An analytical expression for the D.I.P.–P.I.P. flexion interdependence in human fingers

Abstract

Empirical evidence shows that a strong correlation exists between the flexion angles of the distal and proximal interphalangeal(D.I.P., P.I.P.) joints of the human finger. Several authors measured this functional dependence, stating that the interdependence of D.I.P. and P.I.P. flexion is different for healthy individuals and patients displaying pathologies. The purpose of our study is to find an analytical expression for this correlation. Methods: Following closely the anatomical in situ relations, we developed a two-dimensional kinematical model which expresses analytically the D.I.P.–P.I.P. angle correlation. Numerical values for the model were extracted from one healthy and one pathological case data set. Results: The analytical form of the model allows for any P.I.P. angle not only to calculate the corresponding D.I.P. angle, but after first order differentiation with respect to the P.I.P. angle, it also shows the rate of change of the D.I.P. flexion. The model reproduces well the differences in the angular correlation of D.I.P. flexion of the two healthy- pathological data sets. Displaying the rate of change of D.I.P. flexion versus P.I.P. flexion provides an additional, clear-cut discriminatory tool between normal and pathological states. Conclusions: Information on differences between normal and pathological flexion of fingers is more pronounced and easier accessible from the derivatives of the D.I.P.–P.I.P. flexion behaviour than from direct angular correlation data. The analytical form of our model allows one to establish the rate of change of the D.I.P. angles, resulting in a better analysis of the situations at hand.