1. Computational and Systems Biology
  2. Medicine

Topological network analysis of patient similarity for precision management of acute blood pressure in spinal cord injury

  1. Abel Torres-Espín
  2. Jenny Haefeli
  3. Reza Ehsanian
  4. Dolores Torres
  5. Carlos A Almeida
  6. J Russell Huie
  7. Austin Chou
  8. Dmitriy Morozov
  9. Nicole Sanderson
  10. Benjamin Dirlikov
  11. Catherine G Suen
  12. Jessica L Nielson
  13. Nikos Kyritsis
  14. Debra D Hemmerle
  15. Jason F Talbott
  16. Geoffrey T Manley
  17. Sanjay S Dhall
  18. William D Whetstone
  19. Jacqueline C Bresnahan
  20. Michael S Beattie
  21. Stephen L McKenna
  22. Jonathan Z Pan  Is a corresponding author
  23. Adam R Ferguson  Is a corresponding author
  24. The TRACK-SCI Investigators
  1. Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, United States
  2. Division of Physical Medicine and Rehabilitation, Department of Orthopaedics and Rehabilitation, University of New Mexico School of Medicine, United States
  3. San Francisco Veterans Affairs Healthcare System, United States
  4. Computational Research Division, Lawrence Berkeley National Laboratory, United States
  5. Lawrence Berkeley National Laboratory, United States
  6. Rehabilitation Research Center, Santa Clara Valley Medical Center, United States
  7. Department of Psychiatry and Behavioral Science, and University of Minnesota, United States
  8. Institute for Health Informatics, University of Minnesota, United States
  9. Department of Radiology and Biomedical Imaging, University of California, San Francisco, United States
  10. Department of Emergency Medicine, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, United States
  11. Department of Physical Medicine and Rehabilitation, Santa Clara Valley Medical Center, United States
  12. Department of Neurosurgery, Stanford University, United States
  13. Department of Anesthesia and Perioperative Care, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, United States
https://doi.org/10.7554/eLife.68015
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Cite this article
  1. Abel Torres-Espín
  2. Jenny Haefeli
  3. Reza Ehsanian
  4. Dolores Torres
  5. Carlos A Almeida
  6. J Russell Huie
  7. Austin Chou
  8. Dmitriy Morozov
  9. Nicole Sanderson
  10. Benjamin Dirlikov
  11. Catherine G Suen
  12. Jessica L Nielson
  13. Nikos Kyritsis
  14. Debra D Hemmerle
  15. Jason F Talbott
  16. Geoffrey T Manley
  17. Sanjay S Dhall
  18. William D Whetstone
  19. Jacqueline C Bresnahan
  20. Michael S Beattie
  21. Stephen L McKenna
  22. Jonathan Z Pan
  23. Adam R Ferguson
  24. The TRACK-SCI Investigators
(2021)
Topological network analysis of patient similarity for precision management of acute blood pressure in spinal cord injury
eLife 10:e68015.
https://doi.org/10.7554/eLife.68015
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  3. Download .RIS

Abstract

Background:

Predicting neurological recovery after spinal cord injury (SCI) is challenging. Using topological data analysis, we have previously shown that mean arterial pressure (MAP) during SCI surgery predicts long-term functional recovery in rodent models, motivating the present multicenter study in patients.

Methods:

Intra-operative monitoring records and neurological outcome data were extracted (n = 118 patients). We built a similarity network of patients from a low-dimensional space embedded using a non-linear algorithm, Isomap, and ensured topological extraction using persistent homology metrics. Confirmatory analysis was conducted through regression methods.

Results:

Network analysis suggested that time outside of an optimum MAP range (hypotension or hypertension) during surgery was associated with lower likelihood of neurological recovery at hospital discharge. Logistic and LASSO (least absolute shrinkage and selection operator) regression confirmed these findings, revealing an optimal MAP range of 76–[104-117] mmHg associated with neurological recovery.

Conclusions:

We show that deviation from this optimal MAP range during SCI surgery predicts lower probability of neurological recovery and suggest new targets for therapeutic intervention.

Funding:

NIH/NINDS: R01NS088475 (ARF); R01NS122888 (ARF); UH3NS106899 (ARF); Department of Veterans Affairs: 1I01RX002245 (ARF), I01RX002787 (ARF); Wings for Life Foundation (ATE, ARF); Craig H. Neilsen Foundation (ARF); and DOD: SC150198 (MSB); SC190233 (MSB); DOE: DE-AC02-05CH11231 (DM).

Editor's evaluation

The major strengths of this paper are the use of a combination of relatively novel approaches/applications to the identification of important predictors for recovery after spinal cord surgery. These include various data reduction techniques such as dissimilarity matrices and a subject-centered topological network analysis to identify phenotypes.

https://doi.org/10.7554/eLife.68015.sa0

eLife digest

Spinal cord injury is a devastating condition that involves damage to the nerve fibers connecting the brain with the spinal cord, often leading to permanent changes in strength, sensation and body functions, and in severe cases paralysis. Scientists around the world work hard to find ways to treat or even repair spinal cord injuries but few patients with complete immediate paralysis recover fully.

Immediate paralysis is caused by direct damage to neurons and their extension in the spinal cord. Previous research has shown that blood pressure regulation may be key in saving these damaged neurons, as spinal cord injuries can break the communication between nerves that is involved in controlling blood pressure. This can lead to a vicious cycle of dysregulation of blood pressure and limit the supply of blood and oxygen to the damaged spinal cord tissue, exacerbating the death of spinal neurons. Management of blood pressure is therefore a key target for spinal cord injury care, but so far, the precise thresholds to enable neurons to recover are poorly understood.

To find out more, Torres-Espin, Haefeli et al. used machine learning software to analyze previously recorded blood pressure and heart rate data obtained from 118 patients that underwent spinal cord surgery after acute spinal cord injury.

The analyses revealed that patients who suffered from either low or high blood pressure during surgery had poorer prospects of recovery. Statistical models confirming these findings showed that the optimal blood pressure range to ensure recovery lies between 76 to 104-117 mmHg. Any deviation from this narrow window would dramatically worsen the ability to recover.

These findings suggests that dysregulated blood pressure during surgery affects to odds of recovery in patients with a spinal cord injury. Torres-Espin, Haefeli et al. provide specific information that could improve current clinical practice in trauma centers. In the future, such machine learning tools and models could help develop real-time models that could predict the likelihood of a patient’s recovery following spinal cord injury and related neurological conditions.

Introduction

Spinal cord injury (SCI) may result in motor, sensory, and autonomic dysfunction in various degrees, depending on the injury severity and location. In the USA, the incidence of SCI is around 18,000 new cases per year, with a total prevalence ranging from 250,000 to 368,000 cases (National Spinal Cor Injury Statistical Center, 2021). The dramatic life event of SCI imposes a high socioeconomic burden, with an estimated lifetime cost between $1.2 and $5.1 million per patient (National Spinal Cor Injury Statistical Center, 2021).

Prior retrospective observational single-center studies in humans suggest that lower post-surgery mean arterial pressure (MAP) predicts poor outcome (Cohn et al., 2010; Hawryluk et al., 2015; Saadeh et al., 2017; Ehsanian, 2020), which have resulted in clinical guidelines focused on avoidance of hypotension by maintaining MAP >85 mmHg during the first 7 days of injury (Aarabi et al., 2013). The rational for MAP augmentation to avoid hypotension is based on the hypothesis that decreased spinal cord prefusion leads to ischemia and additional tissue lost (Mautes et al., 2000; Soubeyrand et al., 2014). Importantly, experimentally raising MAP during acute SCI in animals by using vasopressors increases the risk for hemorrhage and consequent tissue damage (Soubeyrand et al., 2014; Streijger et al., 2018; Guha et al., 1987). In acute cervical patients with SCI, spinal cord hemorrhage correlates with poor prognosis for neurological recovery (Miyanji et al., 2007). These findings collectively suggest that hypo- and hypertension must be accounted for in MAP management, but there remains a gap in evidence from clinical studies that definitively informs MAP guidelines (Saadeh et al., 2017).

One of the challenges resulting in the lack of strong evidence for MAP management in patients with acute SCI is the heterogeneity of injury. The heterogeneity of SCIs results in data complexity that benefit from modern analytic tools. Using the machine intelligence approach of topological data analysis, we have previously shown that hypertension during SCI surgery (ultra-acute phase) predicts long-term functional recovery in rodent models (Nielson et al., 2015). These prior cross-species findings motivated the present multicenter study where we apply a data-driven workflow in patients with ultra-acute SCI surgical records from two different Level 1 trauma centers. By employing machine intelligence tools, we show that deviation from an optimal MAP range during surgery predicts lower likelihood of neurological recovery and suggest new targets for therapeutic intervention.

Methods

Retrospective data extraction and cohort selection

Operating room (OR) records from n = 94 patients (98 surgical records, 3 patients with multiple surgeries) from the Zuckerberg San Francisco General Hospital (ZSFG, from 2005 to 2013) and n = 33 patients (33 surgical records) from the Santa Clara Valley Medical Center (SCVMC, from 2013 to 2015) that underwent spinal surgery were collected retrospectively. For ZSFG, monitoring data was extracted from the values manually recorded by the anesthesiologist at 5 min intervals (Q5). For SCVMC, monitoring data was extracted from the Surgical Information Systems (SIS) (Alpharetta, GA) at 1 min intervals (Q1). Demographics and outcome variables were extracted from an existing retrospective registry. AIS (American Spinal Injury Association [ASIA] Impairment Scale) grade at admission (first complete AIS upon admission to the hospital before surgery) and discharge (latest complete AIS grade after surgery before discharge from hospital) were estimated using the available ISNCSCI exams (International Standards for Neurological Classification of SCI) and the neurosurgery, trauma surgery, emergency department, and physical medicine and rehabilitation physical exam notes. To ensure compatibility between centers on the estimated AIS grades, one independent physician conducted the estimates for all the patients in each center (SM for SCVMC and JT for ZSFG) and one independent ISNCSCI certified physician (WW) extracted the AIS grades for all the patients (across centers). In case of conflict between grades, both physicians established a consensus. From the total 131 surgical records, three records were excluded for not having monitoring recorded for both MAP and HR, three were excluded because surgeries were not related to SCI, and seven surgeries were excluded from three patients that were submitted to more than one surgery. The final cohort for exploratory topological data analysis included 118 patients with complete MAP and heart rate (HR) monitoring. For confirmatory regression analysis, 15 patients were excluded because AIS grade could not be extracted either at admission and/or discharge (Figure 2—figure supplement 1). AIS improvement was defined as an increase of at least one AIS grade from admission to discharge. The final list of extracted variables included: MAP and HR continuous monitoring, age, length of surgery in minutes, days from surgery to hospital discharge, estimated AIS grade at admission, estimated AIS grade at discharge and AIS improvement (‘yes’, ‘no’). All data was de-identified before pre-processing and analysis. Protocols for retrospective data extraction were approved by Institutional Research Board (IRB).

Cohort statistics

The differences in the AIS improvers/non-improvers population characteristics were tested at the univariate level using R (see software below). For continuous numerical variables (age, length of surgery, and days from surgery to discharge), the group mean differences were tested using unpaired Student’s t-test (two-sided test). For categorical variables (AIS admission, AIS at discharge, and dichotomized neurological level of injury [NLI]), their levels were compared using Fisher’s exact test (two-sided test). p-Values are presented in Table 1.

Table 1
Cohort demographics split by AIS (American Spinal Injury Association [ASIA] Impairment Scale) improvement.
AIS improve. N/A(n = 15)AIS improve. NO(n = 61)AIS improve. YES(n = 42)Univariate p-value
Age (years)0.12
 Mean (SD)46.0 (17.6)45.3 (19.1)51.4 (19.7)
 Median [min, max]45.5 [19.0, 87.0]47.0 [18.0, 82.0]55.0 [18.0, 86.0]
 Missing1 (6.7%)2 (3.3%)1 (2.4%)
AIS admission0.013
 A1 (6.7%)33 (54.1%)18 (42.9%)
 B0 (0%)5 (8.2%)8 (19.0%)
 C0 (0%)5 (8.2%)11 (26.2%)
 D0 (0%)14 (23.0%)5 (11.9%)
 E0 (0%)4 (6.6%)0 (0%)
 Missing14 (93.3%)0 (0%)0 (0%)
AIS discharge<0.0001
 A0 (0%)35 (57.4%)0 (0%)
 B0 (0%)5 (8.2%)5 (11.9%)
 C1 (6.7%)4 (6.6%)15 (35.7%)
 D0 (0%)14 (23.0%)17 (40.5%)
 E1 (6.7%)2 (3.3%)5 (11.9%)
 Missing13 (86.7%)1 (1.6%)0 (0%)
Surgery duration (min)0.66
 Mean (SD)433 (167)392 (146)407 (181)
 Median [min, max]432 [121, 725]389 [120, 728]343 [151, 950]
 Missing1 (6.7%)2 (3.3%)1 (2.4%)
Surgery to discharge (days)0.33
 Mean (SD)9.50 (2.12)18.8 (20.6)23.4 (23.8)
 Median [min, max]9.50 [8.00, 11.0]11.0 [1.00, 128]14.5 [4.00, 120]
 Missing13 (86.7%)4 (6.6%)2 (4.8%)
 Dichotomized neurological level of injury at admission0.054
 Cervical2.00 (13.3%)36 (59%)33 (78.6%)
 Non-cervical13.00 (86.7%)25 (41%)9 (21.4%)

Topological network extraction and exploration of monitoring data workflow

Monitoring data pre-processing

Two datasets were generated, one for each center. To ensure compatibility, both datasets were harmonized. Given the difference in the sampling frequency of the monitoring data (Q5 for ZSFG and Q1 SCVMC) between centers and protocols for data collection, SCVMC monitoring data was first pre-processed. Briefly, electronic data was exported from the SIS SQL database, de-identified and imported into MATLAB version 2016b (Mathworks Inc, Natick, MA) for filtering. A custom MATLAB script generated by the SCVMC team implemented filtering criteria established by clinicians and researchers to correct for invalid data (e.g., motion artifacts and injections). Thus, MAP values under 10 and above 200 mmHg as well as point-to-point changes greater than 40 mmHg were filtered, as these instances were found to represent data artifacts. This process was validated by comparing clinical curated data and the extracted data from the script with an accuracy of 99.1%. After filtering, SCVMC Q1 monitoring data was downsampled to Q5 by taking the average of five consecutive Q1 intervals for compatibility with ZSFG data. Given that the duration of the monitoring for each patient was different and the continuous time-series data is not aligned between patients (without time dependency on monitoring values), the empirical cumulative distribution function (CDF) for each time-series and each patient was computed. To account for the different scales between MAP and HR, a bin width for CDF was set as a 1% of the range of each measure, producing 100 CDF bins for MAP and 100 bins for HR (Figure 2—figure supplement 2). Additionally, the average MAP (aMAP) and HR (aHR) across time for each patient was calculated for posterior analysis.

Similarity between patients

The CDF bins for both MAP and HR were serialized in one vector per patient and the Euclidean distance (d(p,q)=∑i=1n(pi−qi)2, where p and q are two patients’ CDF vectors and n is the number of CDF bins) calculated for each pair of patients’ vectors. The Euclidean distance matrix was then processed using dimensionality reduction.

Dimensionality reduction

Our goal for dimensionality reduction was to increase the signal-to-noise ratio by mapping to a lower number of dimensions (d) that contained the major information in the dataset. Dimensionality reduction was achieved by using the Isomap algorithm (Tenenbaum et al., 2000). Isomap is a non-linear dimensionality reduction method that uses multidimensional scaling (MDS) with geodesic distances instead of the Euclidean distances as the classic MDS does, and it has been suggested before for health data (Weng et al., 2005). Isomap performs three steps: (1) construct an NNG (near neighbor graph), (2) estimate the geodesic distances from the graph (shortest paths), (3) compute MDS embedding with the geodesic distances. The algorithm takes one parameter (k or e) to set the threshold for the NNG (we used k, the number of near neighbors for NNG). For selecting k, we considered the minimal k the smallest one that produced a connected NNG, in our case k = 3. Then two criteria were established for both k optimization and d selection, distance preservation (RV, residual variance) and topological persistent homology preservation as described (Rieck and Leitte, 2015; Paul and Chalup, 2017). We considered Isomap solutions for k = 3–7 (Figure 2—figure supplement 1). The RV was computed as (Tenenbaum et al., 2000): 1−R2(Dm^,Dy) where R is the standard linear correlation coefficient taken over all entries of D^m and Dy. D^m is the input distance matrix that the algorithm is trying to estimate the real dimensions of (k-geodesic distance matrix for k-Isomap). Dy is the Euclidean distance matrix of the low-dimensional solution. No major differences were observed in RV between the solutions for different k, except for the first dimension where RV increases as k increases. Isomap persistence diagrams were obtained using Vietoris-Rips filtration (Paul and Chalup, 2017) for D^m and Dy for different d solutions (Figure 2—figure supplement 1). Then the topological zero-dimensional and one-dimensional Wasserstein (power = 2) distances (WD0 and WD1, respectively) were computed between D^m and Dy. In persistent homology, dimension 0 measures zero-dimensional holes in the data (the connectivity of the datapoints, i.e., the number of connected sets) and topological dimension 1 measures one-dimensional holes, namely loops. We sought to select the solution (determine d and k) that minimized the WD0 and WD1, indicative of the optimal solution preserving the major topological information (Rieck and Leitte, 2015; Paul and Chalup, 2017). Given that k = 6 and k = 7 showed the lowest WD0 and WD1, we considered k = 6 as the final solution (Figure 2—figure supplement 1). A d = 4 (four dimensions kept in the k = 6 Isomap) was chosen for being the one at the ‘elbow’ of the RV, the one that minimized WD0 in k = 6 Isomap and presented a good compromised WD1.

Network analysis

A network from the k = 6 d = 4 Isomap solution was created for visual representation of the connectivity of patients (similarity) in the low-dimensional space. In this network, nodes represent each patient and edges the connection of two patients that are similar in the Isomap solution. An adjacency (whether two nodes are connected) matrix was obtained by computing a k-NNG for the low-dimensional space. The cutoff threshold for adjacency was set to the minimal k that produced a full-connected network. For network clustering, the walktrap algorithm was used (Pons and Latapy, 2005) as implemented in the igraph R package. Walktrap takes a single parameter, the number of random steps the algorithm uses to determine if nodes are in the same cluster or not. To select the optimal number of steps we computed walktrap solutions of a set of random steps (1–100) and chosen the first solution which maximized modularity (Q) as implemented in igraph R package (Clauset et al., 2004). In network analysis, modularity can be interpreted as the proportion of within cluster compared to the between clusters connectivity (edges). This solution was 47 random steps, producing a dendrogram tree of connectivity which maximal modularity cut the tree in 11 clusters (Figure 2—figure supplement 1). Then the network was contracted for visual representation of a cluster network of patients, where nodes represented the clusters and edges connected clusters that had at least one edge in the similarity network. Both the similarity and the cluster networks were used for exploratory network analysis and hypothesis generation by mapping patient features and visual inspection (Figure 2—figure supplement 1). We used the assortativity coefficient (Ar) to explore the possibility that the network was capturing the association between patients and the time of MAP out of a range (Figure 4; see time MAP out of range). The Ar was calculated using the igraph implementation in R (Newman, 2003) and it can be interpreted as the Pearson coefficient (−1–1) between nodes connectivity and value of a variable.

Regression analysis

Logistic regression

We first used a logistic regression to model the probability of predicting improvement by aMAP. Visual inspection of the plot (Figure 2) suggested a non-linear relationship between aMAP and the probability of improvement. Consequently, the following logistic models were considered (l being the log-odds or logit of the probability of improving): the null model with no predictors (l=β0, the simple model (l=β0+β1x), the two-grade polynomial model (l=β0+β1x+β2x2), the three-grade polynomial model (l=β0+β1x+β2x2+β3x3) and a natural spline model (l=β0+f1(x) )where f1x is the natural spline function with 2 or 3 degrees of freedom (df)). The natural cubic spline was chosen to relax the symmetric constraints of polynomial models given that the visual inspection of the data suggested an asymmetric aMAP range (Figure 2, distribution of aMAP of improvers is skewed to the left). The results of fitting these models and the likelihood comparison between them (by likelihood ratio test) are shown in Table 2. The best fitting model was the two-grade polynomial (Figure 3) and the natural spline (2df) with significant coefficients, confirming our hypothesis. These results were confirmed by leave-one-out cross-validation (LOOCV) (Table 2). To account for the potential confounding effect of AIS grade at admission (given differences between groups, Table 1), aHR, length of surgery (minutes), days from surgery to discharge and age, we fitted the quadratic model with those covariates and LOOCV (Table 3). Considering the independence of the predictors (small correlation coefficients between variables; Table 4), the results of the quadratic term being significant still holds for the covariate model.

Table 2
Logistic regression likelihood ratio test and leave-one-out cross-validation (LOOCV) error (n = 103 patients).
ModelAICResidual dfResidualdevianceDeviancep-ValueLOOCV error
Null model(l=β0)141.26102139.26  0.246
Linear model(l=β0+β1x)134.8101130.808.46(vs. null model)0.0036**(vs. null model)0.231
Quadratic model(l=β0+β1x+β2x2)128.48100122.488.32(vs. linear model)0.0039**(vs. linear model)0.210
Cubic model(l=β0+β1x+β2x2+β3x3)126.9799118.973.50(vs. quadratic model)0.061(vs. quadratic model)0.213
Natural Spline model (df = 2)(l=β0+f1(x))128.29100122.298.50(vs. linear model)0.0035**(vs. linear model)0.210
Natural Spline model (df = 3)(l=β0+f1(x))127.1399119.133.34(vs. quadratic model)0.067(vs. quadratic model)0.213

  1. ** p < 0.01.

Table 3
Evaluation of logistic regression (Wald test) and leave-one-out cross-validation (LOOCV) error.
Model: l=β0+β1x1+β2x12 where x1: average MAP (n = 103 patients)
LOOCV: average observed accuracy = 0.66; average kappa statistic = 0.334
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= –0.550.242–2.2930.02183*
Average MAP (x1)β1= 8.622.9442.9310.00338**
Average MAP (x12)β2= –7.6013.039–2.5010.0123*

  1. *p < 0.05; **p < 0.01.

Table 4
Evaluation of logistic regression with covariates (Wald test) and leave-one-out cross-validation (LOOCV).
Model: l=β0+β11x1+β12x12+β2x2+β3x3+β4x4+β5x5+β6x6+β7x7+β8x8+β9x9, where x1: average MAP; x2 : average HR; x3: length of surgery (min); x4: days to AIS discharge (days); x5: age; x6: AIS admission D (‘yes’,’no’); x7: AIS admission C (‘yes’,’no’); x8: AIS admission B (‘yes’,’no’); x9: AIS admission A (‘yes’,’no’); (AIS admission E was set as the reference level for AIS admission variable and is part of the intercept) (final n = 93)
LOOCV: average observed accuracy = 0.688; average kappa statistic = 0.362
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= –1.530121.8–0.0130.99
Average MAP (x1)β11= 7.3983.1122.3770.017*
Average MAP (x12)β12= –8.0533.530–2.2810.022*
Average HR (x2)β2= –2.0870.0245–0.8510.394
Length of surgery (x3)β3= 0.00110.00150.7280.466
Days to AIS discharge (x4)β4= 0.00370.01090.3440.730
Age (x5)β5= 0.00820.0130.6340.526
AIS admission D (x6)β6= 1.4541.2180.0120.990
AIS admission C (x7)β7= 1.6451.2180.0140.989
AIS admission B (x8)β8= 1.5851.2180.0130.989
AIS admission A (x9)β9= 1.5271.2180.0130.990
 Correlation matrix (Spearman)
 Average MAPAverageHRLength of surgeryDays to AIS dischargeAgeAIS admission
Average MAP1
Average HR–0.1261
Length of surgery–0.1520.1011
Days to AIS discharge0.088–0.0590.1651
Age0.006–0.2450.0110.0221
AIS admission0.0240.003–0.010.258–0.131

  1. *p < 0.05.

Time out of MAP range

We sought to determine a range of MAP in which time outside that range might predict improvement. To consider the time at which MAP was outside a range, we performed an increasing window of MAP for either a symmetric range or an asymmetric one. For the symmetric range, a 1 mmHg range increment at each site of the center (90 mmHg, the mean MAP for improvers) was created. For the asymmetric range, the lower limit was fixed at 76 mmHg and the upper limit was incremented 1 mmHg at the time. The time of MAP (in min) being outside each range was estimated for each patient.

LASSO regression

LASSO (least absolute shrinkage and selection operator) regression (Tibshirani, 1996) was used for selecting a single range of MAP (see time MAP out of range) predictor of the logistic model: l=β0+∑j=1pβjxj, where xj is the jth MAP range. LASSO takes as parameter lambda that sets the amount of shrinkage or regularization (using L1-norm penalty). LOOCV was used to determine the lambda that shrunk the models to one predictor or MAP range. The one-predictor solutions (MAP range of 76–104 for symmetric range model, and 76–117 for the asymmetric range model) were used as the solo predictor of AIS improvers in a logistic regression with LOOCV (see above). It is important to note that given the high multicollinearity in the range data, the Q5 time estimation and the low sample size, the LASSO solution should be taken with caution and as an indicator of the MAP range hypothesis rather than a hard rule for medical decision making.

Prediction modeling

Logistic regression (see above) was used to build prediction models for three binary outcome metrics: AIS improvement of at least one grade from admission to discharge, whether patient was AIS grade A at discharge, or whether the patient was AIS grade D at discharge. For each one of the classification tasks, the following predictors were considered: quadratic aMAP (both linear and quadratic terms), aHR, length of surgery (min), days from surgery to discharge, age, AIS grade at admission, and dichotomized NLI. We performed model selection (a.k.a. feature selection) through an exhaustive search of all potential combinations of at least one of the predictors using the glmulti R package (Calcagno, 2020). The most parsimonious models were selected to be the one minimizing the small-sample corrected Akaike information criteria (AIC) for each task. We then investigated the performance of each one of the most parsimonious models using LOOCV and adjusting the classification threshold to balance prediction sensitivity and specificity. Briefly, each model was trained n (patient) times with an n−1 training sample and tested the performance in the remaining sample. A vector of n probabilities of predictions was then used to measure the LOOCV model performance. Model fitting and prediction performance were conducted using the caret R package (Kuhn et al., 2019). Receiving operating curves (ROC) and area under the curve (AUC) for the LOOCV prediction were obtained using the ROCR R package (Sing et al., 2005).

Software

All data wrangling, processing, visualization, and analysis was performed using the R programming language (R version 3.5.1) (R core team, 2019) and RStudio (RStudio version 1.2.1335) (Team, 2018) in Windows 10 operating system, with the exception of the Q1 OR measures form SCVMC that were preprocessed in MATLAB before downsampling to Q5 in R. The most relevant R functions and packages (beyond the installed with R) used and the references for each function/package and methods are reported in the following table. For more details, see the source code available (Supplementary file 1 and Source code 1).

R packages used

PackageVersionUsageReference
igraph1.2.4.1Building, manage and analyze networksCsárdi and Nepusz, 2006
dplyr0.8.3Data cleaning and wranglingWickham et al., 2018
ggplot23.2.1Data visualization and plottingWickham, 2016
vegan2.5–5For Isomap implementationJari et al., 2019
RColorBrewer1.1–2To control and create colormapsNeuwirth, 2014
TDAstats0.4.0Utilities for topology data analysis for persistent homologyWadhwa et al., 2018
cccd1.5For generating NNGsMarchette, 2015
table11.1Generates table of demographicsRich, 2018
glmnet2.0–18For fitting LASSOFriedman et al., 2010
glmnetUtils1.1.2For fitting LASSOOoi, 2019
caret6.0–84To fit logistic regression with leave-one-out cross-validationKuhn et al., 2019
splines3.5.1To fit the spline modelsR core team, 2019
VisNetwork2.0.7Visualization suit for network graphs using the vis.js JavaScript libraryAlmende, 2019
stats3.5.1Fit generalized linear modelsR core team, 2019
glmulti1.0.8For model searchCalcagno, 2020
ROCR1.0–11For ROC visualization and performanceSing et al., 2005
reshape21.4.3From wide to long view dataframe formattingWickham, 2007

Data and code availability

The final de-identified datasets for analysis are deposited and accessible at the Open Data Commons for SCI (odc-sci.org, RRID:SCR_016673) under DOIs 10.34945/F5R59J and 10.34945/F5MG68. The R code to run all the analysis present in this publication, including visualizations, is available as supplementary material. The code would reproduce the entire analysis and plots when run using the same versions of R, RStudio, and packages specified in this publication. Otherwise results might change.

Results

Exploratory network analysis suggests an upper and lower limit of intra-operative MAP for recovery

Intra-operative monitoring records (MAP, HR) and neurological outcome data were extracted and curated from two Level 1 trauma centers. A final cohort of 118 patients was included (Figure 1a and Table 1). The cohort represents a varied dataset of intra-operative MAP and HR patterns and respective aMAP across time in surgery and aHR across time in surgery values (Figure 1b–c). Using a machine intelligence analytical pipeline (Figure 2a), we extracted a similarity network of patients (Pai and Bader, 2018; Parimbelli et al., 2018) from a low-dimensional space embedded using a non-linear algorithm, Isomap (Tenenbaum et al., 2000), on a distance matrix derived from the MAP and HR records and then performed topological network extraction using persistent homology metrics (Rieck and Leitte, 2015; Figure 2a and Figure 2—figure supplement 1). The results of this dimensionality reduction suggested that four dimensions are enough to capture most of the variance and the topological structures of the original data (Figure 2—figure supplement 1c-e). Clustering the network of patients through a random-walk algorithm, Walktrap (Pons and Latapy, 2005), revealed 11 different clusters where patients were regarded to share intra-operative hemodynamic phenotypes (Figure 2 andFigure 2—figure supplement 1f-h). Importantly, this workflow was unsupervised: only the OR hemodynamic time-series was used to derive patient clustering, and therefore any association captured by the network must be dependent on hemodynamic patterns. Exploratory network analysis showed a gradient distribution of patients by their aMAP (Figure 2b–d) and aHR (Figure 2e–g), confirming that the network captured a valid representation of the raw high-dimensional dataset. We then investigated the association of the clusters to patient recovery as defined by whether the patient improved at least one AIS grade A–D (Roberts et al., 2017) between time before surgery and time of discharge from the hospital. Mapping the proportion of patients with AIS improvement onto the similarity network (Figure 2h–j) revealed that patients with recovery localized to clusters associated with a middle range of MAP (Figure 2k). Those clusters also showed a higher proportion of less severe AIS grades at discharge (AIS C, D, and E) than other clusters (Figure 2—figure supplement 2). In contrast, clusters of patients showing an extreme variation of MAP were highly enriched with patients with no AIS recovery and patients with more severe AIS grades at discharge (AIS A and B, Figure 2—figure supplement 2). This analysis suggested that there is a limited range of MAP during surgery associated with neurological recovery.

Figure 1
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High-frequency monitoring operating room (OR) data.

Flowchart of retrospective study and cohort selection criteria (a). A final cohort of 118 patients were identified and values of mean arterial pressure (MAP) (b) and heart rate (HR), (c) by time (bins of 5 min; Q5) retrospectively extracted from patients’ records. Colormaps represent the MAP (mmHg; green marks normotensive MAP, while blue and red marks hypotension and hypertension, respectively) and HR (beats per min, bpm; dark yellow lowest to purple highest) at each Q5 time, depicting the temporal fluctuation of each measure for each patient (row). The average MAP (aMAP, right plot in b) and average heart rate (aHR, right plot in c) were computed.

Figure 2 with 2 supplements see all
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Topological network analysis of intra-operative monitoring.

Intra-operative mean arterial pressure (MAP) and heart rate (HR) sampled every 5 min (Q5) were curated, processed, and formatted in a unique data matrix (a) (Figure 2—figure supplement 1). The similarity matrix between patients was computed and a four-dimensional subspace extracted using Isomap (Figure 2—figure supplement 1). A network was constructed where nodes represent patients and edges the connection of pairs of patients under a specified threshold of similarity (see Methods). The network was clustered and collapsed (Figure 2—figure supplement 1) by using the walktrap algorithm conveying in 11 clusters. These networks captured both the average MAP (aMAP) (b–d) and the average HR (aHR) (e–g) in a gradient fashion. Similarly, at least one AIS grade gain at discharge (‘yes’, ‘no’) was mapped over the network (h–j, gray: 15 AIS grades could not be extracted). Clusters of higher proportion of patients with recovery had an aMAP in a middle range, while clusters with higher proportion of patients without recovery presented extreme aMAPs (k). The mean cluster aHR showed a less apparent relationship with the proportion of AIS improvers (l).

MAP has a non-linear association with probability of recovery

The exploratory network analysis revealed that clusters with higher proportion of patients that increased AIS of at least one grade were associated with having a middle range aMAP (Figure 2 and Figure 2—figure supplements 1 and 2) and that clusters of patients with aMAP on the extremes contained fewer improvers. We hypothesized that there might be a non-linear relationship between intra-operative MAP and the probability of AIS grade improvement. To confirm this hypothesis, logistic regression models with LOOCV were used (Figure 3, Table 2). We fitted a null model (no predictors) as well as linear, polynomial, and cubic models of aMAP (Figure 3, Table 2) to test the non-linearity of the hypothesis. The linear model showed a significant improvement over the null model with a positive association, suggesting that the higher the aMAP, the higher the probability of AIS grade improvement. However, polynomial logistic regression demonstrated a significant quadratic fit (Table 2) with lower LOOCV error than the linear model, indicating that a quadratic form of aMAP better predicts the probability of improvement. Notably, the cubic model did not show significant improvement over the quadratic one. Exploratory network analysis suggested an asymmetrical function of AIS improvement with respect to aMAP (Figure 2k); we therefore also tested spline models to relax the symmetry of polynomial models. A spline model of degree 2 resulted in a significant fit over the linear model (Table 2) while a spline model of degree 3 resulted in a similar fit as compared to the cubic model. There was no evidence from which to choose between the spline model of degree 2 and the quadratic model. Accordingly, we did not pursue the asymmetric model further, although we explore an asymmetric MAP range below.

Figure 3
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Non-linear relationship of average mean arterial pressure (aMAP) with the probability of improving at least one AIS grade.

Logistic regression models were fitted to study the potential non-linearity of the aMAP predictor as suggested by the exploratory analysis. Six different models were studied: naïve, linear, quadratic, cubic, spline of degree 2, and spline of degree 3. The estimated leave-one-out cross-validation (LOOCV) error for each model showed that both the quadratic and the spline of degree 2 have the minimal cross-validation error (a). This suggests that the linear model did not capture all the potential explainable variance of the response variable by aMAP, while the cubic and spline of degree 3 were probably overfitting the model (Table 2). (b) shows the logit function (blue line) and standard error (gray ribbon) of the quadratic model over the fitted values (points).

Factors influencing MAP association with recovery

We sought to explore additional patient characteristics that might explain or affect MAP association with recovery. To test whether other factors could be responsible for the observed non-linear association, we first compared the quadratic model with aMAP as a predictor alone, a model that also includes several covariates (aHR, length of surgery, days from surgery to discharge, age, and AIS grade at admission), and a model with only the covariates. The significance of the quadratic fit holds even after accounting for the covariates (Table 3, 4), and none of the terms in the covariates-only model had a significant coefficient (Table 5). These results indicate that even in the presence of the other factors, aMAP is still non-linearly associated with AIS grade improvement at discharge.

Table 5
Evaluation of logistic regression covariates only (Wald test) and leave-one-out cross-validation (LOOCV).
Model: l=β0+β2x2+β3x3+β4x4+β5x5+β6x6+β7x7+β8x8+β9x9, where x2 : average HR; x3: length of surgery (min); x4: days to AIS discharge (days); x5: age; x6: AIS admission D (‘yes’,’no’); x7: AIS admission C (‘yes’,’no’); x8: AIS admission B (‘yes’,’no’); x9: AIS admission A (‘yes’,’no’); (AIS admission E was set as the reference level for AIS admission variable and is part of the intercept) (final n = 93)
LOOCV: average observed accuracy = 0.612; average kappa statistic = 0.17
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= –1.585138.2–0.0110.991
Average HR (x2)β2= –0.02090.029–0.9110.362
Length of surgery (x3)β3= 0.00160.001411.1510.250
Days to AIS discharge (x4)β4= 0.01050.01060.9930.320
Age (x5)β5= 0.00520.0120.4240.672
AIS admission D (x6)β6= 1.5111.3820.0110.991
AIS admission C (x7)β7= 1.7151.3820.0120.991
AIS admission B (x8)β8= 1.6431.3820.0120.990
AIS admission A (x9)β9= 1.5741.3820.0110.991

Patients with more severe injuries are more likely to suffer hemodynamic dysregulations (Lehmann et al., 1987). Hence, we studied whether the relationship of MAP and AIS improvement was maintained in the subcohort of patients with an AIS grade of A at admission. We first filtered the data for the subcohort and then fitted a full model as above but without the AIS grade at admission covariate. The resulting model showed the linear aMAP coefficient to be significant and the quadratic term close to significant (p = 0.14) with the second biggest coefficient (Table 6). A likelihood ratio test between a linear model with covariates and a quadratic model with covariates resulted in p-values = 0.07. On the other hand, in the full model with covariates fitted to the entire cohort, none of the AIS grades at admission had significant coefficients, which suggested that the non-linear relationship of MAP with neurological recovery was sustained across injury severity in that model. This apparent divergence in results might be explained by the reduction in power for the AIS A cohort model.

Table 6
Evaluation of logistic regression in American Spinal Injury Association (ASIA) Impairment Scale (AIS) A at admission cohort (Wald test) and leave-one-out cross-validation (LOOCV).
Model: l=β0+β11x1+β12x12+β2x2+β3x3+β4x4+β5x5, where x1: average MAP; x2 : average HR; x3: length of surgery (min); x4: days to AIS discharge (days); x5: age (final n = 51)
LOOCV: average observed accuracy = 0.63; average kappa statistic = 0.197
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= –0.9313.433–0.2710.786
Average MAP (x1)β11= 10.795.0142.1530.031*
Average MAP (x12)β12= –6.734.591–1.4680.142
Average HR (x2)β2= –0.0160.035–0.4680.639
Length of surgery (x3)β3= 0.00390.00261.5040.132
Days to AIS discharge (x4)β4= 0.00670.0140.4770.633
Age (x5)β5= –0.0120.020–0.5990.549

  1. *p < 0.05.

Next, given that the level of the cord injury can be related to different degrees of hemodynamic dysregulation (Lehmann et al., 1987), we studied the effect of the NLI at admission on the association of MAP and patient recovery. Our cohort was very heterogeneous on the NLI, with most patients having cervical injuries and the rest distributed along the mid and lower segments of the cord (Table 7). Thus, we divided the population into two categories: cervical and non-cervical patients. Running the same full model with just the cervical patients resulted in similar results as compared to the full model on the entire cohort, maintaining the quadratic aMAP significance (Table 8). In the non-cervical cohort, we did not find a significant association of the quadratic aMAP to recovery (Table 9). We then performed additional analyses to determine whether this difference in aMAP relationship to recovery between cervical and non-cervical patients was due to differences in the likelihood of recovery between the two NLI populations. A univariate analysis suggested that the proportion of improvers and not improvers in the cervical and non-cervical population were marginally different (Table 1). Moreover, a logistic regression predicting AIS grade improvement by NLI categorization indicated that non-cervical patients were significantly less likely to recover (β = –0.93, p = 0.041). While these results suggest that a quadratic aMAP is important for predicting AIS grade recovery in cervical patients, the lack of significant results in the non-cervical patients must be interpreted with caution due to the reduced number of cases, the heterogeneous distribution, and the low number of improvers in the group.

Table 7
Neurological level of injury cases.
Cervical (n = 71)Non-cervical (n = 32)
NLIC2C3C4C5C6C7C8T2T3T4T5T6T7T8T9T10T11T12S1S5
Cases3324284811331213132462
Table 8
Evaluation of logistic regression in Cervical cohort (Wald test) and leave-one-out cross-validation (LOOCV).
Model: l=β0+β11x1+β12x12+β2x2+β3x3+β4x4+β5x5+β6x6+β7x7+β8x8, where x1: average MAP; x2 : average HR; x3: length of surgery (min); x4: days to AIS discharge (days); x5: age; x6: AIS admission D (‘yes’,’no’); x7: AIS admission C (‘yes’,’no’); x8: AIS admission B (‘yes’,’no’); (AIS admission A was set as the reference level for AIS admission variable and is part of the intercept, no AIS admission E was present in this cohort) (final n = 93)
LOOCV: average observed accuracy = 0.688; average kappa statistic = 0.362
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= 2.7473.0180.910.363
Average MAP (x1)β11= 7.5943.0562.4850.013*
Average MAP (x12)β12= –7.5283.358–2.2420.025*
Average HR (x2)β2= –0.0550.034–1.6080.108
Length of surgery (x3)β3= 0.00140.00190.7200.472
Days to AIS discharge (x4)β4= 0.00220.0120.1820.855
Age (x5)β5= 0.00790.0160.4820.630
AIS admission D (x6)β6= –0.7470.87–0.8400.730
AIS admission C (x7)β7= 0.7450.800.9250.355
AIS admission B (x8)β8= 0.3010.880.3460.401

  1. *p < 0.05.

Table 9
Evaluation of logistic regression in non-cervical cohort only (Wald test) and leave-one-out cross-validation (LOOCV).
Model: l=β0+β11x1+β12x12+β2x2+β3x3+β4x4+β5x5+β6x6+β7x7+β8x8+β9x9, where x1: average MAP; x2 : average HR; x3: length of surgery (min); x4: days to AIS discharge (days); x5: age; x6: AIS admission D (‘yes’,’no’); x7: AIS admission C (‘yes’,’no’); x8: AIS admission B (‘yes’,’no’); x9: AIS admission A (‘yes’,’no’); (AIS admission E was set as the reference level for AIS admission variable and is part of the intercept) (final n = 93)
LOOCV: average observed accuracy = 0.688; average kappa statistic = 0.362
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= –1.883352.4–0.0050.996
Average MAP (x1)β11= –0.2064.713–0.0440.965
Average MAP (x12)β12= –8.0647.643–1.0550.291
Average HR (x2)β2= –0.00020.06490.0040.997
Length of surgery (x3)β3= 0.00180.00540.3360.737
Days to AIS discharge (x4)β4= 0.0760.06131.2400.215
Age (x5)β5= –0.00470.051–0.9210.357
AIS admission D (x6)β6= 1.7273.5240.0050.996
AIS admission C (x7)β7= 3.5575.7820.0050.996
AIS admission B (x8)β8= 1.7383.5240.0050.995
AIS admission A (x9)β9= 1.6863.5240.0050.996

Finally, we sought to determine whether the probability of recovery associated to MAP could be influenced by the time the patient is in the hospital. For that, we break down the potential causal pathway between MAP dysregulation, AIS improvement, and days from surgery to discharge. We first fitted a logistic regression model with AIS improvement as response and days to discharge as the only predictor. This resulted in a non-significant p-value of p = 0.32, suggesting that days to discharge does not associate with probability of improvement. Second, we fitted a linear model with days to discharge as a response and quadratic aMAP (both linear and quadratic terms) as predictors. This resulted as a significant coefficient of the quadratic term (p = 0.047), although the model was not significant (p = 0.13 for the F statistic) and the adjusted R2 was small (0.0217). We also investigated whether days to discharge interacts with MAP and quadratic MAP to predict AIS improvement, with no significant results on the interaction (interaction days to discharge with aMAP: linear term p = 0.61; quadratic term p = 0.91). These suggest that these two factors do not moderate each other. Finally, eliminating days to discharge from the full covariate model predicting AIS improvement does not have a major effect on the model fit. A likelihood ratio test between both models shows a non-significant change in variance explained (p = 0.729) with a deviance difference of ~0.1%. All together indicates that the non-linear relationship between aMAP and AIS improvement is independent of the days from surgery to discharge.

Intra-operative MAP range from 76-[104-117] mmHg predicts recovery

Since aMAP can obscure episodes of high deviation from average (Hawryluk et al., 2015) and has a non-linear relationship with recovery, we hypothesized that there might be a range of intra-operative MAP that better predicts AIS grade improvers. To test this hypothesis, we analyzed the amount of time MAP was out of a specific range (Figure 4). Since our modeling suggested both a symmetric and asymmetric range, we performed two different analyses. First, starting at a MAP of 90 mmHg, we implemented an algorithm to iteratively expand the MAP range symmetrically 1 mmHg higher and lower and calculate the time MAP was outside the range (Figure 4a). Exploratory analysis of the similarity network indicated a high association between the time out of a MAP range of 73–107 mmHg with the topological distribution of patients (Figure 4b and Figure 4—figure supplement 1). To validate this range and the associated lower and upper MAP thresholds, we used a logistic model with LASSO regularization with the predictors being the time outside of each MAP range as in Figure 4b. This allowed us to systematically reduce the number of relevant predictors until only one remained (non-zero coefficient). Interestingly, the logistic LASSO regression with LOOCV revealed that a MAP range from 76 to 104 mmHg was optimal in our dataset since it produced the most reproducible prediction of recovery (average LOOCV prediction accuracy of 61.16%; Figure 4c and Figure 2—figure supplement 2, Table 9). Next, we studied the possibility of an asymmetric range by fixing the lower limit to 76 mmHg and increasing the upper limit by 1 mmHg at the time (Figure 4d). The association of the patient distribution in the network plateau at a range of 76–116 mmHg (Figure 4e and Figure 4—figure supplement 1) and the logistic LASSO found the range 76–117 mmHg be the most predictive of recovery (average cross-validation prediction accuracy of 57.28%; Figure 4f and Figure 4—figure supplement 2a, Table 10). While both the exploratory analysis and the logistic LASSO produced similar ranges, the later analysis is performed through statistical modeling rather than descriptive associations, and therefore we further discuss the results of the LASSO.

Figure 4 with 3 supplements see all
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Range of mean arterial pressure (MAP).

To find the optimal MAP range, a moving MAP range was computed and the time of MAP outside range calculated (a and d, example of the same patient for symmetric and asymmetric map range, respectively). Calculating the assortativity coefficient (Ar) of the network for each range revealed that the distribution of patients in the network was most highly associated with the range 73–107 mmHg for the symmetric range (b, Figure 4—figure supplement 1), and 76–116 mmHg for the asymmetric range study of upper limit threshold (e, Figure 4—figure supplement 1). A logistic LASSO (least absolute shrinkage and selection operator) regression (Figure 4—figure supplement 2a, Figure 4—figure supplement 3) was used as a confirmatory analysis and to obtain the MAP range that most highly predicts AIS grade recovery. For the symmetric range, the time of MAP outside the 76–104 mmHg (c, Table 10) was found to be the ‘last-standing’ predictor during LASSO regularization (Figure 4—figure supplement 2a), suggesting that greater duration outside this range is associated with lower probability of neurological recovery. In the case of the asymmetric range (Figure 4—figure supplement 3), the last non-zero coefficient was for the range 76–117 mmHg (f, Table 11).

Table 10
Least absolute shrinkage and selection operator (LASSO) solution and logistic regression of most predictive symmetric range with leave-one-out cross-validation (LOOCV).
Model: l=β0+β1x1, where x1: time of MAP outside range 76–104 mmHg (n = 103 patients)
LOOCV: average observed accuracy = 0.61; average kappa statistic = 0.158
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= 0.3680.3331.1030.269
Time MAP out 76–104 (x1)β1= –0.0060.0026–2.5660.0103*

  1. *p < 0.05.

Table 11
Least absolute shrinkage and selection operator (LASSO) solution and logistic regression of most predictive asymmetric range with leave-one-out cross-validation (LOOCV).
Model: l=β0+β1x1, where x1: time of MAP outside range 76–117 mmHg (n = 103 patients)
LOOCV: average observed accuracy = 0.5728; average kappa statistic = 0.102
PredictorCoef. estimate (logit)Std. errorz-Valuep-Value
Interceptβ0= 0.28810.2871.0020.316
Time MAP out 76–117 (x1)β1= –0.007880.0027–2.8280.00468**

  1. **p < 0.01.

Altogether, the findings indicate that the time of MAP outside a measurable normotensive range during surgery is associated with lower odds of recovering at least one AIS grade. Our analysis suggests the optimal range for recovery is between 76–104 and 76–117 mmHg. Notice that while range 76–104 mmHg has higher predictive utility than 76–117 mmHg (mean LOOCV accuracy of 61.16 % vs. 57.28%), the difference in variance of the probability of AIS improvement explained by these two predictors is minimal (<4% difference in RV). Therefore, from a modeling perspective, we broadly conclude that the upper limit of the MAP range is probably anywhere between 104 and 117 mmHg.

Building a predictive model of outcome

Finally, we wanted to study the prediction utility of a model including the analyzed features together with other patient characteristics. We focused on three classification tasks: a model predicting AIS improvement of at least one grade at discharge, a model predicting AIS A at discharge, and a model predicting AIS D at discharge. We chose to predict AIS A and D instead of a multiclass prediction of the AIS at discharge in concordance to our previous studies (Kyritsis et al., 2021) and because of the low representation of other grades in our dataset (Table 1). For each of the three classification tasks, we performed an exhaustive search of all possible additive models with at least one of the predictors of interest: quadratic aMAP, aHR, length of surgery, days from surgery to discharge, age, AIS grade at admission, dichotomized NLI (cervical, non-cervical), time of MAP out of range 76–104, and time of MAP out of range 76–117. We selected the parsimonious model as the model that minimized the small-sample corrected AIC (Table 12). Next, for the selected best model for each task, we performed LOOCV performance evaluation and prediction threshold calibration balancing prediction sensitivity and specificity (Figure 5). The model predicting AIS improvement had a cross-validated AUC of 0.74, the model predicting AIS A at discharge had a cross-validated AUC of 0.88, and the model predicting AIS D at discharge had a cross-validation AUC of 0.84. Other metrics of classification performance can be seen in Table 12. Both the parsimonious model predicting AIS improvement and the one predicting AIS A at discharge included quadratic aMAP as an important predictor. The model predicting AIS A also included the time of MAP out of range 76–117 mmHg. The model predicting AIS D did not include any of the MAP associated terms, suggesting that patients discharged with AIS D can be predicted without considering their MAP during OR. In fact, training the same model but with the inclusion of the quadratic aMAP term resulted in slightly worse prediction performance (AUC 0.84 vs. 0.83). Training the models predicting AIS improvement and AIS A at discharge but without a MAP component (quadratic MAP term or time of MAP out of range) reduced the model performance considerably (AUC, AIS improvement: 0.74 vs. 0.52; AIS A discharge: 0.88 vs. 0.78).

Figure 5
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Leave-one-out cross-validation (LOOCV) performance of prediction models.

We built three prediction models, one to predict American Spinal Injury Association (ASIA) Impairment Scale (AIS) improvement of at least one grade at discharge (AIS impro., a), one to predict AIS A at discharge (A at disch., b) and one to predict AIS D at discharge (D at disch., c). The sensitivity and specificity for each model was computed out of the prediction probability of LOOCV, where each leave-one-out patient is predicted with the model that was trained without that patient. For each model, the classification threshold was set at the probability that balances sensitivity and specificity (dashed red line). The receiving operation curve (ROC) and area under the curve (AUC) for the three models are presented in d.

Table 12
Best prediction models of outcome.
Model predicting AIS improvement:l=β0+β11x1+β12x12+β2x2+β3x3+β4x4+β5x5
Model predicting AIS A:l=β0+β11x1+β12x12+β2x2+β3x3+β4x4+β5x5+β6x6+β7x7
Model predicting AIS D:l=β0+β2x2+β3x3+β4x4+β5x5+β8x8+β9x9
where x1: average MAP; x2 : AIS admission A (‘yes’, ‘no’); x3 : AIS admission B (‘yes’, ‘no’); x4 : AIS admission C (‘yes’, ‘no’); x5 : AIS admission D (‘yes’, ‘no’); x6 : NLI non-cervical; x7 : Time MAP out 76–117; x8 : Length of surgery; x9 : Age; (AIS admission E and NLI cervical were set as the reference levels for the corresponding variable and are part of the intercept). All metrics are on LOOCV prediction (n = 93)
 
 Model AIS improv.Model AIS AModel AIS D
PredictorCoef. estimate (logit)Coef. estimate (logit)Coef. estimate (logit)
Interceptβ0= –16.24β0= 20.466β0= 1.558
Average MAP (x1)β11= 7.374β11= 27.031
Average MAP (Cohn et al., 2010) (x1)β12= –8.215β12= –17.138
AIS admission A (x2)β2= 15.54β2= –22.814β2= 2.324
AIS admission B (x3)β3= 16.1818β3= –20.38β3= 0.41
AIS admission C (x4)β4= 16.752β4= –19.01β4= –2.591
AIS admission D (x5)β5= 14.828β5= 0.217β5= –2.624
NLI non-Cervical (x6)β6= –1.228
Time MAP out 76–117 (x7)β7= 0.017
Length of Surgery (x8)β8= –0.0044
Age (x9)β9= 0.03
Model performance metricMetric valueMetric valueMetric value
Accuracy (95% CI)0.73 (0.629, 0.818)0.82 (0.735, 0.898)0.806 (0.71, 0.881)
AUC0.7430.880.87
Kappa0.450.6290.573
Sensitivity0.710.8120.793
Specificity0.740.8360.812
Positive predicted value0.6580.720.657
Negative predicted value0.7880.890.896

Altogether, this suggests that models can be built for predicting AIS improvement or AIS A at discharge and that such the model performance critically depends on MAP during OR. Conversely, we did not find evidence that predicting AIS D at hospital discharge is dependent on intra-operative MAP.

Discussion

Acute hypotension is common in patients with SCI due to neurogenic shock (Lehmann et al., 1987; Krassioukov et al., 2007) and autonomic dysregulation (Lehmann et al., 1987), probably contributing to post-traumatic spinal ischemia (Streijger et al., 2018; Hall and Wolf, 1987), which is known to cause impaired neurological recovery in animal models (Fehlings et al., 1989). Level 4 evidence from a small single-center case series study in the 1990s suggested that MAP augmentation to 85–90 mmHg during the first 5–7 days after injury was linked to neurological recovery in acute SCI (Levi et al., 1993; Vale et al., 1997). These results are the basis of clinical guidelines for avoidance of hypotension in acute SCI management (Aarabi et al., 2013). However, while numerous clinical studies support MAP augmentation, the arbitrary, recommended MAP goal has been controversial (Cohn et al., 2010; Hawryluk et al., 2015; Saadeh et al., 2017). Recent analysis of high-frequency ICU monitoring data (Hawryluk et al., 2015) and systematic meta-analysis of post-surgery management (Saadeh et al., 2017) suggest that the MAP threshold to avoid is actually lower (~75 mmHg) than the current recommendation of 85 mmHg, and that MAP management might be effective at shorter duration (< 5 days post-injury) than the 7-day goal (Saadeh et al., 2017). The present study represents a multicenter, data-driven, and cross-validated re-evaluation in a different setting (during surgery as compared with prior ICU studies).

Our analysis support that there must be a MAP range during surgery at which neurological recovery is maximized, providing further evidence that MAP management for maintaining normotension might be more beneficial for patient outcome than MAP augmentation for hypotension avoidance alone (Ehsanian, 2020; Nielson et al., 2015). The low boundary of 76 mmHg found in our ultra-early analysis further supports previous suggestions for lowering the intervention threshold (Cohn et al., 2010; Hawryluk et al., 2015; Saadeh et al., 2017). On the other side, we find an upper boundary to MAP management between 104 and 117 mmHg, above which the probability of improvement is reduced. Thus, the proposal for MAP augmentation with vasopressors to increase spinal cord perfusion (Saadoun and Papadopoulos, 2016) has a limit since spinal hyper-perfusion pressure can be detrimental (Saadoun and Papadopoulos, 2016). The physiological rational is that high blood pressure induced by vasopressors can translate to increased risk of hemorrhage in the injured spinal cord, exacerbating tissue damage (Soubeyrand et al., 2014; Streijger et al., 2018; Guha et al., 1987). Moreover, the use of some vasopressors might cause more complications in patients (Inoue et al., 2014) while also potentially contributing to intra-spinal hemorrhage. In fact, recent results in acute experimental SCI suggest controlling for hemodynamic dysregulation through a cardiac-focused treatment instead of using standard vasopressors such as norepinephrine (Williams et al., 2020). Specifically, the authors demonstrated that dobutamine can correct for hemodynamic anomalies and increase blood flow to the spinal cord while reducing the risk of hemorrhage compared to norepinephrine. Furthermore, hypertension during surgery in rodent SCI has been associated with lower probability of recovery (Nielson et al., 2015), probably related to higher tissue damage. Our findings together with previous work (Ehsanian, 2020) also translate these animal study results to humans, indicating that prolonged periods of hypertension early after injury can be a predictor of poor neurological recovery in patients with SCI.

An important finding of our study is the indication that level of injury and injury severity modify the association of MAP with neurological recovery. We observed that normotensive MAP during surgery predicts AIS improvement in patients with cervical SCI but not in patients with lower injuries (thoracic, lumbar, and sacral). While the heterogeneity of our population and low sample size for patients with non-cervical SCI sets limitations on interpreting the results, our finding raises a relevant question regarding precision management of patients with SCI. Patients with cervical SCI present more frequently with hemodynamic and cardiac abnormalities than patients with thoracolumbar SCI, increasing the need for treatment (Lehmann et al., 1987). This is due to sympathetic dysregulation in upper cord injuries, which reduces sympathetic tone likely causing reduced heart contractility, bradycardia, and hypotension (Lehmann et al., 1987; Myers et al., 2007; Teasell et al., 2000). This is particularly true for individuals with severe cervical injury (Lehmann et al., 1987). In that context, our results may indicate that those patients with cervical SCI that are more difficult to maintain within a normotensive MAP are probably less likely to improve in neurological function. Alternatively, it could also be the case that more aggressive MAP management treatment is performed in these patients during their course in the hospital, which could increase the chances of aggravating secondary cord injury. Hemodynamic instability early after injury could serve as a prognostic physiology-based biomarker in a subset of the population, providing a potential tool for precision medicine in SCI. Hence, we have established basic prediction models around non-linear features of MAP that could serve as a benchmark for future machine learning development.

Another relevant contribution of this work is the analytical workflow. First, we demonstrate that topology-based analytics can undercover associations for hypothesis generation during exploratory analysis in a cross-species validation. Our group has previously used a similar workflow in data from animal models (Nielson et al., 2015) suggesting that hypertension is a predictor of neurological recovery and providing rational for the present study. Hence, our work constitutes a successful story of translating machine intelligence analytical tools from animals to humans. Second, we provide further illustration that patient similarity networks are useful and interpretable representations of multidimensional datasets that capture associations during exploratory analysis that can then be validated by network-independent confirmatory analysis. Third, we successfully combine Isomap, a non-linear dimensionality reduction method, with topology-based metrics to evaluate embedding solutions. Fourth, our method for finding the MAP range could be expanded and deployed in other settings. Lastly, our workflow captures representations of multidimensional time-series of different lengths into a network that is actionable.

Limitations of this study include the retrospective nature of the analysis, the relatively small sample size (although large for SCI), and the use of an estimated ordinal scale (AIS grade) as an indicator of neurological recovery. An important consideration is the difficulty of determining AIS grade early after injury. Moreover, other factors not considered in this analysis such as MAP levels before or after surgery or the use of vasopressors might influence the results. Future research with more granular data should address these and other important questions.

Data availability

Source data has been deposited to the Open Data Commons for Spinal Cord Injury (odc-sci.org; RRID:SCR_016673) under the accession number ODC-SCI:245 (https://doi.org/10.34945/F5R59J) and ODC-SCI:246 (https://doi.org/10.34945/F5MG68).

The following data sets were generated
    1. Torres-Espin A
    2. Haefeli J
    3. Ehsanian R
    4. Torres D
    5. Almeida C
    6. Huie J
    7. Chou A
    8. Dirlikov B
    9. Suen C G
    10. Nielson JL
    11. Kyritsis N
    12. Duong-Fernandez X
    13. Thomas LH
    14. Hemmerle T
    15. Morozov DD
    16. Sanderson D
    17. Talbott N
    18. Manley J
    19. Dhall GT
    20. Whetstone SS
    21. Bresnahan WD
    22. Beattie JC
    23. McKenna MS
    24. Pan SL
    25. Ferguson JZ
    (2021) Open Data Commons for Spinal Cord Injury
    ASIA Impairment Scale, level of injury, intraoperative time series mean arterial pressure and heart rate after spinal cord injury in patients in a multi-site retrospective TRACK-SCI cohort: site 1 of 2.
    https://doi.org/10.34945/F5R59J

References

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    1. National Spinal Cor Injury Statistical Center
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    Spinal Cord Injury Facts and Figures at a Glance
    National Spinal Cor Injury Statistical Center.

Decision letter

  1. Arduino A Mangoni
    Reviewing Editor; Flinders Medical Centre, Australia
  2. Matthias Barton
    Senior Editor; University of Zurich, Switzerland
  3. Marcel Kopp
    Reviewer
  4. Aaron Phillips
    Reviewer; University of Calgary, Canada

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Decision letter after peer review:

Thank you for submitting your article "Topological network analysis of patient similarity for precision management of acute blood pressure in spinal cord injury" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Marcel Kopp (Reviewer #2).

The Reviewers and Editors have discussed the reviews with one another, and this decision letter is to help you prepare a revised submission.

Essential revisions:

1) Please provide information regarding what covariate adjustment was used in the confirmatory logistic regression models.

2) Can the authors provide an explanation of why they chose the specific forms of clustering to identify patient phenotypes? Other, perhaps simpler and more common unsupervised machine learning algorithms could have been used.

3) Are the results sensitive to the defined outcome of improvement of at least one AIS grade? What happens if this is increased to e.g. 2 grades?

4) Two different approaches to analysis were used – i.e. essentially clustering of some form and also logistic regression (using e.g. quadratic and spline functions). Can the authors comment on whether these 2 approaches can be used interchangeably or whether one would be preferred over to the other to answer the research questions of interest. What advantage does the clustering approach have in terms of the research question?

5) Why was a simple accuracy metric used and not e.g. AUC? Does the accuracy metric account for an imbalance in the outcomes?

6) The LOOCV accuracy was not that high suggesting a lot of other factors might influence outcomes. Is the accuracy really high enough to support the use of MAP being used by clinicians for decision making and/or interventions to control MAP during surgery?

7) What variables were used for the LASSO. The prediction accuracy again seems very low for high-dimensional dataset.

8) Only one dataset was used without splitting the data into a training and validation dataset. Are similar results for the topological network analysis obtained if the data is split for training and validation?

9) What was the modularity of the final network and does it suggest significant clustering?

10) Why was days from surgery to discharge used in the logistic regression models? Might it not be considered a mediator rather than a confounder – and how does its exclusion from the model influence the result?

11) The limitations are mentioned but not discussed or justified. This leads to the following questions: a) Why was the lesion level not included in the analysis? and b) Why did the authors only analyze MAD values during surgery? Because the analysis of MAP data from the ICU period published elsewhere showed similar results regarding the lower limit of MAP, wouldn't it be of interest to know how much overlap there is between the populations with critical MAP values during surgery and during stay in the ICU?

12) Introduction: Neither hypertension nor hypotension following acute SCI has been conclusively demonstrated to impact neurological recovery. Instead, guidelines and more recent work are based purely on observations and post-hoc regression analyses. While the purported mechanism for repeated hypotensive episodes is clear, readers may benefit from at least a brief description of why both hypertension and hypotension could plausibly be important (aside from the fact that, again, non-causal observations demonstrated a relationship in the author's prior work).

13) AIS scores: Based on Table 1 most patients were discharged within 2 weeks after injury. The neurological exam is not so reliable at this point. This is a big limitation of the current work. Although a six month follow-up would be ideal to determine whether neurological recovery occurred, the authors should at least mention this.

14) All the analyses seem to have been conducted on an AIS change. The authors should demonstrate that their analysis holds for a more linear measure of recovery (e.g., total motor score).

15) Based on Figure 2 – Supplement 2, it is difficult to ascertain whether clusters contain a higher proportion of individuals that show an AIS improvement, and those individuals tend to have a MAP > 80 and < 100, is due to these clusters having individuals who were less severe to begin with (i.e., C,D,E) and therefore less likely to be hemodynamically unstable. One way to answer this would be to examine AIS A patients in a separate analysis and determine whether these findings hold. Because, the alternative explanation here is that this analysis is effectively finding a proxy for initial injury severity (i.e., more severe, more hemodynamically unstable) – and not that hemodynamic instability per se is the problem. Another analysis that could help complement this work and avoid this confound would be to use total motor score as the outcome instead of AIS conversion.

16) Logistic regression – Based on Figure 2p the overall trend looks more to be that higher MAP = > Pr(δ AIS grade > 0). The exception is only 2 data points on the top end. It is difficult to determine how robust the notion is that there is a 'too high' component to this data. Indeed it seems that a linear model does quite well for this analysis as well. Please see my comment below but this should be addressed as the concept of also having a 'top cutoff' is an extremely important clinical feature here.

17) Time outside MAP – The authors use an approach that systematically increases their window in both directions to find their optimal range of 76-104. However, what happens if you then hold 76 and only increase on the upper end? Does this rapidly degrade the relationship? If not, again this would suggest that the evidence for a top end cut-off is not as strong. While I understand the authors briefly looked at this (methods) it seems worth exploring further as this is a critical point for clinical management. I do not see a good reason that the time outside the threshold can not at least be plotted to determine this relationship.

18) Data availability – The code and analysis should be made available to the reviewers. It is impossible to determine the accuracy of this type of analysis without it.

19) Discussion – It seems that the authors should discuss the confound of injury severity being linked with worse hemodynamic instability, and also worse neurological recovery. It would be helpful to include some of the suggested analyses to convince the readers that this confound does not explain the results since it is the most likely alternative explanation.

Reviewer #1:

The major strengths of this paper are the use of a combination of relatively novel approaches/applications to the identification of important predictors for recovery after spinal cord surgery. These include various data reduction techniques such as dissimilarity matrices and a subject-centred topological network analysis to identify phenotypes. The weaknesses include its relatively modest prediction accuracy and the lack of internal and external validation in the primary network analysis.

Reviewer #2:

The major strength of the paper is the statistically highly advanced analysis based on high-resolution data from acute SCI care, i.e. intra-operative mean arterial blood pressure (MAP) and heart rate. The steps of data exploration and analysis and their results are presented transparently. In conjunction with the results of previous studies suggesting that the lower threshold of MAP levels to be avoided in the ICU is about 75 mmHg, the main results of the this study imply that the minimum target MAP may be lower than the currently recommended 85 mmHg also during surgery. The analysis, which combines machine learning algorithms with logistic regression models, may serve as a template for data-driven studies also on other aspects of critical care in the field of SCI.

A weakness of the study is that some of the baseline neurological criteria were not included in the analysis. In particular, the neurological level of injury could be important for the research question, because the degree of blood pressure dysregulation also depends on the lesion level. The authors mention this limitation but do not explain why they accept it. Another limitation is the relatively small sample size of the study. Therefore, the specific results might have limited generalizability. Nevertheless, the study is an essential contribution to the readjustment of MAP threshold recommendations in the very acute stage of SCI and provides key information for the design of future precision medicine studies.

Reviewer #3:

The authors present a nice analysis of the relationship between intraoperative mean arterial pressure and neurological recovery after spinal cord injury, and I appreciate the opportunity to review this work. In general, the results are interesting and largely in line with a growing body of evidence that supports the use of hemodynamic monitoring in the acute phase after injury. There are three primary points with regard to this work that the authors can and should address prior to publication.

First, the exclusive use of AIS conversion as the outcome of neurological improvement is not ideal. Demonstrating that these findings are robust to other more continuous measures of neurological improvement such as motor/sensory scores would go a long way towards demonstrating that this finding is robust.

Second, the authors state in the discussion that MAP management may only be needed for <5 days post-injury. There does not appear to be strong data in the paper to support this point. Either more data should be added that supports this contention or this point should be removed.

Third, although the authors briefly discuss the confound of injury severity being linked to hemodynamic instability, the results are compelling enough at the moment to discount a role of injury severity. Individuals with more severe injuries will necessarily have greater hemodynamic instability, particularly in the hyperacute and acute phase after injury. These same individuals are also less likely to exhibit a conversion of their AIS score (e.g., individuals with AIS A/B). The authors control for this in some of their analyses (e.g., including a coefficient of initial AIS score in their regression models), yet their results seem to indicate that the clusters of individuals they focus on are indeed those with less severe injuries to start with. Demonstrating that injury severity is not a factor would require an analysis of only individuals with AIS A injuries at admission. This would be very compelling and enhance the impact of this work.

Overall, this is an interesting analysis that will be of use to the field.

https://doi.org/10.7554/eLife.68015.sa1

Author response

Essential revisions:

1) Please provide information regarding what covariate adjustment was used in the confirmatory logistic regression models.

We adjusted the models by heart rate, length of surgery, days from surgery to discharge, age, and AIS grade at admission. We added text to the Results section that helps to clarify the models and the covariates.

2) Can the authors provide an explanation of why they chose the specific forms of clustering to identify patient phenotypes? Other, perhaps simpler and more common unsupervised machine learning algorithms could have been used.

We have added further explanation to the manuscript. In short, we and others have previously shown that topological analysis drives discovery of biologically meaningful associations with high resolution (Nielson et al., 2015; Nicolau et al., 2011). Here, we use topological network analysis for several reasons. First, physiological data is non-linear, which conforms to a manifold in the multidimensional space. We use Isomap, a well-established non-linear dimension reduction method, to find the low dimensional embedding of the data (Balasubramanian, 2002; Tenenbaum, 2000). Isomap works by constructing a neighbor network to approximate the geodesic distance between observations. Second, to ensure that Isomap approximates the shape of the manifold we use topological metrics. Third, the optimal Isomap solution had 4 dimensions, which makes it challenging for representing data for exploration. We construct the network of patients as networks are efficient data representation methods for multidimensional data. Therefore, using the walktrap clustering algorithm is a natural progression as it is based on the network and its topology.

Indeed, other methods could be used, however, it has been shown that networks (graphs) allow for more efficient data exploration than other approaches as they are capable of representing multidimensional relationships on a single 2D visual space (Benson et al., 2016). Ultimately, the question of which unsupervised method to use in each case is a scholarly question that requires its own dedicated research. Here, we focused on topological methods as we have successfully used them before to explore hemodynamics after SCI in animal models, a direct bench-to-bedside translation of both physiological variables and analytical methods (Nielson et al., 2015).

3) Are the results sensitive to the defined outcome of improvement of at least one AIS grade? What happens if this is increased to e.g. 2 grades?

This is a good question. Unfortunately, we do not have enough data to provide an accurate answer, despite having one of the largest cohorts assembled in SCI (N = 118, greater than 80% of acute SCI studies registered in Clinical trials.gov). Though increasing one AIS grade is clinically meaningful, we acknowledge the limitations of our study and agree with the reviewers that an analysis using a more sensitive outcome such as a continuous metric (e.g. motor/sensory scores) would increase the value of our findings. This is an area for future research that will benefit from the ongoing assembly of ever larger cohorts in the field.

4) Two different approaches to analysis were used – i.e. essentially clustering of some form and also logistic regression (using e.g. quadratic and spline functions). Can the authors comment on whether these 2 approaches can be used interchangeably or whether one would be preferred over to the other to answer the research questions of interest. What advantage does the clustering approach have in terms of the research question?

We have now clarified this in the results and discussion. These two methods are complementary rather than interchangeable. The patient network analysis is unsupervised and was used with the intention of exploratory discovery. It is through this method where we observed the potential double bound (upper and lower limits) for arterial pressure in humans, and the dependence of it to AIS at admission. The logistic regression is used in two ways, one to confirm the hypothesis formulated through the network analysis and two to find a precise MAP threshold through LASSO regularization. The fact that the MAP threshold for prediction of improvement captured through the network is very close to the one found by the LASSO indicates that our network methodology captures valid relationships in the data without previous knowledge of outcome (unsupervised). This suggests that our network method can be used for data discovery in future research including more physiological measures. We take the values obtained through LASSO as more confirmatory because it is a modeling approach, while the network analysis is exploratory. We added text in the manuscript clarifying these points

The use of topological analysis and clustering through networks has some advantages for exploratory analysis and discovery in the question at hand. We show that even though we are technically only including 2 variables in the analysis (MAP and HR), the time series of these two conform to a multidimensional manifold that we approximate by Isomap plus topological metrics. The network allows us to represent that multidimensional space in a 2D visual based on the similarity between patients. This is convenient for fast exploration of the multidimensional space, where relationship between patient similarities and any variable can be easily depicted by mapping the variable values to coloring the nodes. This and other related topological data analysis methods have been described as “Machine Intelligence” approaches as they aid the analyst with expert matter knowledge to perform fast discovery (Carlsson, 2009; Wasserman, 2018).

5) Why was a simple accuracy metric used and not e.g. AUC? Does the accuracy metric account for an imbalance in the outcomes?

We have now performed new analysis on prediction modeling. For these, we have calculated AUC and ROC. We have included new text and a new figure reflecting the new results.

6) The LOOCV accuracy was not that high suggesting a lot of other factors might influence outcomes. Is the accuracy really high enough to support the use of MAP being used by clinicians for decision making and/or interventions to control MAP during surgery?

We have included new analysis for the prediction modeling and added a subsection in the results. In these, we show that the prediction accuracy can be improved through model selection, where MAP is an important feature to maintain in the model for good prediction performance, especially for predicting AIS improvement or AIS A at discharge. It is important to note that all our metrics of performance are for LOOCV, which measures performances over unseen data for n (patients) trained models and thus offers an estimation of the generatability of the data and some protection against model overfitting. In that sense, LOOCV accuracy would be in most cases lower than accuracy of a model that has not been measured with cross-validation, which is the case of most logistic regression in the clinical literature. With the new prediction modeling we included, our model has a LOOCV AUC of 0.75 for predicting AIS improvement at discharge. While we acknowledge the limitations of the study, we think that our prediction models are informative, and indeed are among the first ever to rigorously test ultra-acute predictors of outcome in SCI. These models can provide a benchmark for future prediction modeling in the early level-1 trauma clinical SCI.

7) What variables were used for the LASSO. The prediction accuracy again seems very low for high-dimensional dataset.

We have added the range threshold analysis in its own section in the results and separated the explanation in the methods to address this point. LASSO was used to determine the most predictive MAP range and respective thresholds. The variables included are the time spent out of each one of the MAP ranges. In that sense, we have not used LASSO as supervised predictive ML method but rather as a feature selection method (through the regularization process) to obtain the last standing coefficient and correspondingly the best predicting MAP range. Therefore, we do not expect our use of LASSO to produce the most accurate predictive model but to provide the most predictive MAP range.

8) Only one dataset was used without splitting the data into a training and validation dataset. Are similar results for the topological network analysis obtained if the data is split for training and validation?

We agree with the reviewer about the need to validate the results and have added explicit discussion of this point. Topological network analysis learns the cross-validated data manifold space, through a specific type of validation that subsamples the subspace of all networks. Splitting between validation and training in the exploratory topological analysis presents two major challenges: (1) splitting the data with our sample size can be problematic since would leave relatively few cases for training and testing with precision; (2) training and testing split is normally performed in supervised models to determine how well a trained model can predict unseen data. The topological network analysis process that we implemented is an unsupervised method used to explore the relationship between patients and physiological variables. In that sense, we are not using the network as a model to be “trained” but as a descriptive statistic of the shape of the data manifold. Nonetheless, the metrics of topological descriptions that we use (persistent homology) find the best configuration (most stable) given the data's many potential configurations (Carlsson, 2009). In that sense, we are validating the topological structure of the network for our specific case.

We conducted further validation by (1) performing confirmatory analysis through hypothesis testing (logistic models) and (2) using leave-one-out cross-validation (LOOCV). LOOCV is perhaps the best alternative since splitting the data in this case would leave very few cases for training and testing which would ultimately underpower the analysis.

9) What was the modularity of the final network and does it suggest significant clustering?

The modularity of the final network was Q = 0.837. Modularity has a maximum of 1, representing complete clustering above expected in a random graph with the same structure (same number of nodes and degrees). Our final Q is quite high, suggesting the presence of clusters above what should be expected by chance. We have included this information in the corresponding figure legend.

10) Why was days from surgery to discharge used in the logistic regression models? Might it not be considered a mediator rather than a confounder – and how does its exclusion from the model influence the result?

We now include discussion of this important point.

We use time of surgery to discharge in the model as a covariate, to control for the potential effect in outcome related to the time to discharge. Considering time of surgery to discharge as a mediator is indeed a possibility. That would be true if: (a) time to discharge affects probability of improving (the outcome), and (b) MAP dysregulation during surgery affects days from surgery to discharge. The logical progression in the causal pathway would be as follows: higher MAP OR dysregulation indicates/causes changes in time to discharge, and time to discharge then affects probability of improvement (either increase or decrease). Since we see that MAP dysregulation (or proxies of it) actually reduces probability of improvement, then there are two options: (1) MAP dysregulation during OR directly or indirectly associates with longer time to discharge, and higher time to discharge reduce probability of improvement, or (2) MAP dysregulation associates with shorter time to discharge which in turns, is related to reduced probability of improvement. One would expect that the longer the patient is in the hospital, the more time the patient has to improve before discharge. However, the longer a patient stays in the hospital is probably an indicator of their severity. We have investigated this matter using different models to dissect the potential causal pathway.

First, we fitted a logistic model with AIS improvement as response and days to discharge as the only predictor. This resulted in a non-significant p value of p = 0.32, suggesting that days to discharge doesn’t associate with probability of improvement. Second, we fitted a linear model with days to discharge as a response and quadratic aMAP (both linear and quadratic terms) as predictors. This resulted as a significant coefficient of the quadratic term (p = 0.047), although the model was not significant (p = 0.13 for the F statistic) and the adjusted R2 was small (0.0217). Visual examination of the data indicates that the density of patients that tend to stay longer in the hospital are the ones with a MAP in the normotensive range ~ 80-100. We also investigated whether days to discharge interacts with MAP and quadratic MAP to predict AIS improvement, with no significant results on the interaction, and the inclusion of the interaction do not change the quadratic association of MAP with the response. These suggest that these two factors do not moderate each other. We also performed the same analysis with time MAP out of 76-104 mmHg instead of aMAP as a different proxy for MAP dysregulation, with similar results.

Finally, eliminating days to discharge from the full covariate model predicting AIS improvement doesn’t have a major effect on the model fit. A likelihood ratio test between both models shows a non-significant change in variance explained (p=0.79) with a deviance difference of ~ 0.1%.

Therefore, given the data, we think there is little evidence for considering an effect of MAP dysregulation on AIS improvement mediated (or moderated) by length of stay in the hospital. We have maintained days from surgery to discharge as covariate because although not significant, we still think it is important to adjust the model for differences in length of hospital stay between patients. We have included this analysis in the manuscript as results. In addition, we understand the limitation of the above analysis where all other variables and their relationship have not been considered. Nonetheless, we want to acknowledge the importance of dissecting the correlational observations as a first approximation to determine the causal effects. We will definitely explore these ideas in the near future as larger cohorts of data become available.

11) The limitations are mentioned but not discussed or justified. This leads to the following questions: a) Why was the lesion level not included in the analysis? and b) Why did the authors only analyze MAD values during surgery? Because the analysis of MAP data from the ICU period published elsewhere showed similar results regarding the lower limit of MAP, wouldn't it be of interest to know how much overlap there is between the populations with critical MAP values during surgery and during stay in the ICU?

We thank the reviewers for pointing to these important questions. We have expanded our analysis to include the level of injury. We found that the association of MAP range of AIS grade improvement is dependent on whether the patient had a cervical injury or not. At this time, we do not have enough samples to tackle this question with higher granularity (e.g. per segment level) as our data include very few cases with middle and lower level injuries. This is a limitation due to the infrequent nature of SCI, the difference in injury incidence per segment level, and the slow accumulation of patient cohorts, even at some of the busiest level 1 trauma centers in the country. We have included a new section in the results and expanded the discussion accordingly.

Regarding the analysis of MAP only during surgery, there are some considerations: First, our previous results in animal models suggest that OR hemodynamics is an important predictor of recovery. Second, this is a retrospective cohort in which systematic ICU monitoring is not available for answering the proposed question. Third, and most importantly, monitoring in the OR is perhaps the best controlled scenario for hemodynamic monitoring in these patients. We acknowledge the importance of the question of whether MAP during OR is sufficient as a proxy for patient dysregulation and how it confounds with hemodynamic dysregulation/treatment during ICU. As part of the TRACK-SCI study, we are collecting high-frequency monitoring data in a prospective cohort and we will explore these questions in the future.

12) Introduction: Neither hypertension nor hypotension following acute SCI has been conclusively demonstrated to impact neurological recovery. Instead, guidelines and more recent work are based purely on observations and post-hoc regression analyses. While the purported mechanism for repeated hypotensive episodes is clear, readers may benefit from at least a brief description of why both hypertension and hypotension could plausibly be important (aside from the fact that, again, non-causal observations demonstrated a relationship in the author's prior work).

We have included further details in the introduction describing the importance of both hypertension and hypotension from clinical and animal studies. We agree with the reviewers that a causal link between hemodynamic control and recovery in humans remains elusive, and it should be noted that randomized controlled studies are challenging in this context given the ethical concerns of such studies. Nevertheless, some experimental animal studies 'clamping MAP' at different set points strongly suggest causal effects (Nout et al., 2012), and physician-scientists in the field are conducting ongoing studies that appear strongly supports a potential causal role. Such a causal role is theoretically well-founded, given that in traumatic brain injury and stroke, tissue perfusion/oxygenation, and brain tissue survival are supported by prevention of hypotension, but it is also possible that hypertension can induce 'hemorrhagic conversion' and bleeding into the tissue with devastating effects on lesion expansion. Spinal cord injury is known to involve similar secondary injury processes in both rodent and primate models (Crowe et al., 1997).

13) AIS scores: Based on Table 1 most patients were discharged within 2 weeks after injury. The neurological exam is not so reliable at this point. This is a big limitation of the current work. Although a six month follow-up would be ideal to determine whether neurological recovery occurred, the authors should at least mention this.

We agree with the limitations and have added some text in the discussion. These data are unique in that they reflect ultra-acute data from the level 1 trauma center. This is a moment in the care pathway when a highly heterogeneous patient population is concentrated in one location prior to being dispersed to a broad variety of discharge scenarios (largely depending on insurance status in the US healthcare system). This makes long term follow-up data difficult to obtain. Nevertheless, as the TRACK-SCI prospective study progresses, we are collecting contact information and have funds to track patients out to 12 months follow up together with high granular physiological data both in the OR and ICU. It will take many years to collect a large N, but in the future this dataset will provide a rich source of information to continue researching these important questions.

14) All the analyses seem to have been conducted on an AIS change. The authors should demonstrate that their analysis holds for a more linear measure of recovery (e.g., total motor score).

We agree with the reviewers that AIS change has limitations. We now acknowledge them in the manuscript. We have also added further analysis as a result of this revision. Specifically, we investigated models predicting AIS A and AIS D at discharge in addition to the AIS change analysis we had. Please see the following responses to details on the new analysis.

15) Based on Figure 2 – Supplement 2, it is difficult to ascertain whether clusters contain a higher proportion of individuals that show an AIS improvement, and those individuals tend to have a MAP > 80 and < 100, is due to these clusters having individuals who were less severe to begin with (i.e., C,D,E) and therefore less likely to be hemodynamically unstable. One way to answer this would be to examine AIS A patients in a separate analysis and determine whether these findings hold. Because, the alternative explanation here is that this analysis is effectively finding a proxy for initial injury severity (i.e., more severe, more hemodynamically unstable) – and not that hemodynamic instability per se is the problem. Another analysis that could help complement this work and avoid this confound would be to use total motor score as the outcome instead of AIS conversion.

This is an important consideration. We study the question of injury severity being a driver for the effect in several analyses. First, as suggested by the reviewers, we conducted the model fitting only in patients with AIS A at admission. This resulted in a significant linear MAP term, and a quadratic MAP with the second biggest coefficient and a p = 0.14. Comparing a linear model with the quadratic one in this cohort through a likelihood ratio test resulted in a p = 0.07. This suggests that while the linear term of MAP as predictor of AIS improvement is maintained significantly for AIS A patients, the evidence for a quadratic form is weak in this cohort. However, with the reduction in sample size (n=46) we may be underpowered for detecting such an effect. Second, we have included AIS at admission as a covariate in the full model to adjust for potential differences between different injury severities. In this scenario, the quadratic form of MAP predicting AIS improvement is maintained. All together, this suggests that if non-linear relationship of MAP and AIS improvement depend on initial injury severity we lack the statistical power to fully investigate this question. We have included this analysis in the document pointing out the caveats of it. Future work should address this, as we agree with the reviewers will be important for guiding precision in clinical recommendations.

16) Logistic regression – Based on Figure 2p the overall trend looks more to be that higher MAP = > Pr(δ AIS grade > 0). The exception is only 2 data points on the top end. It is difficult to determine how robust the notion is that there is a 'too high' component to this data. Indeed it seems that a linear model does quite well for this analysis as well. Please see my comment below but this should be addressed as the concept of also having a 'top cutoff' is an extremely important clinical feature here.

We agree with the reviewers that having a ‘top cutoff” is an extremely important clinical feature. Although the linear model performs better than the unconditional model (no predictors), our results show that the polynomial quadratic model or the spline of degree 2 model outperforms the linear model, both in the variance explained and the LOOCV error. We interpret this as indicating that a non-linear association between MAP and the prediction of AIS increase explains the data better than the linear model. We have expanded our explanation in the results to help the reader. Also, please see our answer below regarding the upper limit of the cutoff.

17) Time outside MAP – The authors use an approach that systematically increases their window in both directions to find their optimal range of 76-104. However, what happens if you then hold 76 and only increase on the upper end? Does this rapidly degrade the relationship? If not, again this would suggest that the evidence for a top end cut-off is not as strong. While I understand the authors briefly looked at this (methods) it seems worth exploring further as this is a critical point for clinical management. I do not see a good reason that the time outside the threshold can not at least be plotted to determine this relationship.

We have included further details on the result section about the potential asymmetry of the range. While it is true that we see similar performance of the polynomial quadratic model (symmetric) and the spline model of degree 2 (asymmetric), we did not have strong evidence to justify either model as being 'more correct', so we chose simplicity as spline models will tend to overfit more than a polynomial. For that reason, we used the symmetric window increase in our study of the threshold range. As suggested by the reviewer, we performed the same analysis but holding the lower limit to 76 and increasing the upper limit by 1. This results in the most predictive range to be 76-117. This suggests that our data and methodology is limited to tune the upper level and that it might be between 104 to 117. We have included this analysis in the results and discuss the implication of it.

18) Data availability – The code and analysis should be made available to the reviewers. It is impossible to determine the accuracy of this type of analysis without it.

We are adding the code that reproduces the entire analysis (including figures) as supplementary material, and the data has been uploaded to odc-sci.org, a community-based repository for SCI research data sharing and publication. The data would be available and active upon acceptance with DOIs (10.34945/F5R59J and 10.34945/F5MG68).

19) Discussion – It seems that the authors should discuss the confound of injury severity being linked with worse hemodynamic instability, and also worse neurological recovery. It would be helpful to include some of the suggested analyses to convince the readers that this confound does not explain the results since it is the most likely alternative explanation.

We have performed the suggested analysis when possible and discussed their results. While we agree that there are limitations in our study, we also contend that the findings with the new analyses are important. Although there are caveats to any observational clinical study, this is the largest study to-date on this topic, with a sample size that is 4-fold larger than the last study in this area. The work increases the body of evidence to guide both the clinical conversation and future prospective research.

https://doi.org/10.7554/eLife.68015.sa2

Article and author information

Author details

  1. Abel Torres-Espín

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review and editing
    Contributed equally with
    Jenny Haefeli
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9787-8738

  2. Jenny Haefeli

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Conceptualization, Formal analysis, Investigation, Methodology, Writing – review and editing
    Contributed equally with
    Abel Torres-Espín
    Competing interests
    No competing interests declared

  3. Reza Ehsanian

    Division of Physical Medicine and Rehabilitation, Department of Orthopaedics and Rehabilitation, University of New Mexico School of Medicine, Albuquerque, United States
    Contribution
    Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  4. Dolores Torres

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Data curation, Writing – review and editing, Data curation
    Competing interests
    No competing interests declared

  5. Carlos A Almeida

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Data curation, Writing – review and editing
    Competing interests
    No competing interests declared

  6. J Russell Huie

    1. Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    2. San Francisco Veterans Affairs Healthcare System, San Francisco, United States
    Contribution
    Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  7. Austin Chou

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  8. Dmitriy Morozov

    Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, United States
    Contribution
    Formal analysis, Methodology, Visualization, Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  9. Nicole Sanderson

    Lawrence Berkeley National Laboratory, Berkeley, United States
    Contribution
    Formal analysis, Methodology, Visualization, Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  10. Benjamin Dirlikov

    Rehabilitation Research Center, Santa Clara Valley Medical Center, San Jose, United States
    Contribution
    Data curation, Writing – review and editing
    Competing interests
    No competing interests declared

  11. Catherine G Suen

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Data curation, Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  12. Jessica L Nielson

    1. Department of Psychiatry and Behavioral Science, and University of Minnesota, Minneapolis, United States
    2. Institute for Health Informatics, University of Minnesota, Minneapolis, United States
    Contribution
    Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  13. Nikos Kyritsis

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7801-5796

  14. Debra D Hemmerle

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Data curation, Writing – review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-2796-6107

  15. Jason F Talbott

    Department of Radiology and Biomedical Imaging, University of California, San Francisco, San Francisco, United States
    Contribution
    Conceptualization, Investigation, Methodology, Writing – review and editing
    Competing interests
    No competing interests declared

  16. Geoffrey T Manley

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Conceptualization, Resources, Writing – review and editing
    Competing interests
    No competing interests declared

  17. Sanjay S Dhall

    Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Conceptualization, Resources, Writing – review and editing
    Competing interests
    No competing interests declared

  18. William D Whetstone

    Department of Emergency Medicine, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Data curation, Methodology, Validation, Writing – review and editing
    Competing interests
    No competing interests declared

  19. Jacqueline C Bresnahan

    1. Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    2. San Francisco Veterans Affairs Healthcare System, San Francisco, United States
    Contribution
    Conceptualization, Resources, Writing – review and editing
    Competing interests
    No competing interests declared

  20. Michael S Beattie

    1. Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    2. San Francisco Veterans Affairs Healthcare System, San Francisco, United States
    Contribution
    Conceptualization, Resources, Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  21. Stephen L McKenna

    1. Department of Physical Medicine and Rehabilitation, Santa Clara Valley Medical Center, San Jose, United States
    2. Department of Neurosurgery, Stanford University, Stanford, United States
    Contribution
    Conceptualization, Data curation, Methodology, Resources, Writing – review and editing, Data interpretation
    Competing interests
    No competing interests declared

  22. Jonathan Z Pan

    Department of Anesthesia and Perioperative Care, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    Contribution
    Conceptualization, Data curation, Methodology, Writing – review and editing, Data interpretation
    For correspondence
    jonathan.pan@ucsf.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5814-3707

  23. Adam R Ferguson

    1. Weill Institute for Neurosciences; Brain and Spinal Injury Center (BASIC), Department of Neurological Surgery, University of California, San Francisco; Zuckerberg San Francisco General Hospital and Trauma Center, San Francisco, United States
    2. San Francisco Veterans Affairs Healthcare System, San Francisco, United States
    Contribution
    Conceptualization, Formal analysis, Funding acquisition, Methodology, Supervision, Writing – original draft, Writing – review and editing, Data interpretation
    For correspondence
    adam.ferguson@ucsf.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7102-1608

  24. The TRACK-SCI Investigators

    Competing interests
    No competing interests declared
    1. MS Beattie
    2. JC Bresnahan
    3. JF Burke
    4. A Chou
    5. CA de Almeida
    6. SS Dhall
    7. AM DiGiorgio
    8. X Doung-Fernandez
    9. AR Ferguson
    10. J Haefeli
    11. DD Hemmerle
    12. JR Huie
    13. N Kyritsis
    14. GT Manley
    15. S Moncivais
    16. C Omondi
    17. JZ Pan
    18. LU Pascual
    19. V Singh
    20. JF Talbott
    21. LH Thomas
    22. A Torres-Espin
    23. P Weinstein
    24. WD Whetstone

Funding

National Institute of Neurological Disorders and Stroke (R01NS088475)

  • Adam R Ferguson

National Institute of Neurological Disorders and Stroke (R01NS122888)

  • Adam R Ferguson

National Institute of Neurological Disorders and Stroke (UH3NS106899)

  • Adam R Ferguson

U.S. Department of Veterans Affairs (1I01RX002245)

  • Adam R Ferguson

U.S. Department of Veterans Affairs (I01RX002787)

  • Adam R Ferguson

Wings for Life

  • Abel Torres-Espín
  • Adam R Ferguson

Craig H. Neilsen Foundation

  • Adam R Ferguson

Department of Defense (SC150198)

  • Michael S Beattie

Department of Defense (SC190233)

  • Michael S Beattie

Foundation for Anesthesia Education and Research (A123320)

  • Jonathan Z Pan

Department of Energy (DE-AC02-05CH11231)

  • Dmitriy Morozov

National Institute of Neurological Disorders and Stroke (U24NS122732)

  • Adam R Ferguson

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

Supported in part by NIH/NINDS: R01NS088475 (ARF); R01NS122888 (ARF); UH3NS106899 (ARF); U24NS122732 (ARF); Department of Veterans Affairs: 1I01RX002245 (ARF), I01RX002787 (ARF); Wings for Life Foundation (ATE, ARF); Craig H Neilsen Foundation (ARF); DOD: SC150198 (MSB); SC190233 (MSB); DOE: DE-AC02-05CH11231 (DM).

Ethics

Human subjects: This study constitutes a retrospective data analysis. All data was de-identified before pre-processing and analysis. Protocols for retrospective data extraction were approved by Institutional Research Board (IRB) under protocol numbers 11-07639 and 11-06997.

Senior Editor

  1. Matthias Barton, University of Zurich, Switzerland

Reviewing Editor

  1. Arduino A Mangoni, Flinders Medical Centre, Australia

Reviewers

  1. Marcel Kopp
  2. Aaron Phillips, University of Calgary, Canada

Publication history

  1. Received: March 2, 2021
  2. Accepted: October 23, 2021
  3. Accepted Manuscript published: November 16, 2021 (version 1)
  4. Accepted Manuscript updated: November 17, 2021 (version 2)
  5. Version of Record published: December 2, 2021 (version 3)
  6. Version of Record updated: December 3, 2021 (version 4)

Copyright

© 2021, Torres-Espín et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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  1. Abel Torres-Espín
  2. Jenny Haefeli
  3. Reza Ehsanian
  4. Dolores Torres
  5. Carlos A Almeida
  6. J Russell Huie
  7. Austin Chou
  8. Dmitriy Morozov
  9. Nicole Sanderson
  10. Benjamin Dirlikov
  11. Catherine G Suen
  12. Jessica L Nielson
  13. Nikos Kyritsis
  14. Debra D Hemmerle
  15. Jason F Talbott
  16. Geoffrey T Manley
  17. Sanjay S Dhall
  18. William D Whetstone
  19. Jacqueline C Bresnahan
  20. Michael S Beattie
  21. Stephen L McKenna
  22. Jonathan Z Pan
  23. Adam R Ferguson
  24. The TRACK-SCI Investigators
(2021)
Topological network analysis of patient similarity for precision management of acute blood pressure in spinal cord injury
eLife 10:e68015.
https://doi.org/10.7554/eLife.68015

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