A method for estimating zero-flow pressure and intracranial pressure

Abstract

Background: It has been hypothesized that the critical closing pressure of cerebral circulation, or zero-flow pressure (ZFP), can estimate intracranial pressure (ICP). One ZFP estimation method used extrapolation of arterial blood pressure as against blood-flow velocity. The aim of this study was to improve ICP predictions.

Methods: Two revisions have been considered: (1) the linear model used for extrapolation is extended to a nonlinear equation; and (2) the parameters of the model are estimated by an alternative criterion (not least squares). The method is applied to data on transcranial Doppler measurements of blood-flow velocity, arterial blood pressure, and ICP from 104 patients suffering from closed traumatic brain injury, sampled across the United States and England.

Results: The revisions lead to qualitative (eg, precluding negative ICP) and quantitative improvements in ICP prediction. While moving from the original to the revised method, the ±2 SD of the error is reduced from 33 to 24 mm Hg, and the root-mean-squared error is reduced from 11 to 8.2 mm Hg. The distribution of root-mean-squared error is tighter as well; for the revised method the 25th and 75th percentiles are 4.1 and 13.7 mm Hg, respectively, as compared with 5.1 and 18.8 mm Hg for the original method.

Conclusions: Proposed alterations to a procedure for estimating ZFP lead to more accurate and more precise estimates of ICP, thereby offering improved means of estimating it noninvasively. The quality of the estimates is inadequate for many applications, but further work is proposed, which may lead to clinically useful results.

Figure 1

Distribution of ICP for the University of Washington patients (black), and for the Cambridge patients (red).

Figure 2

Top panel: The time series of FV (solid line) and ABP (dashed line) for one patient. Middle panel: Scatterplot of ABP versus FV (circles), the least-squares fit (dotted line), and the SD line (solid line). The mean ICP for this patient is labeled along the y-axis with an arrow. Bottom panel: same as middle panel, but prior to alignment of the two time series.

Figure 3

The scatterplot of observed ICP versus ZFP (i.e., estimated ICP), for all 104 patients (clusters in different colors), according to the WB method (top) and the revised method (bottom). Each cluster contains 200 points corresponding to 200 different time segments of the time series for that patient. The vertical and horizontal lines denote the grand mean of the observed ICP across all patients. The diagonal line is a line with slope equal to 1 and y-intercept equal to 0.

Figure 4

Comparison of ICP and ZFP for the WB method (top) and the revised method (bottom). The dashed horizontal lines denote the mean, and mean ± 2 standard deviation; They are −4 ± 33 mm Hg, and 0 ± 24 mm Hg, respectively.

Figure 5

A Bland-Altman plot showing the difference between the ZFP estimated by the two methods (WB and revised) as a function of their average. The two estimates appear to have a nonlinear and complex relationship which varies across patients.