MS02 - OTHE-06

A New Wave of Mathematical Modeling in Medicine and Pharmacy (Part 1)

Monday, July 14 at 4:00pm

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Note: this minisymposia has multiple sessions. The other session is: and Part-2.

Sungrim Seirin-Lee (Kyoto University/Graduate School of Medicine), Jaekyoung Kim (KAIST), So Miyoshi (Pfizer)

Description:

Another new wave is transforming the landscape of mathematical biology: its full-scale integration into medicine and pharmacy. The time has come for mathematical research, previously focused on theoretical studies, to make significant strides toward practical applications in collaboration with medical doctors and pharmaceutical researchers. This new paradigm aims to directly connect mathematical modeling to real-world treatment, helping patients in the present rather than only laying the groundwork for future possibilities. As this shift takes place, the role of mathematical approaches is becoming increasingly diverse. The complexities of modern medicine and pharmacy demand that mathematical models not only tackle theoretical challenges but also adapt to the nuances of clinical practice and drug development. This requires integrating multiple perspectives, including data-driven methods, predictive modeling, and tools for interpreting biological systems. Mathematics is no longer an auxiliary discipline-it is evolving into a cornerstone of innovation in medical and pharmaceutical research. Through this initiative, we aim to share cutting-edge developments in mathematical medicine and pharmacy, focusing on transformative approaches that link data, models, and real-world implementation. This mini-symposium represents an opportunity to rethink the possibilities of mathematical modeling and to explore its potential for creating tangible solutions in medicine and drug discovery.

Sungrim Seirin-Lee

Kyoto University

"Pathological State Inference System based on Skin Eruption Morphology for Personalized Treatments in Dermatology"

Skin diseases typically appear as visible information-skin eruptions distributed across the body. However, the biological mechanisms underlying these manifestations are often inferred from fragmented, time-point-specific data such as skin biopsies. The challenge is further compounded for human-specific conditions like urticaria, where animal models are ineffective, leaving researchers to rely heavily on in vitro experiments and sparse clinical observations. In this presentation, I propose a novel mathematical modeling framework that bridges the gap between the visible geometry of skin eruptions and the invisible molecular and cellular dynamics driving them. This interdisciplinary approach integrates mathematical science, data-driven analysis, and clinical dermatology to overcome current limitations in understanding disease pathophysiology. Furthermore, I will introduce an innovative methodology that combines mathematical modeling with topological data analysis, allowing for the estimation of patient-specific parameters directly from morphological patterns of skin eruptions. This framework offers a new pathway for personalized analysis and mechanistic insight into complex skin disorders.

Alexander Anderson

Moffitt Cancer Center

"Adaptive Therapy from Board to Bench to Bedside and Back Again"

Our current approach to cancer treatment has been largely driven by finding molecular targets, those patients fortunate enough to have a targetable mutation will receive a fixed treatment schedule designed to deliver the maximum tolerated dose (MTD). Cancers are complex evolving systems that adapt to therapeutic intervention through a suite of resistance mechanisms, therefore whilst MTD therapies generally achieve impressive short-term responses, they unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during both tumor progression, metastasis and treatment response is becoming more widely accepted. However, MTD treatment strategies continue to dominate the precision oncology landscape. Evolutionary therapy is a new evolution inspired treatment paradigm that seeks to exploit how a cancer evolves under treatment through smart drug dosing and sequencing often informed by mathematical modelling. Adaptive therapy is an evolutionary therapy that aims to slow down the emergence of drug resistance by controlling tumor burden through competition between drug sensitive and resistant cell populations. Adaptive therapy specifically alters the treatment schedule (timing and dose) in response to a patient’s disease dynamics, often stopping therapy or deescalating dose when burden is low and starting therapy or increasing dose when burden is high. This approach was inspired by pest management and developed through mathematical model driven insights and has been shown to work in preclinical animal models (prostate, ovarian, melanoma, breast) and in pilot clinical trials (NCT02415621; NCT05189457; NCT03543969). Recently, phase 2 adaptive therapy trials in prostate (NCT05393791) and ovarian cancer (NCT05080556) are testing the treatment break and treatment deescalation approaches respectively. In this talk we will discuss different aspects of adaptive therapy including (i) How to pick patients who will benefit from it; (ii) How best to optimize the treatment switch threshold; (iii) The importance of appointment frequency; (iv) Robustness when patients miss appointments. We will utilize differential equation and cellular automata models as well as deep reinforcement learning.

Adrien Hallou

University of Oxford

"Spatial mechano-transcriptomics: mapping at single-cell resolution mechanical forces and gene expression in tissues"

Advances in spatial profiling technologies are providing insights into how molecular programs are influenced by local signalling and environmental cues. However, cell fate specification and tissue patterning involve the interplay of biochemical and mechanical feedback. Here, we propose a new computational framework that enables the joint statistical analysis of transcriptional and mechanical signals in the context of spatial transcriptomics. To illustrate the application and utility of the approach, we use spatial transcriptomics data from the developing mouse embryo to infer the forces acting on individual cells, and use these results to identify mechanical, morphometric, and gene expression signatures that are predictive of tissue compartment boundaries. In addition, we use geoadditive structural equation modelling to identify gene modules that predict the mechanical behaviour of cells in an unbiased manner. This computational framework is easily generalized to other spatial profiling contexts, providing a generic scheme for exploring the interplay of biomolecular and mechanical cues in tissues.

Jae Kyoung Kim

KAIST

"Improving Biological Predictions: Rethinking Markovian and Diffusion Assumptions"

Mathematical modeling plays a critical role in understanding complex biological systems and making accurate predictions. However, incorrect probabilistic assumptions embedded in mathematical models can lead to significant errors. In this talk, I will highlight two such cases. First, I will discuss how the unrealistic assumption of Markovian dynamics in modeling the latent period of infectious diseases can produce misleading predictions about the spread of COVID-19, and present methods to overcome this issue. Second, I will address the limitations of the widely-used Fick’s law in describing molecular diffusion within cells. Contrary to experimental observations, Fick’s law cannot accurately reproduce the tracked movement of molecules. Instead, Chapman’s law, which accounts for physical interactions with cellular structures such as the endoplasmic reticulum, provides a more accurate depiction of intracellular protein diffusion.

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Annual Meeting for the Society for Mathematical Biology, 2025.