Intracranial pressure-flow relationships in traumatic brain injury patients expose gaps in the tenets of models and pressure-oriented management

Abstract

Background: The protocols and therapeutic guidance established for treating traumatic brain injury (TBI) in neurointensive care focus on managing cerebral blood flow (CBF) and brain tissue oxygenation based on pressure signals. The decision support process relies on assumed relationships between cerebral perfusion pressure (CPP) and blood flow, pressure-flow relationships (PFRs), and shares this framework of assumptions with mathematical intracranial hemodynamics models. These foundational assumptions are difficult to verify, and their violation can impact clinical decision-making and model validity. Methods: A hypothesis- and model-driven method for verifying and understanding the foundational intracranial hemodynamic PFRs is developed and applied to a novel multi-modality monitoring dataset. Results: Model analysis of joint observations of CPP and CBF validates the standard PFR when autoregulatory processes are impaired as well as unmodelable cases dominated by autoregulation. However, it also identifies a dynamical regime -or behavior pattern-where the PFR assumptions are wrong in a precise, data-inferable way due to negative CPP-CBF coordination over long timescales. This regime is of both clinical and research interest: its dynamics are modelable under modified assumptions while its causal direction and mechanistic pathway remain unclear. Conclusion: Motivated by the understanding of mathematical physiology, the validity of the standard PFR can be assessed a) directly by analyzing pressure reactivity and mean flow indices (PRx and Mx) or b) indirectly through the relationship between CBF and other clinical observables. This approach could potentially help to personalize TBI care by considering intracranial pressure and CPP in relation to other data, particularly CBF. The analysis suggests a threshold using clinical indices of autoregulation jointly generalizes independently set indicators to assess CA functionality. These results support the use of increasingly data-rich environments to develop more robust hybrid physiological-machine learning models.

Keywords: Hagen-Poiseuille flow; Intracranial hemodynamics; cerebral autoregulation; neurocritical care; traumatic brain injury.

FIGURE 1

Hemodynamics relationships associated with ICP In the first relationship (1.), ABP acts as the system inflow pressure with ICP opposing outflow pressure when it exceeds central venous pressure (CVP). In the second (2.), the ABP-ICP difference defines the background pressure gradient (CPP). The third (3.) is the pressure-flow relationship: CBF is determined by the pressure gradient subject under vasoregulation and other influences. The relationship (4.) identifies the co-dependence of functioning CA and CBF (or available oxygen/nutrients beyond the scope of this discussion).

FIGURE 2

Two example experiments with positive PFR. (upper panels of (A,C)) Experiments in this set show consistent, positive coordination between CPP (black) and perfusion (blue) observational data. (lower panels) Model estimated CBF (black, dashed) follows changes in CPP; posterior correction (blue, dashed) preserves the original orientation of the estimate without a change in sign. (panels (B,D)) The associated trajectories in correlation indices show strongly positive Mx values, while PRx may be variable including sign changes.

FIGURE 3

Two example experiments with zero PFR. The layout is the same as in Figure 2. Pressure (solid black) and perfusion (solid blue) data do not consistently coordinate over the 2-h experiment (upper panels of (A,C)). As a result, no suitable choice of Control parameters, corresponding to CA mechanisms, must alternate between positive and negative values to simulate these data for which no single PFR hypothesis suffices.

FIGURE 4

Example experiments with negatively-signed PFR. The layout is the same as the previous figure. Negative coordination between CPP (blue) and perfusion (magenta) observational data persists throughout many 2-h experiments. Model estimated CBF (blue, dashed) follows changes in CPP and requires a sign change in the posterior correction (dashed blue) match observed perfusion. Both Mx and PRx can be highly variable in these cases whose underlying causes are not known.

FIGURE 5

Joint Mx and PRx distributions and their difference Contours show distribution of (PRx, Mx) for pPFR ((A), 27.3K points), zPFR (D), 13.6K points), and nPFR (E), 15.8K points) experiments, excluding unqualified data (PPA $\ge$ 5). For pPFR, the data density is highest at (PRx, Mx) = (0.7,0.75) where both pressure and flow aspects of autoregulation are impaired. Panel (C) shows the difference in densities of pPFR and non-pPFR (C) indices, identifying the region $\text{Mx}=0.43\cdot (1-\text{PRx})$ dominated by pPFR cases. Green lines represent current index thresholds of 0.3 above which CA is assumed to be impaired; delineation based on PFR is a consistent joint consideration of those thresholds. The corresponding zPFR and nPFR distributions are distinct (bottom row). The zPFR data include both strongly positive and negative Mx values, whereas nPFR data consist of near-neutral positive Mx and strongly negative Mx.

FIGURE 6

Distribution of 1-min averaged data in PFR-identified experiments. In the top row, panels (A–E) show ABP, ICP, CPP, PRx, and heart rate (HR), respectively. In the bottom row, panels (F–J) show P_btO₂, SpO₂, EtCO₂, ICT, and respiratory rate (RR), respectively. (C) CPP medians exceed the protocol target range of 60–70 mm  Hg (grey). Both brain tissue oxygenation (F) and ICT (I) are elevated in zPFR relative to other data, although this may also reflect differences in patient care during intervals selected for experiment. Fully characterizing nPFR likely requires finer temporal and patient-specific analysis to identify the respective influences of high and low ICP, EtCO₂, both systemic and brain-tissue metabolic factors.

FIGURE 7

Gaussian process regression fitting of ICP (left) and CBF (right) from 1-s averaged data across the 83 2-h experiment intervals. Box plots give the distribution of scales of predictor influence on a logarithmic scale ordered decreasingly by median. ICHD model variables, indicated in red boxes, have low empirical predictive rank over the 2-h timescale. Importance rank is found by automatic relevance determination (ARD) (MacKay and Neal, 1994; Radford, 2012) using kernel function parameters associated with each predictor’s scale factor. The ranking is robust under alternate regression strategies (e.g., Lasso and Ridge Regression).