Parameter Estimation of Cancer Mathematical Model in Chemoimmunotherapy with Trust-Region Reflective

P Khalili and R Vatankhah, IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY- TRANSACTIONS OF ELECTRICAL ENGINEERING, 49, 1591-1615 (2025).

DOI: 10.1007/s40998-025-00863-w

Studying cancer mathematical models provides a low-cost approach to gainig a deep understanding of how cancer and body cells interact within the tumor microenvironment. This has motivated bioengineers to study and develop more complex models and evaluate their performance using the available data. Estimating the system parameters of such dynamics is one of the major challenging issues since the number of parameters is large, and their values are bounded. This makes implementing the optimization algorithm difficult to implement. This paper considers a recent Ordinary Differential Equation (ODE) model in chemoimmunotherapy for parameter estimation. Meanwhile, a Delay Differential Equation (DDE) model with same states as the ODE model is utilized for data generation instead of performing time-consuming and costly experiments. After adding white noise to the produced data corresponding to different virtual patients, the Trust-Region Reflective algorithm was performed to estimate 47 bounded parameters of the model. The results show that the algorithm successfully estimated the system parameters despite parameter constraints. Subsequently, the model with the newly set of estimated parameters is re-evaluated using other virtual patients' initial conditions. The results show that the algorithm successfully estimates the system parameters, and comparing the model prediction and the virtual patient's data is satisfactory. The paper's findings can be directly applied in practice by substituting the virtual patients' data with real clinical data. This step would begin a new journey to connect pure theoretical models with the available clinical data, leading to personalized drug delivery.

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