Red Blood Cell Dynamics and Microscopy – Lucas Amoudruz

Red Blood Cell Dynamics and Microscopy

August 11, 2026

A few months after I started my PhD, I was part of a team trying to model how red blood cells (RBCs) flow through a microfluidic device.<br>These devices are prime candidates for detecting circulating tumor cells, extremely rare cells that signal cancer metastasis, terribly difficult to catch among the trillions of red blood cells around them.<br>To optimize these devices, we first needed a numerical model that could reproduce the correct physics.

One day, we were comparing two videos, one from a real experiment, and one from our simulations.<br>The trajectories were different, meaning the simulations were wrong.<br>In the simulations, the fluid was modeled with a particle method called dissipative particle dynamics (DPD), and we had a coarse-grained model for the membrane dynamics.<br>At this point, we were not sure whether the mismatch came from the fluid or from the membrane surface model.<br>To rule out the fluid part, I was tasked with writing a boundary-integral method (BIM) code, a trusted method for solving Stokes flows, to compare with the DPD method.<br>I never got to finish it properly since we discovered that increasing the DPD resolution fixed that part.

Recently I made simulations of sedimenting particles in a viscous flow, where a cloud of small particles transformed into a torus before breaking up.<br>This relies on the same principles for solving the Stokes equations, and it made me want to finally implement the boundary-integral method for a red blood cell.<br>I decided to extend my solver to handle the complex membrane dynamics of RBCs, based on my previous research, and combine them with the fluid solver I implemented.

In particular, I have seen several experimental videos of these cells, none of them looking like the visualizations of my "perfect" cells produced numerically.<br>Can we produce similar pictures, with the microscopic artifacts?

Let's first make a few simulations to obtain RBC shapes observed in experiments.

From membrane energies to the stomatocyte-discocyte-echinocyte sequence

Red blood cells are roughly two things: a membrane, enclosing the cytosol, which carries the hemoglobin necessary to transport oxygen efficiently.<br>The cytosol can be modeled as a viscous fluid about 5 times more viscous than the plasma.<br>The membrane is more complicated: it is composed of a cytoskeleton and a lipid bilayer.<br>The former is mainly responsible for shear elasticity, while the latter contributes to bending resistance, area conservation, membrane viscosity, and area-difference elasticity, depending on the surrounding chemical conditions.<br>All these terms can be modeled mathematically on a single surface, and discretized onto a triangle mesh.<br>I'll spare you all the math and energy functionals, but it's described in detail in my previous research 1 2, and has been discretized initially in some of my colleague's work 3 and implemented in Mirheo 4.<br>I show a few of the force terms below.

Loading…

Force magnitude of each term on a discocyte at equilibrium.

The energies are relatively simple to implement, and have analytical solutions on spheres.<br>Forces are derivatives of these energies with respect to positions,<br>much more involved, but validated against finite differences of the energy.<br>I also created functions to compute the Hessian of the energies, which allows computing equilibrium shapes (minimal energy) faster with Newton's method.<br>This was of course all facilitated by LLMs (I mainly used Opus 4.8 from Claude Code), although I gave tight directives so that the design remained under control, performance stayed reasonable, and I adopted a test-driven development approach.

After a bit of back and forth with my agent, tweaking, and parameter tuning, I could reproduce the famous SDE sequence (stomatocyte-discocyte-echinocyte), a sequence of shapes that RBCs take due to a change in the chemical environment, causing an imbalance between the two layers of the lipid bilayer:

Loading…

Stomatocyte

Loading…

Discocyte

Loading…

Echinocyte

Fischer 5 reproduced this sequence experimentally (EDS, reversed!) by changing the albumin concentration. I remember being fascinated by how much the cells deform under this chemical change:

Your browser does not support the video tag.

Video from Fischer (2022) [^5]

This is a microscopic view, very different from the crisp idealized surfaces I showed before.<br>How do they compare?<br>In an ideal world, we would reconstruct the surface from the video.<br>This is far from easy.<br>Instead, let's do the reverse: take our perfect surfaces and model the microscopy.

Microscopy model

The above video uses differential interference contrast (DIC) microscopy.<br>This technique is designed to visualize small, transparent objects that are not visible with conventional microscopy.<br>It relies on the optical path length (OPL) accumulated by light through the sample.<br>More precisely, a system of...