WO2008085179A1

WO2008085179A1 - Quantitative assessment of cardiac electrical events

Info

Publication number: WO2008085179A1
Application number: PCT/US2007/001642
Authority: WO
Inventors: Bosko Bojovic; Ljupco Hadzievski; Vladan Vukcevic; Samuel George
Original assignee: Newcardio, Inc.
Priority date: 2006-01-18
Filing date: 2007-01-18
Publication date: 2008-07-17

Abstract

The application relates to the analysis of ECG data by exploiting computerized three-dimensional spatial presentation of the measured data using the heart vector concept. A three-dimensional presentation of the human heart may be correlated with waveforms specific for standard ECG or derived ECG signals based on the dipole approximation of the heart electrical activity. Additional tools for analyzing ECG data are also provided which may be used to determine the time of cardiac electrical events.

Description

QUANTITATIVE ASSESSMENT OF CARDIAC ELECTRICAL EVENTS

INVENTORS:

BoSko Bojovic, Ljupco Hadzievski, Vladan Vukcevic, Samuel George

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent is related to PCT/US2005/001239 and claims priority to US Provisional Patent Application 60/759,638, filed Jan. 18, 2006, which is herein incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

Technical field

The present invention relates to the field of medical electronics. In particular, it concerns electronic devices for acquisition and presentation of diagnostic data. The invention comprises devices and procedures for acquisition and analysis of electrocardiographic (ECG) data and the three-dimensional visualization of ECG data that enables more precise diagnostic interpretation of the ECG data. According to the International Patent Classification (EPC), the invention is categorized within the A61B 5/00 class, which defines methods or devices for measurement or recording in diagnostic purposes. More precisely, the invention is categorized within the A61B 5/04 class, which defines instruments for measuring or recording bioelectric charges of a body or an organ, such as electrocardiographs.

Technical problem

Although the ECG is a universally accepted diagnostic method in cardiology, frequent mistakes are made in interpreting ECGs, because the most common approach for interpretation of ECGs is based on memorization of waveforms, rather than using vector concepts and basic principles of electrocardiography (Hurst, J. W., Clin. Cardiol 2000 Jan;23(l):4-13). One embodiment of this invention simplifies the vector interpretation concept, and provides a visual three-dimensional presentation of a patient's ECG signal with a three-dimensional model of the human heart, rather than relying on the cardiologist's individual spatial imagination skills. The present invention exploits a dipole approximation of electrical heart activity, in keeping with the basis of the conventional doctrine of ECG interpretation.

Another problem with traditional ECG recordings is that the ECG may not provide adequate indications of electrical activity of certain regions of the heart, especially the posterior region. An embodiment of this invention provides a more accurate approximation of cardiac activity, particularly for regions of the heart, such as the posterior region, that generally were less well ^• represented using prior ECG recordings, and may also provide greater indications of cardiac events such as ischemia.

The timing of cardiac electrical events, and the time intervals between two or more such events, has diagnostic and clinical importance. However, medical diagnosis and drug development has been significantly limited by the lack of adequate ECG measurement tools.

Furthermore, prior analysis of ECG recordings required a substantial amount of training and familiarity with reading of the recorded waveforms. An embodiment of this invention provides analysis tools to aid in the interpretation of cardiac electrical activity.

Background art

• There have been many attempts to extract additional information from the standard 12-lead ECG measurement when measuring the electric potential distribution on the surface of the patient's body for diagnostic purposes. These attempts have included new methods of measured signal interpretation, either with or without introducing new measurement points, in addition to the standard 12-lead ECG points.

Vector ECG

VCG is the oldest approach that includes the improvement of a spatial aspect to the ECG (Frank, E₃, An Accurate, Clinically Practical System For Spatial Vectorcardiography, Circulation 13: 737, May 1956). Like conventional ECG interpretation, VCG uses a dipole approximation of electrical heart activity. The dipole size and orientation are presented by a vector that continuously changes during the heartbeat cycle. Instead of presenting signal waveforms from the measurement points (waveforms), as it is the case with standard 12-lead ECGs, in VCG, the measurement points are positioned in such a way that three derived signals correspond to three orthogonal axes (X, Y, Z), and these signals are presented as projections of the vector hodograph onto three planes (frontal, sagittal, and horizontal). In this way, VCG represents a step towards spatial presentation of the signal, but the cardiologist's spatial imagination skills were still necessary to interpret the ECG signals, particularly the connection to the heart anatomy. Furthermore, a time-dependence aspect (i.e., the signal waveform) is lost with this procedure, and this aspect is very important for ECG interpretation. VCG introduces useful elements which cannot be found within the standard 12-lead ECG, however, the incomplete spatial presentation and loss of the time-dependence are major reasons why VCG, unlike ECG, has never been widely adopted, despite the fact that (in comparison to ECG) VCG can more often correctly diagnose cardiac problems, such as myocardial infarction.

Modifications of Vector ECG

There have been numerous attempts to overcome the drawbacks of the VCG method described above. These methods exploit the same signals as VCG (X, Y, Z), but their signal presentation is different than the VCG projection of the vector hodograph onto three planes:

"Polarcardiogram" uses Aitoff cartographic projections for the presentation of the three- dimensional vector hodographs (Sada, T., et al., J Electrocardiol. 1982; 15(3):259-64). "Spherocardiogram" adds information on the vector amplitude to the Aitoff projections, by drawing circles of variable radius (Niederberger, M., et al., J. Electrocardiol.- d977; 10(4):341-6). "3D VCG" projects the hodograph onto one plane (Morikawa, J., et al., Angiology, 1987; 38(6):449-56. "Four- dimensional ECG" is similar to "3D VCG," but differs in that every heartbeat cycle is presented as a separate loop, where the time variable is superimposed on one of the spatial variables (Morikawa, J., et al., Angiology, 1996; 47:1101-6.). "Chronotopocardiogram" displays a series of heart-activity time maps projected onto a sphere (Titomir, L.I., et al., Int J Biomed Comput 1987;20(4):275-82). None of these modifications of VCG been widely accepted in diagnostics, although they have some improvements over VCG.

Electrocardiographic mapping

Electrocardiographic mapping is based on measuring signals from a number of measurement points on the patient's body. Signals are presented as maps of equipotential lines on the patient's torso (McMechan, S.R., et al., J. Electrocardiol. 1995;28 Suppl: 184-90). This method provides significant information on the spatial dependence of electrocardiographic signals. The drawback of this method, however, is a prolonged measurement procedure in comparison to ECG, and a loose connection between the body potential map and heart anatomy.

Inverse epicardiac mapping includes different methods, all of which use the same signals for input data as those used in ECG mapping; and they are all based on numerically solving the so- called inverse problem of electrocardiography (A. van Oosterom, Biomedizinisch Technik, vol. 42- El, pp. 33-36, 1997). As a result, distributions of the electric potentials on the heart are obtained. These methods have not resulted in useful clinical devices.

Timing of cardiac electrical events

Cardiac electrical activity can be detected at the body surface using an electrocardiograph (ECG), the most common manifestation of which is the standard 12-lead ECG. Typical ECG signals are shown in Fig. 6. The P- wave 10 represents atrial depolarization. The QRS complex 20 represents depolarization of the ventricles, beginning with QRS onset (QRS_0n) 25 and ending at J . point 30. Ventricular repolarization begins during the QRS and extends through the end of the T- wave (Tend) 70. The ST segment 40 extends from J point 30 to onset of the T-wave 50 (T_0n). T- wave 45 extends from T_0n 50 to T_end 70. U waves (not shown) are present on some ECGs. When present, they merge with the end of the T-wave or immediately follow it.

Physiologically, the T-wave is the ECG manifestation of repolarization gradients, that is, disparities in degree of repolarization at a particular time point between different regions of the heart. It is likely that the T-wave originates primarily from transmural repolarization gradients. See Yan and Antzelevitch Circulation 1998;98:1928-1936; Antzelevitch, J. Cardiovasc Electrophysiol 2003; 14: 1259-1272. Apico-basal and anterior-posterior repolarization gradients may also contribute. See Cohen IS, Giles WR, and Noble D Nature. 1976;262:657- 661.

Transmural repolarization gradients arise because the heart's outer layer (epicardium) repolarizes quickly, the mid-myocardium repolarizes slowly, and the inner layer (endocardium) repolarizes in intermediate fashion. Referring to Fig. 6, during ST segment 40, all layers have partially repolarized to a more or less equal extent, and the ST segment is approximately isoelectric. T-wave 45 begins at T_0n 50 when the epicardial layer moves toward resting potential ahead of the other two layers. At the peak of the T wave (T_peak) 60, epicardial repolarization is complete and the transmural repolarization gradient is at its maximum. Subsequently, endocardial cells begin their movement towards resting potential, thereby narrowing the transmural gradient and initiating the downslope of the T wave. Finally, the M cells repolarize, accounting for the latter part of the T- wave downslope. The T wave is complete at T_eπd 70 when all layers are at resting potential and the transmural gradient is abolished.

The QT interval may be estimated from an ECG by measuring time from QRS_0n to T_end- Abnormalities in the QT interval often mark susceptibility to life-threatening arrhythmias. Such abnormalities may be associated with genetic abnormalities, various acquired cardiac abnormalities, electrolyte abnormalities, and certain prescription and non-prescription drugs.

An increasing number of drugs have been shown to prolong the QT interval and have been implicated as causes of arrhythmia. As a result, drug regulatory agencies are conducting increasingly detailed review of drug-induced abnormalities in cardiac electrical activity. The accuracy and precision of individual measurements is highly important for clinical diagnosis of heart disease and for evaluation of drug safety. Drug regulatory bodies worldwide now require detailed information regarding drug effects on cardiac intervals measured from ECG data. See M. Malik, PACE 2004; 27:1659-1669; Guidance for Industry: E14 Clinical Evaluation of QT/QTc Interval Prolongation and Proarrhythmic Potential for Non-Antiarrhythmic Drugs, http ://www.fda. gov/cder/guidance/6922fnl .pdf (accessed 15 January 2007). Improved measurement accuracy and precision would reduce the risk of clinical error and the amount of resources required during drug development to meet regulatory requirements.

This is particularly true for QT interval measurement, but also affects determination of virtually all cardiac electrical events, for example onset of the QRS complex (QRS_0n), the J point, onset of the T wave (T_0n), and U waves.

No computerized QT measurement algorithm has demonstrated a sufficient degree of reliability (M. Malik, J. Electrocardiol 2004; 37: 25-33). Accordingly, the consensus opinion is that . QT intervals should be measured manually by experienced observers. (Anderson M, et al. Am Heart J 2002; 144:769-781. Unfortunately, manual QT measurement is labor intensive and expensive and remains inherently inaccurate (Malik et al., Brit Heart J 1994; 71: 386-390). Problems in manual QT interval determination result in part from lead selection. Measured QT intervals can vary significantly depending upon the ECG lead selected for measurement. Another common problem is finding T_end- This is usually defined as the point at which the measured voltage returns to the isoelectric baseline. However, T-waves are often low-amplitude, morphologically abnormal, fused with a following U-wave, or obscured by noise. The same may apply to J-points, P-waves, U-waves and other important cardiac events.

Thus, accurate and reproducible procedures for cardiac interval measurement are urgently needed. Also needed are procedures that are rapid and simple, and do not require a high degree of medical training and experience to achieve accurate and reproducible results. Such procedures are needed for QT interval and other critical cardiac electrical events, such as QRS_0n, the J point, J-T interval, T_0n, T_on-to-T_end interval, and the like.

BRIEF SUMMARY OF THE INVENTION

The present invention provides accurate, reproducible, and simple methods and articles of manufacture for determining the time of cardiac electrical events and cardiac intervals.

Described herein are methods for determining the time of a cardiac electrical event, comprising providing an ECG lead; selecting from the ECG lead a time interval Δt within a cardiac cycle that includes the cardiac electrical event; determining a time-variable heart vector at a plurality of time points within Δt; determining an angular change in the time- variable heart vector between time points tl and t2 within Δt; wherein the angular change between tl and t2 is equal to or greater than a specified minimum. In some embodiments, the cardiac electrical event is identified as the pair of time points within Δt between which an angular change in the time- variable heart vector is equal to or greater than the angular change determined for any other pair of time points within Δ. In other embodiments, the ECG lead is a virtual ECG lead, and in yet other embodiments, the angular change in the time variable heart vector is determined using an Angle tool as defined herein. In yet other embodiments, the time-variable heart vector is a normalized time- variable heart vector. Also described are methods for determining the time of a cardiac electrical event using the angle between tangents of the trajectory of the heart vector H at two time points, that is

where H = (X, Y, Z) = Xi + Tj + Zk , and the first derivative of H is H₁ (t) = ^Q , the angle γ is: at

cosOO = — ^f-^-÷- — '^—^ , where tl and t2 are any two time points for which H₁ (t) is available. These H₁(U)- H_t(t2) methods comprise providing an ECG lead; selecting from the ECG lead a time interval Δt within a cardiac cycle that includes a cardiac electrical event; determining a time-variable heart vector at a plurality of time points within Δt; determining an angle γ between time points tl and t2 within Δt; wherein the angle γ between tl and t2 is equal to or greater than a specified minimum. In some embodiments, the angle / is equal to or greater than the angle γ determined for any other pair of time points within Δt. In other embodiments, the time-variable heart vector is a normalized time- variable heart vector.

The inventions herein also include methods for determining the time of a cardiac electrical event using the difference between the value of K(t) at two time points of interest, tl and t2, in the cardiac cycle, wherein the second derivative of the heart vector is and K(X) at any time

point t can be calculated from the formula:

₌ (X,² +Y? +Zj)(Xl + Y_tj +zf_t)-(X_tX_tt +Y₁Y_n + Z,Z_tt)² (X? +Y,² +Z?Ϋ

These methods comprise providing an ECG lead; selecting from the ECG lead a time interval Δt within a cardiac cycle that includes a cardiac electrical event; determining a time- variable heart vector at a plurality of time points within Δt; the difference between the value of K(ϊ) between time points tl and t2 within Δt; wherein the difference in K(t) between tl and t2 is equal to or greater than a specified minimum. In some embodiments, the difference in K(t) between tl and t2 is is equal to or greater than the difference in K(t) determined for any other pair of time points within Δt. In other embodiments, the time-variable heart vector is a normalized time-variable heart vector.

Also described are methods for determining the time of a cardiac electrical event, comprising providing a virtual ECG lead; selecting from the ECG lead a time interval Δt that includes a cardiac electrical event; fitting a function with one or more maxima and one or more minima to data points within Δt; identifying the time of a cardiac electrical event a time tl within Δt which corresponds to a maximum or minimum of the function. In some embodiments, the function is a third-order polynomial function. In other embodiments, the function is fit to the ECG data using least-square fitting techniques, and in yet other embodiments, a reference level for the ECG data may be determined by defining a distribution frequency function F (x_n) of voltages within Δt, and setting the reference level equal to the approximate maximum of the distribution frequency function F (x_n) within Δt. In still yet other embodiments, the virtual ECG lead may be a Vo virtual ECG lead, as the Vi₃ virtual ECG lead is defined herein. In some embodiments, a continuous single peak function may be used to approximate F (x_n), for example a Gaussian distribution. In still other embodiments, Δt is chosen to include a QRS_peak or T_peak and an observer marks a fiducial point corresponding to the approximate time of the QRS_peak or T_peak5 and in some embodiments, automated means may be used to adjust the observer placement of the fiducial points to a local maximum within Δt that corresponds to the QRS_peak or T_peak-

The inventions described herein also include methods for determining the time of a cardiac electrical event, comprising providing a virtual ECG lead; selecting from the ECG lead a time interval Δt that includes a cardiac electrical event; fitting a polynomial function with one or more maxima and one or more minima to data points within Δt; identifying the time of a cardiac electrical event a time tl within Δt which corresponds to a maximum or minimum of a third-order polynomial function, and determining a weighted integral of an absolute difference between the polynomial and the ECG lead within Δt. In some embodiments, the weighted integral is Tdiff,

ΛM

Tdiff[%\ = J≤ !00

{N-\) \ VM(t,)-VM{t_N) \

where VMp (ti) are the values of the third-order (Pt) polynomial and the summation is done in the time interval of interest. In other embodiments, a boundary value for Tdiff may be set, and determinations that exceed the boundary value are identified. The boundary value may be, for example, approximately 1%, 2%, 3%, 4%, 5%, 6%, 8%, 10%, 15%, or more. Other embodiments include, for determinations that exceed the boundary value, selecting from the ECG lead a subset Δt' of Δt that includes fewer time points than Δt and includes the cardiac electrical event; fitting a function with one or more maxima and one or more minima to data points within Δt'; identifying the time of the cardiac electrical event as a time tl ' within Δt' which corresponds to a maximum or minimum of the function. Still other embodiments include determining Tdiff within the time interval Δt'identifying determinations of tl' within Δt' wherein the corresponding value for Tdiff exceeds the boundary value; for determinations that exceed the boundary value, selecting from the ECG lead a subset Δt" of Δt' that includes fewer time points than Δt and includes the cardiac electrical event; fitting a function with one or more maxima and one or more minima to data points within Δt"; identifying the time of the cardiac electrical event as a time tl" within Δt" which corresponds to a maximum or minimum of the function.

The inventions herein also include methods for determining the time of a cardiac electrical event, comprising providing an ECG lead; selecting in the ECG lead a time interval Δt that begins at approximately QRSp_ea]_c-4*DQ and ends at approximately a QRS_peak; identifying within Δt a subset of time points at which the value of HWM is less than approximately 0.01 mV/sec; selecting as QRS_0n the time point within the subset that is closest in time to the QRS_peak. The function HWM is as described in detail herein.

The inventions herein also include methods for determining the time of a cardiac electrical event, comprising providing an ECG lead; selecting in the ECG lead a time interval Δt that begins at approximately QRS_peak-4*DQ and ends at approximately a QRS_peak; identifying within Δt a subset of time points at which the value of VA is less than approximately 0.01 sec²/mV²; selecting as QRS_0n the time point within the subset that is closest in time to the QRS_peak- The function VA is as described in detail herein.

The inventions herein also include methods for determining the time of a cardiac electrical event, comprising providing an ECG lead; selecting in the ECG lead a time interval Δt that begins at approximately a QRS_peak and ends at approximately QRS_peak+4*DQ; identifying within Δt a subset of time points at which the value of VA is less than approximately 0.01 sec²/mV²; selecting as a J Point the time point within the subset that is closest in time to the QRS_peak-

The inventions herein also include methods for determining the time of a cardiac electrical event, comprising providing an ECG lead; selecting in the ECG lead a time interval Δt that begins at approximately a QRS_peak and ends at approximately QRS_peak+4*DQ; identifying within Δt a subset of time points at which the value of HWM is less than approximately 0.01 mV/sec; selecting as a J Point the time point within the subset that is closest in time to the QRS_peak.

The inventions herein also include methods for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting a time interval Δt that begins at approximately QRS_Peak-4*DQ and ends at approximately a QRS_peak; identifying within Δt a subset of time points within which the magnitude of Heart Vector Acceleration reaches a maximum; selecting as a QRS_0n a time point within the subset. The term Heart Vector Acceleration is as defined in detail herein.

The inventions herein also include methods for determining the time of a cardiac electrical event, comprising providing an ECG lead; selecting in the ECG lead a time interval Δt that begins at approximately a QRSp_eak and ends at approximately QRS_peak+4*DQ; identifying within Δt a subset of time points at which the magnitude of Heart Vector Acceleration reaches a maximum; selecting as a J Point the time point within the subset that is closest in time to the QRS_peak-

The inventions herein may be used to determine the time of virtually any cardiac electrical event, including but not limited to the beginning and end of the P wave (P_0n and P_enti, respectively); the beginning, peak, and end of the QRS complex (QRS_0n, QRS_peak, and J point, respectively); the beginning, peak and end of the T- wave (T_0n, T_peak, and T_end, respectively), and the beginning and end of the U wave (U_0n and U_end, respectively).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of one version of the device for three-dimensional presentation of ECG data described herein.

FIG. 2 shows the Frank orthogonal coordinate system.

FIG. 3 shows a heart vector hodograph on a three-dimensional heart model.

FIG. 4 shows an isolated hodograph of a heart vector.

FIG. 5 shows an example of a waveform from one of 12 standard ECG leads. FIG. 6 shows an ECG waveform with cardiac electrical events and time intervals noted.

FIG. 7 shows an example of a vector magnitude tracing through approximately one cardiac cycle.

FIG. 8 shows an example graph of a _^' 3 ->rd order polynomial function, with X_max and X_n,;,, indicated.

FIG. 9 shows an example of a vector magnitude tracing, with superimposed line indicating the results of curve fitting and identification of T_peak and T_end with a 3^rd order polynomial function.

FIG. 1OA shows an example of a 12-lead ECG, with FIG. 1OB showing a vector magnitude tracing derived from the same input data as the 12-lead ECG of FIG. 1OA.

FIG. 11 shows the vector magnitude tracing, with the results of the calculated QT interval determination superimposed thereon.

FIG. 12 shows an example of a global ECG lead, obtained from the same input data as the 12-lead ECG of Fig. 1OA, with QRS_0n, T_end, QRS_peak and T_peak superimposed thereon.

FIG. 13 shows a Bland- Altman plot of corrected QT intervals obtained using manual and semi-automated measurements.

FIG. 14A shows a Bland- Altman plot of interobserver variability of corrected QT intervals obtained using semi-automated measurements, and FIG 14B shows a Bland- Altman plot of interobserver variability of corrected QT intervals obtained using manual measurements

DETAILED DESCRIPTION OF THE INVENTION

The devices, systems, articles of manufacture, and methods descried herein allow display and analysis of the electrical activity of a heart by processing cardiac ECG data and by providing different types of analytic tools, including computerized three-dimensional spatial presentations of ECG data recorded from a patient. ECG data is provided, processed, and displayed. Data processing and display may be interactively performed by allowing a user to select different data analysis and display parameters. Cardiac electrical signals derived from the provided ECG data may be displayed as a three-dimensional representation on a model heart; this three-dimensional representation may be manipulated by a user, and may be correlated with two-dimensional representations of cardiac electrical signals, such as standard ECG waveforms. Thus, the cardiac electrical signals may be visualized spatially and temporally. Furthermore, cardiac electrical signals may be analyzed with a variety of tools described herein that may simplify or enhance the analysis of cardiac electrical activity. The ECG analyzer described herein may be used to analyze ECG data as described herein.

A. Acquisition of ECG data

Any appropriate source of patient ECG data may be used. For example, ECG data may be recorded directly from a patient, or it may be provided from stored, previously recorded data. Thus, the present invention may use real-time ECG data, or ECG data from archived sources.

ECG data may be of any appropriate type. ECG data may be recorded from a plurality of lead sites on the surface of the patient's body. In some versions, standard 12-lead ECG recordings are provided (e.g., leads I₅ II, III, aVR, aVF, aVL, Vl, V2, V3, V4, V5 and V6). Any appropriate number of ECG leads, positioned at any appropriate body sites, may be used. Examples of other ECG lead systems include the "Frank" electrode lead system (e.g., 7 electrodes), the McFee- Parungao Lead System, the SVEC III Lead System, Fischmann-Barber- Weiss Lead System, and the Nelson Lead System. Other examples include addition of right-sided precordial leads, posterior leads, leads placed in higher or lower intercostal spaces, and the like. Although the examples of ECG data described herein refer to the standard 12-lead system, it should be understood that any appropriate ECG lead system may be used without altering the basic principles of the invention. In some versions, information about the source of the ECG data may be provided to the ECG analyzer. For example, the ECG analyzer may adapt the configuration of the display and/or analysis tools based on the source of the ECG data, such as the position of the ECG leads with respect to the heart, the body, and/or to other leads.

Different amounts of ECG data may also be provided. For example, an ECG waveform may contain multiple repeated "PQRST" waveforms. In some versions, multiple cycles of PQRST (e.g., describing multiple heartbeats) may be provided. However, as few as a single PQRST (e.g., a single heartbeat) cycle, or even a portion of one cardiac cycle, may be used. In other versions, signal- averaged ECG waveforms (Signal-Averaged Electrocardiography: Expert Consensus Document, J Am Coll Cardiol 1996; 27: 238-49) may be used.

Additional patient data may also be provided, including patient statistics (height, weight, age, etc.), vital signs, medical history, physical exam findings (for example, extra heart sounds, rubs, or murmurs) and the like. Such patient data may be used in conjunction with patient-specific ECG data for data processing and display, or it may be used to correlate information extracted from the ECG data. For example, the orientation of the heart may be calculated based on patient-specific data (e.g., height, weight, torso circumference, etc.) and may be used to orient the heart model and other analytic features.

ECG analyzer

Data may be acquired by the ECG analyzer or it may be obtained from another source (e.g., an ECG recorder, etc.). As used herein, "obtaining ECG data" refers to any appropriate method of obtaining or receiving ECG data, including, but not limited to, directly measuring ECG data, reading ECG data from a recorded (e.g., archived) source, and receiving ECG data from another device. In some versions, the ECG analyzer comprises an acquisition module. An acquisition module may "condition" (or "precondition") data that it receives. For example, an acquisition module may filter, amplify, format, or otherwise operate on ECG data provided from any source, including stored data sources. The ECG analyzer may also receive non-ECG data, including patient data. In some versions, an acquisition module acquires ECG data by direct input from electrical leads connected to a patient.

B. Signal Processing

Patient ECG data may be processed and displayed. Analysis and visualization of the electrical activity of the heart may be simplified by approximating the electrical activity of the heart as an electric dipole. Thus, ECG data may be transformed into a heart vector representing the electrical phenomena in the heart. A heart vector may be defined by three orthogonal projections: X, Y, and Z. If the provided ECG data is not in the form of a heart vector, then the recorded ECG data (actual ECG data) may be used to compute a heart vector (e.g., from a standard 12-lead ECG). The heart vector may be used with a lead vector (approximating tissue attenuation) to calculate "virtual" ECG waveforms. Furthermore, the heart vector may be normalized by a normalization factor so that the resulting normalized heart vector, and any virtual ECG waveforms calculated from the normalized heart vector, may be used to accurately and precisely analyze the cardiac electrical activity of the heart.

1. Computation of the Heart Vector

ECG data provides a time-dependent voltage that reflects the electrical activity of the heart over time; multiple ECG lead sites provide different time-dependent voltage waveforms that reflect this overall electrical activity. Given the spatial location of the ECG leads, a single time- dependent heart vector may be computed by approximating the heart electrical activity as a dipole having an origin near the center of the patient's heart. A time-dependent heart vector that represents the size and orientation of the time- varying electrical dipole may be calculated by approximating the electrical activity of the heart.

As few as three leads (corresponding to four to six electrodes) may be used to obtain the X₅Y₅Z orthogonals of the heart vector. Given a set of leads, any appropriate matrix may be used to convert them to the X₅Y₅Z orthogonal components of the heart vector. For example, a heart vector may be calculated from standard 12-lead ECG data by transforming the 12-leads into X, Y₅Z (e.g., Frank) leads. In one version, a conversion matrix may be used to transform the 12-lead ECG voltages into the three orthogonal components, X₅Y₅ and Z. When converting 12-lead ECG data into a heart vector, an inverse Dower matrix may be used. Examples of the Dower matrix and the inverse Dower matrix may be found in U.S. Patents 4,850,370 and 5,711,304, which are herein incorporated by reference in their entirety. Other types of matrices may be used to transform the ECG data (e.g., 12 lead ECG data) into a heart vector, such as a Levkov matrix (Levkov, C.L., Orthogonal electrocardiogram derived from the limb and chest electrodes of the conventional 12-lead system, Med. Biol Eng. Comput. 1987, 25,155-164). Any appropriate means may be used to convert the ECG data into the heart vector. In some versions, a matrix or conversion paradigm could be derived, e.g., from experimental data. As used herein, unless the context makes it clear otherwise, a matrix is a set of linear equations that define a transformation between two sets of variables.

The heart vector is a dipole representation of the cardiac electrical signal of the heart, and may be calculated from recordings taken at some distance from the surface of the heart (e.g., from body surface electrodes, internal electrodes such as esophageal electrodes, and combinations of internal and external electrodes).

Example 1: Calculation of a Heart Vector from actual ECG data

For example, a heart vector may be calculated from 8 standard ECG leads (recorded at leads I, II, Vi, V₂, V3, V₄, V₅, and Vβ). In this example, an Inverse Dower matrix is used to convert the data from the standard leads into the time variable heart vector that represents the size and orientation of a time varying electrical dipole approximating the electrical current (and voltage) of the heart.

The heart vector is described by H :

H = (X,Y,Z) = Xϊ + Ϋj + Zk (1)

The ECG data from eight independent ECG leads can be described as a vector, V :

V = (I,II,V_λ,V₂,V,, V₄,V₅,V₆) (2) leads I, II, Vi, V₂, V₃, V₄, V₅, and V₆ described the recorded potentials from the ECG recorded at the actual lead sites on the surface of a patient's body.

Using an Inverse Dower matrix (ID), the ECG data may be converted into the heart vector containing three orthogonal components, X₅Y₅Z. In this case, a reasonable Dower matrix is given by:

.156 -.00893. -.173 -.0747 .122 .231 .239 .194

ID= -.223 .875 .056 -.018 -.104 -.0209 .0408 .0476 .0225 .101 -.229 -.310 -.246 -.0626 .0550 .109

(3)

This inverse Dower matrix (3x8) may be applied to ECG signals recorded from the standard positions of the leads (Pettersson et al., J. Cardiol. 28:169, 1995). From, equations (2) and (3), the heart vector may be calculated by matrix multiplication:

H = ID-V (4) which is equivalent (expressed as linear equations) to:

Jr = .l56 -/ -.00893-//-.173- F₁ -.0747- F₂ +.122. F₃ +.231 - F₄ +.239- K₅ +.194 -K₆ (5) Y = -.2Ti- / + .875-7/ + .056- V_x -.018- V₂ -.104 -F₃ -.209- F₄ +.0408- V₅ +.0476- V₆ (6) Z = .225-/ +.101-//-.229- ^ -.310- V₂ -.246- V₃ -.0626- V₄ +.0550- F₅ +.109- V₆ (7) Thus, the X, Y₅ and Z components of the heart vector may be solved at any time point by applying the ECG data into these linear equations.

The dipole approximation of heart activity given by the heart vector offers an approximation of cardiac electrical activity, however the heart vector does not give the electrical activity at any particular body surface. For example, the cardiac electrical signals present in an ECG waveform are typically recorded from the surface of the body (or from some internal body sites some distance from the heart). Thus, electrical activity arising from the heart is attenuated by body tissues between the heart and the point of measurement. An empirically determined "lead vector" may therefore be used to estimate a "virtual" signal waveform (e.g., an ECG waveform) recorded anywhere around the heart.

2. Computation of Signal Waveforms at an Arbitrary Point from a Model Heart In general, a heart vector and a lead vector may be used to derive an ECG signal waveform at any position around the heart. A lead vector, L, may be described by components I_x, l_y, and l_z. The magnitude of a lead vector describes the attenuation factor of body tissue between the source of the electrical phenomenon (the heart) and a "virtual" recording position (H. E. Burger, J. B. van Milaan, Heart Vector and Leads, Brit. Heart J. 10:229, 1948). For example, a lead vector describing the attenuation factors from the heart to points on the body surface may have magnitudes of different values corresponding to different attenuation factors (i.e. distances from the heart center). Thus, any appropriate lead vector may be used to derive virtual ECG recordings. In some versions, the lead vector may be determined based on empirical measurements. As used herein, unless the context makes clear otherwise, the term "lead vector" may refer to both a real electrode measurement (when the parameters of the electrode reflect the direction and attenuation of the signal at the measurement point), and a parameter of a virtual (or imaginary) measurement surface, defined by a direction and an attenuation factor for a point on the virtual surface.

The lead vector may have a direction corresponding to the position of the recording electrode (e.g., an actual recording electrode or a "virtual" recording electrode) on the body surface, and a magnitude approximately equal to some attenuation factor similar to the electrical attenuation between the heart and the surface of the body where the recording electrode would lie. Thus, by scalar multiplication, a cardiac electrical signal (e.g., an ECG waveform) may be determined for any virtual lead, and any position around the heart may be chosen as a virtual lead. For example, a point (virtual lead) may be selected from the surface of a heart model that is centered using the same coordinate origin as the heart vector and the lead vector. Any point around the heart model may be correlated to a lead vector having a direction including that point (e.g., I_x, l_y, and l_z where x, y, and z describe the point). Thus, an arbitrary point selected from the heart model may generate a virtual ECG by scalar multiplication of the time-dependent heart vector and the lead vector having the spatial direction of that point.

The scalar product of the lead vector at that point and the heart vector gives the instantaneous potential of the ECG lead for that electrode position. This relationship may be represented by:

Vi = I_x *¹ X + l_y * Y + l_z * Z - (8)

Where Vi is the time-dependent electric potential at an arbitrary point on the patient's body (the value of the recorded lead signal), I_x, l_y, l_zare the components of the lead vector L from that arbitrary point on the body surface, and X, Y, and Z are the components of the heart vector, i.e., the values in three orthogonal vector leads as they have been defined previously.

Thus, a virtual ECG waveform calculated for a point on a body surface around the heart may be approximated by the scalar product of the heart vector and an attenuation factor (given by a lead vector) at that point.

Both the virtual (simulated) and actual (recorded) ECG waveforms reflect the voltage arising from the heart that is recorded at some point on the body surface. This electrical signal has passed from the heart, through the body tissue, and been attenuated depending upon where on the body surface the ECG waveform is recorded. Thus, it is difficult to accurately compare the magnitudes of electrical signals recorded (or simulated) at different points on the surface of the body to each other, or to an empirical electrical criterion (e.g., ST depression or elevation) useful for analyzing the heart. Furthermore, the magnitudes of derived heart vectors (e.g., Frank vectors) are typically undefined, and correspond only to an imaginary surface centered around the heart. However, the heart vector may be normalized such that the voltage (or current) from ECG waveforms simulated anywhere around the heart may be reliably compared with clinically relevant benchmarks. 3. Normalization of the Heart Vector

The heart vector may be normalized by any appropriate method allowing comparison of the normalized heart vector (or cardiac electrical signals derived from the normalized heart vector) to a clinically relevant benchmark. For example, the heart vector may be normalized by scaling the magnitude of the heart vector over all time by a normalization factor. The normalization factor may be derived from actual ECG data specific to each patient. The normalization factor may define a normalization surface (e.g., a sphere) which is centered at the origin of the heart vector. As used herein, the term "scaling" includes multiplying a vector a normalization factor so that the magnitude of the vector is multiplied by the normalization factor.

In general, the normalization factor is determined by minimizing the difference between actual and virtual voltages recorded at selected leads. Normalization only changes the magnitude (not the direction) of the heart vector.

The heart vector may be normalized so that the magnitude of the heart vector (or virtual ECG waveforms derived from the normalized heart vector) may be comparable to the magnitude of signals recorded from individual precordial leads or any combination of precordial leads. The precordial leads (e.g., leads Vi, V₂, V₃, V₄, V₅, V₆) are well characterized, and a number of clinically relevant benchmarks for cardiac phenomena have been derived from the magnitude of regions of ECG waveforms recorded from standard precordial sites (e.g., ST elevation/depression, R-wave magnitude, and the like). Thus, the leads chosen for normalization should correspond to leads whose recorded signals contribute to the establishment of the particular benchmark (or criterion) that will be used to analyze the virtual heart vector. Thus, although any lead may be used to normalize the heart vector (including non-precordial leads, such as the limb leads), leads that did not correspond to the establishment of the particular benchmark may negatively impact the normalization, and should not be included in normalization for that particular benchmark or criterion.

In one version, a normalization factor (/?) is derived by first calculating an individual normalization lead factor ( p _\) for each actual lead, i. Thus, if the six precordial leads are used to determine the normalization factor, an individual lead normalization factor ( p _\) is calculated for each of the six precordial leads (Vi, where i=l to 6), and the normalization factor p is selected from the range defined by the maximum and minimum value of these six lead normalization factors.

In this example, each lead normalization factor ( p j) is calculated by solving for the minimum value of the least-squares difference between the actual ECG waveform over some time (T) and a virtual ECG waveform calculated from the heart vector at that point (by scalar multiplication to a lead vector, as described above), over the same time (T). In some versions, each lead normalization factor ( p j) is approximately equal to a value that sets the magnitude of a virtual ECG waveform generated using the scaled heart vector to approximately the same magnitude as the actual ECG waveform recorded at the same position around the heart (e.g., the same lead position). The normalization factor ( p) is then selected from within the range of the individually calculated lead normalization factors (pϊ).

Put another way, each lead normalization factor is approximately equal to the ratio (e.g., the least-squares difference) between a cardiac signal derived from the heart vector for a given lead over some time period (e.g., a "virtual" ECG signal recorded at a lead for 5 seconds), and an actual cardiac signal recorded at the same lead for the same time period of time. Thus, a lead normalization factor may be chosen so that error between the recorded and derived leads is minimized. In some versions, the normalization factor is chosen so that difference between the actual and derived leads recorded nearest the chest (e.g., the precordial leads) is minimized. Normalization factors calculated using the precordial leads are appropriate when using an analysis criterion based on a clinically relevant benchmark (e.g., voltage or current) measured for precordial electrodes or electrodes with comparable signals.

Thus, when calculating the normalization factor, a "virtual" signal waveform may be calculated from the heart vector at the position of an actual lead, as described in more detail above.

Example 2: Calculation of a Normalization Factor

In this example, a normalization factor ( p ) is calculated using six standard precordial leads. V_}(f) is the recorded voltage over time from a lead (e.g., the actual voltage from precordial leads 1 to 6, where i=l to 6), and Vd₁(J) is the derived voltage for each of the ECG leads (e.g.; the same leads 1 to 6). As previously described, virtual lead voltages are calculated as a scalar product of the heart vector// and a lead vector, L₁ ,

where L, is defined having the direction of the position of the z-th electrode (e.g., precordial electrode 1 to 6), and p, is an unknown normalization factor for each electrode. When normalizing the heart vector, the derived voltage is set approximately equal to the actual voltage recorded at the same lead:

The unknown factor ρ_t for every lead can therefore be calculated as a minimum of the function:

where T is the recording time (e.g., 5 seconds). From this, we derive the relationship:

Thus, we can calculate the lead normalization factors corresponding to each of the precordial electrodes (i =1 to 6). From all of these normalization factors, we can determine a common normalization factor, p . For example, the common normalization factor may be the average value of the individual normalization factors (e.g., when recorded from the six precordial leads):

6

P=-^- (13).

Although equation (14) illustrates the normalization factor as an average of individual lead normalization factors, a normalization factor may be any value from the range defined by the lead normalization factors (e.g., the range defined by the maximum and minimum lead normalization factors). Furthermore, a normalization factor ( p ) for the heart vector may be any reasonable combination of lead normalization factors. For example, the normalization factor may be equal to the median of a plurality of lead normalization factors. Although example 2 shows the calculation of a normalization factor ( p ) from six precordial leads, a normalization factor may be calculated using only a single lead (e.g., Vj) or any combinations of leads (e.g., V₂, V₃, V₄), including non-standard leads. In particular, the normalization factor may be calculated using the leads (e.g., actual leads) comparable to leads used to derive (or used with) any criterion or benchmark applied by the ECG analyzer.

Furthermore, it should be apparent that the calculation of p does not require the calculation of individual lead normalization factors, p _\. For example, a normalization factor may be calculated from the least-squares difference of the sums of the actual lead waveforms and the virtual lead waveforms, over some time, T.

The heart vector may be normalized by scaling the magnitude of the heart vector with the normalization factor, p :

H_mmAuz_ED (t) = H(t) - p or (14)

H _NORMA_UZED (0 = /K-*f + Yj + Zk) (15)

where H_NomAUZED (t) is the normalized heart vector. From the normalized heart vector, a normalized "virtual" ECG waveform can be calculated at an arbitrary point around the heart, as previously described:

Vι' = p (\_K * X + ly * Y + l_z * Z) (16)

where Vi ' is the normalized time-dependent electric potential at an arbitrary point on the patient's body, and I_x, l_y, l_zare the components of a lead vector L for that arbitrary point on the body surface, and X, Y, and Z are the orthogonal components of the heart vector, and p is the normalization factor. The lead vector, L, may have a constant magnitude, defined by the module of the lead vectors used to calculate the normalization factor. Normalization may allow comparison of cardiac voltage levels anywhere around the heart with clinical benchmarks (e.g., ST-segment shift), or with other regions of the heart. Normalization may be particularly helpful for ECG or other tests that rely, at least in part, on the magnitude of recorded cardiac electrical signals, such as ST segment shift, which is one of the most widely accepted diagnostic tests for ischemia.

While heart vectors may be able to provide information about cardiac electrical activity anywhere around the heart (e.g., away from the recording electrodes), and may be used to generate "virtual" ECG tracings, the magnitudes of these signals may not be adequately analyzed unless they are normalized as described herein. Normalizing the heart vector, and therefore any "virtual" ECG tracings generated from the normalized heart vector, may allow the magnitude of the cardiac electrical data from any virtual recording location around the heart to be compared with clinically proven criterion.

A normalization factor may be calculated for each individual patient ECG data set. Normalization factors may therefore be patient specific or patient ECG-data set specific. Preliminary results suggest that normalization factors calculated using the six precordial leads may be highly variable between patients, emphasizing the importance of normalizing for each set of patient data, so that the same criterion may be used to analyze patient heart data across patient populations. .

Any of these cardiac electrical signals (e.g., heart vectors, normalized heart vectors, etc.) may be presented with a three-dimensional model of the heart that contains both temporal and spatial information about cardiac electrical activity, and may be coordinated with traditional ECG waveforms or the simulated and/or normalized signal waveforms. This displayed information may allow manipulation and further analysis of the cardiac electrical data.

C. Display of Cardiac Electrical Activity

Recorded and simulated cardiac data may be displayed and manipulated by the user in three- dimensional and two-dimensional representations. Cardiac electrical signals may be represented on a three-dimensional model of a heart; this model may be rotated by the user or automatically rotated. A user may select points on the heart for which cardiac electrical signals may be displayed. One or more ECG waveforms may also be displayed along with the three-dimensional model of the heart, e.g., as a two-dimensional plot of voltage over time.

Heart Model

Any suitable model of the heart (e.g., anatomical models) may be used as the heart model, including simulated heart models, and heart models based on actual patient data. In some versions, the heart model may be correlated to actual patient physiology. For example, the heart model may be derived from a medical scanning technique (e.g., CT, MRI, etc.) Thus, the heart model may reflect individual patient anatomy.

In some versions, the heart model may be entirely simulated. Such models may be based on actual patient data (e.g., a composite based on population information). A variety of heart models may be used. For example, classes or categories of heart models may be used that reflect a population that may be matched to the patient whose ECG data is being analyzed. For example, the ECG analyzer may choose which heart model to use based on information provided about the patient, including characteristics from the ECG data and additional information. Thus, there may be typical heart models for gender, weight, age, etc.

The heart model may also be a combination of patient data and simulation. The heart model may include features that reflect an individual patient's anatomy, medical condition, or medical history. For example, the heart model may be a simulated heart that contains markers indicating previous coronary events, scars, or surgical operations.

Presentation of Cardiac Data

Fig. 1 shows one example of a device for providing a three-dimensional presentation of ECG data. A patient 1 is connected to the electrodes and cables 2 for recording standard 12-lead ECG (leads I, II, III, aVR, aVF, aVL, Vl, V2, V3, V4, V5 and V6). Data may be acquired by an acquisition module 3 that amplifies and A/D (analog/digital) converts the electrical signal. It may contain an amplifier level and an A/D converter. Thus, an acquisition module may function as a standard digital ECG device. In this example, signal processing module 4 filters, eliminates the base line fluctuation, and converts the standard 12 ECG leads into three orthogonal vector leads X, Y and Z. Frank vector leads are used for the derived X, Y, and Z leads, as described (Frank, E., An Accurate, Clinically Practical System For Spatial Vectorcardiography, Circulation 13: 737, May 1956). An orthogonal coordinate system with the axis orientation used for the Frank vector system is shown in Fig. 2. An inverse Dower's matrix is used for conversion of 12 leads into X, Y, and Z (Edenbrandt, L., Pahlm, 0., Vectorcardiogram synthesized from a 12-lead ECG: superiority of the inverse Dower matrix, J. Electrocardiol. 1988 Nov;21(4):361-7). The three orthogonal leads X, Y, and Z may be obtained by other conversion matrices or other methods. For example, Kors (Kors, J.A. et al., Reconstruction of the Frank vectorcardiogram from standard electrocardiographic leads: diagnostic comparison of different methods, Eur. Heart J. 1990 Dec;ll(12):1083-92), Levkov (Levkov, C.L., Orthogonal electrocardiogram derived from the limb and chest electrodes of the conventional 12-lead system, Med. Biol. Eng. Comput. 1987, 25,155-164), and the like.

In this example, an interactive visualization module 5 includes a processor 6, a monitor 7, input and output devices (a keyboard 8 and a mouse 9), and memory 10. The visualization module 5 uses signals X, Y, and Z from the signal processing module 4, enabling different ways of visualizing the electrical activity of the heart on the screen 7. Recorded signals, including personal and other diagnostic data of a patient, may be stored in digital form in databases in the memory 10 or used in data processing or display.

The basic assumption enabling visualization of the electrical activity of the heart is that electrical activity can be approximated by an electric dipole. The electrical signal of the heart may be presented on a three-dimensional model of the heart 20, as shown in Figs. 3, 4, and 5. The heart model can include basic anatomic elements, such as the aorta and other major blood vessels. Input and output devices (e.g., the keyboard 8 and the mouse 9) may be used for interactive manipulation of the model 20 and of the presented signals.

The model may be rotated. For example, the model may be interactively rotated around two orthogonal rotation axes (e.g., using the mouse 9), and it may be brought into any position on screen, meaning that any view of the heart and associated signal can be chosen by a user. The heart may be rotated around two imaginary rotation axes (which may not be shown on screen), such as the horizontal and vertical axes in the screen plane. A user may control the movement of the heart model through any appropriate input device (e.g., a keyboard or mouse). For example, by moving a mouse 9, the model may be rotated up-down and left-right. In some versions, the model heart is rotated automatically (e.g., it may center a particular feature such as electrical potential or cardiac abnormality, or it may continuously rotate about one or more axes).

As the model is rotated, any information displayed on the heart model may also be rotated. For example, the coordinate system for the model, the heart vector, and the lead vector may be rotated with the heart model. The coordinate system 21 is linked to the model, and may be shown as three orthogonal axes X, Y, and Z, which are rotated together with the rotation of the heart model, so that the model orientation regarding the patient's body is obvious at any view angle. An orientation guide, or body-referenced coordinate system, may also be included for indicating the orientation of the heart relative to a patient. For example, a small figure of a person may be displayed and oriented to show the heart orientation relative to a patient's body.

The heart model (or portions of the model) can be made transparent. For example, a user may select a command from the keyboard 8 or the mouse 9 to make a portion of the model transparent, revealing basic anatomic structures within the heart (e.g., atria and ventricles).

Visualization of analyzed ECG data may include: (1) graphical presentation of the heart vector hodograph, (2) graphical presentation of the signal waveform at an arbitrarily chosen point on the heart, and (3) graphical presentation of the map of equipotential lines on the heart at a chosen moment.

(1) Graphical presentation of the heart vector hodograph

Graphical presentation of the heart vector, and the heart vector hodograph, is shown in Figs. 3, 4, and 5. When the heart vector hodograph is shown on screen, three elements may be visible: the first element 22 (Fig. 3) shows the heart vector 23 and its hodograph 24 on a three-dimensional heart model 20, i.e., it shows the path line of the top of the heart vector during a single heartbeat cycle; the second element 25 (Fig. 4) shows the hodograph 24 of the heart vector with the heart vector 23 and coordinate system 21 without displaying the heart model; the third element 26 (Fig. 5) gives a waveform 27 of one of the 12 standard ECG leads. The waveform may be selected from either an actual ECG waveform (e.g., from the data presented) or it may be a virtual waveform selected using the heart model. Waveforms from any of the 12 standard ECG leads, which may be presented as in element 26, may be chosen interactively. The heart model may also indicate the location of the lead from which the ECG waveform originated.

These three display elements may be correlated so that when a time or spatial point is selected from one display, the selection (or change) is reflected in the other displays. In Figures 3 and 4, the heart vector is shown by the arrow 23 at the same moment in time. The moment (e.g., the time value for this heart vector) is correlated to the position of the vertical marker line 28 in the ECG waveform in figure 5 (element 26). A user can select any time value. In some versions, the user may select a time value by interactively moving (or placing) a cursor 28 on an ECG waveform. In this way, a major drawback of vector ECG related to the loss of the time axis, i.e., the waveform, as mentioned earlier has been eliminated.

The user may also select the time interval to be displayed on the heart vector hodograph (e.g., the number of heart cycles or amount of a single heart cycle). In Figure 5, element 26, showing the waveform, there are two vertical marker lines 29 (left and right) that can be moved interactively along the waveform, thus defining a time interval (between the two marker lines) shorter that, a complete heartbeat cycle, making only the corresponding portion of hodograph visible. In figure 5, the brackets 29 show that a complete cardiac cycle (PQRST) have been selected, and are displayed as a cardiac hodograph in Figures 3 and 4. In some versions, the user selects the time period of interest. For example, the user may interactively move the brackets 29. When multiple cycles are selected, the hodograph may be computed by processing the data from different cycles so that a single (e.g., averaged or subtracted) hodograph is shown.

The heart model and visualized electrical activity may be moved interactively, and rotation of the different components (e.g., the 3D and 2D elements) may be synchronized. For example, the common axes of the coordinate systems 21 may be kept parallel at any view angle. The same applies to the presentation of the heart vector 23 in the elements 22 and 25. . (2) Graphical presentation of the signal waveform for an arbitrarily chosen lead on the heart

A "virtual" lead may be calculated using the normalized heart vector for any point on the surface of a heart model. The point may be selected by the user. In some versions, the user may select any point on the continuous surface of the heart model. In some versions, regions of the heart model may not be selectable (e.g., regions that are not electrically active). All of these elements, or a subset of these elements, may be displayed, so that a user may see a 3D heart model, an actual ECG waveform, and/or a virtual ECG waveform.

The correlation between the ECG waveform and its position on the heart may be calculated using the heart vector and the normalizing lead vector, as described above. Thus, the electric potential Vl in an arbitrary point on the patient's body, i.e., the value of the recorded lead signal, is given by the scalar multiplication:

Vi = l_x * X' + l_y * Y' + l_z * Z' ^• (17)

where I_x, l_y, I₂ are the components of the lead vector L of an arbitrary point on the body surface, and X', Y', and Z' are the components of the normalized heart vector, i.e., the values in three orthogonal vector leads as they have been defined earlier. The values of the lead vector L at points that correspond to standard ECG leads are used to obtain orthogonal leads X, Y, and Z. By using the equation (1), one can obtain the potential Vi, i.e., the corresponding waveform on the basis of the orthogonal leads for the known value of vector L for each standard measurement point, using the normalizing lead vector. The resulting values are normalized. On the basis of this concept, one can obtain values Vi for any other point, provided that the value of the vector L that corresponds to the position of the point is known. The waveform is obtained using the equation (1) so that for values of the lead vector L that correspond to the position the angle coordinates of the point are used. In this example, the vector module of the lead vector is set to the average value of the vector L module for precordial leads Vl to V6. This means that waveform corresponds to virtual measurement points that would be positioned on a sphere having the same center as the heart model, with the radius corresponding to the average value of the radii of the precordial electrode measurement points (measured as an electrical distance, e.g., attenuation). In any of the visual elements described herein, the user may magnify or "zoom" in or out of the image. For example, the user may zoom in on a region of the heart model, or a region of the ECG signal waveform. For example, the user may zoom out of an image of an actual or virtual waveform so that the time axis shows multiple PQRST waveform cycles; a single region in the time axis (e.g., corresponding to a single PQRST wave) may then be selected, zooming in on the image. When multiple waveforms are displayed, changing the scale of the time axis of one waveform may concurrently change the time axis on all of the waveforms displayed, or each waveform may have a different time axis scale. In some versions, the user may "scroll" through the time axis of one or more waveforms. The voltage axis of the ECG signal waveforms may similarly be controllable by the user and coordinated between the different waveform images.

The interactive display may be part of an ECG analyzer. For example, the ECG analyzer may include modules 3, 4, and 5 (in Fig. 1) as components of a single device. Thus, the ECG analyzer may receive ECG data, process the data, display the data, and respond to user commands. In some versions, the ECG analyzer includes a computer having components such as a monitor or other display device, and one or more command inputs (e.g., from a keyboard or mouse). In some versions, the ECG analyzer includes a computer running software supporting the described procedure of data processing and/or interactive visualization. Additional output devices (e.g., printers, electronic connections, digital storage media, etc.) may be used, for example, for reporting output or printing chosen screen shots obtained during the process of visualization.

An ECG analyzer may include a display (e.g., as part of a display module) or it may present data in a format that may be displayed by an additional device. In some versions, the ECG analyzer does not prepare the processed cardiac data for display, but provides the processed (e.g., normalized) data for storage, or for use by other devices or methods. For example, the ECG analyzer may process ECG data, normalize the ECG data, and present this ECG data to another device or tool. The normalized ECG data may be digital data, vectors, or waveforms, or as any other useful format.

D. Analysis Tools

The heart vector (including the normalized heart vector) may have a direction that is parallel to the direction of current across the heart. Thus, as current moves during cardiac electrical activity, the direction of the heart vector may reflect this movement. However, typical two-dimensional analysis of recorded ECG waveforms provides only a limited understanding of current flow across the heart. Thus, an analysis of the three-dimensional shape and motion of the heart vector may help interpret the electrical activity of the heart, and may provide new diagnostic tools and criterion. An Angle tool may be used to measure the angular difference in the heart vector over a selected time period.

Angle tool (Heart Vector Spatial Angle Difference tool)

The time varying heart vector reflects both the relative magnitude and the direction of the cardiac electrical activity of the heart. Thus, the direction of the heart vector changes over time, as may be seen from a heart vector hodograph, as previously described. An angle analysis tool, called an Angle tool, may be used to measure the difference in the angle between heart vectors in two or more time instants.

In general, the Angle tool compares the angle difference of two or more heart vectors. In one version, the user may interactively select two time points (e.g., from an ECG waveform) and the tool calculates the angular difference in the heart vector from those two time points. Interactive selection of the time points may be highly useful, because time points may be selected from displayed actual or virtual ECG waveforms. In some versions, automatic selection may be used (including waveform analysis to identify characteristic features). The tool may also analyze the heart vectors at the two specified times (or over the range of time). For example, the tool may calculate the variation in the angles of the heart vector over time, map the variation (e.g., differences) in the heart vector over this time. The tool may calculate any appropriate statistic, including but not limited to the rate of movement of the heart vector, the maximum and minimum differences in the heart vector, and the like. In some versions, the tool may display or otherwise provide statistical data. The tool may also display or provide graphical data. For example, the change in angle per unit time may be graphed and displayed, or the three-dimensional movement of the heart vector over the selected time range may be displayed, similar to the hodograph display previously described. As with all of the tools, data may be displayed, transmitted or stored. In a Cartesian coordinate system, the angle between two heart vectors, A (a_x, a_y, a_z), and B (b_x, b_y, b_z), may be calculated from their orthogonal components (a_x, a_y, a_z and b_x, b_y, b_z), from the following formula:

where α is the angle between the two heart vectors. The tool may determine the heart vectors A and B from specified time points (e.g., to and U) using either a normalized or a non-normalized time dependent heart vector.

E. Analysis tools for identifying cardiac electrical events

Presented herein are a series of approaches to precisely determine the time of cardiac electrical events and time intervals between such events.

Timing cardiac electrical events using the heart vector

As described herein, ECG data provides a time-dependent voltage that reflects electrical activity of the heart; multiple ECG leads sites provide different time-dependent voltage waveforms that reflect this overall electrical activity. From such data, a single time-dependent heart vector representing the heart's electrical activity can be calculated at any time point during the cardiac cycle. Any suitable method for determining the heart vector may be used. The heart vector and its hodograph may be presented to the viewer as 2D heart vector hodographs in orthogonal planes or as a 3D hodograph. The visualization module is suitable for this purpose.

The heart vector hodographs may be used to time cardiac electrical events by identifying the event on one or more heart vector hodographs, and correlating that event with events occurring at the same time point on one or more ECG leads (either ECG leads as actually recorded, or a virtual ECG lead). Alternatively, the cardiac electrical event can be identified on one or a plurality of ECG leads, and the temporally-correlated events identified on one or more heart vector hodographs.

Two or more display elements may be correlated so that when any time or spatial point is selected from one display, the selection (or change) is reflected in the other display or displays. Any time point may be selected. Such time points may indicate, for example, the following cardiac electrical events: P_0n, P_end, QRS_0n, QRSpeak, J point, T_0n, T_peak, T_end, and the onset and end of the U wave (U_0n and U_end, respectively).

In some versions, the user may select a time value by interactively moving (or placing) a cursor on an ECG waveform. A specific cardiac cycle or cycles, or portions thereof, containing the electrical event of interest may be selected for detailed examination, for example by using marker lines to select all or part of a cardiac cycle of interest. Multiple cycles may be selected, and a composite 3D hodograph, or composite set of 2D hodographs, computed by any suitable method, e.g., averaging or subtracting. The composite hodographs may be used to identify cardiac electrical events in the same manner as set forth above.

The 3D heart vector hodograph may be rotated interactively, so that the screen displays the orientation where the desired cardiac electrical event is most effectively seen on the screen. This enables the viewer to identify more easily the cardiac electrical event of interest. For example, by rotating the 3D heart vector hodograph, the viewer could identify with precision the beginning of the T- wave heart vector loop. The viewer could then correlate the beginning of the T- wave heart vector loop with the corresponding time on an ECG, and thereby mark with precision the onset of the T- wave, T_0n. Similarly, the viewer could use the 3D heart vector hodograph to identify and mark other cardiac electrical events, including but not limited to QRS_0n, QRS_peak, the J point, T_peak and T_end- The time interval between any two such events is calculated by simple subtraction.

Timing cardiac electrical events using the Angle tool and related approaches.

It is possible to measure the change in angular direction (angular change) in the heart vector over a selected time period. The Angle tool may be used for this purpose. Such measurement of angular change may be used to identify the time point in a particular section of the cardiac cycle where the heart vector changes direction more than a specified criterion. As one of many possible examples, the viewer could identify T_0n as follows: (1) define a time interval Δt = t2 - tl that begins late in the ST segment (tl) and ends in the upslope of the T-wave (t2); (2) determine angular change at a plurality of time points within Δt, for example using the Angle tool; (3) identify a time interval tβ-tα within Δt wherein the angular change equals or exceeds a specified minimum, for example equal to or greater than about 5°, equal to or greater than about 10°, equal to or greater than about 20°, equal to or greater than about 30°, equal to or greater than about 45°, equal to or greater than about 60°, equal to or greater than about 90°, equal to or greater than about 120°, or more. T_0n is present within tβ-t_« , and may be defined as any time point within that interval, if the specified minimum is equalled or exceeded. The optimal specified minimum for a particular cardiac event is determined empirically. Alternatively, the time of a cardiac event may be determined by finding U,- tδ , defined as the time interval within Δt over which the heart vector exhibits a greater angular change than any other pair of time points within Δt.

Measurement of angular change in the heart vector, for example with the Angle tool, is particularly convenient to apply when Δt is a time range that includes the cardiac electrical event of interest, but is not so large as to include other cardiac electrical events associated with substantial angular changes in the heart vector. Continuing with the immediately preceding example, if Δt is selected to begin late in the ST segment and end in the upslope of the T- wave, it will include Ton- T_on may be identified by determining the pair of time points t_β-t_α equalling or exceeding a specified minimum, or by identifying t_c-te, or other suitable method. It is generally preferable to avoid choosing a substantially larger Δt, for example beginning before QRS_0n and ending after T_ends since Δt will then include several major changes in angular direction, thereby increasing analytical complexity and increasing the risk of ambiguity or error.

Since many important cardiac electrical events are associated with angular changes in heart vector direction, determination of such angular changes, for example using the Angle tool, is broadly useful in timing cardiac electrical events. For example, the Angle tool is highly effective in defining cardiac electrical events that are often difficult to identify visually or with other analytical tools.

Cardiac electrical events may also be identified by directional changes in functions derived from the heart vector function. One such approach is referred to herein as the Gamma tool. The angle γ is the angle between tangents of the trajectory of the heart vector H at two time points, that

is where H = (X, Y, Z) = Xi + Ϋj + Zk , and the first derivative of H is H, (t) = ^^ , the angle γ is dt defined herein as:

H, (/I)- H₁ (/2) cos(/) =

H₁ (U) - H, (/2) where tl and t2 are any two time points for which H, (0 is available.

The angle may be used to identify the time point in a particular section of the cardiac cycle where the angle γ is greater than a specified criterion, for example equal to or greater than about 5°, or equal to or greater than about 10°, equal to or greater than about 20°, equal to or greater than about 30°, equal to or greater than about 45°, or more, as determined empirically. Alternatively, the time of a cardiac event may be determined by finding the time interval within Δt over which the angle γ exhibits a greater change than any other pair of time points within Δt. Thus, in a fashion similar to that described for the Angle tool, the Gamma tool may be used to determine the timing of a broad range of cardiac electrical events.

Another derived function from the heart vector function may also be used to time cardiac electrical events. This approach is referred to herein as the Kappa tool. The second derivative of the

heart vector is H_tt(t) = ^- . The value of Kappa, K (square of the curvature), at time point t dr can be calculated from the formula:

The Kappa tool result, ΔK(t), is defined herein as the difference between the value of K(t) at two time points of interest, tl and t2, in the cardiac cycle. The time points of interest may be, for example: tl, the approximate center of the downslope of the T-wave; and t2, a point apparently beyond T_enci but before the onset of the P wave, as identified visually. In this example, T_end may be determined using the Kappa tool as a value of ΔK(t) equal to or greater than a specified minimum. Alternatively, the time of T_end or other desired cardiac event may be determined by finding the time interval within Δt over which ΔK(t) exhibits a greater change than any other pair of time points within Δt. It is readily apparent that functions of the heart vector curvature similar to Kappa are also useful for identifying cardiac electrical events. Timing cardiac electrical events using virtual ECG leads

For the purpose of timing cardiac electrical events, any recorded or standard ECG lead, or a plurality of such leads, are suitable. In addition, virtual ECG leads may be used, such as the heart vector magnitude or the normalized heart vector magnitude.

The heart vector magnitude VM = HL may be calculated at any time point t in the cardiac cycle as:

where X(t) , Y it) , and Z(t) are the scalar values of the heart vector in the x, y, and z-axes, respectively, at time point t.

Fig. 7 shows the value of VM over an entire cardiac cycle. VM may be viewed as a virtual ECG lead formed by contributions from all ECG leads used in calculating X(t) , Y(t) , and Z(J) . Using virtual ECG leads such as VM to time cardiac events offers several key advantages over existing methods. The VM signal is larger than the signal in any recorded ECG lead, and has an overall improved signal to noise ratio. For example, the amplitude of the T wave can be very small, or negligible in some leads. If the T wave exists in any of the 12 leads, it will also exist in the VM signal. Moreover, unlike a recorded ECG lead, T_end in VM cannot be artificially shortened by an orthogonal angle of the heart vector relative to the ECG lead late in the T-wave loop. As a consequence, the T wave duration in VM equals the T wave duration in the lead where this duration is the longest.

Other types of virtual ECG leads may be used to time cardiac electrical events. For example, one could use any virtual ECG lead described herein, such as normalized ST segment vector magnitude (NSTVM). One could also calculate a suitable virtual ECG lead by summing the voltages, or the absolute value of the voltages, from a plurality of ECG leads, for example, 2, 3, 4, 5, 6, 7, 8 or more ECG leads. Alternatively, a suitable virtual ECG lead could be calculated by multiplying two or more ECG leads by an arbitrary constant and calculating their sum, or the sum of absolute values. Another approach would be to determing the square root of the summation of squared recorded voltages from a plurality of ECG leads, e.g., y II² + V₁ ² + Vf ... + V₆ ² for any two or more ECG leads, determined for at least that part of the cardiac cycle containing the events of interest, and preferably at least one cardiac cycle or more.

Another useful virtual lead finds its basis in the concept of the lead vector described by Burger et al, Brit. Heart J. 10:229, 1948. This virtual lead may be derived from the heart vector function by defining a unity vector as the components of the heart vector divided by Vector Magnitude, that is, at any time t, the unity vector is I_x = Xjrø /VM(_t), l_y = Yj(Q /VM(_t), I_x = Zm) /VM_(t).

A virtual ECG lead, referred to herein as V₁₃, may be defined as the scalar product of the heart vector at that moment in time and the unity vector determined at the time of QRS_peak5 that is:

where values for I_x, l_y and l_z are all determined at the time of QRS_peak- Vl 3 may be particularly useful for identifying cardiac electrical events associated with the QRS complex, for example QRS_0n and the J Point.

The Vj₃ virtual ECG lead may be derived as follows. Define tR as time when QRS_peak is reached. At tR the components of the heart vector are: X(tR), Y(tR), Z(tR) and its magnitude is VM(tR). The direction of this heart vector is defined by unity vector: XO=X(tR)/VM(tR), Y0=Y(tR)/VM(tR) and ZO=Z(tR)/VM(tR). The V₁₃ virtual ECG lead is calculated at each point in time as the scalar product of the heart vector at that moment in time and the unity vector. This yields: V,₃(t)=X(t)*X0+Y(t)*Y0+Z(t)*Z0.

The V1₃ virtual lead may be used to define cardiac electrical events in the same manner as described herein for other virtual and recorded ECG leads. For example, a reference level for Vo may be obtained using any of the methods described herein (particularly those described for defining a median isoelectric level) and the V₁₃ waveform fit to a third-order polynomial, using least squares or other suitable curve fitting method, in the time interval from QRS_peak-2.5*DT to QRS_peak - 0.5 *DT (where DT is determined using the Vl 3 lead as the time from QRS_peak to the next point on QRS which is less than or equal to half the voltage at QRS_peak). Then, the minimum of the 3^rd order polynomial is found using a standard formula. Once the minimum is determined, the QRS_0n is found in the intersection between the polynomial and the reference level line to the left of this minimum, for example from the polynomial minimum leftward to QRS_peak - 4*DT

Once the minimum for the 3^rd orer polynomial is thus determined, one may then compare the V i₃ function and the polynomial to the left of this minimum, for example from the polynomial minimum leftward to QRSpeak - 4*DT. If the polynomial function crosses the reference level of Vi3 in this interval, the user may choose to redefine QRS_0n as the time at which this intersection occurs, rather than the time at which the fitted polynomial function reaches a local minimum. In some instances, this adjustment may result in more accurate placement of QRSon.

From such examples, other suitable virtual ECG leads will be readily apparent to one of ordinary skill in the art. Such virtual ECG leads may offer some or all of the key advantages provided by VM, V^ and others described herein in timing cardiac electrical events. This may result in more accurate and precise identification of cardiac electrical events than determinations from a standard ECG lead, or a plurality of such leads.

Timing of cardiac electrical events using curve-fitting functions

Polynomial functions may be used to time key cardiac electrical events, such as P_0n, P_end» QRS_0n, J point, T_0n, T_peak_s and T_end. The methods will be illustrated below using a third order polynomial function, P= &X³ + bX² + cX+ d, but it will be readily recognized that higher order polynomial functions also may be used.

Polynomial interpolation may be used to determine values for the parameters (a, b, c, and d) that make the curve best fit a set of data points, using least squares or other suitable curve fitting method. For example, polynomial interpolation may be used to fit set of data points from any ECG lead. Alternatively, any virtual ECG lead such as VM may be used. The data points chosen for curve fitting can be, for example, points in or near the T-wave from any ECG lead, or from any virtual ECG lead.

For example, to determine the time of T_peak and T_eπd from VM, a section of VM is chosen visually or by computer analysis, the section extending from a time point after T_0n but at or before the apparent T_peak, to a time point at or after the apparent T_end. The section could be chosen to begin coincident with, or about 5 msec, or about 10 msec, or about 15 msec, or about 20 msec, or about 30 msec, or about 60 msec or more, before the apparent T_peak. The section could be chosen to end coincident with, or about 5 msec after, or about 10 msec after, or about 15 msec, or about 20 msec, or about 30 msec, or about 60 msec, more, after the apparent T_end. The section is then fitted to a third order polynomial using least squares or other suitable curve fitting method. T_peak is then readily identified as the time point at which the third order polynomial function reaches a local maximum. Similarly, T_end is the time point at which the third order polynomial function reaches a local minimum. In Fig. 3, such local maximum and minimum are identified as X_max 80 and X_n, j_n 90, respectively. In Fig. 4, T_peak 100 and T_end HO, as determined using the method described in this example, are indicated.

Other functions with one or more minima and one or more maxima are suitable for use in this method, and may be used to determine timing of cardiac electrical events, including, for example, QRS_0n, the J point, T_0n, T_peakj T_end> the beginning and end of U waves, and the beginning and end of the P wave. In addition to the third order polynomial, such functions include but are not limited to higher order polynomials, Legendre, Bessel, and Matheiu functions. See Abramowitcz and Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1970. Functions with one maximum or one minimum, such as a second-order polynomial, may also be used.

Defining α median isoelectric level

When using vector based leads or a virtual lead such as Vector Magnitude (VM) or V13 to evaluate cardiac electrical events, it is useful to define the magnitude, of the heart vector with reference to an approximate isoelectric point or origin of the vector loop in three-dimensional space. Such a point is referred to herein as the reference point or alternatively, the reference level, which approximately corresponds to the voltage level of the isoelectric line (baseline) of ECG signals on a standard or virtual ECG lead.

When a time interval is displayed to an observer, the shape of VM, V₁₃ or other virtual ECG lead may be affected by choice of the reference point. Since alterations in the shape of an ECG curve may in some instances affect timing of cardiac electrical events, it is useful to find a reasonably accurate and reproducible reference point. A reference point may be the common isoelectric baseline of 12 ECG leads. However, because of baseline wandering and electromechanical noise, determining a reference point in this manner can be difficult.

A reference point in 3D vector space that approximately corresponds to the isoelectric baseline level can be determined in the following manner. VM is used an example, but the approach is useful for any recorded or virtual ECG lead. VM is calculated at any time point t in the cardiac cycle as:

where X(O , Y(O , and Z(O (Frank leads) are the scalar values of the heart vector in the x, y, and z- axes, respectively, at time point /. These scalar values are defined as voltage differences:

X(t) = x(t)-x₀ nθ = ^y(O-^y _o

where the point xo, yo, ∑a, defines the reference point or approximate origin of the 3D vector loop, and corresponds approximately to the baseline of ECG signals.

Let the 3 vector ECG signals, x(t), y(t), z(t) be represented as a matrix V(i j), index i representing the lead, and j representing the time instant (of n time instants). The overall range of the signals is divided in N segments in the following way:

Define maximal and minimal values of the signals in the whole matrix: V_max= max(V(ij)) 1=1,3; j=l, n V_mi_n=min(V(ij)) i=l,3; j=l, n

The V_min to V_max interval is divided in N segments (for example, N=IO, or N=IOO, or N=I 000, as desired) of approximately equal duration dV=(V_max-V_mj_n)/N as: l: V_min to V_min+dV,

2: V_min+dV to V_min+2*dV, . . .

. . . and so on, to: N: V_min+(N-l)*dV to V_min+N*dV

For each of the 3 vector signals a distribution frequency function of signal points among these intervals is defined. For example, for the x vector signal, the number of signal points that fall within each interval is determined, that is, for the first interval,

Fmin < V < Fmin+ dV , the second interval Fmin+ dV < V < Fmin+ 2dV , And so on to the last interval N.

Once the number of signal points that fall within each interval is determined, a distribution frequency function F (x_n) is determined, where F is the number of signal points of the matrix V(Ij) inside the interval x_n, and where x is the approximate mean value of the signal in a certain interval:

X_n =Vmin +i*dV-dV/2

A reference level may be set to the approximate mean value of the signal corresponding to the maximum of the distribution frequency function F (x_n). Since F (x_n) is a discrete function whose precision may be limited by the number of discrete signal levels, one may use a continuous single peak function to approximate F (x_n). For example, F (x_n) may be fit to a Gaussian distribution G = GO *exp[- (JC-X₀)² ld\ , and the parameters GO, xo and d may be conveniently determined using least squares method. This approximation may be used to define the approximate maximum of the Gaussian distribution as a reference level for each signal V(Ij). A reference level determined with this procedure may be displayed to the observer as an approximately horizontal line, with the ECG or virtual ECG lead(s) being evaluated.

The above-described approaches for determining a reference level may be used on the whole available ECG signal including one or more heart beats, or may be used on a particular segment. For example, it may in some instances be advantageous to determine the reference level frorri a limited segment corresponding to the time interval from T_end to P_0n, or from P_end to QRS_0n- It may be used for determining reference levels for any recorded or virtual ECG lead, for example conventional 12 leads, vector-based leads, VM, V_]3 and other virtual ECG leads. Computer-based methods for determination of QT interval

Methods described herein may employ any of a variety of calculating tools, such as a personal computer, laptop, or handheld computer. For example, a desktop PC or laptop with a Pentium III or equivalent processor, about 128 MB of RAM, a mouse or pointing device, and a monitor would be suitable. These methods are preferably carried out on a virtual ECG lead such as VM (whether normalized or not), Vo, or the like, but may also be applied to data from one or more ECG leads recorded from a subject.

Data recorded from the eight standard ECG leads can be described as a vector, V = (I, II, V₁ , V₂, V₃, F₄ , V₅ , V₆) . An approximate isoelectric level for each lead is determined by any suitable method. For example, the approximate isoelectric level may be determined using the methods described herein for determining a median isoelectric level, or by having an operator mark the approximate isoelectric level by visual estimation; or semiautomatically, by having an operator mark all or part of the T-P interval; or automatically calculating an average value; or by automatically locating a suitable segment of reasonably uniform voltage from the ECG data and calculating an average value for that segment.

The approximate isoelectric level for each lead is determined by any appropriate method and subtracted from the measured signals (e.g., T = I - 1₀, IP = IP - Ho, . . . V6' = V6 - V6o) to yield

V'= V - V₀. The isoelectric-subtracted ECG data V' may be converted into a heart vector.

Alternatively, the heart vector components (X, Y, Z) may be directly determined, for example by recording from the body surface with a Frank lead system. As an alternative, it is also possible to subtract the approximate isoelectric level from a virtual ECG lead such as VM.

In some embodiments, the operator may mark certain fiducial points on the ECG, such as the approximate peak of the QRS complex (QRS_peak), or the approximate T_peak, or both, on a monitor with a mouse- or keyboard-driven screen cursor. A computer-implemented algorithm may then calcualte QRS_peak and T_emd by a suitable method by finding the local maximum of ECG data from the ECG lead, correcting any operator misplacement of QRS_peak and T_peak if necessary. In marking fiducial points, the operator marks the estimated point (e.g, QRS_peak, T_peak, or other desired point) anywhere within a time interval Δt which contains the marked event. Usual values of Δt may be about 2 msec, or about 5 msec, or about 10 msec, or about 20 msec, or about 50 msec, or about 100 msec, or more. In general, it is preferrable that the value of Δt be set so as not to encompass a second maximum that exceeds the magnitude of desired event (for example, in determining T_peak, it is preferrable that Δt is chosen so that it does not include QRS_peak)-

Figs. 1OA and 1OB illustrate the operation of an embodiment of this invention for computer- based methods of QT determination. Fig. 1OA illustrates a standard 12-lead ECG, obtained as a digital XML file from the Center for Drug Evaluation and Research, United States Food and Drug Administration, Rockville MD. Fig. 1OB illustrates 3 beats of a virtual ECG lead, VM, calculated as described herein, using software incorporating inventions herein (QTinno™). Reference level 120 is calculated automatically using the procedures described herein for determining a median isoelectric level.

In the example shown in Fig. 11, user marks the approximate QRS_peak 130 and T_peak 140. The software then employs the operator input to define the true QRS_peak and T_peak, and proceeds to curve-fit using a third-order polynomial and least-squares curve fitting to define QRS_0n 150 and T_end 160. The QT interval 170 is then calculated by the software and displayed. The software may export the QT result and identifying information to another program such as a spreadsheet or database, and also may load the next ECG file, if a series of files needs to be read. Alternatively, the software may wait for further input, for example when an average QT for 2 or more beats is desired. Other calculations may also be performed, such as correction of the QT interval for heart rate, for example using Bazett's or Fridericia's formula, or other desired correction method.

The accuracy of any calculated QT interval may be assessed by the operator in a variety of ways. For example, Fig. 12 shows a so-called "global" ECG lead, which is the superimposition of all 12 ECG leads on a single X-Y graph. The QTinno™ software shows the location of the fiducial points, and the calculated QRS_0n and T_en_d, on the global lead. By assessing the location OfQRS_0n and Tend in relationship to the global lead, the operator can be assured that the caculated QT interval is reasonable and accurate.

Semi-automated identification of cardiac electrical events

These procedures may be used with any ECG lead, particularly virtual ECG leads such as VM or Vj₃. Using a standard PC and monitor, handheld computer, or the like, an observer may display a suitable ECG waveform and mark a fidicuial point or points, for example the approximate QRS_peak, Tp_eak or both. It is preferable to mark the point or points near the local maxima of the R and T waves. If there are multiple QRS peaks, it is generally preferable to mark the earliest peak (in a typical time-versus-voltage ECG display, the leftmost peak). Such multiple QRS peaks may be observed in conditions such as right bundle branch block, or if virtual leads such as vector magnitude are being used. If a T wave has multiple peaks, the observer may select the peak deemed most suitable, preferably following a predetermined and predictable set of rules to maximize reproducibility. Such a rule may be, for example, the leftmost T_peak unless the rightmost T_peak is more than half the amplitude of the leftmost peak.

Once the user has chosen an approximate fiducial point, the accuracy of placement of the fiducial point may be improved by the computer. For example, if trie user has marked the approximate QRS_peak or Tpeak, a more accurate location of the QRS_peak or T_peak is defined as the local maximum in some time interval around the user-chosen point, for example the local maximum identified within 5 msec, or 10 msec, or 20 msec or more around the user-chosen point. The computed location of the fiducial point may be displayed to the user.

Once the desired fiducial points are established, they can be used to define subsequent points in the ECG that correspond to the fiducial points. For example, having established the location in time of the fiducial QRS peak Rl, subsequent QRS peaks (R2, R3, etc) may be located by a variety of approaches. For example, determine the value R_0-S= R/2, or half amplitude of Rl, and use R_0-5 to find the point R0.₅* (point on the upslope of the next QRS complex) which is the first point to the right starting at QRS_peak+200msec and having the amplitude greater or equal to R₀.₅. The next QRS_Peak, R2, is the local maximum in the interval R_0.5*, Ro.s*+lOOmsec. The RR interval is the time difference between Rl and R2 points. R3, R4, and subsequent QRS peaks may be found in a similar manner.

The fiducial points may also be used to refine reference levels. For example, the reference level may be redefined using the period of time between a T_peak and the next QRS_peak₅ or in a similar time interval, for example T_peak + 100 msec to QRS_peak - 100 msec. In such an approach, the distribution frequency function F (x_n) is limited only to those points falling within the selected time interval. Such a refinement may improve accuracy and reproducibility of certain cardiac electrical events, for example T_end, U_0n, U_end, P_0n and P_end. Fiducial points may be useful as landmarks to improve determination of cardiac electrical events. For example, T_peak may be used to improve accuracy and precision in determining T_0n, T_end, U_0n, and U_end. One may define DT as the time interval between T_peak and first subsequent point where the magnitude falls to less than half the magnitude at T_peak- Using DT, time interval boundaries for searching for T_end with polynomial fitting may be defined as, for example, left boundary approximately T_peak - 0.25*DT, right boundary approximately equal to T_peak + 2.5*DT. It is readily apparent that a similar approach may be used to define time boundaries in which to search for other cardiac electrical events.

Once time boundaries are defined, curve fitting may be used to identify the desired event. For example, to find T_end, a third order polynomial may be fit to the ECG data within DT using a least squares method. In this method, T_end would be identified as the local minimum of the third order polynomial Pt. By limiting the search to DT or other appropriate time interval, the chance for an erroneous determination is decreased.

Evaluating quality and refining estimates

When using the methods disclosed herein to determine the approximate time of a cardiac electrical event, the quality of a determination may be estimated. For example, when determining T_end from the VM virtual lead, using a third-order polynomial curve-fitting, an estimate of quality may be obtained according to formula:

Tdiff[%] =

where VMp (ti) are the values of the third-order (Pt) polynomial, and the summation is done in the time interval between T_peak and T_end- The quality estimate represents the weighted integral of the absolute difference between the polynomial and the original VM curve over the interval, and is approximately equal to the ratio of the surfaces of the difference Pt-VM and the rectangle defined by Tpeak and T_end points.

The observer may set boundaries of acceptability if desired. For example, the observer may establish as acceptable a value for Tdiff of 1%, 2%, 3%, 4%, 5%, 6%, 10%, 15%, or some other value. The determination is accepted if Tdiff is less than the boundary value, and rejected if greater than or equal to the boundary value. In instances where Tdiff exceeds the desired boundary value, the determination may be further refined by shifting the time of T_peak rightward by a minimal amount, for example 1msec or 2msec, then repeating the T_end calculation and redetermining Tdiff. If the boundary value is still exceeded, the time of T_peak is again shifted rightward by a minimal amount and the calculations redone. This procedure continues until the boundary value is met, or some other cutoff is reached (for example, iterations to stop if the magnitude of T_peak being used is less than 90%, or 80%, or 70%, or 60%, or 50%,. or some other fraction of the original T_peak value).

Determining the onset and termination of a QRS complex

An accurate and reproducible determination of QRS onset (QRS_0n) and its termination (J Point) is useful for determining cardiac time intervals such as PR interval, QRS duration, and QT interval. This example provides additional procedures for automated or semi-automated determination OfQRS_0n and the J Point. They are particularly effective when used with virtual ECG leads such as VM, V₁₃ or the like.

Having determined QRS_peak, one can then determine the time between QRS_peak and QRS0.5, which is defined as first point prior to QRS_peak where the magnitude of the VM curve falls to approximately less than 70% (or 60%, 50%, or some other desired value) of the magnitude at QRSpeak- This time interval is defined as DQ. If desired, an upper limit for DQ may be set, for example 50msec, 60msec, 70 msec, or some other value. If QRS₀.₅ is not reached by the preset upper limit for DQ, then DQ is set at the said upper limit.

If desired one may define a new reference level using the time interval between P_end and QRS_0n. This may be done, for example, by limiting the distribution frequency function F (x_n) to values in the interval from approximately [QRS_peak - 4*DQ] to approximately QRS₀.5, or from approximately [QRS_peak - 4*DQ] to any other desired point within the QRS complex. The values of VM or other ECG lead being used are adjusted according to the new reference level. This may adjust the reference point to the approximate level of the PQ segment (interval from P_end to QRS_0n), and may make it easier to accurately identify QRS_0n. The location OfQRS_0n may then be identified and marked by the user, or identified using a curve fitting technique such as fitting to a third-order polynomial or other suitable function. Using derivatives of the heart vector to identify cardiac electrical events

In physiologic terms, QRS_0n reflects the onset of ventricular depolarization, and the J Point reflects its end. These are a sudden and rapid events that are amenable to detection by examining changes in direction and speed of the heart vector. The same is true of several other cardiac electrical events, for example, P_0n, Pend, T_0n and T_end-

Let X(t), Y(i) , and Z(O be components of a heart vector at time t:

Heart Vector = H = (X, Y, Z) = Xi + Yj + Zk

Its magnitude at time t is

VM = H(O = Jx(t)² + Y(O² +z(0²

The heart vector velocity is the first derivative of the Heart Vector

Heart Vector Velocity = HW = dX/dt 7 + dY/dt J + dZ/dt k

which approximately reflects the speed of movement of the point across the 3D loop in the 3D vector space. The magnitude of the heart vector velocity module is the square root of the sum of squares, that is, HVV Magnitude = HWM = sqrt [(dX/dt)²+ (dY/dtf+ (dZ/dt)²]. Using HWM within an appropriate time interval, for example beginning at QRS_peak and proceeding leftward to QRS_Peak-4*DQ, QRS_0n may be identified as the first point with the value less than approximately 0.01 mV/sec, or less than approximately 0.02 mV/sec or similar desired threshold.

An empirically derived function, Velocity Attenuation, may be useful for determining QRS_0n. Velocity Attenuation is defined as: VA =(l/HWM*)*exp(- 5*VM). Using VA, QRS_0n may be found as the first local maximum of the VA function greater than approximately 0.01 sec²/mV² , going from right to left in the approximate time interval QRS_peak to QRS_peak-4*DQ (where DQ is determined as set forth above using QRS₀.₅ of approximately 50%) or similar appropriate time interval. The J point may be found in similar fashion in the approximate time interval QRS_peak to QRSpeak + 4*DQ. It is readily apparent that functions similar to VA are also useful for identifying cardiac electrical events. The second derivative of the heart vector, referred to herein as Heart Vector Acceleration (HVA), is also useful for identifying cardiac electrical events, particularly those in which acceleration is prominent, such as QRS_0n and J Point:

Heart Vector Acceleration = HVA = cPx/d? T + U²YMt² J + cfz/di² k

The magnitude of HVA can be calculated as the square root of the sum of squares of its components in a manner similar to that used for VM and HVVM. The maximum magnitude of HVA in the approximate time interval QRS_peak to QRS_peak - 4*DQ may be used to identify QRS_0n, or may be used to identify J point in the approximate time interval QRS_peak to QRSp_eak + 4*DQ.

These methods are described primarily in terms of the QRS complex, but they are well suited to cardiac electrical events other than the QRS complex, for example T_0n and T_end-

Example

Standard 12-lead ECGs (each approximately 10 seconds in length) were recorded in digital form from 26 healthy volunteers at 4 different times: at baseline, and at 1, 2 and 3 hrs after ingesting a drug known to affect cardiac electrical events. These 104 ECGs are referred to in this Example as the Study ECGs. They were read manually by two trained and experienced readers, and in parallel by devices and computer software incorporating methods disclosed herein, and the results were compared.

For manual reading, the Study ECGs were displayed in random order on a high-resolution computer monitor to two cardiologists, working independently and unaware of the other's results. Readers marked QRS_0n, QRS_peak, T_peak, and T_end on 5 successive QRS complexes that they judged to be the most suitable for analysis. One of the observers repeated the analysis approximately 10 days later, with Study ECGs reordered and without knowledge of prior results.

Semi-automated reading was performed using software, referred to herein as QTinno, that incorporates inventions disclosed herein. A VM virtual lead was derived for each of the Study ECGs, and displayed in random order on a high-resolution computer monitor to two readers working independently and unaware of the other's results. For each VM trace, the readers marked the approximate peak of a QRS complex and the approximate peak of the T wave following the selected QRS complex. The QRS_peak and T_peak closest to the user marks were then determined in automated fashion, as were the next 4 successive QRS_peak and T_peak. For each QRS complex, QRS_0n was identified using methods described for semi-automated determination of cardiac electrical events and for determining the onset and termination of a QRS complex. Results were displayed in graphic fashion to the user, and numerical results exported to a spreadsheet. Intervals were then calculated, including RR and QT intervals, Q_0n to T_peak9 T_peak to T_end. QT intervals were corrected for heart rate using Fridirecia correction. Upon user approval, the next ECG was automatically loaded and presented to the reader, and the process repeated..One of the observers repeated the analysis approximately 10 days later, with Study ECGs reordered and without knowledge of prior results.

Results obtained with manual and semi-automated readings were compared. QTinno was considerably faster in performing the task than manual readers. The total time to read one set of Study ECGs was approximately 2.5 -3 hrs for manual reading, and 15-20 min using the QTinno semi-automated method. On average, this was over 90 sec per ECG during manual read, and less than 10 sec for semi-automated read.

Table 3. Cardiac intervals determined with manual and semi-automated measurements

The data in Table 3 show the mean cardiac intervals obtained. In each instance, the figure is the mean ± standard deviation of 104 determinations (26 determinations made a total of 4 times, 2 times each by 2 observers). Shown are results for RR intervals, QT intervals, and Fridericia- corrected QT intervals (QTc) obtained with manual and semi automated readings.

As may be seen from data in Table 3, the two approaches also returned very similar values for the mean prolongation of QTc produced by the drug. Relative to baseline, mean increase in QTc was estimated at 15 msec at 1 hr by both Manual and QTinno; at 2 hrs, 33 msec for Manual and 36 msec for QTinno; and at 3 hrs, 36 msec for Manual and 38 msec for QTinno.

FIG. 13 shows a Bland- Altaian analysis of QTc determined by manual and semi-automated methods. Each point on the plot represents an individual determination. The x-axis is the average QTc value of manual and semi-automated determination, in msec. On the y-axis, points^on which manual and semi-automate methods returned the same value lie at 0, points where manual returned a higher value are positive, and points where manual returned a lower value are negative. On average, manual determinations were 3.7 msec higher than semi-automated, with a SD for differences of 7.4 msec.

These data show that the semi-automated approach returned results that were closely matched to the "gold standard" of careful manual reading by trained cardiologists, but did so much faster and in a much less labor-intensive manner.

When individual determinations were examined, it was apparent that the precision of semi- automated measurement was substantially higher than for manual measurement. In determining intervals, whether by semi-automated or manual methods, each subject had a total of 15 determinations made. For each interval, a mean and standard deviation was calculated for the 15 determinations. This yielded a total of 104 standard deviations, for which a mean was determined. Table 4. Mean SDs of cardiac interval measurement

Table 4 shows that the mean SDs for QT and QTc were far lower using semi-automated measurements than using a manual approach. Thus, not only was the semi-automated approach faster and easier, it was also more precise and reproducible. This conclusion is reinforced by the data in FIG 14A and 14B, which compares Bland- Airman plots for QTc determined by different observers. For semi-automated measurement, the mean interobserver difference in QTc was 0.1 msec with a SD of 2.1 msec. Of 104 determinations, 56 were identical and 98 were within 4 msec of each other. For manual reading, the mean interobserver difference was 0.3 msec with a SD of 5.0 msec - over two-fold higher than that obtained with semi-automated measurement. Only 1 of 104 determinations was identical, and 36 were different by more than 4 msec.

The greater precision obtained using semi-automated measurement is highly important for clinical diagnosis and for drug safety analysis. For example, the number of subjects needed in a clinical study of drug effects may be calculated according to equation (18):

S² n = 2(Z,_{ϊ +} Z_(ι)² (μ, - μ.)² <¹⁸>

where n is the number of subjects needed, Z_α is the desired significance level, Zβ is likelihood of beta error, μl-μ2 is the expected drug effect on the parameter being studied, and S is the standard deviation for the parameter being measured. Thus, a 2-fold improvement in measurement precision, as measured by S, will result in a 4-fold reduction in n. In a study of drug effects on QTc, the lower SD obtained by semi-automated measurement, shown in Table 4, would reduce the number of subjects needed by 2.5-fold. Although the methods, articles of manufacture, systems, and devices described herein have discussed devices and methods for timing cardiac electrical events, the invention should not be limited to timing cardiac electrical events, and should apply to the analysis, diagnosis or treatment of any cardiac electrical phenomena (for example, abnormalities in cardiac electrical conduction processes, disturbances of heart rhythm or dysrhythmias, location of accessory pathways and reentrant circuits, infarction, cardiomyopathy, cardiac hypertrophy, etc.).

Further, although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity of understanding, it is readily apparent to those of ordinary skill in the art in light of the teachings of this invention that certain changes and modifications may be made thereto without departing from the spirit or scope of the appended claims. Furthermore all references cited herein are intended to be fully incorporated herein in their entirety.

Claims

CLAIMSWhat is claimed is:

1. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting from the ECG lead a time interval Δt within a cardiac cycle that includes the cardiac electrical event; determining a time-variable heart vector at a plurality of time points within Δt; determining an angular change in the time- variable heart vector between time points tl and t2 within Δt; wherein the angular change between tl and t2 is equal to or greater than a specified minimum.

2. The method of claim 1, further comprising: identifying within Δt the pair of time points between which an angular change in the time-variable heart vector is equal to or greater than the angular change determined for any other pair of time points within Δt.

3. The method of claim 2, wherein the ECG lead is a virtual ECG lead.

4. The method of claim 2, further comprising determining the angular change in the time- variable heart vector with an Angle tool.

5. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting from the ECG lead a time interval Δt within a cardiac cycle that includes a cardiac electrical event; determining a time- variable heart vector at a plurality of time points within Δt; determining an angle γ between time points tl and t2 within Δt; wherein the angle γ between tl and t2 is equal to or greater than a specified minimum.

6. The method of claim 5, father comprising: identifying within Δt the pair of time points wherein the angle γ is equal to or greater than the angle γ determined for any other pair of time points within Δt.

7. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting from the ECG lead a time interval Δt within a cardiac cycle that includes a cardiac electrical event; determining a time- variable heart vector at a plurality of time points within Δt; determining ΔK(t) between time points tl and t2 within Δt; wherein ΔK(t) between the time points is equal to or greater than a specified minimum.

8. The method of claim 7, father comprising: identifying within Δt a pair of time points between which ΔK(t) is equal to or greater than ΔK(t) occurring between any other pair of time points within Δt.

9. A method of determining a time of a cardiac electrical event, comprising: providing a virtual ECG lead; selecting from the ECG lead a time interval Δt that includes a cardiac electrical event; fitting a function with one or more maxima and one or more minima to data points within

Δt; identifying the time of a cardiac electrical event a time tl within Δt which corresponds to a maximum or minimum of the function.

10. The method of claim 9, wherein the function is a third-order polynomial function.

11. The method of claim 10, wherein the minimum of the third-order polynomial function is . used to identify T_end.

12. The method of claim 9, father comprising: determining an approximate mean value of a signal corresponding to an approximate maximum of the distribution frequency function F (x_n) within Δt; setting a reference level equal to the approximate maximum of the distribution frequency function F (x_n) within Δt.

13. The method of claim 12, further comprising: using a continuous single peak function to approximate F (x_n).

14. The method of claim 13, wherein the continuous single peak function is a Gaussian distribution.

15. The method of claim 9, wherein Δt is chosen to include a QRS_peak or T_peak and an observer marks a fiducial point corresponding to the approximate time of the QRS_peak or T_peak.

16. The method of claim 15, further comprising: adjusting by automated means the observer placement of the fiducial points to a local maximum within Δt that corresponds to the QRS_peak or T_peak.

17. The method of claim 9, further comprising: determining a weighted integral of an absolute difference between the polynomial and the ECG lead within Δt.

18. The method of claim 17, wherein the weighted integral is Tdiff.

19. The method of claim 18, further comprising: establishing a boundary value for Tdiff; identifying determinations for the time of a cardiac electrical event within Δt wherein the corresponding value for Tdiff exceeds the boundary value.

20. The method of claim 19, further comprising: for those determinations that exceed the boundary value, selecting from the ECG lead a subset Δt' of Δt that includes fewer time points than Δt and includes the cardiac electrical event; fitting a function with one or more maxima and one or more minima to data points within

Δt'; identifying the time of the cardiac electrical event as a time tl ' within Δt' which corresponds to a maximum or minimum of the function.

21. The method of claim 20, further comprising: determining Tdiff within the time interval Δt' identifying determinations of tl' within Δt' wherein the corresponding value for Tdiff exceeds the boundary value; for determinations that exceed the boundary value, selecting from the ECG lead a subset

Δt" of Δt' that includes fewer time points than Δt and includes the cardiac electrical event; fitting a function with one or more maxima and one or more minima to data points within

Δt"; identifying the time of the cardiac electrical event as a time tl" within Δt" which corresponds to a maximum or minimum of the function.

22. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting a time interval Δt that begins at approximately QRS_peak-4*DQ and ends at approximately a QRS_peak; identifying within Δt a subset of time points at which the value of HWM is less than approximately 0.01 mV/sec; selecting as QRS_0n the time point within the subset that is closest in time to the QRS_peak.

23. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting a time interval Δt that begins at approximately QRS_peak-4*DQ and ends at approximately a QRS_peak; identifying within Δt a subset of time points at which the value of VA is less than approximately 0.01 sec²/mV²; selecting as QRS_0n the time point within the subset that is closest in time to the QRS_peak-

24. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting a time interval Δt that begins at approximately a QRS_peak and ends at approximately QRS_peak+4*DQ; identifying within Δt a subset of time points at which the value of VA is less than approximately 0.01 sec²/mV²; selecting as a J Point the time point within the subset that is closest in time to the

QRSpeak-

25. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting a time interval Δt that begins at approximately a QRS_peak and ends at approximately QRS_peak+4*DQ; identifying within Δt a subset of time points at which the value of HWM is less than approximately 0.01 mV/sec; selecting as a J Point the time point within the subset that is closest in time to the

QRSpeak.

26. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting a time interval Δt that begins at approximately QRS_peak-4*DQ and ends at approximately a QRS_peak; identifying within Δt a subset of time points within which the magnitude of Heart Vector

Acceleration reaches a maximum; selecting as a QRS_0n a time point within the subset.

27. A method for determining the time of a cardiac electrical event, comprising: providing an ECG lead; selecting a time interval Δt that begins at approximately a QRS_peak and ends at approximately QRS_peak+4*DQ; identifying within Δt a subset of time points within which the magnitude of Heart Vector Acceleration reaches a maximum; selecting as a J Point the time point within the subset that is closest in time to the

QRSpeak.

28. The method of claim 9, wherein the virtual ECG lead is a V^ virtual ECG lead.