Indices of nonlinearity in finger force interaction.

Abstract

Experiments with force production by subsets of fingers within the human hand have shown that finger interaction may be significantly nonlinear. In particular, this nonlinearity is reflected in the phenomenon of force deficit, a drop of the peak force of a finger when several fingers act simultaneously. We describe nonlinear effects in force relations within finger pairs, triplets, etc. Finger forces are represented as the sums of components resulting from force interactions within all subsets of the explicitly involved (master) fingers. The values of these components computed at extreme values of control signals, zero and unity, are taken as indices of such "elementary" force interactions. Indices of the first order reflect purposeful force production by a single master finger and its effects on forces produced by other fingers (enslaving). Indices of the second order reflect additional influences from pairs of simultaneously recruited master fingers, etc. Force interaction indices were computed based on finger forces measured in earlier experiments. Signs of indices alternated with their order, being positive for the indices of the first order (enslaving), negative for the indices of the second order (force deficit), positive for the indices of the third order, and mostly negative for the indices of the fourth order. Indices of the third and fourth orders reflect phenomena of force interaction not reported earlier. The study emphasizes the importance of nonlinear interactions among finger forces and introduces a set of independent indices that can be used to quantify such interactions in different subpopulations and their possible changes with practice and/or rehabilitation of the hand function.