Modeling pulmonary and CNS O₂ toxicity and estimation of parameters for humans

The power expression for cumulative oxygen toxicity and the exponential recovery were successfully applied to various features of oxygen toxicity. From the basic equation, we derived expressions for a protocol in which PO₂ changes with time. The parameters of the power equation were solved by using nonlinear regression for the reduction in vital capacity (ΔVC) in humans: %ΔVC = 0.0082 × t²(PO₂/101.3)^4.57, where t is the time in hours and PO₂ is expressed in kPa. The recovery of lung volume is ΔVC_t = ΔVC_e × e^{-(-0.42 + 0.00379PO2)t}, where ΔVC_t is the value at time t of the recovery, ΔVC_e is the value at the end of the hyperoxic exposure, and PO₂ is the prerecovery oxygen pressure. Data from different experiments on central nervous system (CNS) oxygen toxicity in humans in the hyperbaric chamber (n = 661) were analyzed along with data from actual closed-circuit oxygen diving (n = 2,039) by using a maximum likelihood method. The parameters of the model were solved for the combined data, yielding the power equation for active diving: K = t² (PO₂/101.3)^6.8, where t is in minutes. It is suggested that the risk of CNS oxygen toxicity in diving can be derived from the calculated parameter of the normal distribution: Z = [In(t) - 9.63 +3.38 × n(PO₂/101.3)]/2.02. The recovery time constant for CNS oxygen toxicity was calculated from the value obtained for the rat, taking into account the effect of body mass, and yielded the recovery equation: K_t = K_e - e^-0.079t, where K_t and K_e are the values of K at time t of the recovery process and at the end of the hyperbaric oxygen exposure, respectively, and t is in minutes.