Mathematical programming applied to the decomposition of EMG signals

Mathematical programming is widely used to solve complex problem, for this reason the aim of this study is to apply this approach to the decomposition of electromyographic signal. When we talk about muscular contraction, we know that is generated by motor units through the use of action potentials. Nerve impulses rule all the human body, but we study their muscular effects because the muscular junction have highly reliability. The aim of this research is to understand the motor control through the solution of the inverse problem which means that we analyze the neural components that are extracted during the movement. We want to obtain the relation between action potentials of the motor units and muscular contraction, it could be not easy to find a solution. Signal is recorded though a clinical exam named electromyography whose output is a matrix in which the rows represent temporal instants. Each element of the column vector is the sum of more than one motor-neuron signal, but to understand the correlation between signal and contraction we have to obtain the single signal components for each motor-neuron. The large size of the output matrix prevents us from using exact algorithms because they may spend a very large computational effort. In this study we analyze existent heuristic and meta-heuristic procedure and we create a personalized approach to find a good solution to the problem in a reasonable amount of time. The purpose of this study is only a step of a bigger aim of the Medicine Department of the University of Brescia.
This study will help the neuro-mechanics and motor control laboratory. The mechanical models of the human movement and the biological knowledge of the human body are very developed but there isn’t a correlation yet between these subjects. To do that, the technique for the decodification of neural control were already used in the past. The recording of the specific muscular control is done through EMG. The spinal neurons create nerve impulses that go to the muscular fibers that contract them self in order to generate muscular movement. Therefore, we can say that muscles don’t generate only force and movement, but they also generate electrical activities that we can record through EMG like a signal. This study may have several applications. The most obvious purpose is to understand the site and the extend of injuries as the muscular dystrophy, myasthenia gravis, carpal tunnel syndrome and the amyotrophic lateral sclerosis. These diseases have symptoms as tingling, numbness, muscle weakness, muscle pain or cramping, paralysis or involuntary muscle twitching like tics. The second application referred to prosthesis, the EMG signal is also studied to be used as a prosthetic command. Therefore, problem analyzed in this study is the decomposition of the EMG signals through the use of the Mathematical Programming. EMG signals are recorded though a diagnostic exam that is the electromyography for a certain number of time instants. The output of this exam is a series of chronological values (one for each time instant is considered). These values are the sum of contributes of more than a single source. The motor-unit is the source that provokes the signal which generates muscular contraction though the use of action potentials. The problem is to find a way to decompose this signal in a reasonable amount of time and in the best possible way in order to understand which sources it is generated by. We formulate the problem as a MIP problem.