Probability of survival during accidental immersion in cold water

BACKGROUND: Estimating the probability of survival during accidental immersion in cold water presents formidable challenges for both theoreticians and empirics. A number of theoretical models have been developed assuming that death occurs when the central body temperature, computed using a mathematical model, falls to a certain level. This paper describes a different theoretical approach to estimating the probability of survival. METHOD: The human thermal model developed by Wissler is used to compute the central temperature during immersion in cold water. Simultaneously, a survival probability function is computed by solving a differential equation that defines how the probability of survival decreases with increasing time. The survival equation assumes that the probability of occurrence of a fatal event increases as the victim's central temperature decreases. Generally accepted views of the medical consequences of hypothermia and published reports of various accidents provide information useful for defining a "fatality function" that increases exponentially with decreasing central temperature. RESULTS: The particular function suggested in this paper yields a relationship between immersion time for 10% probability of survival and water temperature that agrees very well with Molnar's empirical observations based on World War II data. DISCUSSION: The method presented in this paper circumvents a serious difficulty with most previous models--that one's ability to survive immersion in cold water is determined almost exclusively by the ability to maintain a high level of shivering metabolism.