Combining mechanistic modelling with data-driven modelling in mathematical oncology

Mathematical modelling in cancer research has been developing and has contributed valuable insights. By helping to understand the mechanisms of biological processes and predict clinical outcomes, mathematical models can complement empirical cancer research. In chapter 2, we studied the dynamics by explicitly modeling the cancer cell-immune cell conjugate, and comparing the differences in deterministic and stochastic models. We find that explicit consideration of a conjugate compartment can (i) change long-term steady-state, (ii) change the time to reach an equilibrium, (iii) alter the probability of tumor escape, and (iv) lead to very different extinction time distributions. The importance of the conjugate compartment in defining tumor-effector T cell interactions suggests that accounting for transitionary compartments of cellular interactions may better capture the dynamics of tumor control and progression. In chapters 3 and 4, we study the acute lymphoblastic leukemia relapse problem. We investigate the dynamics of residual disease in individual patients to mathematically model leukemia evolution in observed response and relapse kinetics. We developed stochastic and deterministic, patient-specific models that can integrate longitudinal measurable residual disease data to further the understanding of the driving factors of relapse. In addition,  a machine learning approach is implemented to obtain the best-fit model and important features from the data. We found that pre-existing resistant subclone, de novo resistant subclone, or cancer plasticity can be the underlying reason for some early relapses. The initial disease level reduction kinetics are important to predict the relapse. Our modelling provides a framework for better quantifying relapse timing in individual patients and understanding the mechanisms driving relapse through measurable residual disease kinetics. Overall, this thesis shows the exploration of the role of cell conjugation in cancer immune dynamics and the underlying mechanisms of cancer relapse as well as timing in mathematical modelling approaches. The thesis also shows the step-by-step evolution of modeling from building a mechanistic model, integrating data, to learning from data.

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