arXiv subjects

Annabelle Collin

Publications and source records attributed to Annabelle Collin.

3 recordsLinked to original sources

arXiv2023

Deciphering circulating tumor cells binding in a microfluidic system thanks to a parameterized mathematical model

The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their trajectories under the influence of hemodynamic and adhesion forces. We focus on already available in vitro measurements performed with a microfluidic device corresponding to the trajectories of CTCs -- without or with different protein depletions -- interacting with an endothelial layer. A key difficulty is the weak knowledge of the fluid velocity that has to be reconstructed. Our strategy combines a differential equation model -- a Poiseuille model for the fluid velocity and an ODE system for the cell adhesion model -- and a robust and well-designed calibration procedure. The parameterized model quantifies the strong influence of fluid velocity on adhesion and confirms the expected role of several proteins in the deceleration of CTCs. Finally, it enables the generation of synthetic cells, even for unobserved experimental conditions, opening the way to a digital twin for flowing cells with adhesion.

q-bio.TO↗

arXiv2015

Analysis-suitable $G^1$ multi-patch parametrizations for $C^1$ isogeometric spaces

One key feature of isogeometric analysis is that it allows smooth shape functions. Indeed, when isogeometric spaces are constructed from $p$-degree splines (and extensions, such as NURBS), they enjoy up to $C^{p-1}$ continuity within each patch. However, global continuity beyond $C^0$ on so-called multi-patch geometries poses some significant difficulties. In this work, we consider planar multi-patch domains that have a parametrization which is only $C^0$ at the patch interface. On such domains we study the $h$-refinement of $C^1$-continuous isogeometric spaces. These spaces in general do not have optimal approximation properties. The reason is that the $C^1$-continuity condition easily over-constrains the solution which is, in the worst cases, fully locked to linears at the patch interface. However, recent studies by Kapl et al. have given numerical evidence that optimal convergence occurs for bilinear two-patch geometries and cubic (or higher degree) $C^1$ splines. This is the starting point of our study. We introduce the class of analysis-suitable $G^1$ geometry parametrizations, which includes piecewise bilinear parametrizations. We then analyze the structure of $C^1$ isogeometric spaces over analysis-suitable $G^1$ parametrizations and, by theoretical results and numerical testing, discuss their approximation properties. We also consider examples of geometry parametrizations that are not analysis-suitable, showing that in this case optimal convergence of $C^1$ isogeometric spaces is prevented.

math.NA↗

arXiv2015

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria, and the "Minimal model for human Ventricular action potentials" (MV) by Bueno-Orovio, Cherry and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistor- capacitor transmission condition. Various ECGs are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, Wolff-Parkinson-White syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article.

physics.med-ph↗