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5.Mathematical
statement of a problem.
Logged
electrogastroenterography signal is
investigated by various methods of mathematical processing, including
using linear filtering, spectral analysis, wavelet analysis, etc.
5.1.
Spectral
analysis
Spectrum Signal
decomposition is called a signal
on the various systems of orthogonal functions. In this case, the
orthogonal system: 1,cos( ω t), sin ( ω t), cos
(2ωt), sin (2ωt),…, cos(n ωt),
sin (nω t). Here ω:Angular frequency, t : current
time.
This decomposition
can be performed using the
classical discrete Fourier transform (DFT). As a result of the
transformation of time domain signal is converted in frequency from the
spectral components indicates the amount of harmonics, the current at
this frequency.
where S (n) - spectral components in the n-th DFT filter;
N - number of points of DFT;
s (k) - k-th source to run a temporary signal.
Because the signal
is a non-shot, his range is not
calculated for all studies. Instead, choose a segment length of a
continuous signal (10 or 4 minutes), and the method of "sliding
window", with a shift in 1 minute see all of the study. The spectrum is
calculated with each segment. The choice of such a length of the
segment due to the reduction of the various divisions GIT are the bass.
Therefore, it is safe to assume that a change in the amplitude of these
low-frequency components will be even more low.
In favor of this
assumption and said that all the
probabilistic characteristics of the signal in the absence of artifacts
over time, changing very little. Apparent at first glance, the high
unsteadiness signal is actually the result of addition of many
harmonics. In addition, the duration of this segment, provides a good
resolution of the frequency spectral components, which is very
important in the calculation of peripheral computer
electrogastroenterogram.
As for the
calculation of the first range you
want the elapsed time equal to the length of the selected window (10 or
4 minutes), then start all the graphs of spectral analysis of naturally
moves on the start of the study on the duration of the selected window.
5.2.
Wavelet analysis
ÎOne of the most
urgent tasks of digital signal
processing - the task of cleaning the signal from noise. A practical
signal contains not only useful information, but also traces of some
extraneous influences (interference or noise). The model of such a
signal can be written as follows: S(t)=f(t)+σe(t),where f
(t):a useful signal, e (t):noise, σ:the noise level, s
(t):the monitoring signal. In most cases, it can be assumed that the
function e (t) describes a model of white (Gaussian) noise, and
information about the obstacle in the high-frequency spectrum signal,
and useful information - in the low-frequency.
For such a model of
noise removal using the
wavelet transform is carried out in four stages:
1. Decomposition of the signal on basis of wavelets.
2. The choice of noise threshold values for each level of
decomposition.
3. Threshold filtering coefficients of detail.
4. Reconstruction of the signal.
ÑFrom a statistical
point of view, this method is
a nonparametric regression model assessed the signal using an
orthogonal basis. The technique works best on a smooth signals, ie to
signals in the expansion of which only a small amount of detail
coefficients is significantly different from zero.
5.3.
Linear
filtering
Linear digital
system described by equations:
 (2.1)
where x [n]: input sample, y [n]: output sample, h- pulse
characteristic of the system. The transfer function of a linear digital
system is determined by the expression
 (2.2a)
Where
Z:transform input and output signal samples. If you multiply both sides
of equality (2.1) and at zn summarize on n, can be obtained from the
expression for the transfer function of a linear digital system in the
form of
 (2.2á)
where hl; - pulse characterization systembr
A necessary and sufficient condition for stability of linear digital
systems are often written in the form of inequality for the impulse
characteristics of
 (2.3)
Linear digital system is physically realizable if hl =0 for l <0.
Digital devices that perform the type of transformation (2.1) are
called linear digital filters. A linear digital filter is a finite
linear digital system, and, in general, described by the equation
 (2.4)
where { ai,bi } -
coefficients of the filter.
Typically, linear digital filters are divided into low-frequency
filters, high frequency filters, and band transmits and band-barrier
filters, amplitude and phase-corrector filters or comb filters, etc.
The first four types of filters are called the main or basic types of
filters. The designs of linear digital filters are divided into
recursive and no recursive (transversal) filters. The coefficients of
transversal filter or a filter with finite impulse characteristic
satisfy the conditions: {a0 =1, ai =0 for all i # 0).
Digital filters, which are not transversal, called recursive or filters
with infinite impulse characteristic.
The transfer function of a linear digital filter (2.4) has the form
 (2.5) Polynomials facing
in the numerator and the
denominator of this expression can be represented as the product and to
rewrite the transfer function of a linear digital filter (2.4) as
follows:
 (2.6)
The condition of stability of linear digital filter is usually written
in the form of inequality:|αi|<l,i=0,1,...,I ,, the
pole digital filter transfer function must lie inside the unit circle
radius. Regulation of zeros of the transfer function of {βl}on
the stability of the filter is not affected, but the condition
|βl |‹1, l=0,1,...,L defines the minimum-phase
digital filter. Frequency response of digital filter H (w) corresponds
to the transfer function of filter H (z) at  ,
where T - the interval of
digitization, w = 2 * 3.14 ...* f - circular frequency. Since the
exponential function of imaginary argument,
is a periodic function of
frequency with period W = 2 * 3.14 ... / T, a frequency response of
digital filter H (w) is also a periodic function of frequency with
period W.
Calculating the
coefficients of the digital filter
satisfying the given conditions are known as the design (synthesis)
filter, a device or program that performs the conversion of digital
signals - the implementation of the filter.
The problem of designing a digital filter as follows: a priori
specified module or the square of the modulus of the desired frequency
response filter. Find the filter coefficients, the square modulus of
the frequency characteristics of which satisfactorily approximates the
square of the modulus of the desired frequency response for the given
constraints. In particular, such restrictions may include: type of
filter, the number of coefficients (order) filter,the error of
approximation, etc.
6.
Viewing and analysis of signal
electrogastroenterography
6.1.
Viewing and analysis of the schedule alarm.
The device
"Gastroscan-HEV offers the opportunity
to analyze the signal captured by various methods, including by means
of linear filtering and spectral analysis, which are the basic
operations of digital signal processing and have found wide application
in medicine. You can view the schedule captured signal in the time
domain. Below is a sample schedule of the signal.
Figure 5. Example schedule electrogastroenterography signal
You can view and analyze the signals that characterize the motor
activity of the various divisions GIT isolated from the signal captured
using a digital band filter. For digital filtering using conventional
filters with finite impulse characteristic
where Xâûõ(n):n-th readout signal at the output of the digital filter;
Xâõ(k: (k)-th readout signal at the input of digital filter;
h (i): impulse characteristic of digital filters.
The following is an example of scheduling five divisions GIT signals
obtained after digital filtering.
Figure 6. Example graphs electrogastroenterography signals of five
divisions GIT.
Ïðè ÿâëåíèÿõ
"ðàçäðàæåííîãî æåëóäêà" When events
"irritated stomach" there is unevenness and irregularity teeth, teeth
with alternating high and low voltages, the emergence of waves
associated with a reduction in stomach tonic. During the attack of pain
there has been a sharp increase in the amplitude and frequency of
waves. With the development of stenos is janitor teeth are
characterized by particularly high voltage, which can exceed 2 MB.
Reliable connection between the type of EGG and the nature of the
disease can not be, because it reflects the functional changes that do
not always coincide with the pathological process. However electrograph
opens up broad prospects for the study of various therapeutic factors
on motor function of the stomach. In healthy subjects the amplitude of
teeth after breakfast 0,3-0,4 mV, and frequency of waves ~ 3 in 1
minute. Less Hyper Kinetic (0,5-0,8 mV) or hypo-kinetic (<0.2
mV) types EGG.
6.2.
Performance Computer electrogastroenterogram.
6.2.1
The total electrical activity
On the basis of a
result of spectral analysis of
the spectrum curve is determined by the electric power signal. The
program calculates the output signal for each frequency unit P (i) (ie
the frequencies characteristic of the stomach duodenum, colon etc.) and
the total power of PS.
where S (n) - spectral components in the n-th DFT filter;
k1:DPF filter number corresponding to the minimum value of the
frequency of the i-th frequency division;
k2 - DPF filter number corresponding to the maximum frequency of the
i-th frequency division.
6.2.2.
The relative electrical activity
In contrast to the
absolute reliably proved
stable relative electrical activity of R (i) / PS. This indicator is
the ratio of absolute values of electrical activity in each frequency
spectrum to the total activity.A set of five indicators of R (i) / PS
and a major in the decoding of data of peripheral computer
electrogastroenterogram.
6.2.3.
The coefficient of rhythm
The next indicator
of motor GIT - rate rhythm
Kritm, calculated as the ratio of the length of the spectrum envelope
of the department of digestive tube to the width of the spectral plot
at the abscissa axis.
where S (n): spectral components in the n-th DFT filter;
k1 - DPF filter number corresponding to the minimum value of the
frequency of the i-th frequency division;
k2 - DPF filter number corresponding to the maximum frequency of the
i-th frequency division.
6.2.4.
Ratio
Comparison
Of the normal physiology suggests that only an adequate job in all
divisions of the digestive tube provides the proper evacuation of chyme
on intestinal tube. Accordingly, this condition should be stable ratios
to characterize the electrical activity of the divisions GIT. It
appeared 4 the ratio of the electrical activity of the overlying
department to lower P (i) / P (i +1). Here are the normal rates of
computer electrogastroenterogram in healthy investigated.
Table 2. performance
computing electrogastroenterogram studied in healthy
| Division
gastrointestinal tract |
P(i)/PS |
P(i)/P(i+1) |
Kritm |
| Colon |
22,41±11,2
|
10,4±5,7
|
4,85±2,1
|
| Stomach |
2,1±1,2
|
0,6±0,3
|
0,9±0,5
|
| Small
intestine |
3,35±1,65
|
0,4±0,2
|
3,43±1,5
|
| Jejunum |
8,08±4,01
|
0,13±0,08
|
4,99±2,5
|
| Duodenum |
64,04±32,01
|
|
22,85±9,8
|
7.
Synthesis of scientific search and
analysis
Features computer
electrogastroenterogram:
•Non-invasive;
•simplicity of the study;
•o the possibility of the use of different types of
stimulants;
•o Obtaining objective information on the electrical activity
and rhythmic activity in all divisions of the digestive tract, not only
individually, but in the relationship.
The objectives of the computer electrogastroenterogram:
•Determining the type of breach - a functional or mechanical;
•Identification of lesion localization (Department GIT);
•Select a method of treatment;
•selection of corrective therapy.
Indications for study by computer electrogastroenterogram is that
patients with various signs of violations of the motor activity of the
digestive tract.
Constitute the main group studied patients with ulcer disease of
stomach and duodenum. Given the numerous theoretical developments, one
can clearly argue that violations of motor upper gastrointestinal tract
plays a crucial role in the pathogenesis of peptic ulcer disease.
Invariability of the identified motor-evacuative violations (Maine) is
one of the criteria for determining the future strategy of management.
When deciding on surgical treatment, adequate correction of violations
IEF is possible only when there is the original, unbiased information
that can be obtained by computer electrogastroenterogram.
Pathology small intestine so far is an area of medicine where a
decisive role in the diagnosis is clinical experience doctor. For even
those isolated intestinoscop provide information only on the organic
lesion of bowel. Functional same violations found in most cases, little
or no patognomonichno endoscopic picture. Here, computer
electrogastroenterogram has no analogues.
Recently, more attention gastroenterologists took functional violations
of so-called "transition zones" (gastro esophageal reflux reflux,
etc.). Currently, diagnosis of these states is connected with a long
radial load the patient and the doctor-radiologist, or "painful"
swallowing 6-channel probe for ionomanometri that does not stand up to
any comparison with the study of methods of computer
electrogastroenterogram.
In abdominal surgery is often a number of functional disorders of
gastrointestinal tract have to differentiate the mechanical nature of
the disease. In these situations, a matter of time, sometimes for
stretchable clock, is often decisive for the preservation of life of
patients. This 20-30 minute study of the peripheral computer
electrogastroenterogram may help to put all points on the "i". Recent
research has shown that postoperative paresis of intestines, which
affects ~ 65% of patients may be due to various factors:
•violations of electrical activity, as one of the divisions,
and combinations;
•violations of rhythmic activity, as one division, and
combinations.
None of the existing methods of diagnosis, except for computer
electrogastroenterogram, currently can not provide such information.
The treatment of postoperative paresis of the intestines - an area
commonly known and standardized in most clinics and includes all known
drugs that affect motor function. And based on numerous studies, in
some cases, even is contraindicated and can lead to a deterioration of
the patient.
8.
Conclusion
The main object of
study in this work are the
gastrointestinal tract (ZHKT). The study assesses the activity of a
physician in all divisions of the digestive tract and the consistency
of their work. Comparing the results with clinical data and the
endoscopic, radiological, ultrasonic methods of investigation gives the
physician the most complete information about the patient and not only
the correct interpretation of the diagnosis, but also the risk of
further progression of the disease and the development of
complications. Thus, the functional assessment of the doctor examine
the patient with the dialectic of positions and find the best ways to
treat it. Data obtained with electrogastroenterogram not contradict,
and often are ahead of the results of X-ray and endoscopic studies,
which showed a high sensitivity method for the diagnosis of motor
disorders. Using the method electrogastroenterogram can be recommended
in daily clinical practice for diagnosis, differential diagnosis, as
well as to determine the nature of violations of the motor-function
evacuative gastrointestinal tract as a functional and organic genesis.
Non-invasive, simple application of this method can be used in
pediatric practice, including for the required number of follow-up
surveys during observation.
9.
Literature
1. Stupin VA, Smirnova Ã.Î., Baglaenko MV, Siluyanov SV, Zakirov DB
Peripheral electrogastroenterogram in the diagnosis of violations of
the motor-function evacuative the gastrointestinal tract. Treating
physician. - 2005. - ¹ 2, pp. 60-62.
2. Vyskrebentseva SA, Alferov VV, Kovalev NA, Bobryshev DV Pasechnik VD
Electrical activity of the stomach in patients with gastro esophageal
reflux disease. Materials III scientific-practical conference with
international participation, dedicated to the memory of the Honored
Worker of Science Professor LI Geller. 2002, ¹ 1, pp. 76-83.
3. Vasil'ev VA, Popova TS, Tropskaya NS Assessment of motor activity of
the gastrointestinal tract. Russian Journal of Gastroenterology,
Hepatology, coloproctology. 1995, ¹ 4, pp. 48-54.
4. Rebrov VG, Stankovsky BA, Kulanina GI Features of the registration
of electrical activity of the stomach and intestines from the body of
the patient. Russian Journal of Gastroenterology, Hepatology,
coloproctology. 1996, ¹ 2, pp. 48-52.
5. Rachkova NS Functional dyspepsia in adolescents. Principles of
differentiated treatment. Abstract of thesis grace candidate of medical
sciences. Moscow, 2007.
6. Ponomarev AP, Rachkova NS, Belmer SV Havkin AI Peripheral
electrogastroenterogram in pediatric gastroenterology. (Methodological
aspects). / M.: 2007, 48 pp. Download in format pdf, 920 KB
7. Stupin VA Bogdanov AE Mishulin LE Artemiev AS Lavrova NI Belkov AV
Narezkin DV Zakirov DB Siluyanov SV Smirnova Ã.Î. The method of
diagnosing the motor-function evacuative the gastrointestinal tract.
8. http://www.gastroscan.ru
Intragastric pH-metry, elektrogastroenterography and ECG.
9. http://www.lvrach.ru/rub/4607864/
Gastroenterology.
10.http://www.medpanorama.ru/zgastro/
Gastroenterology.
11. http://kronportal.ru/digestive
Gastrointestinal tract.
12. http://en.wikipedia.org/wiki/Electrogastrogram
Electrogastrogram
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