to be maximized: (1) systemic, (2) coronary, and (3) combined systemic and coronary oxygen. Results showed the geometries associated with the favored delivery, the origin of coronary artery flow being driven by the shunt position as well. The results made only sense when the 3D domain was connected to a closed-loop model of the circulation.

• A novel Y-shaped baffle was proposed for the Stage 3 Fontan operation achieving overall superior hemodynamic performance compared with traditional designs. Previously, we investigated if and how the inferior vena cava flow (which contains an important biological hepatic factor) could be best distributed among both lungs. In [41] we proposed a multi-step method for patient-specific optimization of such surgeries to study the effects of boundary conditions and geometry on hepatic factor distribution (HFD). The resulting optimal Y-graft geometry largely depended on the patient left/right pulmonary flow split. Unequal branch size and constrained optimization on energy efficiency were explored. Two patient-specific examples showed that optimization-derived Y-grafts effectively improved HFD.