Fig 1.
Illustration of the model and local coordinate systems.
(A) and (B) Musculotendinous paths from anatomical origins to insertions on the skeleton are illustrated with red lines with selected labels. (C) Coordinate systems for each segment are illustrated with the color-coded cartesian exes in red, yellow, and green for x-, y- and z-axes respectively. Euler angles around these axes represent joint angles. The illustrated posture of the model corresponds to all joint angels at zero. The local coordinate systems are shown only for thumb and index finger. The coordinate systems of the other digits follow the orientation of the coordinate systems for the index finger.
Table 1.
The abbreviations of muscles included in the analyses.
Fig 2.
The difference between r2 values for the correlations between muscle lengths as a function of the number of selected postures.
Error bars show standard deviations around the mean.
Fig 3.
Examples of muscle lengths for the pronator teres, a single 2-DOF muscle originating on the humerus and attaching on the radius, in two subjects.
The data points (circles) correspond to muscle lengths throughout the physiological range of motion for each DOF.
Table 2.
The summary of anthropometric measurements.
All distance measurements, unless indicated otherwise in brackets, were made between the estimated centers of joint rotation.
Fig 4.
Examples of the correlations between muscle lengths in a single subject.
Only significant correlations are plotted (p < 0.05). (A) Pearson correlation coefficient (r) between muscle lengths of all muscle pairs. Blue colors indicate negative correlations; yellow colors indicate positive correlations. (B) Histogram of r-values for each subject across all muscle pairs. The bar plots are binned with 0.2 increments, and only significant values were included in the analysis.
Fig 5.
Hierarchical clustering methodology and examples for two subjects.
(A) Geometric illustration of heterogenous variance explained (HVE). HVE distance is determined by the correlations of musculotendon length between muscle pairs determined by the equation in (B). (B) The equation for calculating HVE distance. The negative regressions (r-) indicate opposite or antagonistic actions of muscle pairs, when the positive ones (r+) correspond to the synergistic or agonistic actions. Insert shows a histogram of HVE values for one subject across all muscle pairs. (C) Examples of hierarchical clustering for individual subjects. Clustering across all muscles is shown in the top two polar dendrograms. The bottom plot shows clustering across only the distal muscles for one of the subjects. Lines emanating from the center indicate the distance between muscle clusters calculated from HVE. The main agonist-antagonist division can be established using a high clustering threshold (2 clusters with dark red and dark blue lines), and further subdivisions are revealed by the progressive lowering of the threshold. Example matching clusters are marked by outside brackets with * or ^.
Fig 6.
Reliability of clustering across subjects.
(A) The average number of unclassified muscles is shown as a function of the number of clusters. Each colored line corresponds to the level of stringency for the variability in classification across subjects, e.g. 100% stringency corresponds to the same classification in all subjects. The right panel shows the same values normalized to the average number of muscles in all clusters. (B) The same analysis as in A for distal muscles only. Vertical black arrow indicates the nontrivial minimum for the number of clusters (11 clusters for all and 6 clusters for distal muscles), which represents the most reliable number of muscle clusters.
Fig 7.
Mean hierarchical clustering across all subjects.
The polar dendrogram illustrates hierarchical clustering as described in Fig 5C. Inserts along the perimeter illustrate the directions of motion (green arrows) produced by the activation of muscles in the model shown in Fig 1. Only muscles that belong to the corresponding cluster are shown on each insert.