=Paper=
{{Paper
|id=Vol-1839/MIT2016-p05
|storemode=property
|title= Improving the efficiency of the human spine diagnostics systems
|pdfUrl=https://ceur-ws.org/Vol-1839/MIT2016-p05.pdf
|volume=Vol-1839
|authors=Nikolay Dorofeev, Konstantin Podmasteriev,Oleg Kuzichkin,Anastasia Grecheneva
}}
== Improving the efficiency of the human spine diagnostics systems==
https://ceur-ws.org/Vol-1839/MIT2016-p05.pdf
Mathematical and Information Technologies, MIT-2016 — Information technologies
Improving the Efficiency of the Human Spine
Diagnostics Systems
Nikolay Dorofeev, Konstantin Podmasteriev, Oleg Kuzichkin, and Anastasia
Grecheneva
Murom Institute (branch) Vladimir State University, Murom, 602200,
23 Orlovskaya st., Russia
DorofeevNV@yandex.ru
http://www.mivlgu.ru
Abstract. The paper proposes a method of recording and measuring
the spatial mutual movement and positioning of the spine segments. As
a basic method, an application of the accelerometer measuring method
of the rotation angles and acceleration is proposed. The research results
show that the use of accelerometer sensor significantly increases the flexi-
bility of the system (scalability and ease of interfacing the accelerometric
diagnostic and rehabilitation system of the spine with other diagnostic
systems) and the accuracy of the results (thanks to additional digital
processing of recorded signals) due to the small size and high precision
of sensors. The proposed method is passive (does not use additional ex-
posure, such as in an ultrasound, X-ray and tomography) and has no
negative impact on patient.
Keywords: biomechanics, human spine, diagnostic system, goniometric
control, accelerometery.
1 Introduction
One important area of medical technology is diagnostic and rehabilitation equip-
ment, especially spinal diagnosis and rehabilitation system [1]. Various deviations
in the relative position of the spine segments affect the functionality of the mus-
culoskeletal system, internal organs, eventually triggering a “chain reaction” of
disorders of organs and systems of the body as a whole [2, 3].
To figure out timely corrections of the deviations in the spine, and prevent-
ing the formation of irreversible pathological processes, a high accuracy primary
diagnosis is required. It should be noted, that during the period of spinal rehabil-
itation to assess the treatment and recovery results, an investigation of patient’s
motion is required.
2 The current state of medical diagnostics of the spine
In the existing medical diagnosis methods, the presence of pain syndrome is a
key reason for the prescription of rehabilitation procedures [4]. Pain is the basis
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Mathematical and Information Technologies, MIT-2016 — Information technologies
for hospitalization, medical appointments actions aimed at rehabilitation, and
often for the adoption of expert solutions (diagnosis). Therefore, the prescrip-
tions for rehabilitation are assigned to the patients that have a partial violation
or substantial loss of functionality, i.e., spine pathology with pain syndrome and
neurological manifestations. In practice, this means one must carry out rehabil-
itation effects only on the patients with acute syndromes and during recovery
periods.
Diseases of the spine are accompanied by impaired mobility of vertebral
joints. For example, studies were carried out on soldiers of the Air Force of
the Ministry of Defense of Russia. The soldiers’ physical state were character-
ized by a high degree of physical fitness and health requirements. The results
of the studies reveal a relatively high level of disorders of the spine functions in
56 % of the cases. The same violations of the biomechanics of the spine were
revealed in 61.3 ± 3.5 % of the patients, with 19 % of the violations were of
moderate to severe degree [5].
For this reason, an important part of solving the problem of diagnosis of
spinal diseases and their treatment is the development of an automated method
of goniometric spine control. The method are to provide a high accuracy and sen-
sitivity, and must be easy applied in practice for estimation of the functionality
of the spinal column.
3 The accelerometer method of geometric spine control
We propose to use accelerometer method of bending angle measurement for
assessing spinal configuration and range of its motion in the sagittal, frontal and
horizontal planes as a method of goniometry in the automated control system
[6]. This instrumental method of the investigation of the curvature and mobility
of the spine is built on the principle of measuring the full acceleration vector
of two accelerometers attached to the vertebrae controlled spinal segments (Fig.
1).
The output of the four signals proportional to the acceleration of the general
point of biokinematic pairs 𝑎 ¯ are obtained as a result of measurement of the
acceleration values of each accelerometer in two coordinate system.
𝑎𝑥 = 𝐾𝑎𝑥 𝑎 cos(𝜙𝐴 ); 𝑎𝑦 = 𝐾𝑎𝑦 𝑎 sin(𝜙𝐴 );
(1)
𝑏𝑥 = 𝐾𝑏𝑥 𝑎 cos(𝜙𝐵 ); 𝑏𝑦 = 𝐾𝑏𝑦 𝑎 sin(𝜙𝐵 ).
where 𝑎𝑥 , 𝑎𝑦 , 𝑏𝑥 , 𝑏𝑦 are the acceleration values of the first and the second ac-
celerometers in the plane 2D coordinate system; and 𝜙𝐴 , 𝜙𝐵 are the angle be-
tween the direction of the acceleration vector of a general point 𝑂 about a pair
of adjacent vertebrae 𝑎 ¯ and measuring systems (¯ 𝑥𝐴 , 𝑦¯𝐴 ) and (¯
𝑥𝐵 , 𝑦¯𝐵 ) the ac-
celerometer, respectively; 𝐾𝑎𝑥 , 𝐾𝑎𝑦 , 𝐾𝑏𝑥 , 𝐾𝑏𝑦 are transform coefficients of the
corresponding accelerometers.
The goniometric angle 𝜙 = 𝜙𝐴 − 𝜙𝐵 is determined on the basis of relations
between the components of the linear acceleration vector in the spine movement
and displacement of the accelerometers. The angle is described by the formulas:
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Mathematical and Information Technologies, MIT-2016 — Information technologies
Fig. 1. The accelerometer method of geometric spine control
(︂ )︂
(𝑏𝑥 𝑎𝑥 )/(𝐾𝑏𝑥 𝐾𝑎𝑥 ) − (𝑏𝑦 𝑎𝑦 )/(𝐾𝑏𝑦 𝐾𝑎𝑦 )
𝜙𝐴 = cos (2)
(𝑎𝑥 /𝐾𝑎𝑥 )2 + (𝑏𝑥 /𝐾𝑏𝑥 )2
(︂ )︂
(𝑏𝑥 𝑎𝑦 )/(𝐾𝑏𝑥 𝐾𝑎𝑦 ) − (𝑏𝑦 𝑎𝑥 )/(𝐾𝑏𝑦 𝐾𝑎𝑥 )
𝜙𝐵 = sin (3)
(𝑎𝑥 /𝐾𝑎𝑥 )2 + (𝑏𝑥 /𝐾𝑏𝑥 )2
As a consequence, the desired value of the angle of rotation of the kinematic
pair is determined from the expression
(︂ )︂
𝑎𝑦 𝑏 𝑥 − 𝑏 𝑥 𝑎𝑥
𝜙 = 𝑎𝑟𝑐𝑡𝑔 (4)
𝑎𝑥 𝑏 𝑥 − 𝑎𝑦 𝑏 𝑦
However, in the process of calculation the resulting error might increase due
to a possible division by zero in the trigonometric arc tangent function argu-
ment. Such an error occurs due to the indeterminacy of the patient motion, and,
consequently, it is a result of receiving different acceleration values, including
zero.
The solution of the problem is to use a phase-measuring method [7], whose
implementation is to compensate the multiplicative instability of the accelerom-
eters branches. Signals from the two-component accelerometers is converted into
the phase sine wave by multiplying the signals 𝑎𝑥 , 𝑎𝑦 , 𝑏𝑥 , 𝑏𝑦 on phase quadrature
signals sin(𝜔𝑡) and cos(𝜔𝑡), whose frequency is a multiple of the frequency of
the reference generator (RG). The obtained signals will be as follows:
𝑎𝑥 = 𝑈 sin(𝜔𝑡)𝐾𝑎𝑥 𝑎 cos(𝜙𝐴 ); 𝑎𝑦 = 𝑈 cos(𝜔𝑡)𝐾𝑎𝑦 𝑎 sin(𝜙𝐴 );
(5)
𝑏𝑥 = 𝑈 sin(𝜔𝑡)𝐾𝑏𝑥 𝑎 cos(𝜙𝐵 ); 𝑏𝑦 = 𝑈 cos(𝜔𝑡)𝐾𝑏𝑦 𝑎 sin(𝜙𝐵 ),
where 𝑈 and 𝜔 are the amplitude and the frequency of the quadrature phase
signals.
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Mathematical and Information Technologies, MIT-2016 — Information technologies
Summing the signals in the adders for the object 𝐴 and object 𝐵, respectively,
we obtain:
𝑎𝐴 = 𝑈 𝐾𝑎𝑥 𝑎 cos(𝜔𝑡 + 𝜙𝐴 + 𝜙𝐾𝑎𝑥 ); 𝑎𝐵 = 𝑈 𝐾𝑏𝑥 𝑎 cos(𝜔𝑡 + 𝜙𝐵 + 𝜙𝐾𝑏𝑥 ). (6)
where 𝜙𝐾𝑎𝑥 and 𝜙𝐾𝑏𝑥 are the phases of misaligment of the measuring branches.
From the relations (5) and (6), the signal value at the input of the main
phase detector will be as follows:
𝑈𝐴 = 𝑈 𝐾𝑎𝑥 (1 + 𝛥𝐾1 )𝑎 cos(𝜔𝑡 + 𝜙𝐴 + 𝜙𝐾𝑎𝑥 );
(7)
𝑈𝐵 = 𝑈 𝐾𝑏𝑥 (1 + 𝛥𝐾2 )𝑎 cos(𝜔𝑡 + 𝜙𝐵 + 𝜙𝐾𝑏𝑥 ).
Since the serial connection circuit is selected, the transform coefficients of ac-
celerometers are 𝐾𝑎𝑥 = 𝐾𝑎𝑦 and 𝐾𝑏𝑥 = 𝐾𝑏𝑦 , respectively, hence the phase error
of the measuring branches 𝜙𝐾𝑎𝑥 = 𝜙𝐾𝑏𝑥 = 0. As a result, phase detector gener-
ates a signal on the output. The signal is proportional to the angle of inclination
of the pair of vertebrae, and it is finally independent of the instability influence
of the coefficients of the measurement branches.
4 The algorithm of collecting and pre-processing the
goniometric control data
Implementation the accelerometric method of rotation angle measuring in the
goniometric control systems is based on an algorithm collecting dynamic data,
which is based on the direct conversion of signals from two-component accelerom-
eters in phase sine wave by multiplying the signal on the phase quadrature signals
(PQS) with a frequency, which is a multiple of the reference oscillator frequency
(RG) (Fig. 2) [8].
fd PQS
RG
sin.ω t cos.ω t
. .
ay
ax &
ax
O ay
φ
by
bx
bx by
O
Fig. 2. The algorithm of collecting and pre-processing goniometric control data
According to the algorithm, the rotation angle of the biokinematic couples
in the accelerometric goniometer is determined by the phase difference between
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Mathematical and Information Technologies, MIT-2016 — Information technologies
the measured and the reference signals. Therefore, a signal proportional to the
angle of biokinematic pairs without affecting instability coefficients transmitter
branches is generated at the output by summing the received harmonic signal.
The multiplicative error is eliminated by means of hardware implementation
of the phase-measuring method, namely, by limiting the signal level by a limiter
circuit and following detection of the phase signal [9].
5 The error compensation method of the digital
accelerometers
The measurement error is determined at the error measurement phase, which
is a part of the application of the phase method for measuring turning angle
in the accelerometric goniometer. The measurement is based on the direct con-
version of signals from two-component accelerometers in the phase sine wave. A
sampling error occurs since the phase measurement is conducted at the discrete
time moments [10]. The sampling error is depended on the frequency ratio of
the reference sine wave produced by programmable generator and the sampling
frequency of the signal obtained from the accelerometric goniometer, with an
algorithm of approximation of the target signal being applied between adjacent
sample time moments. Figure 3 shows the sampling error data of the accelero-
metric goniometer signal.
Fig. 3. The sampling error of the accelerometric goniometer signal
Traditionally, to calculate interval approximation between the samples 𝑈𝑖 (at
the time moment 𝑡𝑖 ) and 𝑈𝑖+1 (at the next time moment 𝑡𝑖+1 ), algorithms of
linear approximation are used:
𝑈 (𝑡) = 𝑘𝑡 + 𝑏, (8)
but the real process is described by
𝑈 (𝑡) = 𝑈𝑚 · sin(𝜔𝑡 + 𝜙), (9)
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Mathematical and Information Technologies, MIT-2016 — Information technologies
where 𝜔 = 2𝜋𝑓 is the frequency of reference oscillator, 𝜙 is a variable phase. The
approximation coefficients are determined by the following relations:
𝑈𝑖+1 − 𝑈𝑖 𝑈𝑖 · 𝑡𝑖+1 − 𝑈𝑖+1 · 𝑡𝑖
𝑘= , 𝑏= , (10)
𝑡𝑖+1 − 𝑡𝑖 𝑡𝑖+1 − 𝑡𝑖
The phase is determined on the base of the equation (10) by the time shift
𝜏 , forming an error of determination of the angle of accelerometric goniometer
through the phase error 𝛥𝜙:
𝑘(𝑡𝑖 + 𝜏 (𝛥𝜙)) + 𝑏 = 0. (11)
The time period expression that determines the measured phase on the base of
𝑛-periods of measurement is as follows:
(2𝜋𝑛 + 𝜙) 𝑈𝑖
𝑇 = = 𝑖 · 𝛥𝑡 − · 𝛥𝑡, (12)
𝜔 𝑈𝑖+1 − 𝑈𝑖
where 𝑓𝑑 = 1/𝛥𝑡 is the sampling frequency.
Assuming that the frequencies are multiples of each other, the ratio of the
oscillator and the sampling frequencies are defined by:
𝐹
= 𝑚. (13)
𝑓𝑑
From (12) and (13), the expression for phase determination, which is based on
the linear approximation, takes the form
(︂ )︂
𝑈𝑖
𝜙 = 2𝜋 𝑚 · 𝑖 − ·𝑚−𝑛 (14)
𝑈𝑖+1 − 𝑈𝑖
The rotation angle of the biokinematic pair in a accelerometric goniometer is
measured by the difference of 𝑈𝑖 and the reference phase signal 𝑈 0 :
(︂ )︂
𝑈𝑖 𝑈0
𝛼 = 𝜙 − 𝜙0 = 2𝜋 · 𝑚 · 0 𝑖 0 (15)
𝑈𝑖+1 − 𝑈𝑖 𝑈𝑖+1 − 𝑈𝑖
For this case, the error in the determination of the angle for the real values of
phases is determined on the base of direct calculation
(︃ )︃
𝑈𝑖0 sin(2𝜋𝑚)
𝛼 = arctan −
0 0
(︃ 𝑈𝑖+1 − 𝑈𝑖 cos(2𝜋𝑚))︃ (16)
𝑈𝑖 sin(2𝜋𝑚)
− arctan .
𝑈𝑖+1 − 𝑈𝑖 cos(2𝜋𝑚)
In this case, the analytical expression for estimating the angle measurement
error in the accelerometric goniometer is as follows:
√ √
2𝜋 · 𝑚 − 1 − 𝑎𝑟𝑐𝑡𝑔( 2𝜋 · 𝑚 − 𝑖)
𝑚𝑎𝑥(𝛥𝛼/𝛼) = . (17)
𝜋·𝑚
As seen from the expression (17), the angle error can be reduced by increasing
the sampling rate with respect to the oscillator frequency.
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Mathematical and Information Technologies, MIT-2016 — Information technologies
6 The system of goniometric spine control
In the standard spine goniometry, there are so-called the support points, which
correspond to the ends of the spinous processes of S4, L4, Th7 and C7 vertebrae
[11].
The following algorithm provides a differentiated picture of movements in the
different parts of the spine. At same time, due to the small size and high preci-
sion of accelerometer sensors and system flexibility, the reliability of the results
are significantly increased especially thanks to an additional digital processing
the recorded signals. In addition, our proposed approach is passive, i.e., it does
not use additional exposure, such as in ultrasound or X-ray method, and has
no negative effects on human body. Moreover, the accelerometer module inter-
face can be coupled with other system modules because of compactness of the
accelerometer module.
Existing systems of biomechanics spine control measure only kinematic pa-
rameters of the skeletal system without taking into account the patient’s neuro-
physiological parameters [12]. So, the process of diagnosis and rehabilitation is
slower due to the absence of biofeedback data. Also, recording the parameters of
evoked potentials makes it possible to determine the pain threshold more accu-
rately, and to identify possible causes of motor neurophysiological abnormalities
[13]. In general, the adaptive system of goniometric automated control can be
represented as a block diagram shown in Figure 4.
Forward-looking
Models Neural Network
estimations
database
Neural Network Mathematical Visualization
model module
Measurement database
Dynamic
The density of Informative Informative brain Noise signals of Angles,
Skeletal characteristics of
the medulla muscle signals signals spine distances
parameters step
Module of
Image Processing Module The signal processing unit
synchronization
Bioelectric Electroencephalogram Noises
potentials
X-ray
Tomography picture Electromyography Electroencephalography Accelerometer
photograph
Dynamometry Piezosensor
Calibration
Patient Control block
unit
Evoked potential Assessment module Database of Database of
processing module of problem areas test signals metodics
Fig. 4. The block diagram of hardware and software support of the automated gonio-
metric control
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Mathematical and Information Technologies, MIT-2016 — Information technologies
After the synchronous processing, the recorded parameters form time series,
which are visualized with various degree of detail.
The time series are the basis of a model of patient. The model is processed
by a neural network and is stored in the model data base. The model that most
closely matches the time series is instantiated. Pain thresholds and threshold
of sensitivity of the patient for generating control signals to the actuators are
determined by neural network algorithms. This is possible via a feedback method
(patient’s reactions to test stimuli). Based on the processed data, operation mode
of the actuators is generated and selected from a database of test techniques.
It should be noted that the above adaptive system of goniometric control
includes both stationary and mobile measuring systems. The number of mon-
itored parameters is determined by the severity of the patient’s pathology. In
case of injuries or low severity of the scheduled examination, the use of portable
goniometers alone is sufficient, as it guarantees the freedom of pationt’s move-
ments. If the presence of more serious violations in the musculoskeletal system
functioning is suspected, the use of the accelerometric goniometer coupled with
X-ray and tomography is recommended.
7 The choice of informative variables for constructing
diagnostic models
The main problem of a model determination for diagnosis of the patient’s health
status is selection of informative variables.
In order to form adequate model instances, the sample data should be repre-
sentative, the data should completely and correctly reflect the diagnostic object.
The representativeness of the samples can only be achieved by selecting data
objectively.
The sample data is represented as a matrix whose dimension is 𝑁 × (𝑛 + 1):
𝑊𝑁 = [𝑋𝑛 |𝑌𝑚 ], (18)
where 𝑁 is the number of cases (matrix rows); 𝑛 is the number of independent
informative input variables; 𝑚 is the number of depended informative output
variables; 𝑋𝑛 {𝑋1 , 𝑋2 , ..., 𝑋𝑖 , ..., 𝑋𝑛 }, 𝑌𝑚 {𝑌1 , 𝑌2 , ..., 𝑌𝑗 , ..., 𝑌𝑚 } are sets of vector
values of inputs and outputs; 𝑋𝑖 {𝑥𝑖,1 , 𝑥𝑖,2 , ..., 𝑥𝑖,𝑁 }, 𝑌𝑖 {𝑦𝑗,1 , 𝑦𝑗,2 , ..., 𝑦𝑗,𝑛 } : 𝑥𝑖,𝑁 ,
𝑦𝑗,𝑁 are 𝑖-th value of the input and 𝑗-th value of the output variable of 𝑁 -row
sample data matrix.
Each data row contains sample values of the input (information on chronic
diseases, data from patient history) and output (current symptoms, the results of
goniometry (accelerometry)) informative variables describing the dynamic state
of a particular patient. Sampling should include a training data sample, which
is used at the stage of model construction of the real diagnosed object. An
important condition for the use of samples is that the stored learning sample
data set and testing data set must be different. This ensures reliability of the
diagnostic decisions.
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Mathematical and Information Technologies, MIT-2016 — Information technologies
The quality of the learning data samples obtained in the spine diagnostic
systems is evaluated according to the following criteria: representativity, infor-
mativity, and reliability.
Table 1. Ranges of standards physiological fluctuations and degrees of spinal disorders
in the goniometric studies
Degree of functional disorders
Position Angle Norm slight moderate considerable
of the spine Less More Less More Less More
Free 𝛼 7-13 5-6 14-16 3-4 17-18 62 >19
vertical 𝛽 10-15 8-9 16-18 6-7 19-20 65 >21
position,° 𝛾 9-14 7-8 15-17 5-6 18-19 64 >20
Maximum 𝛼 60-80 51-59 41-50 640
flexion,° 𝛽 90-115 81-89 – 61-68 – 660 –
𝛾 130-155 121-129 111-120 6110
Maximum 𝛼 0-3 4-6 7-8 >9
extension,° 𝛽 35-52 25-34 – 17-24 – 616 –
𝛾 36-50 26-35 16-25 615
The slopes 𝑏𝑠 30-40 20-29 – 10-19 – 69 –
of the sides,° 𝑏𝑑 30-40 20-29 – 10-19 – 69 –
To determine the degree of correlation between the informative variables, i.e.,
to assess the informativity of sample data, rank correlations are used. The degree
of the relationship is determined by the value of the correlation coefficient, which
can range from -1 to +1 inclusive.
To calculate the minimal sample size, the following formula is used:
𝑁 = 𝑛𝑖𝑛𝑓 · (𝑃 · 𝛼/𝜂 2 ), (19)
where 𝑛𝑖𝑛𝑓 is the number of informative variables, 𝑃 is the representativeness
of the sample data; 𝛼 is the required representativeness of the sample data; 𝜂 is
the resulting information content of the sample data.
The input sample data set consists of training and control subsets having the
ratio of 2:1 and separated randomly to the subsets.
Usage of the accelerometer measurement method as a basis for the hard-
ware and software system implementation of goniometric spine control requires
continuous accounting assigned statistical range of physiological fluctuations of
parameters with respect to the biokinematic norm and degrees of functional
disorders of the spine (Table 1), as the system is intended to be used for opti-
mization of medical biomechanical examination.
Selection of informative variables for the construction of multi-level diagnos-
tic model is based on the medical reference book data(Table 2). These variables
are to reflect the relations between the manifestations of a disease from the
current symptoms and reported violations.
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Mathematical and Information Technologies, MIT-2016 — Information technologies
Table 2. Ranges of standards of physiological fluctuations and degrees of spinal dis-
orders in the goniometric studies
Parameters of vertebra Parameters of segment
Vertebra b, mm Fb, ° Gb,° Hd, mm Db, mm Segment
C2 66,3±1,2 21,4±10,9 19,4±5,2 7,3±1,5 0,6±3,0 C2-C3
C3 23,1±10,1 2,4±5,5 4,4 ±2,0 7,3±3,2 1,6±3,0 C3-C4
C4 21,4 ±0,1 2,0 ±3,5 3,2 ±3,6 6,6 ±2,4 1,3 ±1,0 C4-C5
C5 19,3 ±0,1 5,2±0,1 1,7±7,8 7,4±1,2 0,7 ±1,4 C5-C6
C6 20,7 ±0,2 7,0 ±6,2 5,3 ±1,2 7,6 ±3,7 0,0 ±1,0 C6-C7
C7 24,4 ±0,2 12,2 ±6,7 – – – C7-Th1
In Table 2, 𝐹 𝑏 is the body inclination angle to the vertical; 𝐷𝑏 is the body
displacement of the overlying vertebra relative to the underlying one in the plane
of the disc; 𝐻𝑑 is the disc height; 𝐺𝑏 is the angle between adjacent vertebrae.
8 Conclusion
The practical implementation of the proposed approach in the medical organi-
zation in goniometric spine control reveals new insights into the diagnosis and
rehabilitation of the musculoskeletal system, particularly of the spine. The adapt-
ability of the proposed approaches in early detection of motor function disorders,
as well as its high accuracy, prevents the development of other diseases.
The proposed approach to automation of the spine diagnostics allows medical
stuff to:
- continuously monitor the spine bending without attachment of patient to
a stationary place;
- develop methods of evaluation of the degree of allowable deviation of the
spine and vertebrae, accounting the age groups and possible bends of a healthy
human spine, giving rise of the possibilities to automate the monitoring process
that takes into account the patient’s anatomy;
- derive estimations of quantities characterizing the tolerances segments of
the spine of healthy individuals for each type of bending of the back, increasing
the efficiency of diagnosis and rehabilitation of the spine;
- assess the degree of friction during movement of the vertebrae under the
influence of physical activity, and to identify the critical decrease (changes) of
the intervertebral discs;
- derive estimates of the spectral components of an acoustic signal produced
by the friction of the vertebrae, providing means of improvement of the health
automated diagnostic systems based on acoustic methods of control;
- reduce significantly the risk of injury at the time of rehabilitation;
- optimize the rehabilitation process on the basis of the patient’s physical
abilities and data control, allowing timely load adjustments, exclusion of the
overloads and risks of injury.
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Acknowledgments. This work was supported by RFBR grant 16-08-00992-a.
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