Understanding thermoregulatory transitions during haemorrhage by piecewise regression

Transition points are common in physiological processes. However the 28 transition between normothermia and hypothermia during haemorrhagic shock has 29 rarely been systematically quantified from intensive time series data. We estimated the 30 critical transition point (CTP) and provided confidence intervals for core body 31 temperature response to acute severe haemorrhage in a conscious rat model. 32 Estimates were obtained by traditional piecewise linear regression (broken stick model) 33 and compared to those from the more novel bent cable regression. Bent cable 34 regression relaxes the assumption of an abrupt point transition, and thus allows the 35 capture of a potentially gradual transition phase; the broken stick is a special case of the 36 bent cable model. We calculated two types of confidence intervals, assuming either 37 independent or autoregressive structure for the residuals. In spite of the severity of the 38 haemorrhage, median temperature change was minor (0.8 C; IQR 0.57-1.31 C) and 39 only four of 38 rats were clinically hypothermic (core temperature < 35 C). However, a 40 transition could be estimated for 23 rats. Bent cable fits were superior when the 41 transition appeared to be gradual rather than abrupt. In all cases, assuming 42 independence gave incorrect uncertainty estimates of CTP. For 15 animals, neither 43 model could be fitted because of irregular temperature profiles that did not conform to 44 the assumption of a single transition. Arbitrary imposition of broken stick fits on a 45 gradual transition profile and assuming independent rather than autocorrelated error 46 may result in misleading estimates of CTP. Identification of the onset of irreversible 47 shock will require further quantification of appropriate time-dependent physiological 48 variables and their behaviour during haemorrhage. 49