Red Blood Cell Membrane Mechanics Using Discrete Exterior Calculus (DEC) and Optimization

Area of Science:

• Computational biology
• Biophysics
• Cell mechanics

Background:

• Accurate modeling of red blood cell (RBC) geometry is crucial for understanding cellular processes like ATP release.
• Existing computational frameworks may lack the necessary stability or efficiency for dynamic RBC simulations.

Purpose of the Study:

• To develop a novel, implicit algorithm for computing red blood cell (RBC) geometry.
• To establish a coordinate-invariant computational framework using discrete exterior calculus (DEC) for quantitative modeling.

Main Methods:

• Formulated an implicit algorithm incorporating a Lie-derivative based vertex drift for mesh stability during deformation.
• Employed discrete exterior calculus (DEC) for a coordinate-invariant computational framework.
• Quantified algorithm stability by tracking RBC membrane energy.

Main Results:

• Achieved efficient computation of RBC equilibrium geometries.
• Demonstrated high algorithmic stability through membrane energy analysis.
• Validated equilibrium geometries against in vivo observations and reproduced osmolarity-induced shape changes.

Conclusions:

• The novel DEC-based algorithm provides an efficient and stable method for computing RBC geometry.
• This computational framework advances quantitative modeling of RBC behavior and has broad applications in cell biology.
• Future work will apply this algorithm to fluid-structure interactions of RBCs.