- PhD

## Department:

- Mechanical Engineering

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## Thesis Abstract:

Populations of cells interacting within an extracellular matrix (ECM) exhibit spatiotemporal behaviors that are usually described through complex and extensive mechanisms. However, mechanistic computational models become intractable as the cell population increases. In this proposal, we develop a reduced order agent-based framework derived from the empirical treatment of simulation data obtained from detailed single-cell mechanistic computational models.

The key construct within this approach is the linearization and subsequent superposition of single-cell agent models to explain the emergent behavior among multiple cells. In preliminary work, simulation data is obtained from a detailed single-cell mechanistic computational model. Then using the technique of Partial Least Squares Regression (PLSR) combined with physical modeling theory, a linear state transition equation representing a single-cell agent is formulated in latent variable space. Finally, an algorithm is developed to superpose linearized agents and predict multi-cellular interactions. Using this method, computational expense and time are decreased significantly and sufficient mechanistic detail is retained in the simulation. The method is applied to cell-ECM interactions, and ECM remodeling during cell migration.

Current work includes analysis of the theoretical validity of the proposed approach and consideration of more than one reduced order model to describe the dynamic behavior of a single cell. This is in order to ensure adaptation to various initial conditions that may be present in the surrounding environment. Ultimately, multiple solutions of single agents will be superposed to predict emergent behaviors of nonlinear interacting agents, which would otherwise be prohibitively complex to compute.

## 5 Recent Papers:

Kim, M.C., **Mayalu, M**., Asada, H.H., (2016), “*Dynamic Modeling of Collective Cell Migration on an Elastic Substrate of Extracellular Matrix fiber network*,” Proceedings of the 2016 American Control Conference

**Mayalu, M**., Kim, M.C., and Asada, H.H., (2016), “*A Reduced Order Systems Approach to Prediction of Emergent Behaviors of Cellular Systems*,” Proceedings of the 2016 American Control Conference

Asada, H.H., Wu, F., Girard, A., **Mayalu, M**.,(2016), “*A Data-Driven Approach to Precise Linearization of Nonlinear Dynamical Systems in Augmented Latent Space*,” Proceedings of the 2016 American Control Conference

**Mayalu, M.N**., and Asada, H.H.,(2015), “*Multi-Model Selection of Integrated Mechanistic-Empirical Models Describing T-Cell Response*,” Proceedings of the 2015 American Control Conference

**Mayalu, M. N**., Kim, M.C., Chan, V., Neal, D., Kim, H.Y., Asada, H.H.,(2014), “*A New Approach to Predicting Emergent Behaviors of Cell-ECM Interactions Using Stochastic Rules Generated from Mechanistic Computational Models*,” Proceedings of the 7th World Congress of Biomechanics