WO2008109185A2

WO2008109185A2 - A noninvasive method to determine characteristics of the heart

Info

Publication number: WO2008109185A2
Application number: PCT/US2008/003207
Authority: WO
Inventors: Kenneth R. Kensey; Daniel J. Cho
Original assignee: Individual
Current assignee: Individual
Priority date: 2007-03-06
Filing date: 2008-03-06
Publication date: 2008-09-12
Anticipated expiration: 2009-09-06
Also published as: WO2008109185A3

Abstract

A method for estimating/determining the work of the heart of a patient that includes calculating the cardiac output based on estimated or measured pulsatile pressure profile and blood flow characteristics of a patient.

Description

A NONINVASIVE METHOD TO DETERMINE WORK OF THE HEART, COMPLIANCES OF THE VASCULAR SYSTEM, AND PERIPHERAL VASCULAR RESISTANCE

CLAIM OF PRIORITY

[0001] The present application is based on and claims priority to U.S. Provisional Patent Application Serial No. 60/893,158, filed on March 6, 2007, entitled WORK OF THE HEART, COMPLIANCES, AND PERIPHERAL VASCULAR RESISTANCE, the disclosure of which is incorporated by reference.

FIELD OF THE INVENTION

[0002] The present invention relates generally to a method of determining the work of the heart, proximal and distal compliances, and peripheral vascular resistance.

BACKGROUND OF THE INVENTION

[0003] Every organ in the human body needs oxygen, which is supplied by blood through the work of the heart. Diseases such as ischemia or hypoxemia often result from the lack of oxygen through improper work of the heart. Furthermore, in order to compensate the ischemia or hypoxemia, the heart works harder and pumps blood with a greater pressure, increasing the blood pressure. Thus, hypertension is a consequence of increased work of the heart. Hypertension, if not corrected, becomes a cause of vascular occlusive disease that increases the peripheral vascular resistance, thus creating a condition of ischemia or hypoxemia. The heart attempts to overcome vascular resistance by pumping blood with greater pressure, which increases the work of the heart and promotes hypertension. [0004] Also, arteriosclerosis (i.e., hardening of arterial wall) or atherosclerosis (i.e., partial blockage of lumen) can have a profound effect on the work of the heart. When a coronary artery is partially blocked, the myocardial muscle of the heart does not receive enough oxygen for normal myocardial motion. In order to compensate the lack of oxygen at the myocardium, the heart works harder, thus increasing the work of the heart.

[0005] When hypertension persists and the work of the heart is consistently large over a number of years, the heart (more specifically the left ventricle) grows in size to respond to the increased workload. An oversized left ventricle is often referred as congestive heart failure (CHF). When the left ventricle becomes oversized, the heart cannot pump blood out efficiently as the left ventricular muscles cannot contract all the way. Thus, the cardiac output significantly drops, resulting in the congestion of blood in the venous system. An example is a swelling of veins in the lower extremities.

[0006] By monitoring the work of the heart, one can detect the increased workload of the heart and start the treatment at the early stages of CHF. Thus, it is desirable to estimate/determine the work of the heart. The contractility of the left ventricle - a second important parameter for representing the motion of the heart — can be estimated through information on the work of the heart.

[0007] The currently available method for determining the work of the heart is invasive. Specifically, the currently available method uses a cardiac function analyzer (e.g., Leycom CFA-512), which measures the transient pressure P(t) and the left ventricular volume V(t). A pressure-volume loop can be constructed using the transient pressure and left ventricle volume data as shown in Fig. 1. The area enclosed by the pressure- left ventricle volume loop is mathematically determined by integration, which indicates the work of the heart per a cardiac cycle. This method requires the measurement of the transient motion of the left ventricle, which requires the injection of a special dye into the arterial system for the angiography of the left ventricle. The introduction of the dye requires the penetration of a catheter, a non-trivial procedure which is conducted only when there is an absolute need for the procedure.

[0008] It is desirable to have a noninvasive method to determine the work of the heart.

SUMMARY OF THE INVENTION

[0009] According to the present invention, a noninvasive method is used to determine the work of the heart based on estimated or measured pulsatile pressure (e.g. measured from the upper exteremities, i.e. the arm, of a patient) and data related to the whole blood viscosity of the patient.

[0010] According to the preferred embodiment of the present invention, the cardiac output (i.e. blood flow rate) of the heart of the patient can be calculated based on fluid dynamic principles. Once the pulse pressure and cardiac output are determined, the work of the heart can be estimated by the integration of the product of the cardiac output and the pulsatile pressure over a cardiac cycle. According to the preferred embodiment, a modified Windkessel model is used to simulate the cardiovascular system. A modified Windkessel model according to the present invention includes vascular hemodynamic impedance parameters such as proximal and distal compliances, and peripheral vascular resistance (PVR). Thus, according to another aspect of the present invention, vascular hemodynamic and impedance parameters can also be calculated in addition to the work of the heart.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Fig. 1 illustrates two examples of a pressure-volume loop obtained using a method according to the prior art.

[0012] Fig. 2 illustrates steps in a method according to the present invention.

[0013] Fig. 3A illustrates schematically parts of a cardiovascular system.

[0014] Fig. 3B illustrates an equivalent circuit diagram for a modified Windkessel model used as a basis for a method according to the present invention.

[0015] Fig. 4 illustrates a method according to the first embodiment of the present invention.

(0016] Fig. 5 illustrates a method according to the second embodiment of the present invention.

[0017] Fig. 6 provides values for the power of the heart of nine human subjects calculated using a method according to the present invention.

[0018] Fig. 7 reports the values from Fig. 6 broken into four subgroups.

[0019] Fig. 8 provides ten pairs of values for Casson model constants selected randomly and used in a method according to the present invention to obtain values for the power of the heart.

[0020] Figs. 9A-9C graphically illustrate the relationship between the power of the heart and Casson model constants.

DETAILED DESCRIPTION OF THE INVENTION

[0021] A method according to the present invention non-invasively determines the work of heart, the power of the heart, and other cardiovascular characteristics of a patient using data related to the blood viscosity of a patient.

[0022] Referring to Fig. 2, in a method according to the present invention, the work of the heart of a patient can be calculated by providing a value for the pulsatile pressure S l , which can be estimated or measured, providing the blood viscosity of the patient S2 (for example, blood viscosity at a high shear rate (e.g. 300/s)), providing yield stress S3, calculating blood flow rate (cardiac output) S4 based on the values provided at S l , S2, S3, and calculating the work of heart of the patient S5 based on values obtained at S l and S4. [0023] A value for the pulsatile pressure can be the patient's aortic pressure, which can be measured by taking the pulse of the patient at his/her upper extremity (e.g. forearm). The blood viscosity of the patient and the yield stress can be determined using, for example, a scanning capillary tube viscometer, or any other desirable method. The blood flow rate can be calculated using the patient's pulsatile pressure, blood viscosity of the patient, and the yield stress using preferably a mathematical relationship as disclosed herein (see Equation (6) below), and the work of the heart of the patient can be estimated/determined by first determining the power of the heart of the patient, and then integrating the power of the heart of the patient over a cardiac cycle as mathematically demonstrated below.

Flow Characteristics of Blood

[0024] Blood is a non-Newtonian fluid which means that its viscosity varies with the shear rate of the flow thereof. Thus, it is known that as shear rate increases, whole blood viscosity decreases, which is referred to as the "shear-thinning characteristic" of whole blood.

[0025] A reason for the variation in blood viscosity with varying shear rate is that blood consists of a number of suspended particles such as erythrocytes, leukocytes, and platelets. Red blood cells, the main component of whole blood, cause blood's non- Newtonian behavior.

[0026] It is known that the heart pumps blood out of the left ventricle only during systole and the aortic valve is closed during diastole. Such a flow is a time-dependent pulsatile flow. During systole, blood moves at a relatively high velocity, resulting in a high shear rate condition, whereas during diastole, blood moves relatively slowly, resulting in a low shear rate condition. Thus, blood viscosity is small during systole (high shear rate) and large during diastole (relatively lower shear rate). In other words, the blood viscosity significantly varies in each cardiac cycle. [0027] The Casson model is the best known and most widely used model for analyzing the viscosity of whole blood. The Casson model can be given as

[0028] The Casson model contains two parameters: τ _y (yield stress) and k (the Casson model constant). These parameters can be obtained using a scanning capillary tube viscometer SCTV (available from Rheologics, Exton, PA, USA), or any other suitable method. The SCTV produces whole blood viscosity data (more specifically viscosity vs. shear rate) of a patient over a wide range of shear rates. In terms of blood viscosity, one can rewrite the above Casson model equation as

Note that the constants f| and f₂ represent two Casson model constants, k and τ_y, where fi represents the blood viscosity at a high shear rate (i.e., shear rate greater than 300 s^{* 1}) and f₂ represents the yield stress.

[0029] Viscosity, which is a measure of resistance to flow, critically affects the magnitude of peripheral vascular resistance (PVR). Thus, as whole blood viscosity increases, the value of peripheral vascular resistance also increases, thereby reducing blood flowrate if the blood pressure remains constant. In most practical cases, the cardiac output (blood flow rate) must remain constant as the body needs a constant perfusion over time. Hence, when blood viscosity increases, the blood pressure increases.

[0030] When blood viscosity decreases, whole blood becomes thinner and blood flow rate increases in the arterial system. Consequently, with the reduction of whole blood viscosity, the circulation of blood improves (particularly in microvessels and peripheral vessels) and the delivery of oxygen and nutrients to the tissue level increases. Moreover, the heart consumes less mechanical energy to circulate blood throughout the body, thus decreasing the work of the heart. For these reasons, whole blood viscosity can be an important hemodynamic factor in blood flow and consequently the work of the heart.

Power of the Heart

(0031] The power of the heart (POH) can be estimated by the product of the pressure change in the left ventricle during a cardiac cycle and the cardiac output according to the following equation:

where SP is the aortic pressure at the peak systole, DP_Lv is the left ventricular pressure at the end of diastole, and CO is a cardiac output [ml/min]. The left ventricular pressure at the end of diastole is approximately 5 mmHg for most people. The aortic pressure at peak systole varies widely from person to person, but can be approximated by the systolic blood pressure measured at the forearm. It has been shown that the cardiac output CO can be estimated using a person's body weight W as

CO = 3.33 W^{0 75} (4)

where CO is in [ml/s] and W is in [kg].

[0032] Note that the power of the heart has a unit of [J/s]. Hence, the work of the heart can be obtained by multiplying the period of a cardiac cycle T (which is measured in seconds) to the power of the heart POH as

Work of the Heart = Power of the Heart x T (4a)

where the period of a cardiac cycle T [s] can be determined by the heart rate as

T = 60/(Heart Rate per min) (4b)

In order to describe how whole blood viscosity is related to the work of the heart, a fully developed laminar flow in a circular tube can be used as a model. Such a flow regime, if described by the Poiseuille flow equation, can be given as

AP = ≡≠ (4c) πd

where the left hand side ΔP represents a pressure drop due to friction between the moving fluid and the tube wall over a length L of a tube with an inside diameter d. When we apply this Poiseuille equation to blood flow in a relatively healthy arterial vessel, the blood pressure can be described as the product of the cardiac output and blood viscosity for a given geometry circulatory system, i.e., with fixed diameter and length. More specifically, since blood leaves the heart (i.e., left ventricle) only during systole, blood pressure can be replaced by the aortic blood pressure during systole minus the left ventricle pressure at the end of diastole, which is relatively small compared to the peak aortic pressure at the peak systole. Hence, the aortic blood pressure at the peak of systole minus the venous pressure, or simply systolic pressure, ΔP can be qualitatively described as the product of the cardiac output, Q, and blood viscosity, μ.

Systolic pressure ( AP ) - Cardiac output (Q) x Blood viscosity (μ) (4d)

Therefore, using Equations (3) and (4a), the power of the heart can be given as

Power of the heart (POH) ~ (Cardiac Output)² x Blood viscosity x Cardiac Period (4e)

Since the cardiac output is the volumetric flow rate of blood per minute, it is the time- averaged value over a cardiac cycle, which is often constant and does not vary over time at resting conditions for most people. Hence, the work of the heart can be simply expressed as a function of the whole blood viscosity as

Work of the heart (WOH) - Blood viscosity (μ) (4f)

When one considers the pulsatile nature of blood flow, both the instantaneous cardiac output Q(t) and the instantaneous aortic blood pressure P(t) vary with time. Therefore, one can determine the work of the heart using an integration of the product of the two over time as

where T is the period of a cardiac cycle. In a method according to the present invention, the above integration (Eq. 4g) of the product of the cardiac output and blood pressure (e.g. aortic pressure) over time (e.g. a cardiac cycle) is used to estimate the work of the heart.

[0033] In order to quantitatively determine the instantaneous volumetric flow rate (i.e. cardiac output (Q)) and aortic pressure (P) in pulsatile blood flow, the Navier-Stokes equation Eq. (4h) can be used which describes a balance between the inertial force and viscous force in a pressure-driven flow regime occurring in a circular tube. du. du, u_a du, du dP 1 d ( duΛ

P ^■ + w. ^■ + u = - — + μ- — \ r— M 4(h) dt ^r dr r dθ ^z dz oz r dr y or J

Where the left-hand side represents the inertial force (i.e., acceleration) of a fluid particle, and the two terms in the right-hand side represent contributions from pressure gradient and viscous force.

The Modified Windkessel Model

[0034| The human arterial system is a network of vessels that converts the intermittent flow pumped out of the heart into steady flow through the capillaries and the venous system. One of the most elementary modeling approaches is the Windkessel model, where compliance, pressure wave reflection, vascular resistance, and inertance are the key parameters in the analysis of the pulsatile arterial flow. A great deal of research has been performed to approximate these parameters, and a number of modified models have been created for this purpose. More complex models, however, have failed to capture the phenomenon and have limitations in reflecting the behavior of the real system. Furthermore, in these complex approaches, each model that represents a segment of the whole arterial system is combined with the next segment model in series, forming a lumped parameter model to increase the accuracy of the model. However, the lumping of parameters increases the uncertainty of the uniqueness of the solution.

[0035) In a method according to the present invention, a modified Windkessel model is used to analyze vascular hemodynamic impedance parameters that indicate the progressive state of the cardiovascular disease. Referring to Figs. 3 A and 3B, the modified Windkessel model uses the proximal compliance of the aorta, C_/, and the peripheral vascular resistance, R_s, to simulate the inertia (often called inertance) of blood, L. The inertance L relates to the recoil effect of the arterial wall as the pressure wave propagates through the arterial system in each cardiac cycle. In a method according to the preferred embodiment of the present invention a value of L = 0.017 (mmHg S²AnI) can be used.

[0036| In a modified Windkessel model, it is assumed that a hypothetical arterial system between the compliant aorta and the compliant distal vessels has a rigid and noncompliant characteristic for mathematical simplicity. In other words, the contribution due to the recoil effect seen in a hypothetical arterial system is assumed to be in the value of the blood inertia. In addition, the frictional effect is assumed to be negligibly small in the hypothetical arterial system. Furthermore, the modified Windkessel model uses another parameter, the distal compliance, C₂, whose alteration is particularly sensitive to cardiovascular diseases associated with hypertension, diabetes mellitus and atherosclerosis, ultimately affecting the work of the heart.

Mathematical Procedures

[0037] The three equations derived from the modified Windkessel model are as follows:

Pi(O is the instantaneous pressure at the aorta, i.e. the pulsatile pressure Pι(t). Since the modified model assumes the venous pressure to be negligible for simplicity, Pi(O actually means the pressure difference between the aorta and the vein. Note that P _\(t) represents aortic pressure, which can be mathematically described in three different ways, Eqs. (5a), (5b), and (5c). Fig. 3B indicates the three different paths for the aortic pressure to propagate, and each path is marked by the corresponding equation number, Eqs. (5a), (5b), or (5c) in Fig. 3B. Fig. 3B illustrates, using an equivalent circuit diagram, the respective locations of the parameters in the modified Windkessel model as used in Eqs. 5(a)-(c). Qιn(t) is the flow rate of blood pumped out of the left ventricle LV of the heart during systole. Qm{t) is made of two components: the blood flow moving in the aorta, Qi(O _> and the blood flow that is stored in an stretched aorta.

is the flow rate of blood in an aorta, which simulates the blood moving in a hypothetical rigid arterial system toward the peripheral arterial system during systole. The difference between the two, i.e., Qm(t) - Qi(O , indicates the amount of blood stored in the expanded space of the compliant proximal artery, i.e., the aorta. Thus, according to an aspect of the present invention, the proximal compliance, C_/, during systole can be determined from Qm{t) - Q\{t) . In summary, the proximal compliance Cl can be expressed as:

C₁ = ^{c p}:i^:' ^'d\ (5d)

[0038J Qz(O '^s the flow rate of blood moving at the distal region of the peripheral arterial system. Since the distal artery is also considered to be compliant, it expands during systole. The blood stored in the expanded space of the peripheral arterial system is given by

- Qj{t) . Thus, using a modified model according to an aspect of the present invention, the distal compliance, C₂ , can be obtained from the difference between the flowrate into the peripheral vascular system

and the flowrate at the distal region, Qi(t) .

[0039] Each of the above three Equations 5a-5c represents the blood flow passing through each path shown in the circuit diagram of the modified Windkessel model (Fig. 3B). Thus, Eq. 5(a) describes the proximal blood pressure (i.e., aortic pressure),

as

a sum of the pressure drop occurring at the hypothetical rigid arterial system L and dt the pressure drop in the peripheral arterial system Q₂ (t)R_s (T) . The proximal blood pressure, Pi(O , is often clinically assumed to be equivalent in magnitude to that measured in the brachial artery.

[0040) In a method according to the present invention, preferably, a pulse pressure measured at the brachial artery is used. Once the pulse pressure is determined, the blood flowrate at the hypothetical rigid arterial system,

, can be estimated based on the fluid mechanics principle. With the continuity equation and the momentum equation for a rigid circular pipe, the mathematical form for the relation between

and Q\{t) can be given using the Casson viscosity model by the following equation:

where Qι(t) is the volume flow rate from the left ventricle, k and τ_y are the Casson model constants (see Eq. (I)), R is the radius of vessel, Pi is the aortic pressure, z_/ is a characteristic dimension for the whole arterial system. From Equation (6), the stroke volume of the left ventricle can be obtained by integrating the Qm(t) curve over time for the period of a cardiac cycle. In other words, the area under the Qm(t) curve during a cardiac cycle represents the stroke volume. Since the blood volume stored in the compliant proximal arterial wall is always constant from one cycle to another cycle, the integration of the Qm(t) curve must be equal to the integration of the Q\{t) as shown below.

[0041] The peripheral vascular resistance R_s(t) can be obtained from the momentum equation using the Casson model as follows:

168*z₂

*, (') = π[nR⁴ - 48*³⁵(rJ⁰⁵ + 2SRⁱ{r_c)- {r_c)⁴ }

where k and τ_y are the Casson model constants (see Eq. (I)), R is the radius of vessel, z₂ is another characteristic dimension for the whole arterial system, and r_c is the radial distance where the shear stress is equal to the value of the yield stress τ_y. hi general, the pressure drop is proportional to the product of the flowrate and the resistance in a pipe flow, which is Pi{l) = Qi{t)R_s{t) . Since the product of the peripheral resistance R_s(t) and Qi{t) represents the pressure drop at the peripheral arterial system, one can obtain ζh(/) by substituting Rs{t) , Equation (7), into Equation (5a) because the pulse pressure Pi(Z) and the pressure drop at the hypothetical rigid arterial systems are already determined at this point.

J0042] The compliance of an elastic artery is defined as the rate of change of vessel volume to the pressure change as shown next:

AP AP Thus, from the definition of the compliance, the mathematical expression for the distal compliance, Cι{t), can be given as follows:

where AP₂(C) = Pι(t + At) - P₂(t) . Combining Pi(t) and Equation (8), one can obtain the distal compliance, Cι(t).

[0043] Once Qi(t) and Ci{t) are obtained in equation (5a), they should also satisfy Equation (5b) with the same values of Q\(t) and Pi(O . By differentiating Equation (5a) and rearranging it, one can obtain the following equation:

Differentiating Equation (5c), one can have the following equation:

With an initial guess for Cι(/) , Qm(t) can be obtained from Equation ( 10). Then, preferably, iteration is used whereby more values are guessed for Ci(O until the flowrate estimated by the area under the curve of Qm(t) is equal to the area under the curve of Q\{t) . As mentioned before, the flow rate ejected from the heart should be the same as the amount passing through the arterial system during one cardiac cycle. Using this "flow balance" concept in a closed system, one can confirm the validity of the results obtained using the mathematical approach set forth herein.

[0044) In a human body, whole blood viscosity is one of the variables that dictates how hard the heart must work. Similar to Eq. 4(g), the important relationship between the circulating whole blood viscosity and the work of the heart can be mathematically expressed as follows:

Where WOH is the work of the heart [J] in a cardiac cycle, subscripts 1 and in indicate the location identified by Pi in Figs. 3A and 3B (i.e., at the ascending aorta) and the integrand, Qι(t)Pι(t), represents an instantaneous power of the heart POH(i).

POH(O = Q_x (I)P₁ (O [J/s] (12)

If Eq. (12) is integrated over time, e.g. during a cardiac cycle, and divided by the period of a cycle, an average power of the heart can be calculated as follows:

POH(avg) [J/s] (13)

where T is the period of a cardiac cycle [s], and POH is the power of the heart [W].

[0045] The circulating whole blood viscosity is an implicit variable in Equations (1 1 - 13). Equations (1 1-13) show that the work of the heart depends on the aortic blood pressure and cardiac output, which is dictated by the peripheral vascular resistance and whole blood viscosity. Note that whole blood viscosity directly correlates with blood pressure through the peripheral vascular resistance as mentioned earlier. Hence, the work of the heart which is needed to overcome the peripheral vascular resistance can be estimated by using the blood flow rate, aortic blood pressure and viscosity of a patient's blood. When the whole blood viscosity is elevated, one can expect that the work of the heart increases. Similarly, when the blood pressure is elevated, one can expect that the work of the heart increases. A method according to another aspect of the present invention allows for the calculation of the changes in the work of the heart due to the elevated blood viscosity as indicated by Eq. (4f). EXAMPLE 1

[0046] A simple method to estimate the power of the heart is given below: Consider a patient who has 120/80 mmHg for systolic and diastolic blood pressures, 5 mmHg for the end diastolic pressure of left ventricle, and a cardiac output of 5 1/min. Then, the power of the heart POH can be simply estimated as

POH = (120-5) [mmHg] x 5 [1/min] = 525 [mmHg.l/min] = 1.17 [J/s] (14)

Note that a conversion factor of 1 mmHg = 133.3 Pa is used in the above calculation.

EXAMPLE 2

[0047] When the instantaneous blood pressure profile P|(t) is available through actual measurement, for example, at the forearm of the patient, the power of the heart can be determined using the procedure shown in Fig. 4. Thus, as illustrated, the aortic pressure is measured SlO by, for example, taking the patient's systolic and diastolic blood pressures at his/her forearm, the blood viscosity (f|) and the yield stress (f₂)values are obtained S12 by analyzing the patient's blood, the cardiac output (blood flow rate) Q is calculated S14 using Eq. 6 based on values obtained at steps SlO, S 12. From the cardiac output values obtained at S 14 average cardiac output can be calculated S16 by integrating the instantaneous blood flow rate Q(t) over time during a period of time, for example, a cardiac cycle (e.g., Eq. 6a can be used to obtain an average over one minute), instantaneous POH values can be calculated S18 (see Eq. (12)), and average POH can be calculated S20 (see Eq. (13)). Note that by obtaining the area under a curve constructed using the instantaneous values of POH (i.e. by integrating the POH), the work of heart of the patient may be obtained.

EXAMPLE 3

[0048] Referring to Fig. 5, in a method according to the second embodiment, the instantaneous blood pressure profile P|(t) is not used. Rather, initially the pulsatile pressure profile is estimated S22. Using the estimate from S22, the instantaneous blood flow rate Q(t) is calculated S24 using Eq. 6 and the blood viscosity information for the patient S26, i.e. fl and f2 from Eq. 2 . Then, the average blood flow rate over a cardiac cycle Q_nvg is calculated S28 by integrating the instantaneous blood flow rate Q(t) over time during the cardiac cycle. The cardiac output CO estimated from the body weight, Eq. (4), is compared with that obtained using Eq. 6 S30. If the estimated CO and calculated CO from step S24, S28 are not close (i.e., difference is greater than 5%) a multiplying factor mf is obtained S32. For example, an mf = 1.1 is selected for each iterative step in order to increase the pressure profile by 10% in each iteration when the calculated CO is less than the estimated CO. The mf is multiplied by the initial estimated pulsatile pressure 34 to obtain a new estimated pulsatile pressure, and the procedure in steps S24, S28, S30 is continued until the cardiac output estimated from the body weight S36 is almost equal (i.e., difference is less than 5%) to the average cardiac output obtained using the Navier-Stokes Eq. 6 based on the estimated pulsatile pressure value, whereby it can be concluded that the estimated pulsatile pressure profile is reasonably correct for the patient. Thereafter, an mf is determined S38, a pressure profile is determined S40 such that the calculated CO is equal to the estimated CO, where the patient's blood viscosity data S26 is used in the calculation procedure. Now, that both Q(t) and P(t) are determined, one can calculate the instantaneous power of the heart POH(i) S42 and average POH S44 using Equations 12 and 13, respectively. Note that, as with the previous embodiment, the work of the heart can be obtained by integrating the power of the heart.

EXAMPLE 4

In a method according to the third embodiment, the Casson model constants fl and f2 are determined from the whole blood viscosity curve using, for example, a viscometer such as a scanning capillary tube viscometer, and used along with the following values to calculate Work of the heart [J], Power of the heart [W], Cardiac output [1/min], Proximal compliance Ci [ml/mmHg], Distal compliance C₂ [ml/mmHg], Peripheral vascular resistance R_s [mmHg/ml]. Note that while work of the heart, the power of the heart and the cardiac output can be calculated using the first and the second embodiment, the remaining values can also be calculated. Note that Ci can be obtained using Eq. (5d); C₂ can be obtained using Eq. (8), and R_s can be obtained using Eq. (7).

Density of blood : 1.04 g/ml

Characteristic length of arterial system : Z| = 200 [cm] (a preferred value)

Characteristic length of peripheral arterial system : Z₁ = 0.9 [cm] (a preferred value)

Inertance of hypothetical rigid arterial system : L = 0.016 - 0.017 [mniHg s²/ml] (a preferred value)

Characteristic diameter of arterial system : D) = 0.7 [cm] (a preferred value)

To carry out a method according to any one of the embodiments of the present invention, a general purpose computer, such as a personal computer, can be programmed to automatically calculate the work of the heart upon receiving the required input values such as shear rate, yield stress, estimated initial pulsatile pressure or measured pulsatile pressure profile.

Results

[0049] Figure 6 shows results of tabulation of two Casson model constants fl, f2 obtained from nine whole blood samples of human subjects. f| represents a value for high shear viscosity of blood, which varies widely from 2.76 to 5.63. f> is a value representing the yield stress of blood, which also varies widely from 2.55 to 18.32. Using these two hemorheological data obtained from nine human subjects, the average power of the heart POH was determined using the aforementioned modified Windkessel model illustrated by Figs. 3A and 3B and a method according the second embodiment. The time-average POH was found to vary from 0.892 to 1.794 [W]. [0050] Referring to Fig. 7, the nine human subjects were grouped into four subgroups: women, men, polycythemia patients, and regular blood donors. Using the POH values shown in Fig. 6 , the average POH for each subgroup was calculated as shown in Fig. 7. As expected, the subgroup representing polycythemia shows the highest value of POH, whereas the group representing blood donors shows the lowest value. The POH for men was 1.2 [W], which is slightly greater than the value for women 1.1 [W].

[0051 ] Referring to Fig. 8, the two Casson model constants fi and f₂ vary much more widely in reality than the data shown in Figure 6. Often, the value of f| varies from 2 to 6, whereas the value of f₂ varies from 2 to 20. Thus, ten pairs of data for fi and f₂ were selected randomly and the POH value was determined for each pair of f| and f₂. Figure 8 tabulates 10 pairs of data for fi and f₂ and corresponding POH values.

[0052] Figs. 9A-9C show three graphs: POH vs. f, (Fig. 9A), POH vs. f₂ (Fig. 9B), and POH vs. f|²+f₂° ⁷⁵ (Fig. 9C). As one can see, there is a linear relation between PΟΗ and f|, which represents a high shear blood viscosity. Also, there is a strong one-to-one correlation between POH and f|²+f₂° ⁷⁵. However, POH was almost independent of f₂.

[0053] Although the present invention has been described in relation to particular embodiments thereof, many other variations and modifications and other uses will become apparent to those skilled in the art. It is preferred, therefore, that the present invention be limited not by the specific disclosure herein.

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Claims

WHAT IS CLAIMED IS:

1. A method for determining the work of heart of a patient, comprising: providing a value of pulsatile pressure of said patient; calculating blood flow rate based on said value of said pulsatile pressure, and blood flow characteristics of said patient; and calculating a value for power of heart of said patient based on said value of said pulsatile pressure and said calculated blood flow rate.

2. The method of claim 1 , wherein said blood flow characteristics includes blood viscosity of said patient.

3. The method of claim 1 , wherein a Casson model is used to obtain said blood viscosity characteristics.

4. The method of claim 1, wherein a scanning capillary tube viscometer is used to determine said blood viscosity characteristics.

5. The method of claim 1 , wherein said value of said pulsatile pressure is estimated.

6. The method of claim 1 , wherein said value of said pulsatile pressure is measured.

7. The method of claim 1, wherein said value of said pulsatile pressure is the aortic blood pressure of said patient.

8. The method of claim 1 , further comprising calculating a work of heart of said patient based on said calculated value for power of heart of said patient.

9. The method of claim 8, wherein said work of heart of said patient is calculated over a cardiac cycle of said patient's heart.

10. The method of claim 1 , further comprising calculating an average value for said power of heart of said patient.

1 1. The method of claim 10, wherein said average value is calculated over a cardiac cycle of said patient's heart.

12. A method to determine the characteristics of a vascular system of a patient, comprising: obtaining blood from said patient; determining a blood flow characteristic of said blood; and calculating a value for a characteristic of a cardiovascular system of said patient.

13. The method of claim 12, wherein said cardiovascular characteristic is peripheral vascular resistance.

14. The method of claim 12, wherein said cardiovascular characteristic is a proximal compliance of said cardiovascular system.

15. The method of claim 12, wherein said cardiovascular characteristic is a distal compliance of said cardiovascular system.

16. The method of claim 12, wherein said blood flow characteristic is a Casson model constant.

17. The method of claim 12, wherein said blood flow characteristic is blood viscosity.