=Paper=
{{Paper
|id=Vol-2843/shortpaper35
|storemode=property
|title=Iterative Models of Bioimpedance in Intelligent Systems for Early Diagnosis of Infectious Diseases (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2843/shortpaper035.pdf
|volume=Vol-2843
|authors=Andrey V. Miroshnikov,Alexey V. Kiselev,Roman A. Krupchatnikov,Olga V. Shatalova
}}
==Iterative Models of Bioimpedance in Intelligent Systems for Early Diagnosis of Infectious Diseases (short paper)==
https://ceur-ws.org/Vol-2843/shortpaper035.pdf
Iterative Models of Bioimpedance in Intelligent Systems
for Early Diagnosis of Infectious Diseases *
Andrey V. Miroshnikov1, Alexey V. Kiselev1[0000-0001-7228-0281], Roman A.
Krupchatnikov2[0000-0002-4951-8607] and Olga V. Shatalova1[0000-0002-0901-9272]
1
Southwest State University, 94, st. 50 years of October, Kursk, 305040, Russian Federation
shatolg@mail.ru
2
I. I. Ivanov Kursk State Agricultural Academy, 70A, Karl Marx Street, Kursk, 305021, Rus-
sian Federation
roman0406@yandex.ru
Abstract. As a result of the study, fundamentally new results have been ob-
tained, which make it possible to create intelligent decision support systems for
the diagnosis of infectious diseases. A bioimpedance analysis model has been
created, based on multifrequency bioimpedance measurement, which allows
decomposition of biomaterial impedance into structural elements. On the basis
of the proposed model, descriptors were formed, intended for classifiers exe-
cuted on trained neural networks. To obtain descriptors, multifrequency sound-
ing of the biomaterial was carried out, on the basis of which Cole's graphs were
constructed. Using iterative algorithms and these graphs, Voight models of the
biomaterial impedance were obtained. The parameters of these models are used
as descriptors for the trained classifiers.
Keywords: Infectious Diseases, Bioimpedance Model, Multifrequency Sens-
ing, Trainable Classifier, Iterative Algorithm, Training Set.
1 Introduction
The disease of infectious diseases is systemic in nature. For its diagnosis, in particu-
lar, early diagnosis, requires the search for new markers and the creation of new intel-
ligent technologies [1-4]. The use of instrumental and laboratory research methods
takes a significant amount of time and is associated with the influence of harmful
factors on the body, which does not allow their use with high frequency and greatly
complicates the study of the pathological process in dynamics. This is due to the in-
troduction into practice of a number of innovative diagnostic technologies. However,
the accuracy of identifying the risk of infectious diseases using these methods does
not meet the requirements of modern medicine.
*
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License Attribu-
tion 4.0 International (CC BY 4.0).
2 Materials and methods
The method of classification of biological objects is based on a method based on bio-
impedance analysis, in which, to classify a segment of a biological object, its model is
built in the form of a passive two-terminal, electrodes are applied to the selected seg-
ment of the biomaterial, and multifrequency sounding is carried out at as many fre-
quencies as is required to determine the parameters of the model of a passive two-pole
model. The classification of a biological object is carried out according to the ob-
tained parameters of a two-port network [5-10]. As a model of a biomaterial segment,
Voight's recursive model [11] is used, shown in Figure 1.
С1 С2 СL
R1 R2 … RL
Fig. 1. The structure of the Voight model.
The impedance of the model in Figure 1 is determined by the formula
R jC
L
1 1
Z VOIT ( ) (1)
1
Where is the frequency of the probing current, at which the impedance of the
model is determined, R and C are the parameters of the model, L is the number of
RC - two-poles in the Voight model.
Considering that the impedance is a complex quantity, equation (1) can be repre-
sented as a system of two real equations
L
R
a( ) 1 R C
1
2 2
2
L (2)
R2 C
b( ) 2 2 2
1 1 R C
Where Z VOIT a( ) jb( ) .
Bioimpedance can be measured at a variety of frequencies i , i 1, N . Substi-
tuting these results into the left-hand sides of equation (2) and solving the correspond-
ing system of equations, we can determine a set R ,C that can be used as descrip-
tors for classifiers of the risk of infectious diseases.
To construct the Voigt model, the graph of the dependence of the impedance of the
biomaterial under the corresponding electrodes on the frequency in the frequency
range from Ωmin to Ωmax is experimentally determined. An example of such a graph is
shown in Figure 2. Each abscissa in this graph gives the values of two components of
bioimpedance. Thus, each frequency value in this graph allows us to write two equa-
tions (2) with 2L unknowns. Therefore, to build a Voight model with L links, it is
necessary to determine the impedance of the biomaterial at least at L frequencies, that
is, N> L.
6000
4000 1
2000
Resistance, Ohm
2
0
Frequency, kHz
3
- 2000
- 4000
- 6000
Fig. 2. A plots of the dependence of the impedance of a biomaterial on frequency: 1-modulus
of complex resistance, 2-real part of complex resistance, 3-imaginary part of complex resis-
tance.
For example, to represent the impedance of a biomaterial by the Voigt model in the
form of a single link, equation (2) will take the form:
R1
a ;
1 C12 R12
2
2 (3)
C1 R1
b .
1 2 C12 R12
To solve (3), it is sufficient to measure the bioimpedance at only one frequency, for
example, at . In this case, it is necessary to make sure that such a model is ade-
quate, that is, the impedances of this model at frequencies different from are equal
to the impedances obtained as a result of experimental studies.
For this purpose, a recursive procedure for solving systems of nonlinear equations
(2) is performed to determine the parameters of the model, starting from the single-
link Voight model and sequentially increasing the links in the Voight model. In each
Voigt model, a set j is defined C i ,Ri j, where i is the link number in the j-th iteration
of the Voigt model. The iterative process is performed until the functional of the ap-
proximation error of the experimental data by the Voigt model reaches an acceptable
value. The error is determined by comparing the simulation results according to (1)
with the results of experimental studies presented in the form of a graph in Figure 2.
Voigt's models are constructed by solving a system of nonlinear equations obtained
on the basis of the graphs shown in Figure 2. Voigt's model allows theoretically ob-
taining the amplitude-frequency characteristic (AFC) according to equation (1), with
the set elements calculated from the system of equations (2) R ,C . The AFC
model is compared with the experimental AFC. The approximation error ε is deter-
mined, for example, by the Euclidean distance, and is compared with the allowable
error εadd. If the error is less than the allowable, then the iterative process of building
the model ends. Otherwise, one more link is added to the model and Voight's model is
rebuilt, that is, a new system of nonlinear equations (2) is solved with the addition of
the next frequency - two values of the impedance parameters at the next frequency of
the graphs Figure 2. Before incriminating the parameter L, it is checked for its output
beyond the limit value. When this parameter goes beyond the limit value, the parame-
ters of the Voight model are not redefined, but are displayed as a space of informative
features.
3 Results
Voight's model for a two-link model uses two points in the graph in Figure 2 and has
the form
R1 R2
a1 1 ;
1 12 C12 R12 1 12 C 22 R22
R1 R2
a 2 2 2 2 2
2 2 2
;
1 2 C1 R1 1 2 C 2 R2
(4)
1C1 R12 1C 2 R22
b1 1 ;
1 12 C12 R12 1 12 C 22 R22
2 C1 R12 2 C 2 R22
b2 2 .
1 22 C12 R12 1 22 C 22 R22
After solving equation (4), we obtain new parameters of two-port networks in the
Voigt model and repeat the procedures for solving system (4). If the approximation
accuracy is not satisfactory, then we add two more equations to the system of equa-
tions (4), solve it and build the model (1) anew.
To construct a classifier for this space of informative features, we use trainable
neural networks with a hierarchical structure [12-16]. The output of the neural net-
work of the first hierarchical level shows confidence in the biomaterial belonging to
the class of functional state for which the neural network was trained. The neural
networks of the first hierarchical level are trained using the same training samples.
The outputs of the neural networks range from zero to one. In this case, the classifica-
tion is carried out in two classes "class of interest" and the class "everything else". At
the second hierarchical level, there is only one neural network with one output and the
number of inputs equal to the number of neural networks at the first hierarchical level.
As an example, a group of patients with pneumonia with a clearly defined diagno-
sis (radiography, X-ray tomography, laboratory analysis data) and a group of volun-
teers without pulmonary pathologies were taken. Diagnoses are coded with the char-
acters "0" and "1". Control samples are formed from the obtained training sample by
the rolling exam method. To obtain bioimpedance analysis data, an electrode belt is
put on the patient's chest and impedance curves of the type shown in Figure 2. Each
impedance curve corresponded to a certain combination of electrodes. The process of
obtaining them is illustrated in Figure 3.
Indicators of the quality of diagnostics in the "pneumonia - no pneumonia" classes
for one of the control samples are presented in Table 1.
Table 1. Indicators of the quality of forecasting on the control sample.
Surveyed Bioimpedance studies X-ray examinations
DS DSp DE DS DSp DE
n 1 1 60 75% 83% 87% 66%
2 79% 77%
n1 60 83% 75% 66% 87%
The indicators of the quality of diagnostics of the proposed method were com-
pared, as with the prototype, with the indicators of the quality of X-ray studies on the
same control sample.
Fig. 3. Illustration of the process of classification of biomaterial in an in vivo experiment.
4 Discussion
Analyzing Table 1, we come to the conclusion that in this control sample both meth-
ods have practically the same diagnostic efficiency, but bioimpedance studies are
superior to radiological studies in specificity and are somewhat inferior in sensitivity,
which allows them to be recommended for clinical practice.
Thus, to classify a biomaterial for the presence of infectious diseases, descriptors
are used, which are determined by representing the model of a biomaterial in the form
of a multi-link bipole, the parameters of the links of which are determined on the
basis of multipart sensing. The obtained multidimensional model of descriptors is
used to train neural networks that perform the functions of a biomaterial classifier. As
a result of the study, the results were obtained that allow the creation of intelligent
decision support systems for the prediction and diagnosis of infectious diseases. The
possibility of multifrequency sensing will make it possible to construct algorithms for
differential control of tissue impedance and fluid impedance, which will make it pos-
sible to obtain new decisive rules for diagnosing pathological conditions of the body
(cardiovascular, infectious and oncological diseases).
5 Conclusion
The scientific novelty of the study lies in the fact that descriptors are used to classify a
biomaterial for the presence of infectious diseases, which are determined by repre-
senting the biomaterial model in the form of a multi-link bipole, the parameters of the
links of which are determined on the basis of multipart sensing. The obtained multi-
dimensional model of descriptors is used to train neural networks that perform the
functions of binary classifier of biomaterial.
As a result of the study, the results were obtained that allow the creation of intelli-
gent decision support systems for the prediction and diagnosis of infectious diseases.
The possibility of multifrequency sensing and the use of iterative biomaterial models
will allow the construction of algorithms for differential control of tissue impedance
and fluid impedance by non-invasive methods in in vivo experiments. This will con-
tribute to obtaining new decisive rules for the diagnosis of pathological conditions of
the body (cardiovascular, infectious and oncological diseases).
6 Acknowledgments
The reported study was funded by RFBR, project number 20-38-90063.
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