Physiological Complexity of Acute Traumatic Brain Injury in Patients Treated with a Brain Oxygen Protocol: Utility of Symbolic Regression in Predictive Modeling of a Dynamical System

Predictive modeling of emergent behavior, inherent to complex physiological systems, requires the analysis of large complex clinical data streams currently being generated in the intensive care unit. Brain tissue oxygen protocols have yielded outcome benefits in traumatic brain injury (TBI), but the critical physiological thresholds for low brain oxygen have not been established for a dynamical patho-physiological system. High frequency, multi-modal clinical data sets from 29 patients with severe TBI who underwent multi-modality neuro-clinical care monitoring and treatment with a brain oxygen protocol were analyzed. The inter-relationship between acute physiological parameters was determined using symbolic regression (SR) as the computational framework. The mean patient age was 44.4±15 with a mean admission GCS of 6.6±3.9. Sixty-three percent sustained motor vehicle accidents and the most common pathology was intra-cerebral hemorrhage (50%). Hospital discharge mortality was 21%, poor outcome occurred in 24% of patients, and good outcome occurred in 56% of patients. Criticality for low brain oxygen was intracranial pressure (ICP) ≥22.8 mm Hg, for mortality at ICP≥37.1 mm Hg. The upper therapeutic threshold for cerebral perfusion pressure (CPP) was 75 mm Hg. Eubaric hyperoxia significantly impacted partial pressure of oxygen in brain tissue (PbtO 2 ) at all ICP levels. Optimal brain temperature (T br ) was 34–35°C, with an adverse effect when T br ≥38°C. Survivors clustered at \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$${ \rm PbtO}_2\, \cong\, 25 { \rm mm}$$ \end{document} Hg vs. non-survivors \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$\cong $$ \end{document} 18 mm Hg. There were two mortality clusters for ICP: High ICP/low PbtO 2 and low ICP/low PbtO 2 . Survivors maintained PbtO 2 at all ranges of mean arterial pressure in contrast to non-survivors. The final SR equation for cerebral oxygenation is: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$PbtO_ {2} = 6.32774 + \cos ( - 12.9753*CPP ) + \frac {23.2796} {FiO_ {2}} - 1.32622*ICP$$ \end{document} . The SR-model of acute TBI advances new physiological thresholds or boundary conditions for acute TBI management: PbtO 2 ≥25 mmHg; ICP≤22 mmHg; CPP≈60–75 mmHg; and T br ≈34–37°C. SR is congruous with the emerging field of complexity science in the modeling of dynamical physiological systems, especially during pathophysiological states. The SR model of TBI is generalizable to known physical laws. This increase in entropy reduces uncertainty and improves predictive capacity. SR is an appropriate computational framework to enable future smart monitoring devices.

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