Method and apparatus for determination of left ventricular stroke volume and cardiac output using the arteries of the forearm by means of integration technique
An apparatus a method for determining stroke volume by bioimpedance from a person having two or more spaced apart alternating current flow electrodes positionable on a person and two or more spaced apart voltage sensing electrodes positionable on the person and between the alternating current flow electrodes. A constant magnitude alternating current source is electrically connectable to the alternating current flow electrodes. A voltmeter is electrically connectable to the voltage sensing electrodes and configured to generate a voltage signal Z from a voltage sensed by the voltage sensing electrodes. A processing unit is electrically connectable with the voltmeter and configured to determine a stroke volume (SV) using the voltage signal Z and at least one of six equations.
1. An apparatus for determining stroke volume by bioimpedance from a person, comprising:
two or more spaced apart alternating current flow electrodes positionable on a person;
two or more spaced apart voltage sensing electrodes positionable on the person and between the alternating current flow electrodes;
a constant magnitude alternating current source electrically connectable to the alternating current flow electrodes;
a voltmeter electrically connectable to the voltage sensing electrodes and configured to generate a voltage signal Z from a voltage sensed by the voltage sensing electrodes;
a processing unit electrically connectable with the voltmeter and configured to determine a stroke volume (SV) using the voltage signal Z and at least one of the following six equations:
Q
.
Z
=
C
·
[
∫
t
B
t
0
+
dZ
(
t
)
dt
dt
+
∫
t
0
t
X
-
dZ
(
t
)
dt
dt
]
Z
0
=
C
·
dZ
(
t
)
total
Z
0
(
1
)
Q
.
Z
=
C
·
+
dZ
(
t
)
+
-
dZ
(
t
)
Z
0
=
C
·
dZ
(
t
)
total
Z
0
(
2
)
SV
Z
=
C
·
[
∫
t
B
t
0
+
dZ
(
t
)
dt
+
∫
t
0
t
X
-
dZ
(
t
)
dt
]
Z
0
=
C
·
[
+
Z
+
-
Z
]
Z
0
(
3
)
SV
Z
=
C
·
[
+
Z
+
-
Z
]
Z
0
=
C
·
Z
total
Z
0
(
4
)
SV
Z
=
Q
=
C
·
∫
t
B
t
X
dZ
(
t
)
dt
total
Z
0
=
C
·
Z
total
Z
0
(
5
)
SV
=
C
·
∫
t
B
t
X
dZ
(
t
)
dt
Z
0
=
C
·
Z
Z
0
(
6
)
wherein:
{dot over (Q)} Z =impedance-derived blood flow velocity (mL/s)
∫=definite integral over time intervals from t B to t 0 and t 0 to t X that collectively are a systolic flow time, where t B is a beginning point of cardiogenically-induced transradioulnar impedance pulse, t 0 is a maximum point of cardiogenically-induced transradioulnar impedance pulse, and t X is an ending point of cardiogenically-induced transradioulnar impedance pulse
dZ
(
t
)
dt
=
cardiogenically
-
induced
rate
of
change
of
the
transradioulnar
impedance
pulse
variation
dZ
(
t
)
dt
ma
x
=
peak
rate
of
change
of
the
cardiogenically
-
induced
transradioulnar
impedance
pulse
variation
dZ(t)=cardiogenically-induced transradioulnar impedance pulse variation
C=constant person-specific mass-based allometric equivalent of volume
Q Z =transradioulnar impedance-derived stroke volume
Z 0 =quasi-static transradioulnar base impedance.
2. The apparatus for determining stroke volume of claim 1 , further comprising:
a data input device in communication with the processing unit for receiving the person's weight W, wherein the processing unit is configured to determine the constant person-specific mass-based allometric equivalent of volume C using the following equation:
C
=
[
[
a
n
W
b
]
·
[
k
1
k
2
(
dZ
/
dt
ma
x
·
Z
0
-
1
)
0.5
]
·
[
dZ
/
dt
ma
x
Z
0
]
·
T
SF
∫
t
B
t
X
dZ
(
t
)
dt
Z
0
]
wherein a is at least 5 and no greater than 10, n is at least 2 and no greater than 4, W is the person's weight, b is at least 1 and no greater than 2, k 1 ·k 2 collectively are a dimensionless constant at least 0.04 and no greater than 0.3, dZ/dt max is a peak time rate of change of a transradioulnar impedance pulse variation, Z 0 is a transradioulnar quasi-static base impedance, T SF is a systolic flow time, and Vc is cM d where c is at least 30 and no greater than 50, M is the person's weight and d is at least 1 and no greater than 2.
3. The apparatus for determining stroke volume of claim 2 , wherein the constant k 1 ·k 2 comprises:
an impedance constant k 1 at least 0.08 and no greater than 0.2, and
a calibrating temporal constant k 2 at least 0.5 and no greater than 1.5.
4. The apparatus for determining stroke volume of claim 1 , wherein the processor is configured to:
determine heart rate from the voltage signal; and
determine cardiac output (CO) by using the following formula: CO=(heart rate)×(SV).
5. The apparatus for determining stroke volume of claim 4 , further comprising:
a band configured to wrap around and secure to a person's wrist, wherein the processing unit is mounted to the band.
6. The apparatus for determining stroke volume of claim 5 , further comprising:
a display mounted to the band, wherein the display is electrically connected to the processing unit and configured to display at least one of the determined stroke volume and the determined cardiac output.
7. The apparatus for determining stroke volume of claim 4 , further comprising:
an exercise machine being one of a stationary bicycle, a treadmill, an elliptical pedaling device and a stair-climbing machine, wherein the exercise machine includes a display operatively connectable to the processing unit and configured to display at least one of the determined stroke volume and the determined cardiac output.
8. The apparatus for determining stroke volume of claim 7 , wherein the operative connection between the display and the processing unit comprises a cable.
9. The apparatus for determining stroke volume of claim 7 , wherein the operative connection between the display and the processing unit comprises a wireless connection.
10. The apparatus for determining stroke volume of claim 7 , wherein the alternating current source, a voltmeter and the processing unit are mounted to the exercise machine.
11. The apparatus for determining stroke volume of claim 1 , further comprising:
an exercise machine being one of a stationary bicycle, a treadmill, an elliptical pedaling device and a stair-climbing machine, wherein the exercise machine includes a display operatively connectable to the processing unit by a wireless connection and configured to display at least one of the determined stroke volume and the determined cardiac output.
12. The apparatus for determining stroke volume of claim 1 , further comprising:
an adhesive strip on which the two or more spaced apart alternating current flow electrodes and the two or more spaced apart voltage sensing electrodes are affixed.
13. A method of determining stroke volume by bioimpedance from a person, comprising:
positioning two or more spaced apart alternating current flow electrodes on the forearm of a person;
positioning two or more spaced apart voltage sensing electrodes on the forearm of the person and between the alternating current flow electrodes;
providing a constant magnitude alternating current flow through the alternating current flow electrodes;
measuring a voltage Z between the voltage sensing electrodes;
determining a stroke volume (SV) using the measured voltage Z and at least one of the following six equations:
Q
.
Z
=
C
·
[
∫
t
B
t
0
+
dZ
(
t
)
dt
dt
+
∫
t
0
t
X
-
dZ
(
t
)
dt
dt
]
Z
0
=
C
·
dZ
(
t
)
total
Z
0
(
1
)
Q
.
Z
=
C
·
+
dZ
(
t
)
+
-
dZ
(
t
)
Z
0
=
C
·
dZ
(
t
)
total
Z
0
(
2
)
SV
Z
=
C
·
[
∫
t
B
t
0
+
dZ
(
t
)
dt
+
∫
t
0
t
X
-
dZ
(
t
)
dt
]
Z
0
=
C
·
[
+
Z
+
-
Z
]
Z
0
(
3
)
SV
Z
=
C
·
[
+
Z
+
-
Z
]
Z
0
=
C
·
Z
total
Z
0
(
4
)
SV
Z
=
Q
=
C
·
∫
t
B
t
X
dZ
(
t
)
dt
total
Z
0
=
C
·
Z
total
Z
0
(
5
)
SV
=
C
·
∫
t
B
t
X
dZ
(
t
)
dt
Z
0
=
C
·
Z
Z
0
(
6
)
wherein:
{dot over (Q)} Z =impedance-derived blood flow velocity (mL/s)
∫=definite integral over time intervals from t B to t 0 and t 0 to t X that collectively are a systolic flow time, where t B is a beginning point of cardiogenically-induced transradioulnar impedance pulse, t 0 is a maximum point of cardiogenically-induced transradioulnar impedance pulse, and t X is an ending point of cardiogenically-induced transradioulnar impedance pulse
dZ
(
t
)
dt
=
cardiogenically
-
induced
rate
of
change
of
the
transradioulnar
impedance
pulse
variation
dZ
(
t
)
dt
ma
x
=
peak
rate
of
change
of
the
cardiogenically
-
induced
transradioulnar
impedance
pulse
variation
dZ(t)=cardiogenically-induced transradioulnar impedance pulse variation
C=constant person-specific mass-based allometric equivalent of volume
Q Z =transradioulnar impedance-derived stroke volume
Z 0 =quasi-static transradioulnar base impedance.
14. The method of claim 13 , further comprising:
determining the constant person-specific mass-based allometric equivalent of volume C using the following equation:
C
=
[
[
a
n
W
b
]
·
[
k
1
k
2
(
dZ
/
dt
ma
x
·
Z
0
-
1
)
0.5
]
·
[
dZ
/
dt
ma
x
Z
0
]
·
T
SF
∫
t
B
t
X
dZ
(
t
)
dt
Z
0
]
wherein a is at least 5 and no greater than 10, n is at least 2 and no greater than 4, W is a person's weight, b is at least 1 and no greater than 2, k 1 ·k 2 collectively are a dimensionless constant at least 0.04 and no greater than 0.3, dZ/dt max is a peak time rate of change of a transradioulnar impedance pulse variation, Z 0 is a transradioulnar quasi-static base impedance, T SF is a systolic flow time, and Vc is cM d where c is at least 30 and no greater than 50, M is the person's weight and d is at least 1 and no greater than 2.
15. The method of claim 14 , wherein the constant k1·k2 comprises:
an impedance constant k1 at least 0.08 and no greater than 0.2, and
a calibrating temporal constant k2 at least 0.5 and no greater than 1.5.
16. The method of claim 13 , wherein the positioning of the two or more spaced apart alternating current flow electrodes on the forearm of the person comprises:
positioning a first of the two or more spaced apart alternating current flow electrodes proximal to the antecubital fossa of the person's forearm; and
positioning a second of the two or more spaced apart alternating current flow electrodes proximal to the wrist of the person.
17. The method of claim 13 , further comprising:
determining heart rate from the measured voltage; and
determining cardiac output (CO) by using the following formula:
CO=(heart rate)×(SV).
18. The method of claim 17 , further comprising:
displaying at least one of the determined stroke volume (SV) and the determined cardiac output (CO) on a visual display.
19. The method of claim 17 , further comprising:
mounting the visual display to the person's wrist.
20. The method of claim 17 , wherein the visual display is included as part of an exercise machine being one of a stationary bicycle, a treadmill, an elliptical pedaling device and a stair-climbing machine.
21. The method of claim 13 , wherein the two or more spaced-apart alternating current flow electrodes and the two or more spaced-apart voltage sensing electrodes are affixed to an adhesive strip.