A “Thermodynamic” Model of Central Commands for Two-Joint Arm Movements in Humans

Previously, we proposed a “thermodynamic” model (T-model) in an attempt to analyze temporal dynamics of the central commands (CCs) coming to the muscles in the course of forelimb movements in humans. The model used electromyography (EMG) data and was tested on a simplified geometric simulation of a human arm with a fixed shoulder joint in the case of parafrontal hand movements under the action of tangential loads. The T-model is based on equations that determine the relationship between infinitesimal changes in the muscle force and length, which, by analogy with the principles of classic thermodynamics, are taken as exact differentials. Thus, our study represents the further development of the T-model, taking into account the CCs coming to the elbow joint muscles, belonging to the subject with known biomechanical parameters of his arm identified via magnetic resonance imaging (MRI). When considering circular planar movements of the subject’s hand against the background of tangential loads, symmetrical sinusoidal force waves develop in the muscles, and the CC waves acquire asymmetric shapes. The proposed method of the equalization/normalization procedure in the T-model allows us to formally consider the inverse transformation of the symmetric force waves into asymmetric CCs, which are the root cause of force generation. This approach was found to be quite effective in describing hysteresis differences of the CCs related to oppositely directed test movements. To analyze these differences using the T-model, we propose a method using multiplicative or additive correction terms to be applied to the muscle stiffness, or force velocity, respectively. The further development of the T-model is discussed concerning the real experimental practice.