[Paper Review] Understanding thermoregulatory transitions during haemorrhage by piecewise regression

Penny S. Reynolds, Grace S. Chiu|arXiv (Cornell University)|Jun 26, 2010

Thermal Regulation in Medicine12 references3 citations

TL;DR

This study uses piecewise regression—specifically broken stick and bent cable models—to identify critical transition points (CTPs) in core body temperature during acute haemorrhage in conscious rats. It finds that bent cable regression better captures gradual thermoregulatory transitions than abrupt models, and that assuming independent residuals leads to incorrect uncertainty estimates, highlighting the need for autocorrelated error structures in physiological time series analysis.

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.

Motivation & Objective

• To systematically quantify the transition from normothermia to hypothermia during acute haemorrhagic shock using intensive time series data.
• To compare the performance of traditional broken stick regression with the more flexible bent cable regression in modeling physiological transitions.
• To evaluate the impact of residual error structure—assuming independence versus autoregressive correlation—on confidence interval estimation for the critical transition point (CTP).
• To assess whether the observed temperature changes during severe haemorrhage are consistent with a single, identifiable transition phase.
• To identify limitations in model applicability due to irregular or non-monotonic temperature profiles in a subset of animals.

Proposed method

• Employed piecewise linear regression (broken stick model) to estimate a single abrupt transition point in core temperature during haemorrhage.
• Applied bent cable regression as a more flexible alternative that allows for a gradual transition phase, relaxing the assumption of an instantaneous shift.
• Calculated two types of confidence intervals for the CTP: one assuming independent residuals and another assuming an autoregressive structure for error terms.
• Used time series data from 38 conscious rat models subjected to acute severe haemorrhage to estimate temperature response dynamics.
• Assessed model fit quality by comparing residual sum of squares and visual inspection of fitted curves against observed data.
• Excluded animals with irregular temperature profiles that did not conform to a single transition assumption, limiting model applicability to 23 of 38 cases.

Experimental results

Research questions

• RQ1 What is the critical transition point (CTP) in core body temperature during acute haemorrhage in conscious rats, and how accurately can it be estimated?
• RQ2 How do bent cable and broken stick regression models compare in capturing the thermoregulatory transition from normothermia to hypothermia?
• RQ3 Does assuming independent residuals lead to biased or incorrect confidence intervals for the CTP compared to an autoregressive error structure?
• RQ4 To what extent do individual physiological profiles deviate from a single-transition model, and what are the implications for model reliability?
• RQ5 What are the implications of gradual versus abrupt transitions for identifying the onset of irreversible shock in haemorrhagic shock models?

Key findings

• Only 4 out of 38 rats became clinically hypothermic (core temperature < 35°C), with a median temperature change of 0.8°C (IQR 0.57–1.31°C), indicating mild overall hypothermia despite severe haemorrhage.
• A critical transition point (CTP) could be estimated in 23 out of 38 rats, suggesting that a single transition model is applicable in a majority but not all cases.
• Bent cable regression provided superior fit when the transition appeared gradual, demonstrating its advantage over the broken stick model in capturing non-abrupt physiological shifts.
• Assuming independent residuals led to incorrect uncertainty estimates for the CTP in all cases, underscoring the necessity of modeling autocorrelation in time series data.
• Fifteen animals had irregular temperature profiles that violated the single-transition assumption, rendering both models inapplicable and highlighting limitations in model generalizability.
• Arbitrary imposition of broken stick models on gradual transitions, along with incorrect error assumptions, may lead to misleading CTP estimates, emphasizing the need for model selection based on data structure.