Mathematical Modeling Applied to Pharmaceutical Sciences Problems

Monday, June 14 at 09:30am (PDT)
Monday, June 14 at 05:30pm (BST)
Tuesday, June 15 01:30am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS01" time block.
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Carl Panetta (St. Jude Children's Research Hospital, US), Helen Moore (Laboratory for Systems Medicine, University of Florida, US)


The use of mathematical modeling in pharmaceutical sciences began more than 50 years ago with the use of differential equations to quantify plasma drug disposition (pharmacokinetics) and drug exposure effects (pharmacodynamics). As computing power increased, more complex models and methods have been developed to address challenging problems in this field. These include mechanistically /physiologically based models; optimal control methods for designing effective drug scheduling; sensitivity analysis methods to quantify the impact of parameter uncertainty on model outputs; and machine learning and artificial intelligence methods to help with the ever-growing amount of available data. Mathematical modeling is currently used throughout pharmaceutical sciences from early drug development (e.g., exploring effective drug targets via mechanistic pathway models), to designing efficient clinical trials (e.g., pharmacokinetic/pharmacodynamic and efficacy/toxicity modeling), to therapeutic drug monitoring (e.g., defining optimal safe and effective individualized treatments). This mini-symposium, organized by members of the International Society of Pharmacometrics--- an organization which supports quantitative work in the pharmaceutical sciences, includes four speakers who will provide an overview of several specific mathematical modeling areas in pharmaceutical sciences. The primary aim of this mini-symposium is to initiate discussion between mathematical modelers and researchers in pharmaceutical sciences in an effort to develop stronger collaborative ties.

C.J. Musante

(Pfizer, US)
"A Few Open Mathematical Modeling Problems in Drug Discovery & Development"
Now, more than ever, pharmaceutical companies are relying on mathematical modeling & simulation to inform drug discovery and development decisions. In many cases, particularly for novel compounds, targets, and/or combinations, modelers must rely on incomplete data and/or extrapolation beyond existing data to address key questions, such as dose and dose regimen selection for clinical trials. In this talk, I will present a few case studies and related mathematical challenges that my team has faced and discuss why developing a better understanding of these problems is important in the context of drug discovery & development.

Jane Bai

"Conducting sensitivity analysis and uncertainty analysis for QSP needs more than mathematical computation"
In quantitative systems pharmacology (QSP) modeling, sensitivity analysis is often conducted to identify a set of sensitive parameters to avoid overparameterization for robust calibration and validation. There are different global sensitivity analysis methods to choose from. Furthermore, for each model output, sensitivity analysis generates a rank-ordered list. Combining individual lists of rank-ordered sensitive parameters from all model outputs in a QSP model to obtain the final list may be subject to modeler’s judgement. Capturing variability in a trial population through uncertainty analysis and virtual patient trials can improve the predictive performance of a model and inform trial designs for a drug development program. However, multiple different algorithms can be used. This talk will discuss methodological considerations when applying sensitivity analysis and uncertainty analysis to QSP modeling for drug development.

Freya Bachmann

(Department of Mathematics and Statistics, University of Konstanz, Germany)
"Computing the Individualized Optimal Drug Dosing Regimen Using Optimal Control"
Providing the optimal dosing strategy of a drug for an individual patient is an important task in pharmaceutical sciences and daily clinical application. By solving an optimal control problem (OCP) especially tailored to pharmacokinetic-pharmacodynamic (PKPD) models the optimal individualized dosing regimen can be computed for substantially different scenarios with various routes of administration. The aim is to compute a control that brings the underlying system as closely as possible to a desired reference state by minimizing an objective function. In PKPD modeling the controls are the administered doses and the reference state can be the disease progression. Therefore, the objective function which shall be minimized is quantifying the difference between a desired disease state and the actual state generated by a particular treatment. Drug administration at certain time points gives a finite number of discrete controls, the drug doses, determining the drug concentration and its effect on the disease state. Hence, it is possible to construct a finite-dimensional OCP depending only on the doses and apply robust quasi-Newton algorithms from finite-dimensional optimization.

Tongli Zhang

(Department of Pharmacology & Systems Physiology, College of Medicine, University of Cincinnati, US)
"Coping with the Challenge of Heterogeneity with Integrated Modeling, Machine Learning, and Dynamical Analysis"
Heterogeneity among individual patients presents a fundamental challenge to effective treatment, since a treatment protocol would only work for a portion of the population. We hypothesize that a computational pipeline integrating mathematical modelling and machine learning could be used to address this fundamental challenge and facilitate the optimization of individualized treatment protocols. We tested our hypothesis with the neuroendocrine systems controlled by the hypothalamic-pituitary-adrenal axis. With a synergistic combination of mathematical modelling and machine learning, this integrated computational pipeline could indeed efficiently reveal optimal treatment targets that could significantly improve the treatment efficacy of a heterogeneous individuals, despite of the challenge that the simultaneous changes of multiple parameters result in complex dynamical patterns. Dynamical Analysis of the computational results then revealed mechanistic insights that connect heterogeneous behavior to model structure. We believe that this integrated computational pipeline, properly applied in combination with other computational, experimental and clinical research tools, can be used to optimize treatment targets against a broad range of complex diseases.

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Virtual conference of the Society for Mathematical Biology, 2021.