Ventricular activation (RR) entropy change as a predictor of sudden cardiac death in cardiac resynchronization therapy patients

Abstract

A method of determining health and mortality includes obtaining a ventricular activation (RR) time series from a subject for multiple temporal intervals. The method also includes calculating a cardiac entropy in the RR time series over the temporal intervals using coefficient of sample entropy (COSEn). Additionally, the method includes comparing the cardiac entropy between the intervals to determine health and mortality. The absolute and relative changes in entropy over a patient's follow up period provide dynamic information regarding health and mortality risk. The determination of health and mortality can then be used to create a treatment plan for the subject.

Claims

1. A method for determining increased risk of mortality of a patient, comprising: measuring a first cardiac rhythm of a patient at a first time; identifying at least one segment of said first cardiac rhythm; calculating a first entropy measurement for the at least one segment; measuring a second cardiac rhythm of said patient at a second time subsequent to said first time; identifying at least one segment of said second cardiac rhythm; calculating a second entropy measurement for the at least one segment of said second cardiac rhythm; calculating a change in entropy by comparing said second entropy measurement with said first entropy measurement; and determining that said patient is at an increased risk of mortality when said change in entropy is above a predetermined value.

2. The method of claim 1, wherein the entropy measurement is a measurement of absolute entropy.

3. The method of claim 2, wherein the absolute entropy measurement is a coefficient of sample entropy (COSEn).

4. The method of claim 3, wherein the at least one cardiac rhythm arises from at least a deterministic process.

5. The method of claim 3, wherein the at least one cardiac rhythm arises from a combination of both deterministic and stochastic physiological processes.

6. The method of claim 3, wherein the at least one segment comprises a series of beats having a statistically homogeneous time interval between beats.

7. The method of claim 4, wherein each at least one cardiac rhythm comprises a heart rate time series such as would be provided by non-invasive devices that do not use a conventional ECG signal.

8. The method of claim 3, wherein the heart rate time series comprises a number of beats, and wherein COSEn is calculated at least every 50 beats.

9. The method of claim 3, wherein the at least one cardiac rhythm comprises an RR-interval series, and wherein the step of calculating COSEn for at least one segment comprises: calculating a mean RR-interval for the RR-interval series; using the mean RR-interval as a continuous variable; unit mean normalizing the RR-interval series by dividing each observation by the mean RR-interval; and calculating COSEn as an entropy rate or entropy of the unit mean normalized RR interval series.

10. The method of claim 3, wherein the at least one cardiac rhythm comprises an RR-interval series, and wherein the step of calculating COSEn for at least one segment comprises: calculating the differential quadratic entropy rate using a sample entropy (SampEn) algorithm; calculating a mean RR-interval for the RR-interval series; and subtracting the natural logarithm of the mean RR-interval from the differential quadratic entropy rate to obtain COSEn.

11. The method of claim 1, wherein said first cardiac rhythm is measured when said patient is in normal sinus rhythm (NSR).

12. The method of claim 1, wherein said second time is on the order of months subsequent to said first time.

13. The method of claim 1, wherein calculation of a change in entropy comprises calculating a rate of entropy change.

14. The method of claim 13, wherein calculation of a rate of entropy change comprises measuring a slope of a linear regression fit to values at a baseline measurement and subsequent measurements of cardiac rhythm.

15. The method of claim 11, wherein said change in entropy is a rising entropy of NSR.

16. The method of claim 1, wherein determining that said patient is at increased risk of mortality further comprises use of a multivariable model that employs entropy measures.

17. An apparatus comprising: a programmable computer, programmed to measure a first cardiac rhythm of a patient at a first time; identify at least one segment of said first cardiac rhythm; calculate a first entropy measurement for the at least one segment; measure a second cardiac rhythm of said patient at a second time subsequent to said first time; identify at least one segment of said second cardiac rhythm; calculate a second entropy measurement for the at least one segment of said second cardiac rhythm; and calculate a change in entropy by comparing said second entropy measurement with said first entropy measurement.

18. The apparatus of claim 17, wherein the entropy measurement is a measurement of absolute entropy.

19. The apparatus of claim 18, wherein the absolute entropy measurement is a coefficient of sample entropy (COSEn).

20. The apparatus of claim 19, wherein the at least one cardiac rhythm comprises an RR-interval series, and wherein calculating COSEn for at least one segment comprises: calculating a mean RR-interval for the RR-interval series; using the mean RR-interval as a continuous variable; unit mean normalizing the RR-interval series by dividing each observation by the mean RR-interval; and calculating COSEn as an entropy rate or entropy of the unit mean normalized RR interval series.

21. The apparatus of claim 19, wherein the at least one cardiac rhythm comprises an RR-interval series, and wherein calculating COSEn for at least one segment comprises: calculating the differential quadratic entropy rate using a sample entropy (SampEn) algorithm; calculating a mean RR-interval for the RR-interval series; and subtracting the natural logarithm of the mean RR-interval from the differential quadratic entropy rate to obtain COSEn.

22. The apparatus of claim 17, wherein said first cardiac rhythm is measured when said patient is in normal sinus rhythm (NSR).

23. The apparatus of claim 17, wherein said second time is on the order of months subsequent to said first time.

24. The apparatus of claim 17, wherein calculation of a change in entropy comprises calculating a rate of entropy change.

25. The apparatus of claim 24, wherein calculation of a rate of entropy change comprises measuring a slope of a linear regression fit to values at a baseline measurement and subsequent measurements of cardiac rhythm.

26. The apparatus of claim 22, wherein said change in entropy is a rising entropy of NSR.

27. A computer program product comprising a non-transient computer readable storage medium storing computer-executable instructions causing a computer to: receive a measurement of a first cardiac rhythm of a patient taken at a first time; identify at least one segment said first cardiac rhythm; calculate a first entropy measurement for the at least one segment; receive a measurement of a second cardiac rhythm of said patient taken at a second time subsequent to said first time; identify at least one segment of said second cardiac rhythm; calculate a second entropy measurement for the at least one segment of said second cardiac rhythm; and calculate a change in entropy by comparing said second entropy measurement with said first entropy measurement.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The accompanying drawings provide visual representations, which will be used to more fully describe the representative embodiments disclosed herein and can be used by those skilled in the art to better understand them and their inherent advantages. In these drawings, like reference numerals identify corresponding elements and:

(2) FIG. 1A illustrates fractal temporal processes of a healthy RR according to an embodiment of the present invention. FIG. 1B illustrates wavelet analysis of healthy RR time series of >1500 beats (x-axis is time, y-axis is wavelet scale (5 to 300 secs) according to an embodiment of the present invention. FIG. 1C illustrates the wavelet amplitudes according to an embodiment of the present invention.

(3) FIGS. 2A-2E illustrate an RR time series demonstrating quantifiable nonlinear dynamics that are distinct within patients with OSA, as illustrated in FIGS. 2A-2C, and also distinct within healthy individuals at high altitude, as illustrated in FIGS. 2D-2E according to an embodiment of the present invention.

(4) FIG. 3 shows analysis of heart rate variability.

(5) FIG. 4 shows graphs of calculated change in entropy over time for patients at risk of SCD, in accordance with an aspect of the invention.

(6) FIG. 5 is a diagram illustrating vital demographics of patients in an observational study in accordance with the invention.

(7) FIG. 6 shows Kaplan-Meier survival curves for the patients in FIG. 5.

(8) FIG. 7 shows Hazard Ratios for multiple parameters of SCD patients.

(9) FIG. 8 shows Hazard Ratios for multiple parameters of patient death in the study due to all causes.

(10) FIG. 9 is a block diagram of an illustrative computer system capable of implementing the methods of the present invention.

DETAILED DESCRIPTION

(11) The presently disclosed subject matter now will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the inventions are shown. Like numbers refer to like elements throughout. The presently disclosed subject matter may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Indeed, many modifications and other embodiments of the presently disclosed subject matter set forth herein will come to mind to one skilled in the art to which the presently disclosed subject matter pertains having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the presently disclosed subject matter is not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims.

(12) In accordance with an aspect of the present invention, a method allows for the nonlinear assessment of health and mortality. In order to nonlinearly determine health and mortality, ventricular activation (RR) time series from a subject for a temporal interval are obtained. A first and second cardiac entropy in the RR time series over the temporal interval are determined. The first and second cardiac entropy are compared, to determine health and mortality. This information can then be used to determine a treatment plan for the subject, such as increased monitoring for pathophysiological states.

(13) In accordance with another aspect of the invention, a method is provided for assessing the risk of sudden cardiac death (SCD) by comparing cardiac RR interval rate of entropy change over a predefined time interval for a patient receiving Cardiac Resynchronization Therapy (CRT) to determine changes in entropy of normal sinus rhythm (NSR) and determining increased risk of SCD when the NSR entropy of the patient has increased.

(14) The coefficient of entropy is a calculation of an entropy rate (or entropy) of an RR interval series after it has been unit mean normalized (dividing each observation by the mean of the series). This is analogous to the coefficient of variation, which is the standard deviation after normalization by the mean. In practice, the calculation of the coefficient of entropy is accomplished by subtracting the natural logarithm of the mean from the original entropy calculation. The coefficient of entropy calculated for Q in this way is especially effective and we give it the name coefficient of sample entropy or COSEn for short and denote it by Q*.

(15) The dynamics of cardiac rhythms can be quantified by entropy and entropy rate under the framework of continuous random variables and stochastic processes. The entropy of a continuous random variable X with density ƒ is
H(X)=E[−log(ƒ(X))]=∫.sub.−∞.sup.∞−log(ƒ(x))ƒ(x)dx
If X has variance σ.sup.2, then Y=X/σ a has variance 1 and density σƒ(σy). So the entropy of Y is related to the entropy of X by
H(Y)=∫.sub.−∞.sup.∞−log(σƒ(σy))σƒ(σy)dy=H(X)−log(σ)
which shows that reduced entropy is indicative of reduced variance or increased uncertainty.

(16) Another important property of entropy is provided by the inequality

(17) $H\left(X\right)\le \frac{1}{2}\left(\log \left(2\pi e\right)+\log \left({\sigma }^2\right)\right)=H\left(\sigma Z\right)$
where Z is a standard Gaussian random variable. This result shows that the Gaussian distribution has maximum entropy among all random variables with the same variance. Thus, an estimate of entropy that is substantially lower than this upper bound for a random sample (with sample variance used as an estimate of σ.sup.2) provides evidence that the underlying distribution is not Gaussian. This type of distribution is a characteristic of some cardiac arrhythmias, such as bigeminy and trigeminy, that are multimodal and is another reason entropy is important for this application.

(18) Letting X denote the random sequence X.sub.1, X.sub.2, X.sub.3, . . . , the entropy rate of X is defined as

(19) $H\left(X\right)=\underset{n.fwdarw.\infty }{\lim }\frac{H\left(X_1,X_2,\mathrm{.Math.},X_n\right)}{n}$
where the joint entropy of m random variables X.sub.1, X.sub.2, . . . , X.sub.m is defined as
H(X.sub.1,X.sub.2, . . . ,X.sub.m)=E[−log(ƒ(X.sub.1,X.sub.2, . . . ,X.sub.m))]
and ƒ is the joint probability density function ƒ. For stationary processes, an equivalent definition is

(20) $H\left(X\right)=\underset{m.fwdarw.\infty }{\lim }{H}_m\left(X\right)=\underset{n.fwdarw.\infty }{\lim }H\left(X_{m+1}|X_1,X_2,\mathrm{.Math.},X_m\right)$
so entropy rate is the entropy of the conditional distribution of the present observation given the past. The entropy rate for i.i.d. sequences reduces to the entropy of the common distribution.

(21) Estimating the entropy rate for sequences depends on estimates of its densities of order m. Let X.sub.1, X.sub.2, . . . , X.sub.n denote a stationary random sequence and X.sub.i(m) denote the template consisting of the m×1 vector (X.sub.i−m+1, X.sub.i−m, . . . , X.sub.i).sup.T. For notational simplicity, let X.sub.n=X.sub.n(n) denote the whole sequence and X=X.sub.∞ denote the limiting infinite sequence. The sequence X.sub.m(m), X.sub.m+1(m), . . . , X.sub.n(m) is not independent, but many methods developed to analyze independent vector data are applicable. In particular, the m.sup.th-order probability density function of the sequence, ƒ, and entropy
E[−log(ƒ(X.sub.1,X.sub.2, . . . ,X.sub.m))]
can still be estimated empirically. These are the fundamental calculations in ApEn and SampEn.

(22) We define the COSEn as the sample entropy of a series after being normalized by the mean. This is equivalent to subtracting the natural logarithm of the mean from the original entropy. To see this, note that if X has mean μ, then Y=X/μ has mean 1 and density μƒ(μy). So the entropy of Y is related to the entropy of X by
H(Y)=∫.sub.−∞.sup.∞−log(μƒ(μy))μƒ(μy)dy=H(X)−log(μ)
as stated. Similar results can be shown for all Renyi entropy rates and in particular for the differential quadratic entropy rate Q calculated using the SampEn algorithm. This leads to the calculation
Q*=Q−log(μ)
where Q* is the coefficient of sample entropy.

(23) Current clinical measures, including ECG metrics, are insufficient for SCD risk stratification, and the effect of CRT on SCD is debated. Little is known about the prognostic value of ECG entropy in short-term time series of RR and QT intervals. Entropy is fundamentally different from heart rate variability (HRV) in that entropy quantifies the degree to which heart rate fluctuation patterns repeat themselves. As shown in FIG. 3, “self-similar” fluctuations in heart rate are indistinguishable in moment statistics and frequency domain measures of HRV.

(24) In accordance with the invention, RR intervals were collected from 5-min surface ECGs of 134 consecutive patients who were in NSR at time of biventricular ICD implantation (baseline), and at 6-month clinic visits (4±2 mean number of visits) until ICD shock if occurred (N=44; 6±5 mo). The patients (age 51±12 yrs, male 66%, white 82%, DM 26%, HTN 46%, ICM 32%, EF 20±8%, NYHA class 2.3±0.8) were well treated medically for heart failure. Entropy was measured using coefficient of sample entropy (COSEn), based on Kolmogorov-Sinai entropy with roots in chaos theory. For each patient, rate of entropy change (δE/δt) was measured as the slope of linear regression fit to values at baseline and subsequent clinic visits excluding shock. ICD shocks or deaths from ventricular tachyarrhythmias (VT/VF) were used as a specific surrogate for SCD.

(25) As shown in FIG. 4, for each patient, entropy change was measured as ΔE/Δt, the change in entropy over two routine 6 month clinical visits preceding an ICD shock (and excluding the clinical visit after the ICD shock). As shown, the ΔE/Δt for the time interval preceding an ICD shock was a strong predictor of increased risk of SCD (where ICD shock is used as a surrogate for SCD). FIG. 5 is a graph illustrating the demographics of the N=134 patients. Of the N=45 patients who died or experienced ICD shock, N=28 or 62% experienced ICD shock or died from SCD. FIG. 6 shows Kaplan-Meier curves for these patients, per quartile of ΔE/Δt. As shown, patients in the 4.sup.th quartile for ΔE/Δt had the lowest survival probability. FIG. 7 shows hazard ratios for SCD for multiple parameters, and FIG. 8 shows hazard ratios for all deaths for multiple parameters. As shown, ΔE/Δt alone as a predictor had a confidence interval (CI) of 95%.

(26) Over 53±22 months of follow-up, entropy rose in patients who had shocks for VT/VF (δE/δt=+0.025±0.041/mo) but fell in those with no shocks (−0.0075±0.039) or only inappropriate shocks (−0.013±0.025; p=0.002). In contrast, there were no significant changes in heart rate or heart rate variability analyses (i.e., SDNN, RMSSD). In multivariate analyses, δE/δt was the strongest predictor of SCD (p<0.001) after taking age, gender, risk factors, NYHA class, duration of follow-up, medications, biomarkers, and ejection fraction into account. The C-statistic for δE/δt alone was 0.73 (p<0.001), a multivariable model using the clinical variables was 0.77 (p=0.019), and a model using all parameters was 0.86 (p<0.001), suggesting an entropy-based measure has utility in clinical care.

(27) Turning to FIG. 9, it is contemplated that embodiments of the invention may be practiced using a computer system. FIG. 9 is an illustrative block diagram for a computer system 100 for implementation of an exemplary embodiment or portion of an embodiment of present invention. For example, a method or system of an embodiment of the present invention may be implemented using hardware, software or a combination thereof and may be implemented in one or more computer systems or other processing systems, such as personal digit assistants (PDAs). In an example embodiment, the invention was implemented in software running on a general purpose computer 100 as illustrated in FIG. 1. The computer system 100 may include one or more processors, such as processor 104. The Processor 104 is connected to a communication infrastructure 106 (e.g., a communications bus, cross-over bar, or network). The computer system 100 may include a display interface 102 that forwards graphics, text, and other data from the communication infrastructure 106 (or from a frame buffer not shown) for display on the display unit 830.

(28) The computer system 10 may also include a main memory 108, preferably random access memory (RAM), and may include a secondary memory 110. The secondary memory 110 may include, for example, a hard disk drive 112 and/or a removable storage drive 114, representing a floppy disk drive, a magnetic tape drive, an optical disk drive, a flash memory, etc. The removable storage drive 114 reads from and/or writes to a removable storage unit 118 in a well-known manner. Removable storage unit 118, represents a floppy disk, magnetic tape, optical disk, etc. which is read by and written to by removable storage drive 114. As will be appreciated, the removable storage unit 118 includes a computer usable storage medium having stored therein computer software and/or data.

(29) In alternative embodiments, secondary memory 110 may include other means for allowing computer programs or other instructions to be loaded into computer system 100. Such means may include, for example, a removable storage unit 122 and an interface 120. Examples of such removable storage units/interfaces include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as a ROM, PROM, EPROM or EEPROM) and associated socket, and other removable storage units 122 and interfaces 120 which allow software and data to be transferred from the removable storage unit 122 to computer system 100.

(30) The computer system 100 may also include a communications interface 124. Communications interface 124 allows software and data to be transferred between computer system 100 and external devices. Examples of communications interface 824 may include a modem, a network interface (such as an Ethernet card), a communications port (e.g., serial or parallel, etc.), a PCMCIA slot and card, a modem, etc. Software and data transferred via communications interface 124 are in the form of signals 828 which may be electronic, electromagnetic, optical or other signals capable of being received by communications interface 124. Signals 128 are provided to communications interface 124 via a communications path (i.e., channel) 126. Channel 126 (or any other communication means or channel disclosed herein) carries signals 128 and may be implemented using wire or cable, fiber optics, blue tooth, a phone line, a cellular phone link, an RF link, an infrared link, wireless link or connection and other communications channels.

(31) In this document, the terms “computer program medium” and “computer usable medium” are used to generally refer to media or medium such as removable storage drive 114, a hard disk installed in hard disk drive 112, and signals 128. These computer program products are means for providing software to computer system 100. The computer program product may comprise a computer useable medium having computer program logic thereon. The invention includes such computer program products. The “computer program product” and “computer useable medium” may be any computer readable medium having computer logic thereon.

(32) Computer programs (also called computer control logic or computer program logic) may be stored in main memory 108 and/or secondary memory 110. Computer programs may also be received via communications interface 124. Such computer programs, when executed, enable computer system 100 to perform the features of the present invention as discussed herein. In particular, the computer programs, when executed, enable processor 104 to perform the functions of the present invention. Accordingly, such computer programs represent controllers of computer system 100.

(33) In an embodiment where the invention is implemented using software, the software may be stored in a computer program product and loaded into computer system 100 using removable storage drive 114, hard drive 112 or communications interface 124. The control logic (software), when executed by the processor 104, causes the processor 104 to perform the functions of the invention as described herein.

(34) The features and advantages of the invention are apparent from the detailed specification, and thus, it is intended by the appended claims to cover all such features and advantages of the invention which fall within the true spirit and scope of the invention. Further, since numerous modifications and variations will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the invention.