Mathematical Modeling of Sperm Survival: Analysis of Interactions Between Thermal Stress, Oxidative Doses, and ROS Kinetics

Background: Reactive oxygen species (ROS) are required for normal sperm function, but when they accumulate, they cause oxidative stress, DNA damage, impaired motility, and loss of viability. Heat stress—scrotal hyperthermia, in particular—also degrades sperm quality. How thermal and oxidative stress jointly lead to sperm dysfunction is still poorly understood, which hinders the setting of evidence-based occupational exposure limits and the design of sperm preservation protocols. Objective: We developed a mathematical framework that combines oxidative stress (ROS kinetics) with thermal stress (heat diffusion) to estimate sperm survival and to derive dose–response relationships. The model is meant to generate hypotheses that independent experiments can test; it is not a validated clinical predictor of male infertility. Materials and methods: Exposure ranges, biological thresholds, and dose–response parameters were taken from published in vitro studies on human and animal sperm (1995–2024). Records were retrieved from PubMed and Web of Science with the search terms “ROS sperm”, “thermal stress male reproduction”, and “hydrogen peroxide spermatozoa”. Studies were retained if they quantified ROS concentration, H2O2 exposure, or thermal dose in relation to sperm motility, viability, or DNA integrity; reviews, single case reports, and studies without quantitative dose–response data were excluded. Each data set was labeled by species (human, rat, bull, and others) and by sperm source (ejaculated or testicular), and differences in experimental conditions, medium composition, and temperature were recorded. A probit model was combined with a diffusion–reaction equation for ROS and with Fourier’s heat equation to simulate predefined exposure scenarios. The Python 3.14.5 script was compiled in the online interface, was used for probit fitting and plotting. To reflect differences in cellular antioxidant capacity, protected, normal, and vulnerable sperm were modeled as three separate phenotypic populations. Results: Predicted survival depended mainly on ROS concentration, thermal dose, and exposure time. Changing the rates of ROS generation and degradation altered the predicted oxidative exposure and survival probability appreciably. In the thermal simulations, viability declined with increasing dose, and the critical thermal distance varied inversely with thermal severity. The model separated four biological zones: signaling (about 100 nM H2O2), impaired motility (15 μM H2O2, roughly 1–2 h of exposure), DNA damage (50 μM H2O2), and lethality (≥200 μM H2O2). Antioxidant capacity and exposure duration strongly shaped the response to both oxidative and thermal stress. Conclusions: Sperm survival depends strongly on the magnitude and duration of oxidative and thermal exposure. The framework offers a quantitative basis for studying stress-dependent changes in sperm viability and yields hypotheses that can be tested experimentally. Before any clinical use, it needs independent validation under standardized, prospectively defined protocols; for now, it serves as a research tool for generating hypotheses and comparing exposures.