A calculation method for inert gas tension based on a multi-tissue model

Abstract

Introduction: This study developed a mathematical model capable of accurately estimating inert gas tension within human tissues under continuously changing ambient pressure. Methods: Based on Haldane's decompression theory and a multi-tissue model, and grounded in the principle that the rate of gas diffusion is proportional to the pressure gradient, a differential equation was derived and solved. Analytical solutions were obtained for four prototypical ambient pressure patterns: constant pressure, exponential compression, linear compression, and linear decompression. The model's validity was confirmed by comparison with the piecewise approximation method using a sufficiently small step interval. Results: The model allows precise calculation of theoretical tissue inert gas tension at any given time. In air-breathing fast buoyant ascents, for fast tissues with half-times of 30 s and 80 s, the inert gas tensions calculated using the conventional method (374 kPa and 233 kPa) were notably higher than those obtained via the proposed model (331 kPa and 217 kPa), with a maximum difference of 13%. The proposed model closely matched the piecewise method (1 s interval), differing by only 1 kPa. For tissue half-times exceeding 5 min, all three methods produced similar results. In a standard air diving decompression schedule, both the proposed and conventional methods yielded initial decompression stop depths rounded to 18 m, showing no significant difference. Conclusions: The model demonstrates clear advantages for fast tissues, and under varying ambient pressures, establishes a theoretical foundation for the dynamic prediction of tissue inert gas tension across diverse diving scenarios. It can be utilised in safety assessments of fast buoyant ascent, offering substantial theoretical relevance and practical applicability.