Authors:

Alex Author

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About Paper:

Understanding the shape of deformable cells is crucial for advancements in lab-on-chip technology, which relies on precise manipulation of cellular structures. This study presents an approach to modeling the shapes of deformable cells using linear combinations of spherical harmonics. Spherical harmonics are a set of orthogonal polynomial functions that are made up of the Legendre Polynomials. A key challenge addressed in this work is ensuring the modeled cells maintain a constant volume, an essential biological constraint. To enforce this volume conservation, we derive an additional constraint on the linear combination of spherical harmonic coefficients. The volume integral in the context of spherical harmonics is derived and used to plot the shapes of deformed cells that maintain constant volume. To validate our volume integral, we employ a Monte Carlo integration method to verify that the deformed cells maintain a constant volume. Keywords: Mathematical Modeling; Applied Mathematics; Spherical Harmonics

Source:

Purdue University / 2024

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Co-authors:

Alex Author