Patent Application
20090270739
Arterial blood pressure based methods for the determination of cardiac output (CO) are based on the relationship that exists in the arterial system between pulsatile flow and pulsatile pressure. Most known arterial blood pressure based systems rely on the pulse contour method (PCM), which calculates an estimate of CO from characteristics of the beat-to-beat arterial pressure waveform. In the PCM, “Windkessel” (German for “air chamber”) parameters (characteristic impedance of the aorta, compliance, and total peripheral resistance) are used to construct a linear or non-linear hemodynamic model of the aorta. In essence, blood flow is analogized to a flow of electrical current in a circuit in which an impedance is in series with a parallel-connected resistance and capacitance (compliance). The theoretic pressure that determines stroke volume, i.e., cardiac output, is the proximal aortic pressure. Unfortunately, proximal aortic pressure is not routinely clinically available because the central aortic pressure signal cannot be obtained without complicated clinical procedures involving cardiac catheterization. Clinically, the arterial pressures (e.g., radial, brachial, and femoral) are used instead. The radial artery is the most commonly utilized site because of ease of cannulation and low risk of complications.
Differences in pressure are known to exist within the systemic arterial system mainly as a result of differences in wave reflection. The effect of wave reflection is that the pulse pressure does not have the same amplitude for the central and peripheral arteries, but rather is amplified toward the periphery. In normal hemodynamic conditions, the arterial pulse pressure is higher in the peripheral arteries than in the aorta. This phenomenon of increased arterial pressure amplitude is well established and peripheral pressure is routinely used with correction factors in calculations of cardiac output.
Methods for the detection of a vascular condition in a subject are described. The vascular condition includes different cardiovascular hemodynamic conditions and states, such as, for example, vasodilation, vasoconstriction, peripheral pressure/flow decoupling, conditions where the peripheral arterial pressure is not proportional to the central aortic pressure, and conditions where the peripheral arterial pressure is lower than the central aortic pressure. One method of detecting a vascular condition in a subject involves receiving a signal corresponding to an arterial blood pressure and calculating a cardiovascular parameter from the arterial blood pressure. The cardiovascular parameter is calculated based on a set of factors including one or more parameters effected by the vascular condition. Examples of parameters effected by the vascular condition include (a) a parameter based on the area under the systolic portion of the arterial blood pressure signal, (b) a parameter based on the duration of systole, and (c) a parameter based on the ratio of the duration of the systole to the duration of the diastole. Additional parameters can be used in calculating the cardiovascular parameter including one or more of (d) a parameter based on the shape of the arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater, (e) a parameter corresponding to the heart rate, and (f) a set of anthropometric parameters of the subject. The cardiovascular parameter is then monitored for a statistically significant change over time with the detection of a statistically significant change in the cardiovascular parameter indicating the vascular condition.
Further methods of detecting a vascular condition in a subject involve receiving a signal corresponding to an arterial blood pressure and calculating a first cardiovascular parameter and a second cardiovascular parameter from the arterial blood pressure. The first cardiovascular parameter is calculated based on a first set of factors including one or more of (a) a parameter based on the shape of the beat-to-beat arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater, (b) a parameter based on a heart rate of the subject, and (c) a set of anthropomorphic parameters of the subject. The second cardiovascular parameter is calculated based on a second set of factors including one or more parameters effected by the vascular parameter. Examples of parameters effected by the vascular parameter include (a) a parameter based on the area under the systolic portion of the arterial blood pressure signal, (b) a parameter based on the duration of systole, and (c) a parameter based on the ratio of the duration of the systole to the duration of the diastole. Finally, the first cardiovascular parameter is subtracted from the second cardiovascular parameter to create a difference factor or a ratio between the second cardiac parameter and the first cardiovascular parameter is determined. A difference factor of greater than a predetermined threshold value or a ratio greater than a predetermined value indicates the vascular condition.
Methods for the detection of a vascular condition in a subject are described. The vascular condition may include different cardiovascular hemodynamic conditions and states, such as, for example, vasodilation, vasoconstriction, peripheral pressure/flow decoupling, conditions where the peripheral arterial pressure is not proportional to the central aortic pressure, and conditions where the peripheral arterial pressure is lower than the central aortic pressure. As used herein, the phrase vasodilation means a condition in which the arterial and peripheral arterial pressure and flow are decoupled from the central aortic pressure and flow, and the term peripheral arteries is intended to mean arteries located away from the heart, e.g., radial, femoral, or brachial arteries. Decoupled arterial pressure means that the normal relationship between arterial, peripheral arterial, and central pressure is not valid and the arterial and peripheral arterial pressure can not be used to determine the central arterial pressure. This also includes conditions in which the peripheral arterial pressure is not proportional or is not a function of the central aortic pressure. Under normal hemodynamic conditions, blood pressure increases the further away from the heart the measurement is taken. Such a pressure increase if shown in
This normal hemodynamic relationship of pressures, i.e., an increase in pressure away from the heart, is often relied upon in medical diagnosis. However, under hyperdynamic conditions, this relationship can become inverted with the arterial pressure becoming lower than the central aortic pressure. This reversal has been attributed, for example, to arterial tone in the peripheral vessels, which is suggested to impact the wave reflections discussed above. Such a hyperdynamic condition is shown in
In general, these methods involve monitoring a cardiovascular parameter that implicates a vascular condition in a subject to detect a change that indicates the vascular condition. An example of such a change is a statistically significant change in the cardiovascular parameter, such as a change of greater than one standard deviation. Another example of a change that indicates a vascular condition is a difference between a cardiovascular parameter impacted by hyperdynamic conditions and a cardiovascular parameter not impacted by hyperdynamic conditions of greater than a predetermined threshold. A further example of a change that indicates a vasodilatory condition is a ratio between a cardiovascular factor impacted by hyperdynamic conditions and a cardiovascular parameter not impacted by hyperdynamic conditions that is greater than a predetermined value. These cardiovascular parameters are calculated and the above listed changes are monitored continuously as a subject's arterial blood pressure is monitored. The cardiovascular parameter can be, for example, arterial compliance, arterial elasticity, peripheral resistance, arterial tone, arterial flow, stroke volume, or cardiac output. The detection of vascular conditions such as vasodilation in a subject indicates, for example, the occurrence of hyperdynamic cardiovascular conditions, hyperdynamic decoupling of the arterial pressure from the central aortic pressure, that the arterial pressure is lower than the central aortic pressure, or that the arterial pressure is not proportional to the central aortic pressure.
More specifically, a method of detecting a vascular condition in a subject involves receiving a signal corresponding to an arterial blood pressure and calculating a cardiovascular parameter from the arterial blood pressure. The cardiovascular parameter is calculated based on a set of factors including one or more parameters effected by the vascular condition. Examples of parameters effected by the vascular condition include (a) a parameter based on the area under the systolic portion of the arterial blood pressure signal, (b) a parameter based on the duration of systole, and (c) a parameter based on the ratio of the duration of the systole to the duration of the diastole. The factors used to calculate the cardiovascular parameter can further include one or more of (d) a parameter based on the shape of the arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater, (e) a parameter corresponding to the heart rate, and (f) a set of anthropometric parameters of the subject. The cardiovascular parameter is then monitored for a statistically significant change over time with the detection of a statistically significant change in the cardiovascular parameter indicating the vascular condition. The statistically significant change is, for example, a change of greater than one standard deviation or a change of greater than one standard deviation of a parameter when compared to the distribution of the parameter in normal subjects not experiencing the vascular condition.
Another method of detecting a vascular condition in a subject involves receiving a signal corresponding to an arterial blood pressure and calculating a first cardiovascular parameter and a second cardiovascular parameter from the arterial blood pressure. The first cardiovascular parameter is calculated based on a first set of factors including one or more of (a) a parameter based on the shape of the beat-to-beat arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater, (b) a parameter based on a heart rate of the subject, and (c) a set of anthropomorphic parameters of the subject. The second cardiovascular parameter is calculated based on a second set of factors including one or more parameters effected by the vascular condition. Examples of parameters effected by the vascular condition include (a) a parameter based on the area under the systolic portion of the arterial blood pressure signal, (b) a parameter based on the duration of systole, and (c) a parameter based on the ratio of the duration of the systole to the duration of the diastole. Finally, the first cardiovascular parameter is subtracted from the second cardiovascular parameter to create a difference factor. A difference factor of greater than a predetermined threshold value indicates the vascular condition. The predetermined value can represent a statistically significant change in the difference factor over time, e.g., a change of greater than one standard deviation of a parameter when compared to the distribution of the parameter in normal subjects not experiencing the vascular condition. Examples of predetermined threshold values include 1.5 L/minute or greater, 1.6 L/minute or greater, 1.7 L/minute or greater, 1.8 L/minute or greater, 1.9 L/minute or greater, 2 L/minute or greater, 2.1 L/minute or greater, 2.2 L/minute or greater, 2.3 L/minute or greater, 2.4 L/minute or greater, and 2.5 L/minute or greater.
A further method of detecting a vascular condition in a subject involves receiving a signal corresponding to an arterial blood pressure and calculating a first cardiovascular parameter and a second cardiovascular parameter from the arterial blood pressure. The first cardiovascular parameter is calculated based on a first set of factors including one or more of (a) a parameter based on the shape of the beat-to-beat arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater, (b) a parameter based on a heart rate of the subject, and (c) a set of anthropomorphic parameters of the subject. The second cardiovascular parameter is calculated based on a second set of factors including one or more parameters effected by the vascular condition. Examples of parameters effected by the vascular condition include (a) a parameter based on the area under the systolic portion of the arterial blood pressure signal, (b) a parameter based on the duration of systole, and (c) a parameter based on the ratio of the duration of the systole to the duration of the diastole. A ratio of the second cardiovascular parameter to the first cardiovascular parameter of greater than a predetermined value indicates the vascular condition. Examples of predetermined values include 1.1 or greater, 1.2 or greater, 1.3 or greater, 1.4 or greater, 1.5 or greater, 1.6 or greater, 1.7 or greater, 1.8 or greater, 1.9 or greater, and 2.0 or greater.
The cardiovascular parameters used in the methods described herein are calculated from signals based on arterial blood pressure or signals proportional to arterial blood pressure. The calculation of cardiovascular parameters, such as arterial compliance (arterial tone), is described in U.S. patent application Ser. No. 10/890,887, filed Jul. 14, 2004, which is incorporated herein by reference in its entirety. The factors and data used in calculating the cardiovascular parameters for use with the methods disclosed herein, including the parameters discussed in U.S. patent application Ser. No. 10/890,887, are described below.
Signals useful with the present methods include cardiovascular parameters based on arterial blood pressure or any signal that is proportional to arterial blood pressure, measured at any point in the arterial tree, e.g., radial, femoral, or brachial, either invasively or non-invasively. If invasive instruments are used, in particular, catheter-mounted pressure transducers, then any artery is a possible measurement point. Placement of non-invasive transducers will typically be dictated by the instruments themselves, e.g., finger cuffs, upper arm pressure cuffs, and earlobe clamps. Regardless of the specific instrument used, the data obtained will ultimately yield an electric signal corresponding (for example, proportional) to arterial blood pressure.
As illustrated in
Now consider an ordered collection of m values, that is, a sequence Y(i), where i=1, . . . (m−1). As is well known from the field of statistics, the first four moments μ1, μ2, μ3, and μ4 of Y(i) can be calculated using known formulas, where μ1 is the mean (i.e., arithmetic average), μ2=σ2 is the variation (i.e., the square of the standard deviation σ), μ3 is the skewness, and μ4 is the kurtosis. Thus:
μ1Yavg=1/m*Σ(Y(i)) (Formula 1)
μ2=σ2=1/(m−1)*Σ(Y(i)−Yavg)2 (Formula 2)
μ3=1/(m−1)*Σ[(Y(i)−Yavg)/σ]3 (Formula 3)
μ4=σ/(m−1)*Σ[(Y(i)−Yavg)/σ]4 (Formula 4)
In general, the β-th moment μp can be expressed as:
μβ=1(m−1)*1/σβ*Σ[(Y)(i)−Yavg)]β (Formula 5)
where i=0, . . . , (m−1). The discrete-value formulas for the second through fourth moments usually scale by 1/(m−1) instead of 1/m for well-known statistical reasons.
The methods described herein utilize a compliance factor or an arterial tone factor that is a function not only of the four moments of the pressure waveform P(k), but also of a pressure-weighted time vector. Standard deviation σ provides one level of shape information in that the greater σ is, the more “spread out” the function Y(i) is, i.e., the more it tends to deviate from the mean. Although the standard deviation provides some shape information, its shortcoming can be easily understood by considering the following: the mean and standard deviation will not change if the order in which the values making up the sequence Y(i) is “reversed,” that is, Y(i) is reflected about the i=0 axis and shifted so that the value Y(m−1) becomes the first value in time.
Skewness is a measure of lack of symmetry and indicates whether the left or right side of the function Y(i), relative to the statistical mode, is heavier than the other. A positively skewed function rises rapidly, reaches its peak, then falls slowly. The opposite would be true for a negatively skewed function. The point is that the skewness value includes shape information not found in the mean or standard deviation values—in particular, it indicates how rapidly the function initially rises to its peak and then how slowly it decays. Two different functions may have the same mean and standard deviation, but they will then only rarely have the same skewness.
Kurtosis is a measure of whether the function Y(i) is more peaked or flatter than a normal distribution. Thus, a high kurtosis value will indicate a distinct peak near the mean, with a drop thereafter, followed by a heavy “tail.” A low kurtosis value will tend to indicate that the function is relatively flat in the region of its peak. A normal distribution has a kurtosis of 3.0; actual kurtosis values are therefore often adjusted by 3.0 so that the values are instead relative to the origin.
An advantage of using the four statistical moments of the beat-to-beat arterial pressure waveform is that the moments are accurate and sensitive mathematical measures of the shape of the beat-to-beat arterial pressure waveform. As arterial compliance and peripheral resistance directly affect the shape of the arterial pressure waveform, the effect of arterial compliance and peripheral resistance could be directly assessed by measuring the shape of the beat-to-beat arterial pressure waveform. The shape sensitive statistical moments of the beat-to-beat arterial pressure waveform along with other arterial pressure parameters described herein could be effectively used to measure the combined effect of vascular compliance and peripheral resistance, i.e., the arterial tone. The arterial tone represents the combined effect of arterial compliance and peripheral resistance and corresponds to the impedance of the well known 2-element electrical analog equivalent model of the Windkessel hemodynamic model, consisting of a capacitive and a resistive component. By measuring arterial tone, several other parameters that are based on arterial tone, such as arterial elasticity, stroke volume, and cardiac output, also could be directly measured. Any of those parameters could be used to detect vascular conditions such as, for example, vasodilation, vasoconstriction, or peripheral pressure decoupling.
When the first four moments μ1P, μ2P, μ3P, and μ4P of the pressure waveform P(k) are calculated and used in the computation of the arterial tone factor, where μ1P is the mean, μ2P P=σP2 is the variation, that is, the square of the standard deviation σP; μ3P is the skewness, and μ4P is the kurtosis, where all of these moments are based on the pressure waveform P(k). Formulas 1-4 above may be used to calculate these values after substituting P for Y, k for i, and n for m.
Formula 2 above provides the “textbook” method for computing a standard deviation. Other, more approximate methods may also be used. For example, at least in the context of blood pressure-based measurements, a rough approximation to νP is to divide by three the difference between the maximum and minimum measured pressure values, and that the maximum or absolute value of the minimum of the first derivative of the P(t) with respect to time is generally proportional to σP.
As
T(j)=1,1, . . . , 1,2,2, . . . , 2,3,3, . . . , 3,4,4, . . . , 4
This sequence would thus have 25+50+55+35=165 terms.
Moments may be computed for this sequence just as for any other. For example, the mean (first moment) is:
μ1T=(1*25+2*50+3*55+4*35)/165=430/165=2.606 (Formula 6)
and the standard deviation σT is the square root of the variation μ2T:
SQRT[1/164*25(1-2.61)2+50(2-2.61)2+55(3-2.61)2+35(4-2.61)2]=0.985
The skewness μ3T and kurtosis μ4T can be computed by similar substitutions in Formulas 3 and 4:
μ3T={1/(164)*(1/σT3)Σ[P(k)*(k−μ1T)3]} (Formula 7)
μ4T={1/(164)*(1/σT4)Σ[P(k)*(k−μ1T)4]} (Formula 8)
where k=1, . . . , (m−1).
As these formulas indicate, this process in effect “weights” each discrete time value k by its corresponding pressure value P(k) before calculating the moments of time. The sequence T(j) has the very useful property that it robustly characterizes the timing distribution of the pressure waveform. Reversing the order of the pressure values P(k) will in almost all cases cause even the mean of T(j) to change, as well as all of the higher-order moments. Moreover, the secondary “hump” that normally occurs at the dicrotic pressure Pdicrotic also noticeably affects the value of kurtosis μ4T; in contrast, simply identifying the dicrotic notch in the prior art, such as in the Romano method, requires noisy calculation of at least one derivative.
The pressure weighted moments provide another level of shape information for the beat-to-beat arterial pressure signal, as they are very accurate measures of both the amplitude and the time information of the beat-to-beat-arterial pressure signal. Use of the pressure weighted moments in addition to the pressure waveform moments can increase the accuracy of the of arterial tone determination.
One cardiovascular parameter useful with the methods described herein is the arterial tone factor K, which can be used as a cardiovascular parameter by itself or in the calculation of other cardiovascular parameters such as stroke volume or cardiac output. Calculation of the arterial tone K uses all four of the pressure waveform and pressure-weighted time moments. Additional values are included in the computation to take other known characteristics into account, e.g., patient-specific complex pattern of vascular branching. Examples of additional values include, heart rate HR (or period of R-waves), body surface area BSA, or other anthropometric parameters of the subject, a compliance value C(P) calculated using a known method such as described by Langwouters, which computes compliance as a polynomial function of the pressure waveform and the patient's age and sex, a parameter based on the shape of the arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater, a parameter based on the area under the systolic portion of the arterial blood pressure signal, a parameter based on the duration of the systole, and a parameter based on the ratio of the duration of the systole to the duration of the diastole.
These last three cardiovascular parameters, i.e., the area under the systolic portion of the arterial blood pressure signal, the duration of the systole, and the ratio of the duration of the systole to the duration of the diastole, are impacted by arterial tone and vascular compliance and, thus, vary between subjects in normal hemodynamic conditions and subjects in hyperdynamic conditions. Because these three cardiovascular parameters vary between normal and hyperdynamic subjects the methods described herein can use these cardiovascular parameters to detect vasodilation or vasoconstriction in the peripheral arteries of a subject.
The area under the systolic portion of an arterial pressure waveform (Asys) is shown graphically in
The duration of the systole (tsys) is shown graphically in
A further parameter that varies between normal and hyperdynamic subjects is the ratio of the duration of the systole (tsys) and the duration of the diastole (tdia), as shown graphically in
In principle, each of these parameters could be monitored individually to detect hyperdynamic conditions. However, such changes are complex and a multivariate model can often provide a more accurate indication. For example, a compliance or arterial tone factor K can be calculated using a set of parameters including one or more of the area under the systolic portion of the arterial blood pressure signal, the duration of the systole, and the ratio of the duration of the systole to the duration of the diastole.
Determining a cardiovascular parameter using an empirical multivariable statistical model involves several steps. First, an approximating function relating a set of clinically derived reference measurements to the cardiovascular parameter is determined. The set of clinically determined reference measurements of the cardiovascular parameter represents clinical measurements of the cardiovascular parameter, e.g., arterial tone, from both subjects not experiencing the vascular condition and subjects experiencing the vascular condition. The approximating function is a function of one or more of (a) a parameter based on the area under the systolic portion of the arterial blood pressure signal, (b) a parameter based on the duration of systole, (c) a parameter based on the ratio of the duration of the systole to the duration of the diastole, and (d) a parameter based on the shape of the arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater. Next a set of arterial blood pressure parameters from the arterial blood pressure signal is determined. The set of arterial blood pressure parameters includes one or more of (a) a parameter based on the area under the systolic portion of the arterial blood pressure signal, (b) a parameter based on the duration of systole, (c) a parameter based on the ratio of the duration of the systole to the duration of the diastole, and (d) a parameter based on the shape of the arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater. Finally, the cardiovascular parameter is estimated by evaluating the approximating function with the set of arterial blood pressure parameters. The set of arterial blood pressure parameters derived from subjects experiencing the vascular condition can optionally be given more weight in the model than the data derived from subjects not experiencing the vascular condition.
An example of a multivariate model to determine an arterial factor impacted by a vascular condition such as vasodilation to be used as a cardiovascular parameter in the methods described herein, involves the use of the following multivariate model (the hyperdynamic model), which uses many of the parameters discussed above and includes the area under systole (Asys), the duration of systole (tsys) and the duration of the diastole (tdia):
K
h=χh(Asys,tsys,tdia,μT1,μT2, . . . μTk,μP1,μP2, . . . μPk,C(P),BSA,Age,G . . . ) (Formula 9)
where:
To increase the accuracy of the calculations, the predictor variables set for the multivariate model χh are related to the “true” vascular tone measurement (determined as a function of CO measured through thermodilution and the arterial pulse pressure) for a population of test or reference subjects that includes subjects in normal hemodynamic conditions, i.e., not experiencing the vascular condition, and subjects in hyperdynamic conditions, i.e., experiencing the vascular condition, e.g., low arterial tone and marked peripheral decoupling of arterial pressure and flow. Additionally, to further highlight the change from normal hemodynamic conditions to hyperdynamic conditions, the model χh is statistically weighted with the data from the hyperdynamic subjects, i.e., the data from the hyperdynamic subjects is weighted more heavily in the model than the data from the normal subjects. The multivariate approximating function is then computed, using known numerical methods, that best relates the parameters of χh to a given suite of CO measurements in a predefined manner and weighted on the hyperdynamic side. A polynomial multivariate fitting function is used to generate the coefficients of the polynomial that gives a value of χh for each set of the predictor variables. Thus, such a multivariate model has the following general form:
where Ah1 . . . . Ahn are the coefficients of the polynomial multi-regression model, and Xh, are the model's predictor variables:
To determine an arterial tone factor to be used as a cardiovascular parameter that does not take into account the parameters identified above that are not impacted by peripheral decoupling, a multivariate model also is used (the normal hemodynamic model) that involves several steps. First an approximating function relating a set of clinically derived reference measurements to the cardiovascular parameter, e.g., arterial tone, is determined. The set of clinically determined reference measurements of the cardiovascular parameter represents clinical measurements of the cardiovascular parameter from subjects not experiencing the vascular condition. The approximating function is a function of one or more of (a) a parameter based on the shape of the arterial blood pressure signal including calculating at least one statistical moment of the arterial blood pressure signal having an order of one or higher, (b) a parameter based on the heart rate, and (c) a set of anthropometric parameters of the subject. Next a set of arterial blood pressure parameters from the arterial blood pressure signal is determined. The set of arterial blood pressure parameters includes one or more of the shape of the arterial blood pressure signal and at least one statistical moment of the arterial blood pressure signal having an order of one or greater, and the heart rate. Next a set of anthropometric parameters of the subject is determined. Finally, the cardiovascular parameter is estimated by evaluating the approximating function with the set of arterial blood pressure parameters and the set of anthropometric parameters of the subject.
An example of such a multivariate model to determine an arterial tone factor not impacted by the vascular condition to be used as a cardiovascular parameter in the methods described herein, involves the use of many of the parameters discussed above but excludes the area under systole (Asys), the duration of systole (tsys) and the duration of the diastole (tdia), i.e., those parameters impacted by the vascular condition:
K=χ(μT1,μT2, . . . μTk,μP1,μP2, . . . μPk,C(P),BSA,Age,G . . . ) (Formula 12)
Where the parameters K, χ, μ1T, . . . μkT, μ1P . . . μkP, C(P), BSA, Age, and G are the same as described above for the hyperdynamic model.
Similar to that discussed above, the predictor variables set for computing the vascular tone factor K, using the multivariate model χ, is related to the “true” vascular tone measurement, determined as a function of CO measured through thermo-dilution and the arterial pulse pressure, for a population of test or reference subjects. This creates a suite of vascular tone measurements, each of which is a function of the component parameters of χ. A multivariate approximating function is then computed, using known numerical methods, that best relates the parameters of χ to a given suite of CO measurements in a predefined manner. A polynomial multivariate fitting function is used to generate the coefficients of the polynomial that gives a value of χ for each set of the predictor variables. Thus, such a multivariate model has the following general form:
where A1 . . . An, are the coefficients of the polynomial multi-regression model, and χ are the model's predictor variables:
Vascular conditions such as vasodilation, vasoconstriction, peripheral pressure decoupling, conditions where the peripheral arterial pressure is not proportional to the central aortic pressure, and conditions where the peripheral arterial pressure is lower than the central aortic pressure can be detected in a subject using χ and χh As a first example, the difference (Δχ) between χh and χ can be monitored.
χ=χh−χ (Formula 14)
The difference between χ and χh indicates the vascular condition because χh uses the additional arterial pressure waveform parameters Asys, tsys, and tdia that are sensitive to the vascular condition. Thus, an increasing Δχ shows changes in parameters Asys, tsys, and tdia that indicate the vascular condition. This is because the model χh was approximated (during the numerical fitting) using combined data from patients in normal hemodynamic conditions and patients in extreme hyperdynamic conditions with peripheral decoupling, while the model χ was approximated using data only from patients with normal hemodynamic conditions. For this reason, the difference Δχ will be small for patients in normal conditions and it will be high for patients in hyperdynamic conditions when arterial tone is low and the peripheral pressure and flow are decoupled.
Another way to monitor vascular conditions in a subject is to calculate the ratio of χh to χ. When the ratio exceeds a predetermined value vasodilatory conditions are indicated. As an example, for the values of χh and χ shown in
Other parameters based on the arterial tone factor such as, for example, Stroke Volume (SV), Cardiac Output (CO), Arterial Flow, or Arterial Elasticity can be used to monitor vascular conditions in a subject. As an example, Stroke Volume (SV) can be calculated as the product of the arterial tone and the standard deviation of the arterial pressure signal:
SV=χ·σP (Formula 15)
where:
The difference in SV computed with the two different model could be used to detect the vascular condition, as follows:
ΔSV=(χh−χ)·σP (Formula 16)
The analog measurement interval, that is, the time window [t0, tf], and thus the discrete sampling interval k=0, . . . , (n−1), over which each calculation period is conducted should be small enough so that it does not encompass substantial shifts in the pressure and/or time moments. However, a time window extending longer than one cardiac cycle will provide suitable data. Preferably, the measurement interval is a plurality of cardiac cycles that begin and end at the same point in different cardiac cycles. Using a plurality of cardiac cycles ensures that the mean pressure value used in the calculations of the various higher-order moments will use a mean pressure value Pavg that is not biased because of incomplete measurement of a cycle.
Larger sampling windows have the advantage that the effect of perturbations such as those caused by reflections are typically reduced. An appropriate time window can be determined using normal experimental and clinical methods well known to those of skill in the art. Note that it is possible for the time window to coincide with a single heart cycle, in which case mean pressure shifts will not be of concern.
The time window [t0, tf] is also adjustable according to drift in Pavg. For example, if Pavg over a given time window differs absolutely or proportionately by more than a threshold amount from the Pavg of the previous time window, then the time window can be reduced; in this case stability of Pavg is then used to indicate that the time window can be expanded. The time window can also be expanded and contracted based on noise sources, or on a measure of signal-to-noise ratio or variation. Limits are preferably placed on how much the time window is allowed to expand or contract and if such expansion or contraction is allowed at all, then an indication of the time interval is preferably displayed to the user.
The time window does not need to start at any particular point in the cardiac cycle. Thus, t0 need not be the same as tdia0, although this may be a convenient choice in many implementations. Thus, the beginning and end of each measurement interval (i.e., t0 and tf) may be triggered on almost any characteristic of the cardiac cycle, such as at times tdia0 or tsys, or on non-pressure characteristics such as R waves, etc.
Rather than measure blood pressure directly, any other input signal may be used that is proportional to blood pressure. This means that calibration may be done at any or all of several points in the calculations. For example, if some signal other than arterial blood pressure itself is used as input, then it may be calibrated to blood pressure before its values are used to calculate the various component moments, or afterwards, in which case either the resulting moment values can be scaled. In short, the fact that the cardiovascular parameter may in some cases use a different input signal than a direct measurement of arterial blood pressure does not preclude its ability to generate an accurate compliance estimate.
The signals from the sensors 100, 200 are passed via any known connectors as inputs to a processing system 300, which includes one or more processors and other supporting hardware and system software (not shown) usually included to process signals and execute code. The methods described herein may be implemented using a modified, standard, personal computer, or may be incorporated into a larger, specialized monitoring system. For use with the methods described herein, the processing system 300 also may include, or is connected to, conditioning circuitry 302 which performs normal signal processing tasks such as amplification, filtering, or ranging, as needed. The conditioned, sensed input pressure signal P(t) is then converted to digital form by a conventional analog-to-digital converter ADC 304, which has or takes its time reference from a clock circuit 305. As is well understood, the sampling frequency of the ADC 304 should be chosen with regard to the Nyquist criterion so as to avoid aliasing of the pressure signal (this procedure is very well known in the art of digital signal processing). The output from the ADC 304 will be the discrete pressure signal P(k), whose values may be stored in conventional memory circuitry (not shown).
The values P(k) are passed to or accessed from memory by a software module 310 comprising computer-executable code for computing whichever of the parameters μ1T . . . μkT, μ1P . . . μkP, etc. are to used in the chosen algorithm for calculating a cardiovascular parameter, such as χ and Xh. Even moderately skilled programmers will know how to design this software module 310.
The patient-specific data such as age, height, weight, BSA, etc., is stored in a memory region 315, which may also store other predetermined parameters such as Kprior. These values may be entered using any known input device 400 in the conventional manner.
Cardiovascular parameters χ and χh, are calculated by calculation modules 320 and 330. Calculation modules 320 and 330 include computer-executable code and take as inputs the various moment and patient-specific values, then performs the chosen calculations for computing χ and χh. For example, the modules 320 and 330 could enter the parameters into the expression given above for χ and χh, or into some other expression derived by creating an approximating function that best fits a set of test data. The calculation modules 320 and 330 preferably also select the time window [t0, tf] over which each χ and χh estimate is generated. This may be done as simply as choosing which and how many of the stored, consecutive, digitized P(t) values P(k) are used in each calculation, which is the same as selecting n in the range k=0, . . . , (n−1).
Further calculation modules 340 and 350 can be included to calculate Δχ and χh/χ as needed. The input to these calculation modules is from modules 320 and 330. The output of these modules is sent to the display 500 as desired.
As mentioned above, it is not necessary for the system according to the methods described herein to compute each of χ, χh, Δχ, and χh/χ if these values are not of interest. In such case, the corresponding software modules will of course not be needed and may be omitted. For example, the methods described herein could monitor only χh, in which case modules 320, 340, and 350 would not be needed. As illustrated by
For each of the methods described herein, when the vascular condition is detected, a user can be notified of the vascular condition. The user can be notified of the vasodilatory conditions by publishing a notice on display 500 or another graphical user interface device. Further, a sound can be used to notify the user of the vascular condition. Both visual and auditory signals can be used.
Exemplary embodiments of the present invention have been described above with reference to a block diagram of methods, apparatuses, and computer program products. One of skill will understand that each block of the block diagram, and combinations of blocks in the block diagram, respectively, can be implemented by various means including computer program instructions. These computer program instructions may be loaded onto a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions which execute on the computer or other programmable data processing apparatus create a means for implementing the functions specified in the blocks.
The methods described herein further relate to computer program instructions that may be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus, such as in a processor or processing system (shown as 300 in
Accordingly, blocks of the block diagram support combinations of means for performing the specified functions, combinations of steps for performing the specified functions, and program instruction means for performing the specified functions. One of skill will understand that each block of the block diagram, and combinations of blocks in the block diagram, can be implemented by special purpose hardware-based computer systems that perform the specified functions or steps, or combinations of special purpose hardware and computer instructions.
The present invention is not limited in scope by the embodiments disclosed herein which are intended as illustrations of a few aspects of the invention and any embodiments which are functionally equivalent are within the scope of this invention. Various modifications of the apparatus and methods in addition to those shown and described herein will become apparent to those skilled in the art and are intended to fall within the scope of the appended claims. Further, while only certain representative combinations of the apparatus and method steps disclosed herein are specifically discussed in the embodiments above, other combinations of the apparatus components and method steps will become apparent to those skilled in the art and also are intended to fall within the scope of the appended claims. Thus a combination of components or steps may be explicitly mentioned herein; however, other combinations of components and steps are included, even though not explicitly stated. The term “comprising” and variations thereof as used herein is used synonymously with the term “including” and variations thereof and are open, non-limiting terms.
This application claims the benefit of priority to U.S. Provisional Application No. 61/024,638, filed on Jan. 30, 2008, which is incorporated by reference herein in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 61024638 | Jan 2008 | US |
