Modeling investigation of learning a fast elbow flexion in the horizontal plane--prediction of muscle forces and motor units action.

Experimental investigation of practicing a dynamic, goal-directed movement reveals significant changes in kinematics. Modeling can provide insight into the alterations in muscle activity, associated with the kinematic adaptations, and reveal the potential motor unit (MU) firing patterns that underlie those changes. In this paper, a previously developed muscle model and software (Raikova and Aladjov, Journal of Biomechanics, 35, 2002) have been used to investigate changes in MU control, while practicing fast elbow flexion to a target in the horizontal plane. The first trial (before practice) and the last trial (after extensive practice) of two subjects have been simulated. The inputs for the simulation were the calculated external moments at the elbow joint. The external moments were countered by the action of three flexor muscles and two extensor ones. The muscles have been modeled as a mixture of MUs of different types. The software has chosen the MU firing times necessary to accomplish the movement. The muscle forces and MUs firing statistics were then calculated. Three hypotheses were tested and confirmed: (1) peak muscle forces and antagonist co-contraction increase during training; (2) there is an increase in the firing frequency and the synchronization between MUs; and (3) the recruitment of fast-twitch MUs dominates the action.

Analysis of the unfused tetanus course in fast motor units of the rat medial gastrocnemius muscle.

The course of unfused tetani with the sag effect in fast motor units of rat medial gastrocnemius was studied. The analysis of the course of successive contractions within these tetani showed that the high peak force at the beginning of tetanus before the sag resulted from temporary, very efficient sum mation of contractions at this phase, both in FF (fast fatigable) and FR (fast resistant to fatigue) units. The process of summation developed in spite of parallel shortening of the contraction and relaxation. The peak of tetanus force was visible on the average at the 2nd contraction in FF units and at the 5th contraction in FR units. After the tetanus peak the process of the efficient summation was completed and the force decreased what was visible as a sag. In the following part of the tetanus, mainly in FF units, the potentiation occurred and the force of successive contractions increased. The rise of force was visible in spite of shortening of the contraction time and was due to prolongation of the relaxation in this part of the tetanus. These observations indicated that the processes of the summation of successive contractions before sag and during the potentiation underwent different mechanisms discussed in this paper. Considerable release of Ca2+ ions from the sarcoplasmic reticulum was proposed as a possible mechanism responsible for a very efficient summation at the beginning of the tetanus whereas phosphorylation of regulatory light chain of myosin (RLC) in muscle fibers was considered as the reason of potentiation. Moreover, the present analysis revealed that previously found differences in tetani profiles between FF and FR units resulted from faster development of described changes in the course of contractions summating into the tetanus in FF motor units.

Comparison between two muscle models under dynamic conditions.

One fundamental problem when trying to calculate the force developed by one muscle during a motor task is the muscle model. Usually, one control signal is juxtaposed to one musclotendon unit. The question is how is this signal connected to the activation of the motor units (MUs) that compose the muscle and fire differently. The aim of the paper is to compare a Hill-type muscle model to a model composed of MUs. A fast elbow flexion performed by only one muscle is considered. The activation necessary for performing the motion and the corresponding frequencies are calculated for cases of fast and slow muscles using Hill-type model. Then the muscle is modelled as a mixture of [774 MUs] with uniformly distributed twitch parameters. Using MotCo software the moments of impulsation of all MUs and their mechanical responses are predicted. The activation characteristics obtained by the two muscle models are compared. It is concluded that there are two essential parameters for proper muscle modelling: the lead-time and the MUs composition.

Simulation of the motor units control during a fast elbow flexion in the sagittal plane.

The fact that muscles are composed of different Motor Units (MUs) is often neglected when investigating motor control by macro models of human musculo-skeletal-joint systems. Each muscle is associated with one control signal. This simplification leads to difficulties when mechanical and electrical manifestations of the muscle activity are juxtaposed. That is why a new approach for muscle modelling was recently proposed (Journal of Biomechanics 2002;35:1123-1135). It is based on MUs twitches and a Hierarchical Genetic Algorithm (HGA) is implemented for choosing the moments of activation of the individual MUs, thus simulating the control of the nervous system. Its basic benefit is obtaining the complete information about the mechanical and activation behaviour of all MUs, respectively muscles, during the whole motion. Its possibilities are demonstrated when simulating fast elbow flexion. Three flexor and two extensor muscles, each consisting of approximately real number of different types of MUs, are modelled. The task is highly indeterminate and the optimization is performed according to a fitness function that is an assessed combination of criteria (minimal deviation from the given joint moment, minimal total muscle force and minimal MUs activation). The influence of the weight of the first criterion (the one that reflects the importance of the movement accuracy on the predicted results), is investigated. Two variants concerning the muscle MUs structure are also compared: each muscle is composed of four distinct types MUs and the MUs twitch parameters are uniformly distributed.

Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses.

There are different opinions in the literature on whether the cost functions: the sum of muscle stresses squared and the sum of muscle stresses cubed, can reasonably predict muscle forces in humans. One potential reason for the discrepancy in the results could be that different authors use different sets of model parameters which could substantially affect forces predicted by optimization-based models. In this study, the sensitivity of the optimal solution obtained by minimizing the above cost functions for a planar three degrees-of-freedom (DOF) model of the leg with nine muscles was investigated analytically for the quadratic function and numerically for the cubic function. Analytical results revealed that, generally, the non-zero optimal force of each muscle depends in a very complex non-linear way on moments at all three joints and moment arms and physiological cross-sectional areas (PCSAs) of all muscles. Deviations of the model parameters (moment arms and PCSAs) from their nominal values within a physiologically feasible range affected not only the magnitude of the forces predicted by both criteria, but also the number of non-zero forces in the optimal solution and the combination of muscles with non-zero predicted forces. Muscle force magnitudes calculated by both criteria were similar. They could change several times as model parameters changed, whereas patterns of muscle forces were typically not as sensitive. It is concluded that different opinions in the literature about the behavior of optimization-based models can be potentially explained by differences in employed model parameters.

Some mechanical considerations on muscle coordination.

This commentary emphasizes three points of discussion. (a) The terminology: The terms multifunctional, synergisic, antagonistic muscles, and synergistic and antagonistic coactivations are discussed and the conclusion is drawn that they could not be used without mentioning the particular joint motion. (b) The importance of the external joint moments for activation of the muscles is confirmed on the basis of logical and mechanical considerations. Not all-experimental results, however, could be explained by this means. (c) The optimization criterion: Prilutsky's conclusion concerning the predicted muscle force proportionality to the muscle moment arm and PCSA is confirmed using a simple analytical solution of the optimization problem. It is shown, however, that the proportionality to the PCSA is a consequence of the chosen optimization criterion.