Musculoskeletal Network Analysis for Physiological Data
PhysioMSKNet applies network science to the human musculoskeletal system. It implements hypergraph representations of muscle-bone connections, perturbation-based impact scoring, community detection, cross-modal mapping (EMG, IMU, MoCap), clinical outcome prediction, and neuromechanical coupling analysis. The theoretical foundation follows Murphy et al. (2018) doi:10.1371/journal.pbio.2002811.
The package exports 88 functions organized into 10 functional categories, providing a comprehensive toolkit for translational musculoskeletal research spanning biomechanics, rehabilitation, and neuroscience.
Features
Hypergraph Representation
The MSKHypergraph class models the musculoskeletal system as a hypergraph where bones are vertices and muscles are hyperedges connecting their origin and insertion sites. This representation preserves the many-to-many topology lost in standard graph projections.
| Function | Description |
|---|---|
MSKHypergraph() |
Construct a hypergraph from an incidence matrix |
vertexDegree() |
Number of muscles attached to each bone |
hyperedgeDegree() |
Number of bones spanned by each muscle |
projectMuscleGraph() |
Project to muscle co-activation graph |
projectBoneGraph() |
Project to bone adjacency graph |
mskNullHypergraph() |
Generate a degree-preserving null model |
mskNullEnsemble() |
Generate an ensemble of null models |
loadIncidenceMatrix() |
Load incidence matrix from file |
loadMSKData() |
Load bundled MSK dataset |
loadMuscleMetadata() |
Load bundled muscle metadata |
loadValidationData() |
Load validation dataset |
Network Metrics
| Function | Description |
|---|---|
mskNetworkMetrics() |
Compute all metrics in one call |
mskBetweenness() |
Betweenness centrality |
mskCloseness() |
Closeness centrality |
degreeDistribution() |
Degree distribution analysis |
mskModularity() |
Network modularity score |
mskShortestPaths() |
Shortest path computation |
Physical Simulation
| Function | Description |
|---|---|
mskSimulate() |
Damped harmonic oscillator simulation |
mskReproducePaper() |
Reproduce Murphy et al. (2018) results |
Perturbation-Based Impact Analysis
| Function | Description |
|---|---|
mskImpactScore() |
Perturbation impact for a single vertex |
mskImpactScoreAll() |
Impact scores for all vertices |
mskImpactDeviation() |
Deviation from null model expectation |
mskImpactRecoveryModel() |
Recovery dynamics after perturbation |
Community Detection
| Function | Description |
|---|---|
mskCommunityDetect() |
Detect musculoskeletal communities |
mskConsensusPartition() |
Consensus partition from multiple runs |
mskCommunityProfile() |
Detailed profile of each community |
mskZRand() |
z-score of the Rand index for partition comparison |
Cross-Modal Mapping
Bridge musculoskeletal network topology to physiological signals from EMG, IMU, and motion capture.
EMG Integration:
| Function | Description |
|---|---|
emgToMSKMapping() |
Map EMG channels to MSK network nodes |
emgCommunityCompare() |
Compare EMG synergies to MSK communities |
emgMSKEnrichment() |
Test enrichment of EMG patterns in MSK modules |
emgStructuralCoherence() |
Coherence between EMG and structural topology |
IMU Integration:
| Function | Description |
|---|---|
imuToMSKMapping() |
Map IMU sensors to MSK network nodes |
imuCommunityDynamics() |
Time-varying community structure from IMU |
imuImpactPrediction() |
Predict impact scores from IMU signals |
imuNetworkKinematics() |
Network-informed kinematic analysis |
MoCap Integration:
| Function | Description |
|---|---|
mocapToMSKMapping() |
Map motion capture markers to MSK network |
mocapCommunityDynamics() |
Time-varying community structure from MoCap |
mocapImpactPrediction() |
Predict impact scores from MoCap data |
mocapNetworkKinematics() |
Network-informed kinematic analysis |
Clinical Prediction
| Function | Description |
|---|---|
mskClinicalPredictor() |
Build predictive model from network features |
mskPredictFunctionalOutcome() |
Predict functional outcome scores |
mskDetectResponderStatus() |
Classify responders vs. non-responders |
mskDetectCompensation() |
Detect compensatory movement patterns |
mskDetectRecoveryPlateau() |
Identify recovery plateaus |
mskClinicalEvidence() |
Generate clinical evidence summary |
mskInjuryRiskProfile() |
Compute injury risk from network topology |
mskFunctionalMilestones() |
Track functional milestones |
Compensation Analysis
| Function | Description |
|---|---|
mskCompensationNetwork() |
Build compensation network from deviations |
mskCompensationSummary() |
Summarize compensation patterns |
mskCompensationEvolution() |
Track compensation changes over time |
mskCompensationRiskScore() |
Quantify compensation-related risk |
Recovery and Rehabilitation
| Function | Description |
|---|---|
mskOutcomeReport() |
Generate outcome report |
mskOutcomeSummary() |
Concise outcome summary |
mskOutcomeConfidenceInterval() |
Confidence intervals for outcome metrics |
mskRecoveryTrajectoryFit() |
Fit recovery trajectory models |
mskRecoveryTimeline() |
Projected recovery timeline |
mskLongitudinalTracker() |
Track network metrics over time |
mskMinimalDetectableChange() |
Compute MDC for network metrics |
mskRehabProtocol() |
Generate network-informed rehab protocol |
mskAdaptProtocol() |
Adapt protocol based on progress data |
mskReassess() |
Reassess patient status |
mskCoordinationQualityScore() |
Coordination quality from network metrics |
Neuromechanics Bridge
| Function | Description |
|---|---|
neuromechSummary() |
Integrated neuromechanical summary |
neuromechMuscleSynergy() |
Muscle synergy extraction |
neuromechDirectionalCoupling() |
Directional coupling between signals |
neuromechCorticomuscularCoupling() |
Corticomuscular coherence |
neuromechJointTorque() |
Joint torque estimation |
neuromechMotorDriveTopography() |
Spatial motor drive mapping |
neuromechElectromechanicalDelay() |
EMD estimation |
neuromechIntegratedVulnerability() |
Multi-factor vulnerability index |
mskNeuralAdaptationIndex() |
Neural adaptation quantification |
mskSynergyChangeIndex() |
Synergy change over time |
Annotation and Knowledge Graph
| Function | Description |
|---|---|
mskAnnotate() |
Annotate network nodes with anatomical metadata |
mskEnrichKG() |
Knowledge graph enrichment analysis |
mskKGSummary() |
Knowledge graph summary for a network |
mskPathwayQuery() |
Query anatomical pathways |
mskHomuncCorrelation() |
Correlation with somatotopic organization |
OpenSim Integration
| Function | Description |
|---|---|
opensimToMSKHypergraph() |
Convert OpenSim model to MSK hypergraph |
opensimNetworkAnalysis() |
Full network analysis from an OpenSim model |
opensimForceToImpact() |
Map OpenSim muscle forces to impact scores |
opensimCompareModels() |
Compare network topology across models |
Visualization
| Function | Description |
|---|---|
plotMSKNetwork() |
Network graph visualization |
plotDegreeDistribution() |
Degree distribution plot |
plotHomunculus() |
Body map with network overlay |
plotCommunityStructure() |
Community detection results |
plotImpactVsDegree() |
Impact score vs. degree scatter |
plotImpactVsRecovery() |
Impact vs. recovery time |
Statistics
| Function | Description |
|---|---|
mskRobustRegression() |
Robust regression for network predictors |
Installation
From R-universe
# the containers build on Bioconductor, so its repositories are needed too
install.packages("BiocManager", repos = "https://cloud.r-project.org")
install.packages("PhysioMSKNet",
repos = c("https://x-biosignal.r-universe.dev", BiocManager::repositories()))Quick Start
library(PhysioMSKNet)
# --- Build the musculoskeletal hypergraph from bundled data ---
# Bones are vertices; muscles are hyperedges joining their attachment sites.
inc <- loadIncidenceMatrix()
hg <- MSKHypergraph(inc)
hg
# --- Degrees and structural network metrics ---
head(sort(vertexDegree(hg), decreasing = TRUE)) # most-connected bones
metrics <- mskNetworkMetrics(hg)
head(sort(metrics$degree, decreasing = TRUE))
metrics$density
# --- Project the hypergraph to muscle and bone graphs ---
muscle_graph <- projectMuscleGraph(hg)
bone_graph <- projectBoneGraph(hg)
dim(muscle_graph)
# --- Perturbation-based impact scoring (damped harmonic oscillator model) ---
sim <- mskSimulate(hg)
probe <- c(1, 5, 10)
impact <- vapply(probe, function(i) mskImpactScore(sim, muscle_index = i), numeric(1))
names(impact) <- hg$muscle_names[probe]
impact
# --- Degree distribution ---
plotDegreeDistribution(hg)Community detection, betweenness centrality, and network plotting use the optional igraph package; the guard keeps the block inert when it is absent:
# install.packages("igraph")
if (requireNamespace("igraph", quietly = TRUE)) {
comm <- mskCommunityDetect(hg)
comm$n_communities
comm$modularity
bw <- mskBetweenness(hg)
head(sort(bw, decreasing = TRUE), 3)
plotMSKNetwork(hg, community = comm)
}Cross-modal mapping (emgToMSKMapping(), mocapToMSKMapping()), clinical prediction (mskClinicalPredictor()), and the neuromechanics bridge (neuromechMuscleSynergy(), neuromechSummary()) take physiological signal inputs; see the function help pages for worked examples.
Dependencies
- R (>= 4.2)
- Matrix (sparse matrix operations)
Optional (Suggests)
| Package | Purpose |
|---|---|
| igraph | Graph algorithms for advanced network analysis |
| MASS | Robust statistical methods |
| ggplot2 | Enhanced visualization |
| readxl | Excel data import |
| xml2 | OpenSim XML parsing |
| PhysioAnnotationHub | Anatomical annotation and knowledge graph |
| PhysioCrossModal | Cross-modal signal integration |
| PhysioEMG | EMG signal processing |
| PhysioMoCap | Motion capture data handling |
| PhysioOpenSim | Native OpenSim model access |
| SummarizedExperiment | Bioconductor data containers |
Theoretical Background
The musculoskeletal network model is based on:
Murphy AC, Muldoon SF, Baker D, Lastowka A, Bennett B, Yang M, Bhatt P, Bassett DS (2018). “Structure, function, and control of the human musculoskeletal network.” PLOS Biology, 16(1): e2002811. doi:10.1371/journal.pbio.2002811
The human musculoskeletal system is modeled as a hypergraph where bones are vertices and muscles are hyperedges connecting their attachment sites. This representation enables network-theoretic analysis of structural vulnerability, functional modularity, and injury impact propagation.
Ecosystem
PhysioMSKNet is part of the PhysioExperiment ecosystem, a suite of R packages for multi-modal physiological signal analysis.
Related packages:
| Package | Role |
|---|---|
| PhysioExperiment | Core data model and signal processing |
| PhysioOpenSim | Native OpenSim C++ integration |
| PhysioAnnotationHub | Anatomical knowledge graph |
| PhysioMoCap | Motion capture I/O and analysis |
| PhysioEMG | EMG signal processing |
Governance & support
Part of the Physio ecosystem. Community and policy documents live in the umbrella repository: