Modelling noninvasively measured cerebral signals during a hypoxemia challenge: steps towards individualised modelling

Abstract

Noninvasive approaches to measuring cerebral circulation and metabolism are crucial to furthering our understanding of brain function. These approaches also have considerable potential for clinical use "at the bedside". However, a highly nontrivial task and precondition if such methods are to be used routinely is the robust physiological interpretation of the data. In this paper, we explore the ability of a previously developed model of brain circulation and metabolism to explain and predict quantitatively the responses of physiological signals. The five signals all noninvasively-measured during hypoxemia in healthy volunteers include four signals measured using near-infrared spectroscopy along with middle cerebral artery blood flow measured using transcranial Doppler flowmetry. We show that optimising the model using partial data from an individual can increase its predictive power thus aiding the interpretation of NIRS signals in individuals. At the same time such optimisation can also help refine model parametrisation and provide confidence intervals on model parameters. Discrepancies between model and data which persist despite model optimisation are used to flag up important questions concerning the underlying physiology, and the reliability and physiological meaning of the signals.

Figure 1. Typical input traces.

(%, top panel), mean ABP (mmHg, middle panel) and (mmHg, bottom panel) for a typical subject (Subject 6) following the resampling and filtering described in the text. Each experiment lasted 30–40 minutes in total.

Figure 2. Examples of behaviour of the input signals.

In both figures, arrows indicate the start of each hypoxemic challenge. Left. The mean arterial blood pressure trace for Subject 2 showing a marked increase during the experiment. Right. The end tidal tension for Subject 5 was maintained relatively constant across the hypoxemic challenges.

Figure 3. Schematic of the model optimisation methodology.

Healthy subjects undergo a hypoxemic challenge, during which systemic and cerebral data is gathered noninvasively. The systemic data is fed into the physiological model, which then predicts expected values of the cerebral signals. The difference between measured and predicted values of these signals is used to construct an objective function, and minimisation of this function is used to reparametrise the model.

Figure 4. Best and worst performance of the unoptimised model and optimisation results for each signal.

Bold lines are the model output post optimisation, grey lines are the unoptimised model output, while the dashed lines are measured data. The best fit prior to optimisation is on the left, while the worst fit is on the right. The weighted distances are on the bottom left of each plot, while the subject and challenge are on the bottom right (e.g., “2(a)” means “Subject 2, first challenge”).

Figure 5. Error in predicted TOS during two challenges for Fit 1 and Fit 2.

The TOS error is defined as TOS (model) - TOS (data). TOS error is shown following Fit 1 (dashed line) and Fit 2 (bold line) for two example challenges (Subject 2, challenge 1 and Subject 8, challenge 2). The plots illustrate that optimisation 2 considerably reduced the error in the prediction of TOS by reducing the expected drop in TOS during the hypoxemic challenge.

Figure 6. Two examples of measured and model-predicted during an experiment.

The model predictions are without optimisation. In each case the dashed line is as a ratio, while the bold line is normalised to its initial value. Left. Subject 1. This is a fairly typical trace. Right. Subject 5. Both and are more variable, but again the model predicts that changes follow the trends in .