(182m) Rigorous Parameter Estimation for Model Validation in Oncological Systems

The application of quantitative and formal methods from the physical sciences, engineering, and mathematics to physiological systems, provides an immense opportunity for novel and high-impact discovery. Specifically, such approaches in cancer research may enable a fundamental understanding of the limitations of conventional therapies, uncover novel treatment strategies, and someday help optimize therapy for individual patient outcomes. Recently, the normalization of tumor blood vessels has been proposed to improve the the delivery of nanomedicines [1, 2, 3, 4]. However, enhancing the delivery of nanomedicines is a multi-faceted engineering problem, and so a model-based systems engineering approach is proposed to better understand the underlying physical phenomena and complex relationships of the biological system.

Characterizing the fundamental transport properties of nanomedicines in tumors is paramount to developing highly-effective targeted drug delivery cancer therapies. For this purpose, a physics-based modeling approach must be taken. Baxter and Jain originally developed a one-dimensional spherical tumor model that describes vascular and transvascular transport [5, 6, 7, 8]. Further, a two-dimensional percolation-based tumor vasculature network model has also been established, that describes more details about the transmural coupling of fluid flow in the tumors [1, 9]. To enhance the predictive capabilities of models and provide confidence in their utility for the model-based approach for drug and therapy development, formal methods for model validation are required.

In this work, we propose using deterministic global optimization to solve the parameter estimation problem and provide a rigorous quantitative foundation for model discrimination. This approach requires solving a nonconvex optimization problem constrained by the physics-based tumor transport model as a partial-differential equation (PDE). A simulation-based feasible-path approach is taken and the PDE-constrained optimization problem is reformulated as a box-constrained nonlinear program with implicit functions embedded [10]. The objective function is the sum of squared error between the experimental data and the PDE model prediction.

In this study, we utilize a new experimental dataset of the dynamic transport of liposomes in solid tumors in mice. The data is in the form of the intensity profile over the spatial domain of the tumor for 1h and 24h discrete time points. Using distance-based anomaly detection, the data is filtered to eliminate outliers and obtain better results from solving the parameter estimation problem. We select the 1-D Baxter and Jain model for this study because the intensity data exists over the entire tumor domain consistent with this model [5, 6, 7, 8]. We apply a partial-factorial design of experiments approach to estimate the relative global sensitivities of the model parameters and identify the important parameters for consideration in the parameter estimation problem. The problem is solved using the open-source EAGO package[11] for global optimization with implicit functions in Julia [12].

Our work seeks to enhance the practicability and predictive capabilities of tumor transport models using data-driven model validation and rigorous methods in global optimization for stronger model-based systems engineering approaches in cancer research. The information obtained through this approach aides in the development of better models and provides deeper insight into the physical behavior of molecular transport in tumors to guide drug development and delivery.

References

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