Structure, function, and control of the human musculoskeletal network

Abstract

The human body is a complex organism, the gross mechanical properties of which are enabled by an interconnected musculoskeletal network controlled by the nervous system. The nature of musculoskeletal interconnection facilitates stability, voluntary movement, and robustness to injury. However, a fundamental understanding of this network and its control by neural systems has remained elusive. Here we address this gap in knowledge by utilizing medical databases and mathematical modeling to reveal the organizational structure, predicted function, and neural control of the musculoskeletal system. We constructed a highly simplified whole-body musculoskeletal network in which single muscles connect to multiple bones via both origin and insertion points. We demonstrated that, using this simplified model, a muscle's role in this network could offer a theoretical prediction of the susceptibility of surrounding components to secondary injury. Finally, we illustrated that sets of muscles cluster into network communities that mimic the organization of control modules in primary motor cortex. This novel formalism for describing interactions between the muscular and skeletal systems serves as a foundation to develop and test therapeutic responses to injury, inspiring future advances in clinical treatments.

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.

Fig 2. Hypergraph structure.

(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.