Non-linear Dynamical Analysis of Intraspinal Pressure Signal Predicts Outcome After Spinal Cord Injury

Abstract

The injured spinal cord is a complex system influenced by many local and systemic factors that interact over many timescales. To help guide clinical management, we developed a technique that monitors intraspinal pressure from the injury site in patients with acute, severe traumatic spinal cord injuries. Here, we hypothesize that spinal cord injury alters the complex dynamics of the intraspinal pressure signal quantified by computing hourly the detrended fluctuation exponent alpha, multiscale entropy, and maximal Lyapunov exponent lambda. 49 patients with severe traumatic spinal cord injuries were monitored within 72 h of injury for 5 days on average to produce 5,941 h of intraspinal pressure data. We computed the spinal cord perfusion pressure as mean arterial pressure minus intraspinal pressure and the vascular pressure reactivity index as the running correlation coefficient between intraspinal pressure and arterial blood pressure. Mean patient follow-up was 17 months. We show that alpha values are greater than 0.5, which indicates that the intraspinal pressure signal is fractal. As alpha increases, intraspinal pressure decreases and spinal cord perfusion pressure increases with negative correlation between the vascular pressure reactivity index vs. alpha. Thus, secondary insults to the injured cord disrupt intraspinal pressure fractality. Our analysis shows that high intraspinal pressure, low spinal cord perfusion pressure, and impaired pressure reactivity strongly correlate with reduced multi-scale entropy, supporting the notion that secondary insults to the injured cord cause de-complexification of the intraspinal pressure signal, which may render the cord less adaptable to external changes. Healthy physiological systems are characterized by edge of chaos dynamics. We found negative correlations between the percentage of hours with edge of chaos dynamics (-0.01 ≤ lambda ≤ 0.01) vs. high intraspinal pressure and vs. low spinal cord perfusion pressure; these findings suggest that secondary insults render the intraspinal pressure more regular or chaotic. In a multivariate logistic regression model, better neurological status on admission, higher intraspinal pressure multi-scale entropy and more frequent edge of chaos intraspinal pressure dynamics predict long-term functional improvement. We conclude that spinal cord injury is associated with marked changes in non-linear intraspinal pressure metrics that carry prognostic information.

Keywords: Lyapunov; chaos theory; complexity theory; critical care unit; detrended fluctuation analysis; entropy; monitoring; spinal cord injury.

Figures

Figure 1

ISP monitoring technique. (A) Schematic showing intradurally placed ISP probe. (B) Pre-operative T2 MRI of a patient with TSCI at C6-7. (C) Postoperative T2 MRI of same patient. (D) Postoperative CT of same patient with ISP probe in situ. (E) Examples of ABP (yellow) and ISP (white) signals. Percussion peak (a), dicrotic notch (b), dicrotic peak (c). (F) Examples of ABP, ISP, and sPRx recordings.

Figure 2

Detrended fluctuation analysis of ISP signal. (A) Example of raw (white, top) and integrated detrended (yellow, bottom) ISP signal. (B) Log F(n) vs. Log n plot and trend-line (R = 1.00, slope = α). (C) Raw (white, left) and integrated detrended (yellow, right) ISP signals with increasing α. (D) ISP vs. α (green). Trend-line R = −0.18. (E) SCPP vs. α (blue). Trend-line R = 0.19. (F) sPRx vs. α (black). Trend-line R = −0.98. For (C–E)n = 49 patients, mean±standard error.

Figure 3

Entropy analysis of ISP signal. (A) Coarse-graining process: For each 1 h long ISP signal, multiple coarse-grained time series are generated by averaging data points xi within non-overlapping windows of increasing time length to obtain yj. (B) Examples of two raw ISP signals (red, top) and their corresponding sample entropy (MSE) vs. scale plots (green, bottom). (C) ISP vs. MSE (green). Trend-line R = −0.94. (D) SCPP vs. MSE (blue). Trend-line R = 0.93. (E) sPRx vs. MSE (black). Trend-line R = −0.90. For (C–E)n = 49 patients, mean±standard error.

Figure 4

Stability analysis of ISP signal. (A) Concept of Lyapunov exponents: In phase space, a small n-dimensional sphere with radius p1(0) = p2(0) = … = pn(0) at time 0 becomes an ellipsoid with radii p1(t), p2(t), …, pn(t) at time t. The i-th Lyapunov exponent is defined as λi=limt→∞(1t)logpi(t)pi(0). (B) Examples of stable (left, blue, λmax < -0.01) and chaotic (right, red, λ = 0.06) ISP signals with their respective phase space trajectories (insets, 10 s time delay embedding). (C) % hours which are at edge of chaos (circles, −0.01 ≤ λmax ≤ 0.01), stable (triangles, λmax < −0.01), or chaotic (squares, λmax > 0.01) vs. ISP. Trend-line R = −0.86 (edge of chaos), 0.87 (stability), −0.36 (chaos). (D) % hours which are at edge of chaos (circles, −0.01 ≤ λmax ≤ 0.01), stable (triangles, λmax < −0.01), or chaotic (squares, λmax > 0.01) vs. SCPP. Trend-line R = 0.89 (edge of chaos), −0.84 (stability), 0.10 (chaos). (E) % hours which are at edge of chaos (circles, −0.01 ≤ λmax ≤ 0.01), stable (triangles, λmax < −0.01), or chaotic (squares, λ > 0.01) vs. sPRx. Trend-line R = 0.19 (edge of chaos), −0.76 (stability), 0.91 (chaos). For (C–E) 49 patients.

Figure 5

Relations between α, MSE, λmax, and functional outcome. (A) α vs. days after TSCI. (B) % patients who improved vs. α. Trend-line R = 0.92. (C) MSE vs. days after TSCI. (D) % patients who improved vs. MSE. Trend-line R = 0.92. (E) λ vs. days after TSCI. (F) % patients who improved vs. % hours at edge of chaos (−0.01 < λmax < 0.01) . Trend-line R = 0.98. For (A,C,E) Patients who improved by ≥1 AIS grade (red, 19 patients, 1,996 h) and patients not improved (blue, 30 patients, 4,068 h), mean±standard error.