Open Access e-Journal Cardiometry - No.14 May 2019

5
( )−
12
5
4 4
− αβ
1 1( 2 + β1) ( α1
− ε1
)+
8
1
+ β α 5 −ε
5
2
2 3 3
f 1 ( ε 1
, α 1
, β 1 )= ε 1 ( 2 + β1
) α1
− ε1
4 1 2
f 2 1 1
5
( 1 1 )
5 3 2
( ε )= ε − ε1
+
3 3
• Maximum velocity U 01
for the early diastole period
and U 02
for the atrial systole is computed as given below:
U
01
3
36787. 5t01 5ε1
− 2 27⎤
=
⎣⎢
⎦⎥
5
5ε
− 2 243
1
⎡
( ) −
( ) −
(cm/s)
Velocity U 02
is calculated using the same formula at ε = ε 2
.
• The value of time interval t01 is determined based
on a certain condition. To calculate it we take value t 01
subject to the following equation:
{
5
SSV t U ⎡
01 01 ⎣ε1
1 f ε , α , β f ε
− − + ( )− ( )
( )} =
5
+ U ε −1 0
02 2
1 1 1 1 2 1
⎤
⎦ +
• The RV1 blood volume, entering the heart ventricle
in the phase of the early diastole, expressed as a percentage
of the filling volume, is found as given below:
RV1
=
U
5
100U
⎡
01 ⎣ε1
− 1+
f1
( ε1, α1,
β1)− f ⎤
2( ε1
) ⎦
5
⎡
⎣ε
− 1+
f1
( ε1, α1,
β1
)− ( ) ⎤
⎦ + 5
f U −
2
ε1 02
ε2
1
01 1
( )
(%)
• The RV2 blood volume, entering the heart ventricle
in the phase of the atrial systole, expressed as a percentage
of the filling volume, is calculated as follows:
RV2 = 100 – RV1 (%)
• Provided that a balance between the blood input volume
during the diastole and the blood output volume
during the systole is kept, it may be assumed that the
condition of the equal volumes in the filling and the
ejection is met. Then, knowing the stroke volume SV
value, it is possible to determine absolute (in ml) values
of diastolic phase volumes PV1 and PV2:
PV1 = SV ∙ RV1 / 100 (ml)
PV2 = SV ∙ RV2 / 100 (ml)
In the process of research, the relative phase volumes
of blood (RV1 ÷ RV5) to express a percentage
of the absolute value of each phase volume to
the stroke volume SV, have been also calculated and
analyzed. The hemodynamic parameters, the values
of which are expressed as a percentage of the stroke
volume, are pronounced markers of the contribution
of each phase process to the formation of cardiac
output.
Conclusions
• An original mathematical model of an optimal hydraulic
system for transportation of multi-phase fluids,
similar to blood, in the most economically efficient
"third" mode has been developed as a pioneering
theoretical basis for studying the peculiarities of the
circulatory system performance.
• Russian researchers G. Poedintsev and O. Voronova
have succeeded in creating a unique mathematical
model of human hemodynamics, which fully describes
the main laws of the transport function in the
circulatory system.
• Based on the above mathematical model concept,
elaborated has been a new noninvasive method for
determining volumetric parameters of the central hemodynamics
in each cardiac cycle phase with the use
of the cardiac cycle phase-related durations according
to an ECG curve. The theoretical concept has been
translated into a new product: PC-assisted hemodynamic
analyzer Cardiocode.
• The hemodynamic phase-related volumetric parameters
are the most informative characteristics of
the performance of the human circulatory system,
since they reflect the joint operation capability of the
heart and blood vessels. By identifying their correlation
and linking the latter with the anatomical and
functional state of the heart and blood vessels, we
obtain fresh possibilities to provide a new-type of
high-accuracy, reliable diagnostics of the circulatory
system performance and pathology, if any. In addition,
the developed method can be successfully used
to assess effectiveness of therapeutic and preventive
measures.
Statement on ethical issues
Research involving people and/or animals is in full
compliance with current national and international
ethical standards.
Conflict of interest
None declared.
Author contributions
All the authors read the ICMJE criteria for authorship
and approved the final manuscript.
References
1. Voronova OK. Development of models and algorithms
for automated assessment of the transport
14 | Cardiometry | Issue 14. May 2019