Bending Energy Schemes for Discrete-Spring-Network Structural Modelling of Red Blood Cells

Authors

Osayomwanbor Ehi-Egharevba, Technological University DublinFollow
Mingzhu Chen, Technological University DublinFollow
Fergal Boyle, Technological University DublinFollow

Author ORCID Identifier

https://orcid.org/0009-0006-7626-6974

Document Type

Article

Publication Details

International Journal for Numerical Methods in Biomedical Engineering

Abstract

Red blood cells (RBCs) undergo large structural deformation, including bending, when passing through capillaries. They also exhibit a range of complex shapes such as stomatocytes, discocytes and echinocytes that form due to altered blood pH and salt levels, ingested drugs and adenosine triphosphate depletion. Discrete-spring-network structural models of RBCs employ different numerical treatments of the continuum bending energy. This affects bending accuracy and the prediction of accurate RBC shapes. This research compares three representations called bending energy scheme (BES) A, B and C to evaluate their accuracy in shape predictions. BES A, seen throughout the literature, is based on the formulations of Kantor and Nelson, while BES B and BES C are, respectively, spring-based and node-based curvature calculation methods based on the formulations of Jülicher. Flat and enclosed spring-network membrane test cases are presented, and predictions using the schemes are compared. The flat membrane test cases explored the bending of stiff and soft membranes while the enclosed membrane test cases evaluated equilibrium vesicle and RBC shape prediction, including predictions of the stomatocyte-to-discocyte-to-echinocyte sequence. Predictions showed that BES A and BES B have limitations and can underestimate the true bending deformation. Additionally, BES A and BES B are also unable to capture the necking behaviour critical to the accurate prediction of complex RBC shapes. BES C on the other hand was seen to be accurate and robust and predicted shapes closely matched expected biological shapes. Based on this research, BES C is recommended for all future spring-network RBC structural modelling.

DOI

10.1002/cnm.70114

Recommended Citation

Ehi-Egharevba O, Chen M, Boyle FJ. Bending Energy Schemes for Discrete-Spring-Network Structural Modelling of Red Blood Cells. Int J Numer Method Biomed Eng. 2025 Nov;41(11):e70114. doi: 10.1002/cnm.70114. PMID: 41258818; PMCID: PMC12628744.

Funder

Fiosraigh Scholarship

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.