Topological data analysis for discovery in preclinical spinal cord injury and traumatic brain injury methods
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TDA reveals forelimb outcomes most sensitive to cervical SCI
To test the application of TDA combined with SVD to SCI, we assembled raw data from several common SCI models, including hemisections, weight-drop and force-driven hemi-contusion injuries to the cervical spinal cord (;, dropdown). Grooming behaviour and paw preference in a cylinder reveal graded levels of recovery ( ), that map to lesion size, tissue sparing and deformation (;, dropdown). However, measures of open-field locomotion for both forelimb (;, dropdown) and hindlimb (, dropdown) do not show much variability in recovery of function. In the syndromic topology, grooming function has the strongest visual mapping to lesion size (;, dropdown), whereas recovery of paw preference in the cylinder shows a stronger visual mapping with white matter sparing. Little to no variability is seen in the hindlimb open field (, dropdown), most likely because it was designed to measure h...
Visually guided data exploration uncovers drug effects
We identified the nodes within the topology that stood out as having poor functional recovery on grooming and forelimb open field (, circles), despite nodes in this region showing less-severe injuries based on the degree biomechanical tissue deformation (, circle). This sub-network was also significantly enriched for 12.5 mm weight-drop contusions, yet we noticed that not all injuries of this type performed so poorly. To probe factors that might contribute to abnormally bad function, we drilled into this effect. We compared subjects in these nodes with 12.5 mm contusions that performed well on forelimb open field using a ranked Kolmogorov-Smirnov (KS) test. The ranked KS test is analogous to a gene-set enrichment analysis here applied to identify predictor and outcome metric sets (rather than gene sets) that are most sensitive to group conditions (hypothesis testin...
Cross-validation and confirmation of hypertension hypothesis
The data-driven discovery of hypertension as a major predictor of SCI recovery from semi-structured big-data could potentially represent a 'capitalization on chance'. To explicitly rule this out, we performed two waves of additional analyses. First, we independently cross-validated the TDA-based data-driven discovery, by curating an additional data set from subjects with less-severe injuries (12.5 mm) from a separate round of the MASCIS trial (1994-1995, N =154) ( ) queried from the VISION-SCI repository. Nodes within the network that received thoracic 12.5 mm weight-drop injuries showed distinct subpopulations with significant differences in BBB locomotor recovery (, circles, P =0.01). KS testing of the good versus bad recovery subgroups within this network confirmed that hypertensive events (maximum MAP) during surgery predicted lower locomotor recovery in...
Cross-validation and confirmation of hypertension hypothesis
Second, we explicitly tested the formal hypothesis that perioperative hypertension predicts long-term outcome using a repeated measures general linear model (GLM) on the 1996 and the 1994-1995 data sets. Explicit hypothesis testing separately confirmed the hypothesis that perioperative MAP (covariate) predicted poorer functional recovery of BBB (dependent) between 1 and 6 weeks post injury (repeated measure). In both data sets, post-injury MAP (15 min after SCI) significantly predicted the main effect of recovery of BBB locomotion following injury (1996, F(5,20)=3.701, P =0.02; 1994-1995, F(5,110)=2.671, P =0.03).
TDA-based data-driven discovery versus traditional tools
The fact that TDA-guided discovery uncovered a novel finding that was hiding in plain sight in 20-year-old data, provides strong potential support for this approach. However, we wondered whether a similar set of results could have been revealed using traditional analytics. To test this, we pooled all data from MASCIS ( N =334) in the VISION-SCI repository and performed side-by-side bivariate correlational analysis and TDA ( ). Pearson correlation confirmation of the significant inverse correlation between elevated perioperative blood pressure and BBB functional recovery was performed by plotting a bivariate correlation matrix for MASCIS OSU trial subjects ( N =334) for all measures of survival, histology, perioperative vitals and blood gases, functional recovery, bladder health and weight over 1-6 weeks post SCI ( ). Blood pressure measures showing the most significant inverse c...
TDA-based data-driven discovery versus traditional tools
Although visualization and interpretation of the complex interactions between all the variables in this data set can, in theory, be achieved by simple correlation, this approach does not identify clusters of subjects that are most sensitive to these interactions across the full spectrum of variables. Navigating the same data set with TDA creates a syndromic map of all subjects based on the full network of correlations, enabling rapid comparative hypothesis testing about factors such as injury condition, recovery rate, autonomic factors or even gender differences (,, dropdown). All outcomes measured over time, including BBB locomotion, bladder function, weight, and perioperative blood pressure and blood gases were mapped onto the network for each time point (, dropdown). Additional mapping of enrichment for gender differences in the network revealed that subjects within the nodes th...
Methods
TDA was used to rapidly analyse and visualize clustering of individuals based on their similarity across hundreds of variables simultaneously ( ). TDA is an adaptation of the methods of topology, the mathematical discipline which studies robust methods of measuring and representing shape, to create compact visual representations of high-dimensional data sets. This is performed automatically within the software, by deploying an ensemble machine learning algorithm that iterates through overlapping subject bins of different sizes that resample the metric space (with replacement), thereby using a combination of the metric location and similarity of subjects in the network topology. After performing millions of iterations, the algorithm returns the most stable, consensus vote for the resulting 'golden network' (Reeb graph), representing the multidimensional data shape. The applicat...
TDA applied to graded unilateral cervical SCI in rats
Variables that were analysed included all endpoint data, excluding predictor information about categorical injury condition, gender or treatment. Endpoint data used for,, include a standardized measure of tissue compression for injury biomechanics across different contusion devices, terminal tissue pathology measured by lesion size and white/grey matter and MN sparing, and 6-week time-course data points for measures of daily or weekly weight change, CatWalk, grooming, paw preference in the cylinder, BBB hindlimb locomotion, a 4-point measure of forelimb locomotion and the IBB scale for object manipulation. Topologies were colour coded for each injury model, PC1 and PC2 distributions, histopathology and a few key examples of functional outcomes (grooming, paw preference, forelimb and hindlimb open field) at 7, 21 and 42 DPL. These were exported from the cloud into an HTML viewer...
Measurement outputs
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Gait recovery and locomotor function
- Raw artifact
- Per-run gait capture with paw placement, timing, and stride features for each animal
- Processed artifact
- Cleaned gait metrics table and recovery trend summary across timepoints
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- Group comparisons of gait indices, stride metrics, or recovery curves
Analysis plan
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Acquisition
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inferred from protocolPreprocessing / cleaning
Review raw outputs for quality, remove unusable captures, and organize the data into a comparison-ready table or image set.
inferred from protocolScoring or quantification
Quantify the primary readouts for this experiment: Gait recovery and locomotor function.
from paperStatistical comparison
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inferred from protocolReporting output
Report representative outputs alongside summary comparisons for Gait recovery and locomotor function.
inferred from protocolSource and audit
What supports the facts on this page?
Evidence quotes (8)
To test the application of TDA combined with SVD to SCI, we assembled raw data from several common SCI models, including hemisections, weight-drop and force-driven hemi-contusion injuries to the cervical spinal cord (;, dropdown). Grooming behaviour and paw preference in a cylinder reveal graded levels of recovery ( ), that map to lesion size, tissue sparing and deformation (;, dropdown). However, measures of open-field locomotion for both forelimb (;, dropdown) and hindlimb (, dropdown) do not show much variability in recovery of function. In the syndromic topology, grooming function has the strongest visual mapping to lesion size (;, dropdown), whereas recovery of paw preference in the cylinder shows a stronger visual mapping with white matter sparing. Little to no variability is seen in the hindlimb open field (, dropdown), most likely because it was designed to measure hindlimb coordination following bilateral thoracic injuries, whereas these subjects received various grades of unilateral cervical injuries. There was some variance in the measure of forelimb open field for the most severe injuries (, circle), however, it did not map to the full range of lesion pat...
We identified the nodes within the topology that stood out as having poor functional recovery on grooming and forelimb open field (, circles), despite nodes in this region showing less-severe injuries based on the degree biomechanical tissue deformation (, circle). This sub-network was also significantly enriched for 12.5 mm weight-drop contusions, yet we noticed that not all injuries of this type performed so poorly. To probe factors that might contribute to abnormally bad function, we drilled into this effect. We compared subjects in these nodes with 12.5 mm contusions that performed well on forelimb open field using a ranked Kolmogorov-Smirnov (KS) test. The ranked KS test is analogous to a gene-set enrichment analysis here applied to identify predictor and outcome metric sets (rather than gene sets) that are most sensitive to group conditions (hypothesis testing). KS tests between nodes within the high and low functioning groups uncovered an external predictor (not included in the generation of the network) that could account for functional differences: subjects were part of a preclinical trial of two anti-inflammatory drugs: minocycline and MP and no-dr...
The data-driven discovery of hypertension as a major predictor of SCI recovery from semi-structured big-data could potentially represent a 'capitalization on chance'. To explicitly rule this out, we performed two waves of additional analyses. First, we independently cross-validated the TDA-based data-driven discovery, by curating an additional data set from subjects with less-severe injuries (12.5 mm) from a separate round of the MASCIS trial (1994-1995, N =154) ( ) queried from the VISION-SCI repository. Nodes within the network that received thoracic 12.5 mm weight-drop injuries showed distinct subpopulations with significant differences in BBB locomotor recovery (, circles, P =0.01). KS testing of the good versus bad recovery subgroups within this network confirmed that hypertensive events (maximum MAP) during surgery predicted lower locomotor recovery in the chronic phase (KS=0.6, P =0.0009).
Second, we explicitly tested the formal hypothesis that perioperative hypertension predicts long-term outcome using a repeated measures general linear model (GLM) on the 1996 and the 1994-1995 data sets. Explicit hypothesis testing separately confirmed the hypothesis that perioperative MAP (covariate) predicted poorer functional recovery of BBB (dependent) between 1 and 6 weeks post injury (repeated measure). In both data sets, post-injury MAP (15 min after SCI) significantly predicted the main effect of recovery of BBB locomotion following injury (1996, F(5,20)=3.701, P =0.02; 1994-1995, F(5,110)=2.671, P =0.03).
The fact that TDA-guided discovery uncovered a novel finding that was hiding in plain sight in 20-year-old data, provides strong potential support for this approach. However, we wondered whether a similar set of results could have been revealed using traditional analytics. To test this, we pooled all data from MASCIS ( N =334) in the VISION-SCI repository and performed side-by-side bivariate correlational analysis and TDA ( ). Pearson correlation confirmation of the significant inverse correlation between elevated perioperative blood pressure and BBB functional recovery was performed by plotting a bivariate correlation matrix for MASCIS OSU trial subjects ( N =334) for all measures of survival, histology, perioperative vitals and blood gases, functional recovery, bladder health and weight over 1-6 weeks post SCI ( ). Blood pressure measures showing the most significant inverse correlations to BBB recovery were confirmed, with elevated diastolic blood pressure at the time of injury, showing the most significant negative correlations at multiple time points (3-6 weeks), with MAP and systolic blood pressure only showing a significant correlation to BBB deficits at 5 wee...
Although visualization and interpretation of the complex interactions between all the variables in this data set can, in theory, be achieved by simple correlation, this approach does not identify clusters of subjects that are most sensitive to these interactions across the full spectrum of variables. Navigating the same data set with TDA creates a syndromic map of all subjects based on the full network of correlations, enabling rapid comparative hypothesis testing about factors such as injury condition, recovery rate, autonomic factors or even gender differences (,, dropdown). All outcomes measured over time, including BBB locomotion, bladder function, weight, and perioperative blood pressure and blood gases were mapped onto the network for each time point (, dropdown). Additional mapping of enrichment for gender differences in the network revealed that subjects within the nodes that showed the strongest relationship between perioperative hypertension and BBB recovery were mostly males. Due to bladder complications being more pronounced in males following SCI, and the strong correlation between bladder function and health and recovery of locomotion, males may be more sensiti...
TDA was used to rapidly analyse and visualize clustering of individuals based on their similarity across hundreds of variables simultaneously ( ). TDA is an adaptation of the methods of topology, the mathematical discipline which studies robust methods of measuring and representing shape, to create compact visual representations of high-dimensional data sets. This is performed automatically within the software, by deploying an ensemble machine learning algorithm that iterates through overlapping subject bins of different sizes that resample the metric space (with replacement), thereby using a combination of the metric location and similarity of subjects in the network topology. After performing millions of iterations, the algorithm returns the most stable, consensus vote for the resulting 'golden network' (Reeb graph), representing the multidimensional data shape. The application of this method to our data sets creates clusters of subjects which appear as nodes (points) and relations among clusters are represented as interconnections ('edges' or lines) between the nodes ( ). Once the topological network is developed, rapid exploration of the full neurotrauma syndro...
Variables that were analysed included all endpoint data, excluding predictor information about categorical injury condition, gender or treatment. Endpoint data used for,, include a standardized measure of tissue compression for injury biomechanics across different contusion devices, terminal tissue pathology measured by lesion size and white/grey matter and MN sparing, and 6-week time-course data points for measures of daily or weekly weight change, CatWalk, grooming, paw preference in the cylinder, BBB hindlimb locomotion, a 4-point measure of forelimb locomotion and the IBB scale for object manipulation. Topologies were colour coded for each injury model, PC1 and PC2 distributions, histopathology and a few key examples of functional outcomes (grooming, paw preference, forelimb and hindlimb open field) at 7, 21 and 42 DPL. These were exported from the cloud into an HTML viewer to monitor recovery of each outcome over time in relation to injury model and tissue pathology (Supplementary Software 2, dropdown). Heat maps for the colour schemes of the flares represent the range of highest values (red) to lowest values (blue) for each respective outcome being visualized (for ex...
Machine-readable layer
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