A bone-wise approach for modeling the human hind-midfoot. Part I: kinematics

Multi-line segment foot models propose a triple-line segmentation into hindfoot, midfoot and forefoot; oftentimes, the midfoot is regarded as a rigid line segment. We here begin our presentation of a new model of the hind-midfoot bone complex, regarded as a system of rigid blocks, the bones, with perfect mutual constraints, the bone joints. Firstly, we give a qualitative description of the deformations of the foot per se , as if it were severed from the body or made to move passively in vivo , the talocrural joint being kept locked; the descriptive capabilities of our model are illustrated by progressively locking more and more bone joints. Secondly, we derive two interdependent systems of nonlinear algebraic equations which render the geometrical and kinematic complexity of the hind-midfoot complex: one system locates individual bones in space, the other selects all location sets classifiable as unbroken kinematic chains, that is to say, all admissible hind-midfoot configurations. We define the relative multi-parameter configuration manifold, indicate how to inspect it hierarchically, and furnish a representative example amenable to geometrical description. The accompanying dataset document features graphical information and configurational data helping to motivate our modelling choices, as well as analytical information concerning certain mathematical developments we here omit.