CA2073019A1

CA2073019A1 - Method fof measuring blood pressure with a photoplethysmograph

Info

Publication number: CA2073019A1
Application number: CA002073019A
Authority: CA
Inventors: Paul Harvey Jones; Wei-Min Wang
Original assignee: Individual
Current assignee: Spacelabs Medical Inc
Priority date: 1990-09-06
Filing date: 1991-09-06
Publication date: 1992-03-07
Also published as: WO1992003967A3; DE69119741T2; US5140990A; WO1992003967A2; EP0498885A1; DE69119741D1; EP0498885B1

Abstract

A method and apparatus for determining arterial blood pressures uses a photoplethysmograph (4). The output (22) of which is calibrated to the patient (9) using an auxiliary blood pressure determining instrument (20); a constant (k) particular to the patient's arterial blood pressure-volume relationship is determined and is stored for later use; at the time of measurement information is obtained from the photoplethysmograph output (22); and a computer (24) determines the patient's systolic and diastolic blood pressures.

Description

W~9~03967 PCT/US91/06914 ~7 3~
Description A METHOD OF MEASURING BLOOD PRESSURE WITH A
PHOTOPLETHYSMOGRAP~
Technlcal Field This invention relates generally to blood pressure measurements. More particularly, it relates to a method of non-i~vasively determining blood pressure using a photoplethysmograph.

Back~round of the Invention Arterial blood pressure measurements provide valuable information about a patient's condition. The heart's cyclical action produces a blood pressure maximum at systole, called systolic pressure, and a minimum pressure at diastole, called diastolic pressure. While the systolic and diastolic pressures are themselves important in gauging the patient's condition, other useful parameters are the mean (average) blood pressure during a heart cycle, and the pulse pressure, which is the arithmetic difference between the systolic and diastolic pressures.
The importance of arterial blood pressure has spurred the development of numerous methods of determining it. The most widely used method is probably the familiar blood pressure cuff, which consists of an expandable ring (l) inflated to stop arterial blood flow and (2) then gradually contracted. Using a stethoscope, medical personnel listen to the artery to determine at what pressure blood flow begins, establishing the systolic pressure, and at what pressure flow is unrestricted, establishing the diastolic pressure. More advanced blood pressure monitoring systems plot the arterial blood pressure through a complete heart cycle. Typically, these systems use catheters having piezoelectric pressure transducers that produce output signals dependent upon the S-18STITUl E SHEET

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W092/03~67 ~ 9 PCT/US91iO6914 ~ ~Q~ ~ 2 instantaneous blood pressure. The output signals are monitored and used to determine the arterial blood pressures over a complete heart cycle. These systems are advantageous in that the blood pressure is continuously measured and displayed.
While prior art methods are useful, they have disadvantages. Cuff-type systems require restricting arterial blood flow and are not suitable for continuous use. The piezoelectric-type systems generally require undesirable invasive techniques, costly disposable materials, and time and skill to set-up. However, during certain critical periods, such as surgery, continuous arterial blood pressure monitoring is highly desirable.
Therefore, it would be beneficial to have a method of continuously and non-invasively measuring a patient's blood pressure.
Photoplethysmographs are well-known instruments which use light for determining and registering variations in a patlent's blood volume. They can instantaneously track arterial blood volume changes during the cardiac cycle. Since photoplethysmographs operate non-invasively, much work has gone into using them to determine blood pressure. In 1983, inventor Warner was issued U.S. Patent No. 4,418,700 on a method of determining circulatory parameters, wherein signals from a photoplethysmograph were used to determine arterial blood pressure.
Significant problems were found when investigating the Warner method. Therefore, it is clear that the need for a practical method of continuously and non-invasively monitoring arterial blood pressure has remained.

Summarv of the Invention It is an object of this invention to provide an improved method for continuously and non-invasively measuring arterial blood pressure.
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It is another object of the present invention to provide an improved method and system for non-invasively determining arterial systolic and diastolic blood pressures with a photoplethysmograph.
These and other objects, which will become apparent as the invention is more fully described below, are obtained b~ providing a method and apparatus for determi~ing arterial blood pressures using a photoplethysmograph. The inventive method comprises the steps of calibrating the photoplethysmograph output with a patient's arterial blood pressure to determine an arterial constant k in the formula, ~ ~inf(l~KeXp(-kp)~
where ~ is the arterial blood volume, ~inf is a conversion lS constant corresponding to arterial blood volume at infinite pressure, K and k are arterial constants for the patient, and P is the instantaneous arterial blood pressure; gathering data from the photoplethysmograph output during a measurement period; and computing the arterial systolic and diastolic pressures at the measurement period using the evaluated arterial constant k and the data gathered during the measurement period.

Brief Description of the Drawinqs Figure l is a partial cutaway view, partial application depiction, and partial block diagram illustrating a preferred method in operation.
Figure 2 is a sketch of the output waveform from a photoplethysmograph receiver over two cardiac cycles.
Figure 3 is a block diagram illustrating the basic procedural steps of the preferred method of Figure l.
Figure 4 is a flow diagram of the pref erred procedure for calibrating the photoplethysmograph output to a patient according to the inventive method.

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Figure 5 is a flow diagram of thP output monitoring and data acquisition steps according of the inventive method.
Figure 6 is a flow diagram outlining the preferred procedural steps for arterial blood pressure determination according to the inventive method.
Figure 7 is a flow diagram of an alternative procedure for calibrating the photoplethysmograph output to a patient according to the inventive method.
Figure 8 is a flow diagram outlining alternative -~
procedural steps for arterlal blood pressure determination according to the inventive method.

Detailed Descri~tion of the Invention -~
A preferred embodiment of the present invention, shown in Figure 1, uses a transmitter 2 portion of a photoplethysmograph 4 to cause monochromatic light 6, preferably in the red and IR ranges, to be emitted from a photodiode light source 8. The emitted monochromatic light 6 travels through a patient 9, along a light path which includes blood 10 in an artery 12, to a photodiode light detector 14. While artery 12 has been described, and is shown in Figure 1, as a single artery, in all practical cases the light path actually passes through many arteries. These arteries can be lumped together and treated as if only one artery 12 existed. Therefore, for simplicity, the remainder of this application will only discuss one artery 12, but it is to be understood that it represents the composite effects of many individual arteries. The light path is also through background tissue 16. The transmitter 2 controls the amount of monochromatic liyht 6 emitted by varying the amount of current through the light source 8. In the preferred embodiment, the transmitter 2 regulates the monochromatic light 6 at a fixed level.
As the monochromatic light 6 travels along its light path it is partially absorbed by the background SUBSTITUTE SHEET

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~ 5 207~ 9 tissue 16 and the blood 10. A portion of the monochromatic light 6 is not absorbed and impinges on the light detector 14, creating electrical signals which are applied to a receiver 18 of the photoplethysmograph 4.
The magnitudes of these electrical signals depend upon the amount of monochromatic light emitted by the light source 8, the path lengths through the background tissue 16 and the blood 10, the amount of light absorbed per unit length by the blood lo and tissue 16, the conversion efficiency of the light detector 14, and various lumped losses such as poor focusing of the monochromatic light 6.
Since the artery 12 i5 pliant, as blood pressure increase so does the volume of blood 10 within the artery 12. As the heart beats, its cyclical action causes the arterial blood pressure to change. This causes the electrical signals to change since the path length through the blood 10 changes, causing the amount of monochromatic light 6 absorbed by the blood 10 to change. Therefore, the electrical signals from the light detector 14 applied to the receiver 18 is a function of the arterial blood pressure.
The receiver 18 amplifies the electrical signals to a usable level and applies them as analog signals, via a receiver line 22, to an analog-to-digital converter A/D
23. The A/D 23 converts the outputs of the receiver 18 to time sampled digital signals which are applied to the computer 24 via a computer bus 25.
The signals on the receiver line 22 can be represented by the photoplethysmograph output waveform 26, shown in Figure 2 for two cardiac cycles. The horizontal axis designates time and, in the present apparatus, the vertical axis designates volts, but current levels would also be suitable. Times tO and tl, denoting the beginning of each cardiac cycle, are clearly marked. The waveform 26 can be described mathematically as a function of time, with the description being f(t). The voltage waveform is inverted from the common pressure waveform becaus~ the SUBSTITUTE SHEET

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~, W092/03967 ~ PCT/~S91/0~914 voltage corresponds to transmitted light. The highest voltage obtained over a cardiac cycle, Vd, coincides with the diastolic pressure and the lowest voltage, Vs coincides with the systolic pressure. Between Vs and V
is a mean pressure voltage Vm, which corresponds to the mean, or average, arterial pressure over a full cardiac cycle. The duration of the cardiac cycle, td is the time between reoccurrences of the diastolic or systolic voltages. The area between the waveform function f(t) and the diastolic voltage line, shown in crosshatch in Figure 2, is called the IIARCo 1l The particular values for Vs~ Vm, Vd, as well as the waveform function f(t) and the area A~C, change with different patients, photoplethysmographs, sensor locations, and photoplethysmograph settings. However, these parameters are functions of the arterial blood pressure.
In a preferred method of the present invention, three major steps are used to determine arterial blood pressure, shown in Figure 3. The first, shown in block 310, is the calibration of the photoplethysmograph output to the patient. Referring now to Figure l, the calibration is accomplished by matching the photoplethysmograph output on the computer bus 25 at the time of calibration with the systolic, Psl and diastolic Pd, blood pressures from the auxiliary blood pressure instrument 20. In the preferred embodiment, these blood pressure measurements are entered via a keyboard to the computer 24. However, preferably this information would be entered directly via an instrument bus 28. The photoplethysmograph output is compared with the systolic and diastolic pressures, Ps and Pd, from the auxiliary blood pressure instrument 20 and several constants are determined, as is subsequently discussed.
~s is shown in Figure 3, block 320, the next step is the measurement of the phokoplethysmograph outputs during a measurement period to determine various information. This information includes the systolic, SUBS~ITUTE SHEET

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~ 7 mean, and diastolic photoplethysmograph voltages Vs~ Vm and Vd, respectively, the cardiac duration td, and the ARC. The final steps, shown in Figure 3, blocks 330 and 340, are the calculations of the systolic and diastolic blood pressures, Ps and Pd, respectively, using the determined photoplethysmograph information and the constants determined in blocks 320 and 310. After the systolic and diastolic blood pressures are determined, the information is output to medical personnel on a display 30. If more measurements are desired, decision block 350 causes blocks 320, 330, and 340 to be repeated. However, only one calibration phase 310 is required. These major steps are expanded upon below.

Derivation of the Mathematical Model The principle of the inventive method is derived from the Beer-Lambert law of analytical chemistry. The Beer-Lambert law gives the rela-tionship between the absorption of monochromatic light by a concentration of a material in a solution as a function of the path length through the solution. Mathematically, the Beer-Lambert law is expressed as:

I = IOexp cex where I is the intensity of transmitted light, Io is the intensity of incident light, c is the concentration of material, e is the extinction coefficient of monochromatic light at a wavelength ~, and x is the light path length through the medium.
The present invention analogizes blood lO and tissue 16 density to concentration, modifies the Beer-Lambert law so that the light intensity terms are given in terms of receiver 18 output voltages, and breaks the light SUBSTITUTE SHEET

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path into individual lengths containing the background tissues 16 and the arterial blood 10. Therefore, the modified version of the Beer-Lambert law is:

V = ZI exp(~Ctetxt - c e x ) where the t refers to the background tissues 16, a refers to the blood 10 in the artery 12, V is an equivalent transmission voltage corresponding to the transmitted light, and Z is a constant relating light intensity to the receiver 18 output voltage.
This can be simplified to:
V AOexp~ Ctetxt)exp(-cae x ) where Ao = ZIo-This version has separable components, AOexp( Ctetxt) which relates to the conversion constant and the background tissues 16, and exp( Caeaxa)~ which relates to the arterial blood 10. For simplicity, the first component can be given as VO = AOexp( Ctetxt)~ the background transmission voltage. Therefore, the equivalent transmission voltage can be calculated as:

V = VOeXp( a a a) -~

It is convenient to express the above formula in terms of arterial blood volume rather than light path length. Therefore, letting ~ be the arterial blood volume, and substituting for the light path xa V = VOexp (-b~
where b is equal to caea(4/~L)~, and L is the light path width through the artery 12. Taking the natural logarithm results in:

lnV = -b~ + lnVO

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W092/039~7 PCT/US91/06914 9 2 a7 ~ O l9 This version becomes more useful after incorporation of the arterial volume-pressure relationship~

~ = ~inf(l~KeXp(-kP)) where ~ is still the arterial blood volume, ~inf is a conversion constant corresponding to the blood volume at infinite blood pressurP, and K and k are constants for the artery 12, and P is the instantaneous arterial blood pressure. This arterial volume-pressure relationship is a good approximation at the pressures of interestO
Substituting this formula for ~ in the logarithmic version:
lnV = -b(~inf)~ Kexp(-kP))~ + lnVO
This can be expanded using a Taylor series.
Expanding and eliminating higher terms results in:

lnV = f + (n)exp(-kP) where f is equal to lnVO - b(~inf)~, and n is equal to (Kb(~inf)~)/2. This can be converted to:

V = (u)exp((n)exp(-kP)) where u is equal to exp(f~. In terms of systolic, diastolic, and mean pressures:

Vs = (u)exp((n)exp(-kPs)) for systolic Pressure ~ = (u)exp((n)exp(-kPd)) for diastolic Pressure V~ = (u)exp((n)exp(-kPm)) for mean Pressure ~ ~
Vinf = U ~ '' V0 = (u)exp(n) Vo/Vinf = exp(n) SUBSTITUTE SHEET

W092/039~7 PCT/US9~/06914 Where Vinf is the equivalent receiver voltage at infinite pressure and V0 is the equivalent receiver voltage at zero pressure.
Establishing various ratios:

Vd/Vs = exp((n)(exp(-kpd)-exp(-kps))) Vd/Vm = eXP((n)(eXp(-kPd)-exp(-kpm))) ln(Vd/Vs) = ~n)(exp(-kPd)-exp(-kPs)) ln(Vd/Vm) = (n)(exp(-kPd)-exp(-kPm)) and ln(V0/Vlnf) = n leads to useful ratios: ~-ln(Vd/Vm) exp(-kPd)~eXP(~kpm) =
ln(Vd/Vs) exp(-kPd)-eXp(-kps) 1-exp(-kPp/3) 1-exp(-kPp) and:
ln(Vd/Vs) = exp(-kPd)-eXp(-kps) ln(Vo/Vinf) = [exp(-kPd)](l-exp(-kPp) where Pp is termed "pulse pressure" and is equal to Ps - Pd~
. -Details of the Preferred Method The previous ~ection derived various .
relationships useful in the preferred method as outlined .
in Figure 3. The step of calibrating the photoplethysmograph outputs to the patient 9, shown in Figure 3, block 310 is shown in expanded detail in Figure ~:
4. The first two steps, shown in block 410 and block 420 SUBSTITUTE SHEET ~-~,~

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are the determination and entering of the systolic and diastolic blood pressures, Ps and Pd, respectively, at calibration into the computer 24. As previously indicated and as shown in Figure 1, these blood pressures are determined by an auxiliary blood pressure instrument 20, preferably an accurate blood pressure cuff having direct inputs to the computer 24 via the instrument bus 28.
The next two steps, shown in blocks 430 and 440 of Figure 4 are the determination of the photoplethysmograph voltages, Vs and Vd, from the receiver 18 output at the calibration systolic and diastolic blood pressures, respectively. These photoplethysmograph voltages are readily determined since they are the minimum and maximum output signals, respectively, from the A/D converter 23. Next, as shown in block ~50, the duration of the cardiac cycle, td is determined from the output of the A/D converter 23. This is also readily accomplished by using a counter to determine the time between the diastolic voltages, times to and t1 of Figure 2.
To determine various patient arterial constants, the preferred method requires that the area between the diastolic voltage Vd and waveform function f(t), or ARC, be determined. This step is shown in block 460 and is preferably accomplished by determining the integral of the photoplethysmograph voltages over the cardiac cycle using: tl ARC - (Vd)(tl ~ to) f(t)dt tO
where ARC is the area bet1 ~een the waveform f(t) and the diastolic voltage line Vd, time to is the time at the start of a cardiac cycle, t1 is the time at the start of the next cardiac cycle and (tl - to) is the cardiac cycle duration td. The calculation of ARC is easily performed using a digital computer since the output of the A/D
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~,Q~ 3~-9 12 photoplethysmograph signals over time. Using the Simpson approximation to determine the integral is particularly expedient because the digital magnitudes can be multiplied by the sampling time between readings, then summed, to arrive at ARC. While ARC is preferablv determined using integral equations, other methods of determining it are also acceptable.
Next, as shown in block 470, the photoplethysmograph voltage, Vm corresponding to the mean pressure is determined from the formula Vm = Vd - (ARC/td) i where all terms are as previously given.
With Vm known, the next steps, shown in block 480 and 490, are to determine the patient's arterial constant k, solved numerically, and the ratio Vo/Vinf solved using either algebraic or numeric methods:
ln(Vd/Vm) exp(-kPd)~eXP(~kpm) ln(Vd/Vs) exp(-kPd)-exp(-kps) and ln(Vd/Vs) = exp(-kPd)-eXP(~kPs) ln(Vo/Vinf) With the above patient arterial constant k and Vo~Vinf in memory, the patient's arterial blood pressures can be determined only from the photoplethysmograph output. This requires that various information be determined during a measurement period, as shown in block 320 of Figure 3 and with expanded detail in Figure 5.
35 Referring to Figure 5, when arterial blood pressures are ~-to be determined, the computer 24 monitors the photoplethysmograph outputs to determine, at the time of measurement, the systolic voltage Vs~ the diastolic voltage Vd, the duration of the cardiac cycle td and the SUBSTITUTE SHEET

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ARC, as shown in blocks 510, 520, 530 and 540, of Figure 5 respectively. With the information Vd, td and ARC
determined, the computer 24 th~n determines, as shown in block 550, the equivalent photoplethysmograph voltage Vm usi.ng the formula:

Vm = Vd - (ARC/td) With the arterial constant k and the ratio Vo/Vinf determined according to th~ flow chart of Figure 4, and the photoplethysmograph information determined according to the flow chart of Figure 5, the computer 24 determines the patient's systolic and diastolic blood pressures as shown in the flow chart of Figure 6, which is a more detailed description of blocks 330 and 340 of Figure 3. The most efficient method of determining systolic and diastolic blood pressures appears to be, as shown in block 610, to first calculate the pulse pressure Pp, using numerical methods, from the formula:

ln(Vd/Vm) 1 - exp(--kPp/3) ln(Vd/vs) 1 - exp(-kPp) Next, the diastolic blood pressure Pd is determined, as shown in block 620, using the formula ln(Vd/vs) = [exp(-kPd) ] [l-eXp(-kPp) ]
30ln (vo/vinf ) The determination of the systolic blood pressure Ps~ is then readily accomplished, as shown in block 630, using the equatiOn Ps = Pd + Pp-While the above is the preferred method of calculatingarterial systolic and diastolic blood pressures from the photoplethysmograph outputs, other schemes are possible.
The systolic and diastolic blood pressures are then available for output to medical personnel as shown in SUBSTITUTE SHEET

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block 640, in a variety of way such as by digital or analog readouts, chart recorders, voice synthesis, or as in the present embodiment on a display monitor 30. If another sPt of measurements is desired then decision block 650 causes the flow shown in Figures 5 and 6 to be repeated.
The preferred embodiment described above is useful, can be readily implemented on a digital computer, and provides accurate and rapid measurements of arterial blood pressures non-invasively and in a manner suitable for continuous measurements. However, in some patients and under some conditions, the preferred method leads to inaccuracies because of time variations in Vinf, the equivalent receiver voltage at infinite pressure. Vinf, in the preferred method was part of the ratio Vo/V
determined during calibration and presumed constant. The preferred embodiment can be modified to compensate for changes in Vinf but at the expense of additional computation difficulty and time.
The alternative embodiment follows the same three major steps as shown in Figure 3 for the preferred embodiment. However, the calibration procedure of Figure 4 is modified to that shown in Figure 7. These calibration procedures, shown in Figure 7 blocks 710 through 780, are identical until Vinf is determined in block 790. It can be shown that Vinf is determinable by the following formula~

Vinf = exp{[ln(Vs) - (lnVd)exp(-kPp)]/[l-exp(-kpp)]}
With Vinf thus determined in block 790, V0, the equivalent receiver voltage at zero pressure, is determined, as shown in block 799, from the formula:
ln(vd/vs) - - = [exp(-kPd)][l-exp(-kPp)]
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After the photoplethysmograph output is calibrated according to the alternative embodiment, as shown in Figure 7, the patient constants k and V0 are known.
According to the alternative embodiment, the data gathering steps depicted in Figure 5 remain the same.
However, during blood pressure determination, the flow diagram of Figure 6 is modified to the procedural steps shown in Figure 8. Referring now to Figure 8, after determination of the pulse pressure Pp in block 810, in the same manner as it was determined in block 610, the Vin~ at the time of measurement is determined, as shown in block 820, from equation:

Vinf = exp{ln(Vs) - [exp(-kPp)]lnvd]/~l-exp(-kpp)]}

where Vs and Vd are also the values at the time of measurement.
This new Vinf is then used in the equation of block 830, along with the previously stored value of V0, to determine the diastolic pressure Pd. This alternative embodiment reduces the effects of changes in Vinf. The calculation of the systolic pressure Ps~ shown in Block 840, and the output of the systolic and diastolic pressures, Pd and Psl respectively, as shown in block 850 are performed in the same manner as they were in blocks 630 and 640, respectively, of E'igure 6. Likewise, the decision block 860 operates in the same manner as the decision block 650 in Figure 6.
The apparatus for practicing the present invention uses a modified pulse oximeter-type photoplethysmograph 4 having numerous user controls, such as receiver 18 gain and light source 8 current settings.
It outputs an analog voltage representation of the photodiode output to an analog-to-digital converter A/D 23 which digitizes the receiver 18 output and applies it to an IBM-AT type personal computer 24 under the control of - SUBSTITUTE SHEET

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From the foregoing, it will be appreciated that the invention, as described herein for purposes of illustration, provides an advancement in non-invasive blood pressure instruments. Although alternative embodiments have been described herein, various modifications may be made without departing from the spirit and scope of the present invention. Accordingly, the scope of the invention extends to the broad general meaning of the appended claims.
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Claims

1. A method of determining arterial blood pressures using a photoplethysmograph having light passing through an artery of a patient, the method comprising the steps of:
(a) calibrating during a calibration period the photoplethysmograph output to the patient by evaluating and storing the arterial constant k in the formula, ? = ?inf(1-Kexp(-kP)) where ? is the arterial blood volume, ?inf is a conversion constant corresponding to the blood volume at infinite pressure, K and k are arterial constants for the patient, and P is the arterial blood pressure at said calibration period;
(b) gathering data from the photoplethysmograph output at a measurement period; and (c) computing the arterial systolic and diastolic pressures for said measurement period using the arterial constant k determined in step (a) and the data gathered in step (b).

2. The method of claim 1, wherein the data gathered in step (b) includes the duration of the cardiac cycle, td at said measurement period; the systolic photoplethysmograph output, Vs at said measurement period; the diastolic photoplethysmograph output, Vd at said measurement period; and the ARC at said measurement period.

3. The method of claim 2, wherein step (a) includes the steps of:
(d) determining the arterial systolic and diastolic blood pressures, Ps and Pd, respectively, at said calibration period;
(e) determining the photoplethysmograph outputs at systole, Vs, and at diastole, Vd,at said calibration period;

(f) determining the mean photoplethysmograph output Vm at said calibration period; and (g) calculating k from the relationship, where Vd, Vs, Pd, Pm, and Ps are their respective values at said calibration period.

4. The method of claim 3, wherein step (f) is determined by the following steps:
(h) determining the duration of the cardiac cycle, td at said calibration period;
(i) determining ARC at said calibration period; and (j) calculating Vm at said calibration period from the relationship:

Vm = Vd - (ARC/td).

where Vd, ARC, and td are their respective values at said calibration period.

5. The method of claim 3, wherein step (a) further includes the steps of calculating and storing the ratio Vo/Vinf at said calibration period in memory from the formula, where Vd, Vs, Pd, and Ps are their respective values at said calibration period.

6. The method of claim 5, wherein step (c) includes the steps of:
(k) determining pulse pressure Pp at said measurement period;
(l) determining diastolic pressure, Pd at said measurement period; and (m) determining systolic pressure, Ps at said measurement period.

7. The method of claim 6, wherein step (k) is determined by the steps of:
(n) recalling said arterial constant k from memory;
and (o) calculating Pp at said measurement period from the formula;

where Vd, Vm, and Vs are their respective values at said measurement period.

8. The method of claim 7, wherein step (l) is determined by the steps of:
(p) recalling said arterial constant k from memory;
(q) recalling said ratio Vo/Vinf from memory; and (r) calculating Pd at said measurement period from the formula, where Vd, Vs, and Pp are their respective values at said measurement period.

9. The method of claim 3, wherein step (a) further includes the steps of:
(s) determining Vinf at said calibration period from the relationship, Vinf = exp{[ln(Vs) - (lnVd)exp(-kPp)]/[1-exp(-kPp)]};

(t) determining V0 from the relationship, ;

where Vd, Vs, Pp, Pd, Ps, and Vinf are their respective values at said calibration period; and (u) storing V0 in memory.

10. The method of claim 9, wherein step (c) includes the steps of:
(v) determining pulse pressure Pp at said measurement period;
(w) determining diastolic pressure, Pd at said measurement period; and (x) determining systolic pressure, Ps at said measurement period.

11. The method of claim 10, wherein step (v) is determined by the steps of:
(y) recalling said arterial constant k from memory;
and (z) calculating Pp from the formula;

where Vd, Vs, and Vm are their respective values at said measurement period.

12. The method of claim 11, wherein step (w) is determined by the steps of:
(aa) recalling said arterial constant k from memory;
(bb) calculating Vinf from the relationship, Vinf = exp{[ln(Vs) - (lnVd)exp(-kPp)]/[1-exp(-kPp)]};

(cc) recalling V0 from memory; and (dd) calculating Pd from the formula, where Vd, Vs, Pp, and Vinf are their respective values at said measurement period.