RU2371084C1 - Method for determining total elasticity of peripheral vascular bed of main arteries - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: invention refers to medicine, namely to diagnostic techniques for vascular bed condition. Patient-specific examination is performed to determine the measuring data of arterial pressure and volume blood flow through main artery mouth within cardiac cycle. Besides within cardiac cycle, there are minimal diastolic pressure Pd, minimum diastolic volume flow Qd, average integral pressure Pc, average integral volume flow Qc and heart rate Ncc are evaluated simultaneously. These data for peripheral vascular bed of main artery provide a basis to determine diastolic resistance as a ratio of minimum diastolic pressure to minimum diastolic volume flow

and average integral volume flow with diastolic resistance as a ratio of average integral pressure to diastolic resistance

Selast is determined as a quotient of diving the difference of average integral volume flow and average integral volume flow with diastolic resistance into product of heart rate Ncc and the difference of average integral and minimum diastolic pressure according to the relation:

EFFECT: method extends range of aids to determine total elasticity of peripheral vascular bed of main artery.

3 cl, 1 tbl, 3 dwg

Description

The invention relates to medicine, namely to methods for diagnosing the state of the vascular bed. The elasticity of the peripheral vascular bed is an important estimate of the severity of atherosclerotic changes in the walls of blood vessels and is defined [1,2] as the coefficient of proportionality between an elementary change in blood pressure dP in the channel and an elementary change in its volume dV:

Determining the elasticity of the peripheral vascular bed is a complex task. It is associated with the isolation and measurement of changes in the volume of the peripheral vascular bed distal to the mouth of the main artery, simultaneously with the measurement of blood pressure in the volume of the channel during the cardiac cycle.

The methods for determining elasticity [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] are numerous and are given for different model ideas about peripheral vascular bed. The methods include the direct determination of total elasticity as a measure of increasing the control volume of the body in vivo simultaneously with the measurement of blood pressure (plethysmography methods) [3]; indirect methods of measuring changes in the total volume - impedance reoplethysmography [3, 9]; methods for determining the overall elasticity and elasticity of a functionally dependent on blood pressure based on Windkessel models, involving the determination of the total peripheral resistance of the vascular bed and the dependence of blood pressure on time [2, 4, 6, 8, 9, 11, 12, 13, 15, 16]; direct methods of measuring the local elasticity of an individual vessel by measuring the geometric dimensions of the vessel in the proximal and distal parts simultaneously with the measurement of blood pressure [5, 14]; indirect methods using the wave theory [7, 17] to determine the elasticity of the walls of the vascular bed by the speed of propagation of a pulse wave in it and so on.

The method is intended to determine the overall elasticity of the peripheral vascular bed of the great arteries.

As prototypes of the invention, the following can be accepted.

. На основании этих данных общая эластичность определяется через общее периферическое сопротивление сосудистого русла Rc, разницу давлений и площадь под кривой давления, определенных для двух точек отсчета времени в течение периода диастолы сердечного цикла. Способ предполагает задание функциональной зависимости давления по времени от конца систолы до конца диастолы по экспоненте. Последнее предположение не вполне корректно, что вызывает последующее усложнение и представление процесса в виде трехэлементной и четырехэлементной Windkessel-модели.1. A method for determining the total elasticity of the peripheral vascular bed [11] within the framework of the two-element Windkessel model (Fig. 1), in which the elasticity value is considered constant (as in the vast majority of methods) and is determined by measuring blood pressure P (t) and the total blood flow volume

. Based on these data, the total elasticity is determined through the total peripheral resistance of the vascular bed Rc, the pressure difference and the area under the pressure curve, determined for two time reference points during the diastole period of the cardiac cycle. The method involves setting the functional dependence of pressure over time from the end of systole to the end of diastole exponentially. The last assumption is not entirely correct, which causes the subsequent complication and presentation of the process in the form of a three-element and four-element Windkessel model.

2. The method [12] of individually determining the elasticity function in the body and continuously determining the living creature’s systemic blood flow by blood pressure, minute volume of blood circulation, through which the body’s total peripheral resistance Rc is determined, and then the time pressure P (t ) using a non-linear model of blood flow. The method is an example of the use of a complicated modified four-element Windkessel model. The disadvantage of these prototypes is the general limitations associated with Windkessel models, determined by the conditional separation of the peripheral network of vessels into deformable and non-deformable parts and the complexity of calculating the elasticity of the deformable vascular bed, associated with the mandatory use in mathematical calculations of the elasticity of nonlinear functional dependences of blood pressure on time P (t )

These disadvantages of the described methods are eliminated by the fact that the proposed method uses a wave model of blood flow [1, 7, 17, 20] to determine the overall elasticity, which differs from the Windkessel models [8, 9, 10, 11, 12, 13] of the peripheral vascular riverbed. The method proposed in the framework of wave theory for determining the total elasticity of the peripheral vascular bed of the main arteries is simple and accurate.

поддерживается на постоянном среднем уровне благодаря постоянной работе деформируемой части периферического русла из эластичных сосудов, деформирующихся и запасающих кровь во время систолы и выталкивающих ее в сосудистое русло артерии во время диастолы (фиг.1)It is known that at the mouth of the aorta the blood flow is intermittent, then due to the elasticity of the walls of the aorta, the discontinuity of blood flow is eliminated and in the main arteries extending from the aorta, the blood flow already has a continuous pulsating wave character. In methods for determining elasticity based on Windkessel models, it is assumed that the volume of blood flow in the peripheral undeformable part of the vascular bed of the main artery

maintained at a constant average level due to the constant work of the deformable part of the peripheral channel from elastic vessels that deform and store blood during systole and push it into the vascular bed of the artery during diastole (Fig. 1)

In the proposed method for determining the total elasticity (Fig. 2), it is assumed that the entire vascular bed is deformable, the constant component of the bloodstream conductivity of the vascular bed is determined by the state of the vascular bed in a minimally deformable diastolic state, and the pulse component of the peripheral vascular bed of the main arteries is associated with fluctuations in the volume of the bed , pressure and speed in it occurs with pressure pulsation (increase in blood pressure above the minimum diastole of natural significance). This component is due to the propagation of pulse waves arising during a heartbeat along the vascular bed until natural attenuation. The basis of the proposed method for determining the total elasticity of the Selast vascular bed is constituted by the data of an individual clinical examination of a patient by measurement:

(далее диастолическое давление);minimum diastolic pressure

(hereinafter diastolic pressure);

(далее диастолического расхода);the average integral value Pc of blood pressure during the cardiac cycle (hereinafter referred to as average pressure); minimum diastolic volumetric flow rate

(hereinafter diastolic flow rate);

average integral Qc during the cardiac cycle of volumetric flow rate (hereinafter referred to as average flow rate);

heart rate Ncc.

This data can be obtained, for example, using duplex scanning and pulse diagnostics. The method takes into account the relationship of these data with the elasticity of the channel. We pass from expression (1), provided that the Selast value is constant, to the mean integral parameters of volume and pressure changes over a single cardiac cycle:

- среднее изменение давления в русле за один сердечный цикл. Диастолическое давление

- это постоянная минимальная составляющая артериального давления в течение сердечного цикла (фигура 3); диастолический расход это

- постоянная минимальная составляющая расхода в течение сердечного цикла. Эти параметры одновременно имеют место в конце фазы диастолы сердечного цикла (см., например, [14, 15]) (фигура 3). В этот момент сосуды периферического русла подвергнуты воздействию минимального трансмурального давления и наименее дилатированы, а периферическое сосудистое русло имеет в этот момент соответственно минимальный объем. Диастолическое сопротивление

имеет максимальное значение, так как согласно уравнению Пуазейля [1] сопротивление кровотоку возрастает пропорционально уменьшению радиуса сосудов в четвертой степени. Согласно уравнению расходаwhere ΔVc is the average change in the volume of the vascular bed for one cardiac cycle.

- the average change in pressure in the channel for one cardiac cycle. Diastolic pressure

- this is the constant minimum component of blood pressure during the cardiac cycle (figure 3); diastolic consumption is

- constant minimum flow rate during the cardiac cycle. These parameters simultaneously occur at the end of the diastole phase of the cardiac cycle (see, for example, [14, 15]) (figure 3). At this moment, the vessels of the peripheral bed are exposed to minimal transmural pressure and the least dilated, and the peripheral vascular bed at this moment has correspondingly minimal volume. Diastolic resistance

has a maximum value, because according to the Poiseuille equation [1], the resistance to blood flow increases in proportion to a decrease in the radius of the vessels to the fourth degree. According to the flow equation

diastolic resistance is equal to:

. Этот объемный расход проходит в расчетной схеме фиг.2 через элемент

.If the volume of the peripheral vascular bed remained the same minimum and unchanged throughout the entire cardiac cycle, then the peripheral resistance of the vascular bed would also be constant (since in the laminar flow regime the resistance is independent of flow) and would equal the diastolic - Rd. The volume flow through the mouth of the arterial bed with an increase in blood pressure would increase only in proportion to the increase in pressure from the minimum diastolic to the current value and would be

. This volumetric flow rate passes in the design scheme of figure 2 through the element

.

возникает целый ряд сложных функциональных изменений в работе периферического сосудистого русла, связанных с эластично-упругой деформацией стенок сети сосудов русла магистральной артерии, их взаимодействием с гемопотоком, суммарно приводящее к вазодилатации и единичному увеличению объема сосудистого русла [1, 7, 17, 20] при каждой пульсации давления. Распространение этих дополнительных объемов вдоль периферического сосудистого русла происходит параллельно основному потоку в виде пульсовых волн и вызывает увеличение объемного расхода по сравнению с величиной

. Элементарное дополнительное приращение объемного расхода Q(t) над расходом

. имеющим место при диастолическом сопротивлении за время dt, равно:In vivo with pressure pulsations P (t) higher

a number of complex functional changes occur in the work of the peripheral vascular bed, associated with elastic-elastic deformation of the walls of the vessels of the main arterial bed, their interaction with the blood flow, resulting in total vasodilation and a single increase in the volume of the vascular bed [1, 7, 17, 20] with each ripple pressure. The distribution of these additional volumes along the peripheral vascular bed occurs parallel to the main stream in the form of pulse waves and causes an increase in volumetric flow compared to

. Elementary additional increment of the volumetric flow rate Q (t) over the flow rate

. taking place with diastolic resistance during the time dt is equal to:

This additional volumetric flow rate passes through the element Rп in the diagram of Fig. 2, the average increment of the volumetric flow rate due to the pulse wave during one cardiac cycle from 0 to tc is

обратно пропорциональна Ncc - частоте сердечных сокращений. С другой стороны, среднее приращение объемного расхода за счет пульсовой волны за время одного сердечного цикла равно ΔVc среднему изменению объема периферического сосудистого русла за один сердечный цикл. Согласно (2), следовательно, имеем:where is the duration of one cardiac cycle

inversely proportional to Ncc - heart rate. On the other hand, the average increment in volumetric flow rate due to the pulse wave during one cardiac cycle is ΔVc the average change in the volume of the peripheral vascular bed per cardiac cycle. According to (2), therefore, we have:

Hence, the elasticity of the peripheral vascular bed of the major artery Selast through the above-mentioned patient examination data is defined as:

и среднеинтегрального объемного расхода при диастолическом сопротивлении, равного отношению среднеинтегрального давления к диастолическому сопротивлению

, величина общей эластичности периферического сосудистого русла магистральной артерии определяется как частное от деления разницы среднеинтегрального объемного расхода среднеинтегрального объемного расхода при диастолическом сопротивлении на произведение частоты сердечных сокращений Ncc и разницы среднеинтегрального и минимального диастолического давления по соотношению

Thus, the method for determining the total elasticity of the peripheral vascular bed of the major artery Selast is based on an individual examination of the patient, determination of blood pressure and volumetric blood flow through the main arterial bed during the cardiac cycle and is characterized in that the minimum diastolic pressure is determined jointly during the cardiac cycle Pd, minimum diastolic volumetric flow rate Qd, mean integral pressure Pc, mean integral volumetric flow rate Qc heart rate Ncc. Based on these data, the values of diastolic resistance of the peripheral vascular bed of the main artery are determined as the ratio of the minimum diastolic pressure to the minimum diastolic volumetric flow

and the average integral volumetric flow rate with diastolic resistance equal to the ratio of the average integral pressure to diastolic resistance

, the value of the total elasticity of the peripheral vascular bed of the main artery is determined as the quotient of dividing the difference in the average integral volumetric flow rate of the average integral volumetric flow rate at diastolic resistance by the product of the heart rate Ncc and the difference in the average integral and minimum diastolic pressure according to the ratio

List of drawings

- переменный по времени расход на входе в сосудистое русло;

- среднеинтегральный по сердечному циклу расход на выходе из периферического сосудистого русла; Rc - среднее периферическое сопротивление сосудистого русла; С - эластичность сосудистого русла.Figure 1. Schematic representation of the Windkessel model and a 2-element electrical analogue of the Windkessel model. P (t) - time-varying blood pressure;

- time-variable flow rate at the entrance to the vascular bed;

- average flow rate integral over the cardiac cycle at the exit from the peripheral vascular bed; Rc is the average peripheral resistance of the vascular bed; C is the elasticity of the vascular bed.

;

- минимальное диастолическое артериальное давление;

- диастолическое сопротивление сосудистого русла; Rп - пульсовое сопротивление русла.Figure 2. Schematic representation of the pulsating wave model and analog circuitry to determine the total elasticity of the peripheral vascular bed of the main arteries; P (t) - variable in time of the heart cycle blood pressure,

;

- minimum diastolic blood pressure;

- diastolic resistance of the vascular bed; Rп - pulse resistance of the channel.

- минимальный диастолический расход;

- максимальный систолический расход;

- среднеинтегральный за сердечный цикл расход;

- минимальное диастолическое давление;

- максимальное систолическое давление;

- среднеинтегральное за сердечный цикл давление.Figure 3. The dependence of the volumetric flow rate and blood pressure during the time of the cardiac cycle at the mouth of the main artery.

- minimum diastolic flow rate;

- maximum systolic flow rate;

- average flow rate for the cardiac cycle;

- minimum diastolic pressure;

- maximum systolic pressure;

- the average integral pressure for the cardiac cycle.

Note that in the proposed method, the average integral values of blood pressure and blood flow volume can be determined exactly by averaging instantaneous values over time during the cardiac cycle, or approximately according to well-known simplified formulas (for example, Hickem's formulas) for average values expressed only through maximum systolic and minimum diastolic values of these quantities. For example, for carotid arteries [21]:

This allows you to use in this method for determining the total elasticity more easily determined maximum systolic values instead of average values, while the total number of parameters determined during the examination of the patient does not change.

величина центрального венозного давления на входе в сердце в приведенных соотношениях принималась равной нулю. Так как значение центрального венозного давления может отличаться от нуля и знакопеременно колебаться около него, то в качестве нулевого значения давления можно принять значение центрального венозного давления

, тогда значения

и Рс необходимо скорректировать, уменьшив их на величину

:When determining the average integral Pc and the minimum diastolic pressure

the value of the central venous pressure at the entrance to the heart in the above ratios was taken equal to zero. Since the value of the central venous pressure can differ from zero and alternately alternate around it, then the value of the central venous pressure can be taken as the zero value of pressure

, then the values

and Pc must be adjusted by decreasing them by

:

;

;

.

.

This leads to an increase in the accuracy of the determination method.

As an example of the application of the described method, we give in table 1 the value of total elasticity determined for the total (OCA) and internal (ICA) carotid arteries by processing data [22] on blood flow, blood pressure and heart rate before and after treatment of a group of patients with hypertension carvedilol, the use of which, as we see, significantly increases the overall elasticity of the vascular bed.

Table 1 Before treatment After treatment Effect WASP Salast (ml / mmHg) 0.085 0.121 + 29.8% ICA Salast (ml / mmHg) 0.0205 0.0288 + 28.9%

LITERATURE

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12. Jeken S., Fele M., Pfeiffer W.Y. "A method for individually determining the body's elasticity function and continuously determining the systemic blood flow of a living creature." RU 2179408 C2.

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14. A. Haluska et al. "A new technique for assessing arterial pressure wave forms and central pressure with tissue Doppler." Cardiovascular Ultrasound 2007, 5: 6

15. K. Hirata et al. "Age-Related changes in Carotid Artery flow and Pressure pulse. Possible implications for cerebral Microvascular disease. " Stroke2006: 37: 2552-56.

16. Bratteli C.W., et al. Apparatus and method for blood pressure pulse waveform contour analysis US. Patent 6689069. February 10, 2004.

17. H. M. Figueroa Roldan. "ESTIMATION OF VESSEL WALL COMPLIANCE USING ACOUSTIC REFLECTOMETRY." Thesis for the degree of MASTER OF SCIENCES, UNIVERSITY OF PUERTO RICO, 2006, pp. 1-135.

18. C. Stefanadis, et al. "Pressure diameter relation of the human aorta. A new method of determination by the application of a special ultrasonic dimension catheter," Circulation 92, pp.2210-2219, 1995.

19. D. Hayoz, et al. "Non-invasive determination of arterial diameter and distensibility by echotracking techniques in hypertension," J. Hypertens 10, pp. S95-S100, 1992.

20. Jiun-Jr Wang, et al. "Time-domain representation of ventricular-arterial coupling as a windkessel and wave system." Am. J. Physiol Heart Circ Physiol 284: H1358-H1368, 2003.

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22. E.P. Svishchenko, L.V. Bezrodnaya, T.N. Ovdienko, O.V. Gulkevich "The effect of carvedilol on physical performance and the state of cerebral circulation in patients with hypertension" http://rql.net.ua / cardio j / 2002/3 / svyshchenko.html

Claims (3)

1. A method for determining the total elasticity of the peripheral vascular bed of the major artery Selast, based on an individual examination of the patient, determination of blood pressure and volumetric blood flow through the mouth of the main artery, during the cardiac cycle, characterized in that the minimum diastolic jointly determined during the cardiac cycle pressure Pd, minimum diastolic volumetric flow rate Qd, average integral pressure Pc, average integral volumetric flow Qc and frequencies heart rate Ncc, based on these data to peripheral vascular main artery diastolic resistance value is determined as the diastolic minimum pressure related to diastolic minimum volumetric flow rate

and the average integral volumetric flow rate with diastolic resistance as the ratio of the average integral pressure to diastolic resistance

, the value of the total elasticity of the peripheral vascular bed of the main artery of Selast is determined as the quotient of dividing the difference in the average integral volumetric flow rate and the average integral volumetric flow rate with diastolic resistance by the product of the heart rate Ncc and the difference in the average integral and minimum diastolic pressure according to the ratio:

2. The method according to claim 1, characterized in that when determining the values of the average integral pressure Pc and the average integral volumetric flow rate Qc, only the maximum systolic and minimum diastolic values of blood pressure and volumetric flow are used. 3. The method according to claim 1, characterized in that when determining the values of the average integral pressure Pc and the minimum diastolic pressure Rp, these values are counted from the value of the central venous pressure.

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