Spatiotemporal Analysis of Skeletal Muscle Temperature Under Dynamic Contractions

Abstract

This study extends Pennes’ bioheat equation to capture the thermal behavior of skeletal muscle undergoing periodic contraction and relaxation. By adopting a moving (Lagrangian) coordinate system and employing Fourier expansion, the model effectively predicts how heat is generated, conducted, and dissipated in actively contracting muscles. It provides a mechanistic explanation for why exercising muscles warm up, how they approach thermal steady state, and how convective cooling at the skin surface influences overall temperature distribution. Using this framework, the three-dimensional temperature profile within skeletal muscle was simulated, starting from a uniform dimensionless temperature representing the relative difference between arterial blood and ambient temperatures. As the simulation progressed, pronounced temperature gradients emerged along the muscle thickness due to the interplay of metabolic heat generation, blood perfusion, and surface heat dissipation. Periodic contractions induced oscillatory variations in local temperature, emphasizing the role of dynamic mechanical deformation on thermal responses. Notably, deeper muscle regions exhibited higher temperature elevations than superficial layers, in agreement with physiological expectations. Overall, this computational approach provides a robust framework for investigating spatiotemporal thermal variations in skeletal muscle, offering valuable insights for applications in thermoregulation studies, sports physiology, thermal therapy, and biomedical device design.