Abstract
A two-dimensional model for red blood cell motion is adapted to consider the dynamics of breast cancer cells in a microfluidic channel. Adjusting parameters to make the membrane stiffer, as is the case with breast cancer cells compared with red blood cells, allows the model to produce reasonable estimates of breast cancer cell trajectories through the channel. In addition, the model produces estimates of quantities not as easily obtained from experiment such as velocity and stress field information throughout the fluid and on the cell membrane. This includes locations of maximum stress along the membrane wall. A sensitivity analysis shows that the model is capable of producing useful insights into various systems involving breast cancer cells. Current results suggest that dynamics taking place when cells are near other objects are most sensitive to membrane and cytoplasm elasticity, dynamics taking place when cells are not near other objects are most sensitive to cytoplasm viscosity, and dynamics are significantly affected by low membrane bending elasticity. These results suggest that continued calibration and application of this model can yield useful predictions in other similar systems.
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Acknowledgements
This work has been partially supported by the Department of Mathematics in the School of Science at IUPUI, the Biomechanics and Biomaterials Research Center, the Integrated Nanosystems Development Institute, and NSF Grant DMS-1522554. We would like to thank H. Yokota and S. Na (bioengineering professors at IUPUI), J. Ryu (mechanical engineering professor at NCSU), and T. TruongVo (research assistant at IUPUI) for discussions regarding their microchannel array experiments and paper. We would also like to thank H. Nakshatri (Marian J Morrison Chair in Breast Cancer Research at IUPUI) for useful discussions on important aspects of breast cancer. Finally, we would like to thank students J. Celaya-Alcala and A. Kovacs who helped us better understand capabilities and limitations of the numerical methods used as well as H. Sledge and C. Bugelholl who helped us investigate the efforts necessary for proper calibration of the model.
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Barber, J., Zhu, L. Two-dimensional Finite Element Model of Breast Cancer Cell Motion Through a Microfluidic Channel. Bull Math Biol 81, 1238–1259 (2019). https://doi.org/10.1007/s11538-018-00557-x
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DOI: https://doi.org/10.1007/s11538-018-00557-x