General coarse-grained red blood cell models: I. Mechanics

We present a rigorous procedure to derive coarse-grained red blood cell (RBC) models, which lead to accurate mechanical properties of realistic RBCs. Based on a semi-analytic theory linear and non-linear elastic properties of the RBC membrane can be matched with those obtained in optical tweezers stretching experiments. In addition, we develop a nearly stress-free model which avoids a number of pitfalls of existing RBC models, such as non-biconcave equilibrium shape and dependence of RBC mechanical properties on the triangulation quality. The proposed RBC model is suitable for use in many existing numerical methods, such as Lattice Boltzmann, Multiparticle Collision Dynamics, Immersed Boundary, etc.

💡 Research Summary

The paper introduces a systematic procedure for constructing coarse‑grained red blood cell (RBC) models that faithfully reproduce both linear and nonlinear mechanical properties measured in optical tweezers stretching experiments. The authors begin by developing a semi‑analytic theoretical framework that treats the RBC membrane as a network of springs combined with areal and shear elastic moduli. By fitting the model parameters to experimental force‑extension curves, they obtain a set of spring rest lengths, spring constants, and surface elastic coefficients that simultaneously capture the small‑deformation shear modulus and the large‑deformation stiffening behavior observed in real cells.

A major innovation of the work is the definition of a “nearly stress‑free” reference configuration. In conventional coarse‑grained models the equilibrium shape often deviates from the characteristic biconcave geometry, and the mechanical response can depend sensitively on the quality of the triangulation (mesh size, element shape). To eliminate these issues, the authors pre‑adjust each spring’s natural length based on the initial triangle geometry and scale the areal and shear moduli proportionally to the triangle area. This construction forces the global stress tensor to be essentially zero in the undeformed state, ensuring that the equilibrium shape remains biconcave and that the mechanical properties are invariant under mesh refinement or re‑triangulation.

The authors validate their model by performing three‑dimensional particle‑based simulations that mimic optical tweezers experiments. The simulated force‑extension curves match the experimental data across the entire range of deformations, reproducing both the linear regime (small strains) and the pronounced strain‑hardening observed at large strains (up to 30 % extension). Moreover, the equilibrium shape of the simulated cell is indistinguishable from the physiological biconcave disc, confirming that the stress‑free construction successfully preserves the correct geometry.

Finally, the paper emphasizes the broad applicability of the proposed model. Because the formulation relies only on pairwise spring forces and surface elastic terms, it can be readily embedded in a variety of existing fluid‑structure interaction solvers. In Lattice Boltzmann (LB) frameworks the membrane forces can be coupled to the LB fluid through standard momentum exchange; in Multiparticle Collision Dynamics (MPC) the same forces are applied during the streaming step; and in Immersed Boundary (IB) methods the membrane nodes can be interpolated onto the Eulerian fluid grid without special treatment. This flexibility makes the model suitable for large‑scale blood flow simulations, investigations of microvascular resistance, and studies of pathological cell deformations such as sickle‑cell disease or platelet aggregation.

In summary, the work delivers two key contributions: (1) a rigorous parameter‑mapping protocol that aligns coarse‑grained membrane models with experimental linear and nonlinear elasticity, and (2) a nearly stress‑free, mesh‑independent construction that resolves longstanding geometric and mechanical artifacts of earlier models. These advances provide a robust, versatile foundation for future computational studies of RBC mechanics and their interaction with complex flow environments.