OTHE-01 Contributed Talks

Arianna Ceccarelli

University of Oxford

"A Bayesian inference framework to calibrate one-dimensional velocity-jump models for single-agent motion using discrete-time noisy data"

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time and could be used to calibrate mathematical models of individual motility. However, experimental data is intrinsically discrete and noisy, and these characteristics complicate the effective calibration of models for individual motion. We consider individuals whose movement can be described by velocity-jump models in one spatial dimension, characterised by successive Markovian transitions between a network of n states, each with a specified velocity and a fixed rate of switching to every other state. We develop a Bayesian framework to calibrate these models to discrete and noisy data, which uses a likelihood consisting of approximations to the model solutions which we previously obtained. We apply the framework to recover the model parameters of simulated data, including the probabilities of switching to every other state. Moreover, we test the ability of the framework to select the most appropriate model to fit the data, including comparisons varying the number of states n.

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Richard Foster

Virginia Commonwealth University

"Practical parameter identifiability of respiratory mechanics in the extremely preterm infant"

The complexity of mathematical models describing respiratory mechanics has grown in recent years, however, parameter identifiability of such models has only been studied in the last decade in the context of observable data. This study investigates parameter identifiability of a nonlinear respiratory mechanics model tuned to the physiology of an extremely preterm infant, using global Morris screening, local deterministic sensitivity analysis, and singular value decomposition-based subset selection. The model predicts airflow and dynamic pulmonary volumes and pressures under varying levels of continuous positive airway pressure, and a range of parameters characterizing both surfactant-treated and surfactant-deficient lung. The model was adapted to data from a spontaneously breathing 1 kg infant using gradient-based optimization to estimate the parameter subset characterizing the patient's state of health.

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Caleb Mayer

Stanford University

"Mathematical Modeling of Circadian Rhythms: Applications to Phase Prediction and Fatigue Reduction"

As consumer-grade wearable technology has become more prevalent in recent years, large-scale collections of data have been made available for researchers. We analyze significant amounts of wearable data to determine the circadian features that differ across groups and time frames. Using wearable activity, steps, and heart rate data, we adapt mathematical models to accurately estimate circadian phase across populations. This has a number of applications, including chronotherapeutic drug delivery, reducing fatigue, and shift work scheduling. We demonstrate applications to estimating circadian phase (dim light melatonin onset, or DLMO) in a home-based cohort of later-life adults, showing that activity-based models perform similarly or better than light-based models in DLMO estimation. We further use these models to provide wearable-based lighting interventions for reducing cancer-related fatigue. In particular, we test whether these lighting interventions, delivered via a mobile app, reduce cancer-related fatigue in a randomized controlled trial with 138 breast cancer, prostate cancer, and hematopoietic stem cell transplant patients. These interventions, based on real-time assessment of circadian rhythm through wearable devices, improve certain measures of fatigue (e.g., daily measurements of fatigue) in cancer patients. Further studies are needed to tune these models and assess the effect of lighting interventions in broader and more diverse cancer care settings.

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Vasilis Tsilidis

Department of Mathematics, University of Patras

"Unveiling the Drivers of Fetal Weight Estimation: Which Ultrasound Measurements Matter Most?"

Fetal weight estimation via ultrasound is performed by measuring biometric parameters such as the biparietal diameter (BPD), head circumference (HC), abdominal circumference (AC), and femur length (FL), which are then used in various mathematical formulas to calculate the estimated weight. But do all parameters matter equally? To assess their contribution on fetal weight estimation, we analyzed 29 published formulas across 26 diverse global datasets. Results show that AC is consistently the parameter of greatest importance, while head measurements (BPD, HC) often add little value, particularly in the later stages of pregnancy. Additionally, nearly half of the formulas include redundant parameters, and two-thirds exhibit a crossover in parameter importance—some transition from low to high significance, while others decline from high to low—over the course of gestation. These findings highlight opportunities to simplify fetal weight estimation for clinicians, prioritizing AC reliability and trimming unnecessary inputs. Our work bridges mathematics and prenatal care, offering clearer guidelines to improve ultrasound-based predictions and support healthier pregnancy outcomes.

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