Method, a system and a computer program product for determining a beat-to-beat stroke volume and/or a cardiac output
View Patent ↗The invention relates to a method 10 for determining a beat-to-beat stroke volume 9 a and/or a cardiac output 9 b based on a measurement 2 of suitable arterial pressure data. At the step 4 a waveform of the arterial pressure pulse is assessed based on data obtained during the measurement of step 2 . At step 6 a compliance or impedance in dependence of at least one measurement of arterial pressure data is computed using a non-linear model 7 . The non-linear model may comprise an arctangent model. The arctangent model may be differentiated numerically or analytically to obtain the compliance or the impedance of an aortic portion. The thus obtained compliance or impedance may then be substituted into a linear model 8 . The linear model 8 may comprise a Windkessel model 8 a , or a Waterhammer model 8 b or any other suitable linear pulse contour model 8 c . As a result, the beat-to-beat stroke volume 9 a and/or cardiac output 9 b are computed.
1. A method for determining a beat-to-beat stroke volume or a cardiac output based on at least one measurement of arterial pressure data, the method comprising the steps of:
obtaining at least one measurement of arterial pressure data using a measurement unit;
providing the at least one measurement of arterial pressure data to a processor; and
causing the processor to perform the steps of:
computing a compliance or impedance in dependence of at least one measurement of arterial pressure data using a non-linear model, said non-linear model being given by the following equation:
A ( p )= Am (0.5+(1/π)arctan(( p−p 0)/ p 1),
wherein A(p) is the pressure-dependent cross-sectional area of the aorta in cm 2 ,
Am is the maximal area of the aorta at very high pressure;
p 0 is a parameter indicating an inflection point of a pressure curve A(p); and
pl is a parameter describing a half-width of the pressure curve;
using said compliance or impedance in a pulse contour method for determining the beat-to-beat stroke volume or cardiac output based on the measured arterial pressure data;
approximating parameters of the non-linear model based on a further model based on a person-specific characteristic;
using the approximated parameters for the non-linear model; and
computing the aortic compliance for an effective pressure, wherein for the effective pressure a mean pressure during systole is selected that is computed beat-to-beat for a contraction frequency of the heart.
2. A method according to claim 1 , wherein for the arterial pressure data an arterial pressure waveform is selected.
3. A method according to claim 2 , wherein said non-linear model is conceived to approximate a pressure dependency of a cross-sectional area of a portion of aorta.
4. A method according to claim 1 , wherein the non-linear model is used to approximate mechanical properties of the total aorta.
5. A method according to claim 4 , wherein the mechanical property is a pressure dependent volume V(p) of the aorta, the pressure dependent volume V(p) of the aorta being approximated by an equation of:
V ( p )= A ( p ) Le,
wherein Le is an effective length of the aorta.
6. A method according to claim 5 , wherein the effective length of the aorta is taken to be about 0.5 a height of the person.
7. A method according to claim 1 , wherein a compliance per unit length is derived from the non-linear model, and wherein a total effective aortic compliance is calculated by the processor by taking into account the compliance per unit length in combination with an effective length of the aorta dependent on the person-specific characteristics.
8. A method according to claim 1 , wherein for the pulse contour method a Waterhammer model is used, given by an equation of:
Z ( w, pe )= Z 0 + R Zc /( R+Zc )
wherein:
Z is a total impedance of the aortic portion;
Z 0 is a characteristic impedance of the aorta;
Zc is 1/jwC;
w=2πf, with f the heart rate in Hz;
R is a resistance;
pe is an effective pressure level for the beat; and
C is an aortic compliance.
9. A method according to claim 8 , further comprising the step of causing the processor to determine a value of the resistance R iteratively.
10. A method according to claim 9 , wherein iterations comprise:
determining a stroke volume for an initial value of the resistance R;
determining a cardiac output from the stroke volume;
determining a further value for the resistance based on a means pressure and a cardiac output;
repeating a new stroke volume computation using the further value of the resistance; and
updating the value for the resistance R based on a new value of the stroke volume.