Sophistication of mathematical models in the pharmacological context reflects the progress being made in understanding physiological, pharmacological, and disease relationships. This progress has illustrated once more the need for advanced quantitative tools able to efficiently extract information from these models. While dynamical systems theory has a long history in the analysis of systems biology models, as emphasized under the dynamical disease concept by Mackey and Glass [Science 197, 287-289 (1977)], its adoption in pharmacometrics is only at the beginning [Chae, Transl. Clin. Pharmacol. 28, 109 (2020)]. Using a quantitative systems pharmacology model of tumor immune dynamics as a case study [Kosinsky et al., J. Immunother. Cancer 6, 17 (2018)], we here adopt a dynamical systems analysis to describe, in an exhaustive way, six different statuses that refer to the response of the system to therapy, in the presence or absence of a tumor-free attractor. To evaluate the therapy success, we introduce the concept of TBA, related to the Time to enter the tumor-free Basin of Attraction, and corresponding to the earliest time at which the therapy can be stopped without jeopardizing its efficacy. TBA can determine the optimal time to stop drug administration and consequently quantify the reduction in drug exposure.
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