Mathematical programming applied to the decomposition of EMG signals

Chapter 2
Introduction
Mathematical programming is widely used to solve complex problem, for
this reason the aim of this study is to apply this approach to the decomposi-
tion of electromyographic signal. When we talk about muscular contraction,
we know that is generated by motor units through the use of action poten-
tials. 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 proce-
dure and we create a personalized approach to find a good solution to the
7
Introduction
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 Bres-
cia. This study will help the neuro-mechanics and motor control laboratory.
The mechanical models of the human movement and the biological knowl-
edge 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 activ-
ities 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 dis-
eases 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 gener-
ates 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 gen-
erated by. We formulate the problem as a MIP problem. The approach that
is used is similar to the Kernel Search, we try to solve the problem reducing
8
Introduction
the input items of the problem. Therefore, in order to obtain a good solu-
tion, we decrease the number of items that the solver has to combine. In
particular, we solve a minimization problem in which the objective function
is the sum of the differences between the EMG signal and the error in a
particular instance of time. The problem is to understand which sources
and in which temporal instant have been activated during the recording of
the electromyography.
In Chapter 3 we contextualize the problem. Firstly, there are the descrip-
tion of the electromyography and of the muscular response that generates
the EMG signals. In this Chapter are brevely also described the kinds of
electrodes that are used to record the signal and how they are located on
the human body. The last Section of this Chapter describes the applications
and the possible uses of the decomposition of EMG signals.
In Chapter 4 we describe the formulation of a generic MIP problem and
its elements. Subsequently we classify the algorithms that can be used to
solve this kind of problem and there is a bibliographical review of main
methods of resolution. Starting from this Chapter we individuate two pos-
sible methods to use for the aim of this study, these methods are the Kernel
Search and the Tabu Search.
To apply one of these methods, we have to formulate the problem. This
problem were previously formulated by Negro et al. in [55], but it is a non-
linear formulation, for this reason we formulate the problem in linear way
in Chapter 5. In this Chapter are described also the problem that has the
EMG signals and why we have to depurate it.
In Chapter 6 there are the descriptions of inputs of this particular case
of study and the approaches that are used to the resolution of the problem.
Last Chapter (7) contains tests of the methods that are presented in
the previous Chapter. In particular, we run each method for four times.
To compare methods proposed, we choose a way to assign a score that is
calculated on both the value of the objective function and the percentage
9
Introduction
of improvement with different weights. In this way we find two methods
that seem work better than others and we try these on 10 new different
instances. This second kind of analysis is done comparing the activated
shifted sources of the optimal solution with the activated shifted sources
found by the algorithms.
10
Chapter 3
The EMG signal
3.1 Electromyography
Electromyography is an electrodiagnostic medicine technique for record-
ing, evaluating and representing the electrical activity produced by skeletal
muscles during their contraction. This diagnostic procedure evaluates the
health condition of muscles and the nerve cells that control them. The nerve
cells, named motor neurons, transmit a neuro signal that cause contraction
of muscles. A neuro signal, physically, is an electrical impulse. The test is
done with some devices, named electrodes, of different types. The result of
an electromyography is an electromyogram that represents an EMG signal.
In this work we want to study the electromyogram with the aim to decom-
pose it in its components. Every component is assigned to a motor unit. We
want to know the contribute of each motor unit that we are monitoring.
The EMG signal is a biomedical signal that measures electrical currents
generated in a muscle during its contraction representing neuro-muscular
activities. The contraction of muscles corresponds to the depolarization/re-
polarization of membrane of singular muscular fibres. There are ionic cur-
rents that go through the muscular cells.
11
The EMG signal
Figure 3.1: Electromyoghraph
3.2 Muscular response
The muscle tissue is composed by fibres with an elongated shape. When a
nerve impulse arrives to the muscular cells a contraction of the muscular
fibres occurs. To understand this research, we have to explain the definition
ofmotorunitwhichconsistsinafunctionalunitthatiscomposedbyamotor
neuron, many terminal branches of its axon and the muscular fibres that
are innervated by them. The motor neuron is located in spinal cord. When
an activation signal reaches the muscle each muscular fibre of the same
motor unit contracts synchronously. The number of motor unit changes
from muscle to muscle.
The nervous system (or a nerve reflex) generates a neural signal that
goes through nerves. When this signal reaches the muscle, the connection
between the nerve fibre and the muscle cell is guaranteed by the neuro-
muscularjunction,alsocalledmyoneuraljunction.Theneuro-muscularjunc-
tion is analogous to the synapse between two neurons. There is not an
electrical continuity between the nerve and the muscle, the signal becomes
chemical. Chemical transmission involves that there are pre-synaptic and
postsynaptic structures.
In resting condition, the internal part of the muscular membrane is in
12
The EMG signal
Figure 3.2: Motor unit
Figure 3.3: Neuromuscular junction
balance with the external part. There is a rest potential of the muscular
fibre membrane between -80 mV and -90mV. This potential difference is
maintained through physiological processes and it makes a negative electric
charge in the muscular fibre compared to the outside. The physiological
processes are done thank to ionic pumps that are situated on the muscular
membrane. In presence of a stimulation by a nerve impulse, there is the
activation of the motor neuron that makes the conduction of the action
potential through its axon. The terminal branches of the axon release a
chemical neurotransmitter called acetylcholine. The presence of this chemi-
calcausestheopeningofthetrans-membranechannels,inthiswayNa+ions
13
The EMG signal
flow inside the fibre, indeed theK
+
ions flow outside, as consequence there
is a depolarization of the membrane compensated by ion exchange through
the activation of the ionic pump. In this way there is a re-polarization of
the membrane.
Figure 3.4: Potential transmission inside muscular fibres
If the membrane potential increases more than a threshold value, the de-
polarization makes a muscular action potential. The potential, that is usu-
ally equal to -80 mV, goes quickly to +30 mV. A fast recovery of the mem-
branepotential(re-polarizationphase)followsthereforeahyper-polarization
occurs. From the part of the membrane affected by ion exchange, the poten-
tial for muscle action spreads along the fibre muscle in both directions. This
excitement causes the release of Ca
++
ions in intra-cellular space. Subse-
quently, there is a contraction of the muscular fibres. The depolarization/re-
polarization cycles make a depolarization wave that moves on the fibre. This
cycle is represented by the Figure 3.4
14
The EMG signal
3.3 Electrodes and measure
Figure 3.5: Potential transmission inside muscular fibres
The relevant parameters for this study are the recruitment of motor units
and them activation frequencies, called firing frequency. The combination of
these terms determines the force that changes from muscle to muscle. The
electrical activity of a muscle depends on the same terms. Both electrical
activity and force depend on recruitment and frequency, so we can say that
a relation between them exists. However, we have to remember that there
are a lot of factors that influence the EMG signal trend like: muscular
fatigue, energy metabolism and oxygen availability. We can observe that:
to an increase of the number of motor units corresponds the increase of the
spike amplitude and to an increase of the activation frequencies corresponds
an increase of the characteristic frequencies of the analysed signal.
The electrodes are real transducers that transform the ionic currents gen-
erated in the muscles into an electronic current that can be manipulated
withelectroniccircuitsandstoredinanalogordigitalformasvoltagepoten-
tial. The electrodes are classified according to several criteria, such as: the
detection site (depth and surface electrodes) and the type of configuration
(monopolar and bipolar electrodes). Electrodes include some common ma-
terials like platinum, stainless steel and silver-silver chloride; the electrodes
differ from the needles they use.
The first distinction is done to the depth of application of the electrodes.
15
The EMG signal
Depth electrodes are inserted into the muscle tissue. They allow the study
of deep muscles. They are able to record a reduced number of motor units
because they have a reduced surface that detects the signal. So, they are
selective. Therefore, these kinds of electrodes permit to investigate different
areas of the same muscle. The main disadvantage is their invasiveness, their
little tolerability by the patient and their costs. Depth electrodes could be
classified in needle electrodes and wire electrodes. Inside needle electrodes
there are one or more conducting wires. The terminal parts of conducting
wire form sensible aureoles. The diameter of these aureoles is of the order
of tenth of a millimeter. The number of aureoles depends from the config-
uration of the electrode: monopolar electrodes have only one aureole and
bipolar electrodes have two aureoles.
Figure 3.6: Needle electrodes
Wire electrodes are the evolution of the needle electrodes. They have
flexible wires inside a hollow needle. The wire diameter is from 25 to 100μm.
Wires are inserted into the muscle through a needle and they are hooked to
the muscle. The advantage of these electrodes is their flexibility, they don’t
break during muscle contraction. They could be used for motor analysis.
Surface electrodes are applied to the skin of the patient. They usually have
the form of a suction cup and they are applied through a bulb. We are
referred to the Figure 3.7. A disadvantage is the attenuation of the signal
due to the passage through the adipose tissue. Sometimes electrolyte gel can
be added to improve the connection. In fact, having low contact impedance
permits to reduce the noise of the EMG signal.
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