Understanding thermoregulatory transitions during haemorrhage by piecewise regression

Abstract

Transition points are common in physiological processes. However the transition between normothermia and hypothermia during haemorrhagic shock has rarely been systematically quantified from intensive time series data. We estimated the critical transition point (CTP) and provided confidence intervals for core body temperature response to acute severe haemorrhage in a conscious rat model. Estimates were obtained by traditional piecewise linear regression (broken stick model) and compared to those from the more novel bent cable regression. Bent cable regression relaxes the assumption of an abrupt point transition, and thus allows the capture of a potentially gradual transition phase; the broken stick is a special case of the bent cable model. We calculated two types of confidence intervals, assuming either independent or autoregressive structure for the residuals. In spite of the severity of the haemorrhage, median temperature change was minor (0.8 C; IQR 0.57-1.31 C) and only four of 38 rats were clinically hypothermic (core temperature < 35 C). However, a transition could be estimated for 23 rats. Bent cable fits were superior when the transition appeared to be gradual rather than abrupt. In all cases, assuming independence gave incorrect uncertainty estimates of CTP. For 15 animals, neither model could be fitted because of irregular temperature profiles that did not conform to the assumption of a single transition. Arbitrary imposition of broken stick fits on a gradual transition profile and assuming independent rather than autocorrelated error may result in misleading estimates of CTP. Identification of the onset of irreversible shock will require further quantification of appropriate time-dependent physiological variables and their behaviour during haemorrhage.