Analysis of the structural organization of the metatarsal bones and toe phalanges of the human foot using anatomical network models

BACKGROUND: The human forefoot, despite its fundamental role in bipedalism, is the least studied part of the foot in most biomechanical and clinical models, where it is often considered a rigid structure. Evolutionary adaptations associated with upright walking have led to a complex morphological structure of the forefoot. Existing concepts of morphological modularity and integration are often limited by the complexity of analyzing multiple relationships. This study suggests solving this problem by applying anatomical network analysis (AnNA) to study the structural organization of the forefoot. AnNA enables formalization of the connections between the components of the foot, revealing patterns of its integration and modularity. AIM: To study the structural organization of the metatarsal bones and toe phalanges of the human foot using AnNA. METHODS: As part of this study, the igraph library in the R programming environment was used to analyze the AnNA network. Modeling and visualization of the network structure were carried out using the Fruchterman–Reingold algorithm, which ensures the optimal placement of nodes. Structural characteristics, including modularity and integration of the AnNA network, were analyzed using the Spinglass algorithm. Osteometric parameters — the length of the metatarsal bones and phalanges of toes I–V of the right foot from 100 middle-aged men — were used as input data for the AnNA analysis. RESULTS: The structural organization of the metatarsal bones and toe phalanges of the human foot consists of several modules: a proximal module (includes metatarsals I–V) and a distal module (includes the phalanges of toes I–V) relative to the longitudinal axis of the foot, and a medial module (includes metatarsals I–III and the phalanges of toes I–III) and a lateral module (includes metatarsals IV–V and the phalanges of toes IV–V) relative to the transverse axis of the foot. Network analysis showed that the distal and medial modules are more complex and less anisomeric than the proximal and lateral modules. The distal module is more complex than the proximal one, while the medial and lateral modules show greater similarity in organizational complexity. Overall, the medial and lateral modules are more similar to each other than are the distal and proximal modules. CONCLUSION: Morphological modularity and integration are organizing principles of the bone architecture of the foot. The structural organization of the metatarsal bones and toe phalanges of the human foot is a system of four modules — a proximal (metatarsal bones) and a distal (toe phalanges) module relative to the longitudinal axis of the foot, and a medial (metatarsals I–III and phalanges of toes I–III) and a lateral (metatarsals IV–V and phalanges of toes IV–V) module relative to the transverse axis of the foot.