Authors:

Brijesh B Patel

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About Paper:

Flow cytometry is used in various biological applications for categorizing different cells. It works by exploiting the inertial focusing of particles in flow. While this effect is well studied for rigid bodies, most cells of interest are deformable. The shape and position of soft cells during flow is not well known, though there is consensus that the elasticity of the cell plays an important role. Typically, cell dynamics are calculated numerically by discretizing the surface of the cell and running simulations of the flow. However, these simulations are computationally expensive and full solutions are only known for a few parameters. Additionally, experimental data is difficult to analyze due to the fast speed and small scale of the particles. Yet the principal factor determining the particle's focusing position is the shape of the particle, which depends on the elasticity of the cell. In order to reduce complexity, we build a reduced order model of the cell using spherical harmonics. Assuming the cell's volume remains constant through deformation, the cell's surface can be approximated with linear combinations of spherical harmonics. We developed an algorithm to fit these data using image processing and optimization, allowing us to analyze the coefficients. We then validate the model against experimental image data and previous simulation work under different elasticities and flow conditions. The data can then be used to construct a catalog of cell shapes to help aid in simulations. Keywords: Math Modelling; Inertial Focusing; Spherical Harmonics; Optimization

Source:

Purdue University / 2025

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Co-authors:

Brijesh B Patel