Fig 1.
Schematic of data representations and computational methods.
(a) The musculoskeletal network was first converted to a bipartite matrix, where 1/0 indicates a present/absent muscle±bone connection. (b) Communities of topologically related muscles are identified by (1) transforming the hypergraph to a muscle±muscle graph, in which each entry encodes the number of common bones of each muscle pair, and (2) subsequently, muscles were broken into communities, in which constituent members connected more densely to other members within their community than to members in other communities. (c) To facilitate perturbations, the musculoskeletal network was physically embedded, such that bones (nodes) are initially placed at their correct anatomical positions. (d) To understand the impact of single muscles on the interconnected system, all nodes linked by a selected hyperedge were perturbed in a fourth spatial dimension.
Table 1.
Muscles with greater and lesser impact than expected in a hypergraph null model.
The muscles on the left side have less impact than expected, given their hyperedge degree: their impacts are more than 1.96 standard deviations below the mean, indicating that they lie outside the 95% confidence interval of the distribution. The muscles on the right side have more impact than expected given their hyperedge degree: their impacts are more than 1.96 standard deviations above the mean, ordered from most to least extreme. This table shows the muscles that had the greatest positive and greatest negative difference in impact, relative to degree-matched controls.
Table 2.
Homunculus categories whose member muscles either all have more impact than expected or all have less impact than expected, compared to null hypergraphs.
Categories on the left are composed entirely of muscles with less impact than expected, compared to degree-matched controls. Categories on the right are composed entirely of muscles with more impact than expected, compared to degree-matched controls.
Table 3.
Homunculus categories and their associated identification numbers.
Table 4.
Muscle injury recovery data.
Table 5.
Primary motor cortex somatotopic representation volume sizes and sources.
Fig 2.
(a) Left: Anatomical drawing highlighting the trapezius. Right: Transformation of the trapezius into a hyperedge (red; degree k = 25), linking 25 nodes (bones) across the head, shoulder, and spine. (b) Adductor pollicis muscle linking 7 bones in the hand. (c) Spatial projection of the hyperedge degree distribution onto the human body. High-degree hyperedges are most heavily concentrated at the core. (d) The musculoskeletal network displayed as a bipartite matrix (1 = connected, 0 otherwise). (e) The hyperedge degree distribution for the musculoskeletal hypergraph, which is significantly different than that expected in a random hypergraph. Data available for (e) at DOI:10.5281/zenodo.1069104.
Fig 3.
Probing musculoskeletal function.
(a) The impact score plotted as a function of the hyperedge degree for a null hypergraph model and the observed musculoskeletal hypergraph. (b) Impact score deviation correlates with muscle recovery time following injury to muscles or muscle groups (F(1,12) = 37.3, R2 = 0.757, p < 0.0001). Shaded areas indicate 95% confidence intervals, and data points are scaled according to the number of muscles included. The plot is numbered as follows, corresponding to Table 4: triceps (1), thumb (2), latissimus dorsi (3), biceps brachii (4), ankle (5), neck (6), jaw (7), shoulder (8), teres major (9), hip (10), eye muscles (11), knee (12), elbow (13), wrist/hand (14). Data available at DOI:10.5281/zenodo.1069104.
Fig 4.
Probing musculoskeletal control.
(a) The primary motor cortex homunculus as constructed by Penfield. (b) Deviation ratio correlates significantly with homuncular topology (F(1,19) = 21.3, R2 = 0.52, p < 0.001), decreasing from medial (area 0) to lateral (area 22). (c) Impact score deviation significantly correlates with motor strip activation volume (F(1,5) = 14.4, R2 = 0.743, p = 0.012). Data points are sized according to the number of muscles required for the particular movement. The plot is numbered as follows, corresponding to Table 5: thumb (1), index finger (2), middle finger (3), hand (4), all fingers (5), wrist (6), elbow (7). (d) Correlation between the spatial ordering of Penfield’s homunculus categories and the linear muscle coordinate from a multidimensional scaling analysis (F(1,268) = 316, R2 = 0.54, p < 0.0001). Data available at DOI:10.5281/zenodo.1069104.