HemoTum++

This is the HemoTum++ project documentation.

1. Introduction

We are interested in the metastasis process …​ Biologists study CTCs spreading in the zebrafish …​ We would like to model and simulate this process …​

2. Mathematical framework and modeling

2.1. Computational Fluid Dynamics

Blood flow modeling

  • incompressible newtonian fluid

  • Reynolds number

  • NS → Stokes model

2.2. Computational Solid Mechanics

Vessel wall modeling

Elasticity:

  • linear

  • non linear

2.3. Fluid-Structure interaction

Blood flow deforms the vessel wall, and the vessel wall’s elastic behaviour has a damping effect on the flow. We model this by coupling the CFD and CSM in what is called FSI.

2.4. Multifluid level set framework

The cells we are interested in are mostly made of a membrane containing a fluid: the cytoplasm. Since they are carried over by blood flow, we can see the membrane as the interface between two fluids (blood outside and the cytoplasm inside).

2.4.1. Level-set method

We describe the level set method here.

2.4.2. Cell mechanics

Vesicle model.

Helfrich energy/foce.

2.4.3. RBC

RBC specific properties and physical parameters. How to apply the vesicle model.

2.4.4. CTC

CTC specific properties and physical parameters. How to apply the vesicle model.

2.5. Contact framework

Cells in blood flow can touch each other and can touch the vessel wall too. In this section we describe how to handle this mechanical process.

2.5.1. Cell to cell contact

2.5.2. Cell to wall contact

3. Meshing

In this section, we describe the meshing techniques and present the produced meshes …​

3.1. 3D meshing

We have produced multiple 3D meshes which fall into two categories: simplified (CAD) geometries and realistic (image-based) ones.

3.1.1. Simplified geometry

Full ZF CAD model

  • FreeCAD

  • GMSH

Small parts with obstacle

Cell as a rigid body deforming the endothelium.

  • case 1

  • case 2

  • case 3

  • …​

3.1.2. Realistic geometry

Built using Angiotk.

Aorta
Full ZF model

3.2. 2D Meshing

To test our cell simulations, we also produced 2D meshes.

3.2.1. Image based meshing

  • image pre-processing

  • contours extraction

  • geometry definition

  • meshing

4. Simulations and results

4.1. FSI simulation in a CAD mesh

4.2. Flow with cell as an obstacle in CAD parts

4.3. Cell in a 2D aorta part

4.4. …​