The Hurst Exponent: A Novel Approach for Assessing Focus During Trauma Resuscitation

Abstract

Current assessment of resuscitation team performance is often based on evaluations using checklists that evaluate verbal communication. However, highly efficient teams may function with several non-verbal cues that may not be measured by current assessment methods. Previous work assessing these non-verbal cues has been accomplished by tracking head movements in providers which however have not been attempted in trauma teams. We sought to perform a preliminary, proof-of-concept study to assess the ability to perform head tracking during a simulated trauma scenario. We enrolled a convenience sample of two simulated trauma teams utilizing undergraduate health professional students from four disciplines available at our institution: 2nd year Radiologic Science (RS), 4th year Physician Assistant (PA), 2nd year Respiratory Care (RT), and 4th year Registered Nurse (RN) students. Each team performed a simulated trauma resuscitation two times while wearing Xsens^® MTw motion trackers to track head movements during the resuscitation. These motions were analyzed using a standard measure of discriminating movement patterns known as the Hurst exponent (H). Pre- and post- communication training movement patterns were compared to establish reliability of H in trainees learning trauma resuscitation. There was no difference between the pre- and post- communication training H values for either roll or yaw for any of the four disciplines indicating that non-verbal communications were avoided. The Hurst exponent reliably measures the direction of focus of the participants during some simulated trauma resuscitation scenarios. Future research will be needed to evaluate this analytic technique across providers and in the clinical setting.

Appendix

5.1.1 A Simplified Approach for the Estimation of the Hurst Exponent

A significant number of applications have been developed for the estimation of the Hurst exponent, with varying degrees of complexity in their applications. An unfettered understanding of the underlying steps behind the estimation of H will be considerably aided by the simplification of application steps. An attempt is made here to outline a chronological approach to the preparation of a time series data file for Hurst exponent estimation, using the rescaled range analysis approach (https://blogs.cfainstitute.org/investor/2013/01/30/rescaled-range-analysis-a-method-for-detecting-persistence-randomness-or-mean-reversion-in-financial-markets/) and a spreadsheet application (Microsoft Excel^®). The following steps serve a dual purpose: outlining a stepwise approach to H estimation and illustrating the ability of the H algorithm to validate randomly generated numbers in Excel as being truly so.

• (a) From a single time series data requiring H estimation, define additional data segments created through the division of the original time series data in constant, increasing multiples, ensuring that the smallest data epoch has enough observations for the performance of standard descriptive statistics (mean, median, mode, skewness, etc.). The choice of epoch size is made at the discretion of the analyst, driven primarily by the size of the time series data available for analysis. The choice of the epoch size can be based on the time scale of the phenomenon in question. Long epoch would refer to events that repeat with a very low frequency or are characterized by fractal attractors of very small magnitude and vice versa.

  Using Microsoft Excel^®, generate a random number using the function, =rand (), and create 100 random observations (Fig. 5.6).

  Fig. 5.6

  

  Microsoft Excel^® random number generation function

  Copy the generated random time series data and paste it on a different spreadsheet column as numerical variables, to prevent the reset of the generated random variables every time the spreadsheet is refreshed.

  Create 4 segments of the original time series data, N. Segment 1 should have all of the variables in the N time series; segment 2 should have two epochs of size N/2 each; segment 3 should have four epochs each of size N/4, while segment 4 should have six epochs of each of size N/6.

• (b) Determine the average values of data in each of the epochs (Fig. 5.7).

• (c) For each of the defined epochs, subtract the mean determined in (b) from each observation in the corresponding epochs, and create a dataset of mean adjusted series, having the same number of observations as the original time series data (Fig. 5.8).

  The mean adjusted series value for the observation in cell L3 is computed using the formula: =B3-$G$3.

• (d) Using data from step (c), create “one-step-behind” cumulative deviation (time) series data, retaining the same number of observations as in steps (a) and (c) (Fig. 5.9).

  The observation in cell Q6 is computed using the formula, =L6+Q5.

• (e) Determine the range values of each of the data epochs from the cumulative deviation series created in step (d) (Fig. 5.10).

• (f) Determine the standard deviation values for each of the original data epochs (Fig. 5.11).

• (g) Divide the range values derived in (e) by the standard deviation values determined in step (f) to compute the rescaled range values (Fig. 5.12).

• (h) Compute the mean values of the rescaled range data and determine the log (to base 10) of the mean rescaled range values (Fig. 5.13).

• (i) Determine the log (to base 10) of the number of observations in each of the data epochs.

• (j) Create a plot of log(Rescaled Range) vs. log(n) and compute the slope of the curve (Fig. 5.14).

Fig. 5.7

Mean epoch values

Fig. 5.8

Mean adjusted series data

Fig. 5.9

Cumulative deviation

Fig. 5.10

Epoch range value determination

Fig. 5.11

Epoch standard deviation determination

Fig. 5.12

Computation of rescaled range in Excel^® with reference to already determined epoch values of range and standard deviation

Fig. 5.13

Computation of the mean rescaled range values for each epoch

Fig. 5.14

Log (rescaled range) vs. Log(n)

The observed slope of 0.48999 is the Hurst exponent estimate of the generated random time series data, which verifies the randomness of the data set (Fig. 5.15).

Fig. 5.15

Hurst estimation of generated random time series data in Excel^®