# 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.

## 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

• 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.

### 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