3D Vessel dataset generation for predicting Navier-Stokes equations with deep learning methods

The Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .

The centre has 40 project teams, 27 of which operate jointly with Paris-Saclay University (15 teams) and the Institut Polytechnique de Paris (12 teams). Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.

The centre also hosts the Institut DATAIA, dedicated to data sciences and their disciplinary and application interfaces.

Key words: computational fluid dynamics, blood flow simulation, deep learning
The internship will be co-supervised by Irene Vignon-Clémentel (Directrice de recherche) and Francesco Songia (PhD student).

TIPS (Transjugular Intrahepatic Portosystemic Shunt) aims to reduce portal hypertension by adding a shunt between the portal vein and inferior vena cava.  The diameter, the angle and the global configuration deeply affect the hemodynamics of the surroundings vessels. For clinicians it is relevant to look at pressure and velocity fields in these vascular structures to optimize and evaluate the design and the position of the TIPS. 

Classical Computational Fluid Dynamics (CFD) methods can provide accurate velocity and pressure fields that satisfy the Navier-Stokes equations. However, they are not suitable for real-time predictions: in clinical settings, surgeons often need to evaluate multiple configurations quickly. To face this issue, deep learning methods can be employed to represent and predict pressure and velocity fields in these domains.

A deep learning model based on graph-neural networks has been already implemented for predicting the solution of Navier-Stokes equations in 2D high variable geometries. This pipeline has to be extended in 3D to be able to deal with realistic 3D vascular domains. The model has to be trained on several geometries with realistic boundary conditions to be able to generalize on unseen domains.

Objectives:

The main goal of this internship is to create a 3D dataset to train the neural networks. Within the team, we have several realistic geometries representing the domain composed by mesenteric, splenic and portal vein and there are also public available datasets.  To create the final (augmented) dataset, these geometries have to be preprocessed and a complete pipeline to generate the mesh, set boundary conditions and solve the Navier-Stokes equations has to be implemented.

Once the dataset will be generated, the second step of the project will consist in improving some modules of the architecture that were first developed for the 2D project. In particular, graph neural networks, transformers and space state models need to be combined.

Main tasks:

• Pre- and post- process real vascular geometries
• Solve Navier-Stokes equations with a CFD solver
• Improve some modules of the existing 2D deep-learning pipeline to solve Navier-Stokes in 3D domains
• Participate in activities of the research group (seminars, meetings, social activities)
• Write a report, present the results to the research group
• Contribute the a journal publication and presentation to a conference depending on the obtained results

The core competences for an ideal candidate are:

• experience in deep learning models
• basic knowledge of computational fluid dynamics methods
• programming skills (C++, python)
• good communication skills in English

Experience with real vascular geometries (segmentation, meshing, preprocessing) will be considered as a valuable addition.

• Sports equipment;
• Transport reimbursement

Gratification