MFBM-01 Contributed Talks

Michael Pan

The University of Melbourne

"Mathematical modelling of subchondral bone adaptation, microdamage, and repair in Thoroughbred racehorses"

Musculoskeletal injuries can significantly impact the careers of racehorses, and are a common cause of lost training days and fatality. Most bone injuries arise from the gradual accumulation of microcracks through repeated training rather than spontaneous events. If severe enough, cracks may propagate through the bone and lead to fractures, often necessitating euthanasia. While training promotes bone adaptation to higher mechanical loads, overtraining can cause excessive damage. To better understand the biological processes underlying bone injury, we developed a lumped parameter model that combines the processes of bone adaptation, microdamage accumulation and bone repair. The model parameters were calibrated to experimental observations of bone volume fraction and time to fracture in racehorses. A sensitivity analysis identified joint loads (arising from training speed) and strides per day (arising from training distance) as key factors contributing to bone damage. Simulations of a typical training program showed that the majority of damage is incurred from training at racing speeds. While some microdamage is repaired during training, our model estimates that this process is insufficient to offset the damage accumulated. These findings emphasise the critical role of regular rest in preventing bone injury.

---

James Holehouse

The Santa Fe Institute

"The Origins of Transient Bimodality"

Deterministic and stochastic models, though often used to describe the same biological systems, can yield qualitatively different predictions. In particular, deterministic bistability does not necessarily imply stochastic bimodality, and vice versa. Multistability and multimodality are typically seen as indicators of distinct system behaviors, often inferred from stochastic simulation trajectories. In this talk, I explore the disconnect between probability modes and behavioral modes in the context of transient bimodality—also known as “adiabatic explosions”—which refers to metastable probability modes that do not correspond to distinct dynamical behaviors at the trajectory level. I present recent findings that link the emergence of these transient modes to a breakdown of the central limit theorem, specifically in the context of first-passage time distributions to absorbing states. I conclude by discussing how transient bimodality challenges conventional interpretations of system behavior in biological contexts and highlight conditions under which this phenomenon becomes particularly relevant.

---

Anthony Pasion

Queen's University

"Long-Lasting and Slowly Varying Transient Dynamics in Discrete-Time Systems"

Mathematical models of ecological and epidemiological systems often focus on asymptotic dynamics, such as equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain variables of interest remain in a slowly evolving state for an extended period before undergoing rapid change. These transient dynamics can have significant implications for population persistence, disease outbreaks, and ecosystem stability. In this work, we analyze long-lasting and slowly varying transient dynamics in discrete-time systems. We extend previous theoretical frameworks by identifying conditions under which an observable of the system can exhibit prolonged transients and derive criteria for characterizing these dynamics. Our results show that specific points in the state space, analogous to transient centers in continuous-time systems, can generate and sustain long transients in discrete-time models. We further demonstrate how these properties manifest in predator-prey models and epidemiological systems, particularly in contexts where populations or disease prevalence remain low for an extended period before experiencing a sudden shift. These findings provide a foundation for understanding and predicting long transients in discrete-time ecological and epidemiological models. (Joint Work with FMG Magpantay)

---

Elmar Bucher

Indiana University / Intelligent Systems Engineering

"PhysiGym : bridging the gap between the Gymnasium reinforcement learning application interface and the PhysiCell agent-based modeling framework"

Reinforcement learning (RL) is a powerful machine learning paradigm in which an RL agent learns to discover optimal strategies in uncertain environments. The RL control strategy has achieved remarkable success in complex tasks such as playing Chess, Go, and StarCraft. For RL, the prevailing application interface (API) standard is Gymnasium, a Python library [1]. Agent-based (AB) modeling is a mathematical, dynamical system modeling approach where the parts of the system, the so-called agents, autonomously act according to agent-type specific rules. PhysiCell is an AB modeling framework written in C++ and was implemented to model multicellular systems based on Newtonian physics. Cells are the agents. The cell type specifies the rule set the agents apply. Tissue structure emerges from the cell interactions. Substrates like oxygen can be modeled with the integrated BioFVM diffusive transport solver. Additionally, intracellular models can be integrated into cell agents [2]. The resulting AB models are 2 or 3-dimensional, off-lattice, center-based, and multiscale in space and time. In this talk, we will introduce PhysiGym, a well-documented and on all major operating systems tested open-source framework written in C++ and Python that allows to control PhysiCell models over the Gymnasium API. After a brief introduction to AB models and RL, we will discuss the implementation and obtained results from our tumor microenvironment model and the RL algorithms we applied to the model. In the future, PhysiGym can be used to learn from simulations possible mechanisms that might explain how biology systems react to similar real-world control. Furthermore, if cancer patient digital twins are written as PhysiCell models, PhysiGym could ultimately be used by oncologists to explore RL reward functions to improve treatment efficacy, reduce side effects, and slow or prevent resistance. References: [1] https://gymnasium.farama.org/ , [2] https://PhysiCell.org

---