A mathematical model of the human thigh and its connection with the torso

Abstract

The estimation of body segment parameters is important for the kinetic and dynamic analysis of human motion. For studying these an accurate modeling of the individual segments of the body is required. One specific problem in that respect that still lacks a satisfactory solution is to model the thigh-torso connection. The point is that one normally models the torso and the thigh with relatively simple geometrical bodies that do not tailor continuously into each other. One shall also take into account the specific geometric properties describing the connections of both. Finally, the modeling shall be done in such a way that the mass of the torso as well as of the thigh is reproduced as closely as possible. The purpose of this work is to improve the mathematical modeling of the human thigh of the Bulgarian males[1], taking into account that the segment is dissected from the torso with a plane passing through the anterior superior iliac spine at an angle of 37° to the midsagittal plane [2]. In our previous research, the thigh was modeled as a frustum of a cone. In the current study, the thigh is modeled with the geometric body being a combination of three elements: i) a frustum of the circular cone on top of which is placed ii) a combination of two elements described in details in the main text cut with a plane making an angle of 53° with respect to its base. This combination of two elements extends in-between anthropometric points omphalion - iliospinale. Using the mathematical model suggested, after deriving the corresponding analytical expressions needed, we calculate analytically and estimate numerically the mass- inertial characteristics of the human body segments: the volume, the mass, center of mass, and the principal moments of inertia. We present a comparison between the results obtained within this model with our previous results reported in [1], as well as with other data for Caucasian reported in the literature. The results obtained and the procedure suggested in the current work allows one to claim that more realistic modeling of the shape of the human thigh is proposed. The model can be used when one needs such mass-inertial parameters in problems appearing in rehabilitation, medicine (orthopedics and traumatology), sports, ergonomics, etc. The last can be done not only for the average Bulgarian male, as calculated in the article, but also for any individual, provided that the anthropometric easily measurable data for that individual are known.