Quantifying the efficacy of first aid treatments for burn injuries using mathematical modelling and in vivo porcine experiments

Computational insights into survival durations and prehospital interventions in accidental cold-water immersion: A comprehensive analysis of fresh and saltwater temperatures

This study examines the complex relationship between scenarios of cold-water immersion, survival durations, and prehospital interventions. It utilizes computational modeling methods to shed light on how different water temperatures affect individuals facing accidental cold-water immersion incidents. The analysis reveals significant variations in survival times based on water temperature. For example, subjects immersed in water at temperatures of 5 °C, 2 °C, and 0 °C had average survival times of 136, 113, and 100 min, respectively, under stable conditions. In flowing water at the same temperatures, survival times decreased to 119, 92, and 81 min, indicating the impact of water movement on cooling rates and survival durations. Likewise, individuals immersed in saltwater at temperatures of 5 °C, 2 °C, 0 °C, and -2 °C showed average survival times of 111, 88, 80, and 66 min, respectively, in static conditions. In flowing saltwater at the same temperatures, survival times decreased to 98, 74, 68, and 57 min, highlighting the influence of water flow on cooling rates and survival durations. A comparison between immersion in pure water and saltwater at 2 °C revealed survival times of 113 and 88 min under stable conditions and 92 and 74 min under dynamic conditions, emphasizing the role of water composition in survival outcomes. The study also challenges the notion that the demise of the Titanic's passengers and crew resulted from hypothermia, asserting instead that severe thermal shock was the primary cause. These numerical findings underscore the importance of considering water temperature, flow dynamics, and prompt medical responses in cold-water emergencies to enhance survival prospects. The study identifies water within the range of 41-43 °C as the most effective active external rewarming fluid for critical hypothermal conditions. By quantifying the impact of these variables on survival times, the study provides data-driven recommendations to improve emergency protocols and outcomes for individuals facing cold-water immersion incidents.

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether these data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second, we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods, we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.

A Bayesian Sequential Learning Framework to Parameterise Continuum Models of Melanoma Invasion into Human Skin

We present a novel framework to parameterise a mathematical model of cell invasion that describes how a population of melanoma cells invades into human skin tissue. Using simple experimental data extracted from complex experimental images, we estimate three model parameters: (i) the melanoma cell proliferation rate, [Formula: see text]; (ii) the melanoma cell diffusivity, D; and (iii) [Formula: see text], a constant that determines the rate that melanoma cells degrade the skin tissue. The Bayesian sequential learning framework involves a sequence of increasingly sophisticated experimental data from: (i) a spatially uniform cell proliferation assay; (ii) a two-dimensional circular barrier assay; and (iii) a three-dimensional invasion assay. The Bayesian sequential learning approach leads to well-defined parameter estimates. In contrast, taking a naive approach that attempts to estimate all parameters from a single set of images from the same experiment fails to produce meaningful results. Overall, our approach to inference is simple-to-implement, computationally efficient, and well suited for many cell biology phenomena that can be described by low-dimensional continuum models using ordinary differential equations and partial differential equations. We anticipate that this Bayesian sequential learning framework will be relevant in other biological contexts where it is challenging to extract detailed, quantitative biological measurements from experimental images and so we must rely on using relatively simple measurements from complex images.