WO1988001773A1

WO1988001773A1 - Means to determine the amplitude of the circulatory and respiratory parameters and the properties of the aortic-valve of a patient

Info

Publication number: WO1988001773A1
Application number: PCT/NL1987/000020
Authority: WO
Inventors: Tom Mostert
Original assignee: Tom Mostert
Priority date: 1986-09-03
Filing date: 1987-09-03
Publication date: 1988-03-10
Also published as: NL8602228A

Abstract

The natural blood pressure or flow curve in the arteries is found to be sinusoidal during the ejection of the heart and exponential during the post-ejection and both curves superponated by an oscillation curve generated by the Aortic valve. The invention provides a way to obtain the separate real pressure or flow curve and the oscillation curve of the Aortic valve. These real or modified curves are used to calculate several conventional heart related parameters with a better accuracy and some new defined parameters in accordance with appropriate formulae.

Description

MEANS TO DETERMINE THE AMPLITUDE OF THE CIRCULATORY AND RESPIRATORY PARAMETERS AND THE PROPERTIES OF THE AORTIC-VALVE OF A PATIENT.

The invention refers to the means for calculating the amplitude of the circulatory and respiratory parameters and the properties of the aorta-valve from the measured and reduced pressure in the arteries.

Several methods are known to calculate and determinate the amplitude of the cardiac-output. One can distinguish the methods for dilution and the curve contour interpretations . A very primitive interpretation was used at the early stage and further development of the physiology of the heart and circulation. It is known for more than a halve a century that the slope at the beginning of the ejection curve depends on ejection velocity of the blood. At the moment this property is used to determine the cardiac-output ( see for example patent nr. EP60116.). Also several other curve contour interpretations are known and based on the integration of parts of the curve.

These methods are all approximations with several experimental determined constants particular for an individual patient. Several so called 'heart related parameters', like cardiacoutput, vascular resistance, and compliance.

These used constants do not appear to be constant but in practise they are acceptable as an indication within certain limits. Yet it appears that these constants deviate at neuronal, hormonal or changes in activity and even so at several lesions. Although the already existing methods are not accurate enough for research and diagnosis, it even is a fact that many reactions and influences upon the peripheral perfusion are not or hardly detectable with these methods. The purpose of the invention is to determine the amplitude of the circulatory and respiratory parameters in a new manner, based on the fundamental and classical mechanics, as much as possible without using constants or patient dependent constants. Also means for detecting the arterial blood pressure or for measures that are derived from this, belong to this. The magnitudes of the parameter are calculated per heart cycle and reproduced on a monitor or to an output module. It is known in physics that an arbitrary induced pressure wave always evoluates to a single or compound sine curve. The invention uses this property and the fact that the pressure drop in an elastic vascular system declines exponentionally during the stage in which no -injection takes place. As a. result of my researches it has been established that every arterial pressure curve is composed of three fundamental parts. Referring to figure 1 these three fundamental parts can be further indicated. The registration on the left is an arbitrary arterial blood pressure curve as detected from a patient. In the registration on the lower right the separated oscillation curve of the aortic valve is plotted, which is subtracted from the original patient's curve with the results shown at the upper right side of figure 1. Also figure 1 shows the basic parameters which will be used for further explication. In the detected curve the maximum pressure is represented by Ps which resembles with the usual term 'systolic pressure', whereby its supremum occurs at the moment ts. The difference between the begin pressure (Pb) and the systolic pressure (Ps) is the pulse pressure (Pp). The end diastolic pressure is marked by Pe. The duration of the selected cardiac cycle or the cardiac interval time is I. From the separated oscillation curve the period time (To) is determined by measuring the time elapsed between succession of the minimum and maximum, multiplied with four. The maximum of the oscillation curve is marked by Omax and the minimum by Omin. After the subtraction of the oscillation curve and possible artefacts from the detected curve a pure sine and an exponential curve remains, which is determined by a maximum amplitude (A) of the sine wave at the moment of the quarter of the period time (Tp). Also the pressure at the moment of the closure of the aortic valve is the begin pressure of the exponential curve. The moment of the closure of the aortic valve is marked by (tv) which is at that moment the existing pressure (Pv). It is clear (see figure 1) that the pulse pressure and the amplitude (A) even differs from each other at the moment of the maximum pressure. The systolic pressure used in medicine is therefore not correct, also because the oscillation, which is superponated on this, damps as proceeding approximally in the arteries and therefore it does not contribute in the perfusion. The invention therefore supplies in the discrimination of the parameters. The three fundamental parts are hereafter explained. a) During the cardiac ejection a single sine-shaped pressure wave is induced until the aortic valve closes. b) From the moment the aortic is closed the pressure drops exponentionally in the arteries. c) The aortic valve causes, by its own mass and elasticity, a superponated pressure wave on the arterial pressure at the moment of opening and closing. The arterial pressure curve consists of a sine- and an exponentially interval, on both a superponaced pressure wave as a result of the oscillation during the opening and closing of the aortic valve. Accordingly, this invention provides means to split the detected or derived blood pressure curve into the pressure wave of the oscillation of the aortic valve and the sine and exponential curve. The amplitude of the pressure wave of the valve oscillation gives an indication of the velocity at the moment of closing and opening of the aortic valve, or the begin and end ejection velocity. The period time of this oscillation gives an indication of the elastic properties of the aortic valve. In cardiology the so called phσnocardiography is already being used, which is based on .the observation of the frequencies of the sound waves caused by turbulences in the blood vessel. With, the here mentioned pressure waves is not meant sound waves, but the mechanic pressure waves.

The sound waves are not detected in this means and will be left out of consideration. After subtracting the detected pressure curve from the oscillation of the aortic valve, the parameters of the sine and exponential curve are determined. The sine curve is indicated by:

Pi= A sin (wt) (1) Here Pi is the actual pressure during the ejection stage and A is the maximum amplitude of the sine, w is the circle frequency in radials per second and t is the time per second.

The amplitude (A) is determined by the reducing the maximum pressure with the begin pressure of the ejection. It should be noticed that the here mentioned maximum pressure is not identical with the usual systolic pressure because the systolic pressure is similar to the mentioned value of signal A plus the signal B of the oscillation of the aortic valve. Because of this summons the moment of the systolic top is not similar to the top of the sine that remains after subtraction of this oscillation. The duration

(Tp) can be determined by multiplying the moment of the f irs t top with four . The circle frequency is given by:

(2)

As the heart muscle are also elastic there is question of a forced ejection wave and the circle frequency of the generated pressure wave in the arteries will be very close to the natural frequency (resonance frequency) of this vascular system. For the resonance frequency is given:

(3)

Here is m the mass of the ejected blood per volume unit and k is the force constant. Within certain limits Hooke's law of the physical spring can be supplied whereby the increase of the reactive force equals the increase of the volume multiplied by the force constant. ΔP = ΔVk and k = ΔP / ΔV (4)

Here is ΔV the ejection volume per volume unit of the cardiac stroke volume and ΔP the increase of the pressure. The mass of the ejected blood equals to the ejection volume per volume unit times the density (d) of the blood, so: m = d ΔV (5)

Substituting (4) and (5) into (3) we obtain: ( 6 )

The force constant k can be calculated now by using the calculated ΔV out of (6) with the formula (4).

The exponential curve is given by :

-tk/R P = Pv e (7)

Where P is the momentary pressure and Po is the pressure at the moment of the closure of the Aortic valve, R is the vascular resistance. Because the pressure curve as well the elapsed time and the force constant k are known, we are able to calculate the mean arterial resistance during a cardiac cycle.

(8)

THE CALCULATION OF THE PERFUSION VOLUME DURING A CARDIAC CYCLE. The perfusion volume is the quantity of blood leaving the arteries. The cardiac ejection volume per volume unit ( V) is the relative quantity of blood ejected by the left ventricle. The perfusion volume is not intrinsically equal to the cardiac ejection volume. Of course the mean of these two parameters equals over a longer period. According to my opinion it has no sense to monitor the ejection volume for each heartbeat, because it gives no information about the periphery. It is therefore the reason of the invention to indicate the relative perfusion volume per cardiac cycle.

The momentary velocity (i) is obtained by the quotient of the momentary pressure and the resistance : i = P/R (9)

The relative perfusion volume or the arterial debit (D) during a specific cardiac cycle is obtained by quotient of the mean pressure and the resistance (R) and multiplying with the interval time (I) of this cycle.

D = IP/R (10) THE CALCULATION OF THE QUALITY FACTOR OF THE ARTERIES.

The quality factor (Q) is determined by the quotient of the total induced energy and the dissipated energy. The calculation of this factor is given by :

Q = wR/k (11) For convenience sake this factor can be expressed in percents of the total induced energy.

(12)

THE CALCULATION OF THE PHASE.

With the phase is meant the relation between the cardiac interval time (I) and the period time (Tp).

Fs = I/Tp (13)

The phase has an extended diagnostic value, particularly for the interaction of the respiration and circulation.

Figure 2 represents a functional block diagram according to the invention, 1 is analog transducer to detect the arterial blood pressure or a measurement from which this can be derived. The signal of 1 is lead to an amplifier 2. The amplified signal is lead through a filter 3 which splits this signal into two signals A and B. Signal B is the pressure wave caused by the oscillation which is generated by the opening and closing of the aortic valve. Signal A, being the fundamental pressure curve, consists of a sine wave during the opened aortic valve and a decline following a exponential function when the aortic valve is closed. 4 and 5 converts the signals A and B into numerical values and send them to the calculator 6, with an interval determined by the clock pulse of the controller unit 9. The calculator is based on a microprocessor but can also be realized by conventional and discrete logical or analogical components. 7 is an output module which can be a screen or printer as a part of the device or as an extern device, as well a standardized computer output. Also the output device 10 can contain a digital to analog converter to output a selected parameter to analog plotter. Further the invention contains an input device 8 provides the possibility to accept numerical or analogical data from other sources, after which they are processed in the same way as being measured from the units 2 and/of 4 and 5. The function unit 3 can be constructed as an electronic filter or by interpretation and separation the signals 3,4 and 5 by software in the calculator 6. The calculator 6 can be constructed as an automatic functioning computer or like a programmable computer.

Claims

1. Apparatus for the determination and monitoring the amplitudes of the circulatory and respiratory parameters and the properties of the Aortic valve of a patient, comprising means to detect the arterial blood pressure (1) or signals from which the arterial blood pressure can be derived (9), comprising means to separate the pressure wave of the aortic valve oscillation from the detected blood pressure curve by means of an electronic filter or by means of a calculator whereby one signal (A) consists of a sine wave during the cardiac ejection, and a pressure drop defined by an exponential function, after the aortic valve is closed, and the other signal (B) being the oscillation wave caused by the opening and closing of the aortic valve, means to convert the to signals (A) and (B) into a numerical value by a analog to digital converter; means to detect the two signals (A and B) and means to process these data by a calculator which calculates for each cardiac cycle the amplitudes from signal (A) the begin pressure, the end pressure, the maximum pressure , the moment of maximum pressure , the mean pressure , the moment of closing of the aortic valve, the pressure at the moment of closing of the aortic valve, the maximum amplitude of the sine wave being the difference of the begin pressure and the maximum pressure, the duration of the cardiac cycle, the period time of the sine wave being the quadruple of the elapsed time from to the moment of the maximum pressure, and from the second signal (B) the maximum amplitude and the frequency of the oscillation wave; means to calculate the amplitudes of the selected parameters and means to output these parameters to monitor or printer or plotter .

2. Apparatus according to claim 1 wherein said selected parameter is the circle frequency of the sine wave of signal (A) and wherein said means of the calculator calculates the circle frequency in accordance with the expression :

W = 2

/ Tp where :

W = circle frequency (radials per second)

Tp = period time in second obtained from the signal (A) of the selected cardiac cycle.

3. Apparatus according to claims 1 and 2 wherein said parameter is ejection volume of the left ventricle and wherein said means of the calculator calculates the ejection volume of the left ventricle in accordance with the expression :

where : ΔV is the increase of the arterial volume per volume unit during the selected cardiac cycle.

ΔP = the maximum amplitude f the sine wave of the signal (A) d = the density of the arterial blood (normally 1.0575 gr/cm3) W = the circle frequency as obtained from claim 2

4. Apparatus according claims 1,2 and 3 wherein said parameter is force constant of the arterial vascular system, wherein said mains of the calculator calculates the force constant in accordance the expression : k = d W where : k = the force constant of the arterial vascular system per volume unit. W = the circle frequency as obtained from claim 2

ΔV = the ejection volume of the left ventricle as obtained from claim 3 d = the density of the arterial blood (normally 1.0575 gr/cm3)

5. Apparatus according claim 1 wherein said parameter is force constant and the arterial resistance, wherein said means of the calculator calculates the ratio of the force constant and the arterial resistance in accordance the expression :

Where :

R = the arterial vascular resistance k = the force constant of the arterial vascular system Δt = the difference of moment the closure of the aortic valve and the duration of the selected cardiac cycle. (The duration of a closed aortic valve in this cardiac cycle) Pe = the end pressure of the selected cardiac cycle Pa = the pressure at the moment of closing of the aortic valve

6. Apparatus according claims 1,4 and 5 wherein said parameter is resistance of the arterial vascular system calculated in accordance the expression :

R

where : R = the arterial vascular resistance k = the force constant as obtained from claim 4

R/k as obtained from claim 5

7. Apparatus according claim 1 wherein said parameter is phase, wherein said means of calculator calculates the phase according the expression :

F = I/Tp where : F = phase I = interval time of the selected cardiac cycle

Tp = the period time of the sine wave from signal (A)

8. Apparatus according claim 1 wherein said parameter; is the amplitude of the phase, wherein said means of calculator calculates the amplitude of the phase according the expression : Fa = C2 ΔP sin (Tp.t) where :

Fa = amplitude of the phase ΔP = the maximum amplitude of the sine wave of signal (A)

Tp = the period time of the sine wave of signal (A) I = the interval time of the selected cardiac cycle

C2 = conversion factor to absolute values

9. Apparatus according claim 1 wherein said parameter is mean pressure during the selected cardiac cycle, wherein said means of the calculator calculates the mean pressure during the selected cardiac cycle by integrating the numerical values from signal (A) divides by the number of numerical values.

10. Apparatus according claims 1 and 6 wherein said parameter is the mean perfusion velocity per volume unit during the selected cardiac cycle wherein said means of calculator calculates the mean perfusion velocity in accordance the expression :

where :

v = the mean perfusion velocity per volume unit during the selected cardiac cycle. n = the total numerical values of the selected cardiac cycle from signal (A).

Pi = the momentary pressure of the signal (A) of the cardiac cycle. R = resistance of the arterial vascular system as obtained from claim 6.

11. Apparatus according claims 1 and 10 wherein said parameter is the perfusion volume during the selected cardiac cycle, wherein said means of calculator calculates the perfusion volume during the selected cardiac cycle according the expression :

Vp = C4vl where : v = the mean perfusion velocity as obtained from claim 10.

Vp = perfusion volume per volume unit during the selected cardiac cycle.

I = the total interval time of the cardiac cycle.

C4 = conversion factor to absolute values.

12. Apparatus according claims 1,2,4 and 6 wherein said parameter is the relative quality factor of the arterial vascular system, wherein said means of calculator calculates the relative quality factor of the arterial vascular system in accordance the expression :

where :

Qr = the relative quality factor of the arterial vascular system. k = the force constant as obtained from claim 4. w = the circle frequency as obtained from claim 2.

R = the resistance of the arterial vascular system as obtained from claim 6.

13. Apparatus according claims 1 and 3 wherein said parameter is the absolute ejection volume of the left ventricle, of the heart, wherein said means of calculator calculates the absolute ejection volume from the relative ejection volume as obtained from claim 3 multiplied by the volume of the arteries and by a correction factor.

14. Apparatus according claims 1 and 11 wherein said parameter is the absolute perfusion volume, wherein said means of calculator calculates the absolute perfusion volume from the relative perfusion volume as obtained from claim 11 multiplied by the volume of the arteries and by a correction factor.