Classifications

• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B5/00—Measuring for diagnostic purposes; Identification of persons
  • A61B5/02—Detecting, measuring or recording for evaluating the cardiovascular system, e.g. pulse, heart rate, blood pressure or blood flow
  • A61B5/024—Measuring pulse rate or heart rate
  • A61B5/02405—Determining heart rate variability
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B5/00—Measuring for diagnostic purposes; Identification of persons
  • A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
  • A61B5/316—Modalities, i.e. specific diagnostic methods
  • A61B5/318—Heart-related electrical modalities, e.g. electrocardiography [ECG]
  • A61B5/346—Analysis of electrocardiograms
  • A61B5/349—Detecting specific parameters of the electrocardiograph cycle
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B5/00—Measuring for diagnostic purposes; Identification of persons
  • A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
  • A61B5/316—Modalities, i.e. specific diagnostic methods
  • A61B5/318—Heart-related electrical modalities, e.g. electrocardiography [ECG]
  • A61B5/346—Analysis of electrocardiograms
  • A61B5/349—Detecting specific parameters of the electrocardiograph cycle
  • A61B5/352—Detecting R peaks, e.g. for synchronising diagnostic apparatus; Estimating R-R interval
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B5/00—Measuring for diagnostic purposes; Identification of persons
  • A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
  • A61B5/316—Modalities, i.e. specific diagnostic methods
  • A61B5/318—Heart-related electrical modalities, e.g. electrocardiography [ECG]
  • A61B5/346—Analysis of electrocardiograms
  • A61B5/349—Detecting specific parameters of the electrocardiograph cycle
  • A61B5/366—Detecting abnormal QRS complex, e.g. widening
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B5/00—Measuring for diagnostic purposes; Identification of persons
  • A61B5/02—Detecting, measuring or recording for evaluating the cardiovascular system, e.g. pulse, heart rate, blood pressure or blood flow
  • A61B5/024—Measuring pulse rate or heart rate
  • A61B5/0245—Measuring pulse rate or heart rate by using sensing means generating electric signals, i.e. ECG signals

Definitions

• the present invention relates to non-invasive high-resolution diagnostics of cardiac ischemia based on processing of body-surface electrocardiogram (ECG) data.
• ECG electrocardiogram
• the invention's ' quantitative method of assessment of cardiac ischemia may simultaneously indicate both cardiac health itself and cardiovascular system health in general.
• Heart attacks and other ischemic events of the heart are among the leading causes of death and disability in the United States.
• the susceptibility of a particular patient to heart attack or the like can be assessed by examining the heart for evidence of ischemia (insufficient blood flow to the heart tissue itself resulting in an insufficient oxygen supply) during periods of elevated heart activity.
• ischemia insufficient blood flow to the heart tissue itself resulting in an insufficient oxygen supply
• the measuring technique be sufficiently benign to be carried out without undue stress to the heart (the condition of which might not yet be known) and without undue discomfort to the patient.
• the measuring technique be useful for patients of varying degrees of health, including patients without detectable ischemia, those with moderate levels of ischemia, and patients with coronary artery disease.
• the cardiovascular system responds to changes in physiological stress by adjusting the heart rate, which adjustments can be evaluated by measuring the surface ECG R-R intervals.
• the time intervals between consecutive R waves indicate the intervals between the consecutive heartbeats (RR intervals).
• This adjustment normally occurs along with corresponding changes in the duration of the ECG QT intervals, which characterize the duration of electrical excitation of cardiac muscle and represent the action potential duration averaged over a certain volume of cardiac muscle ( Figure 1).
• an average action potential duration measured as the QT interval at each ECG lead may be considered as an indicator of cardiac systolic activity varying in time.
• QT interval dispersion alone, without simultaneous measurement of T - wave alternation, is said to be a less accurate predictor of cardiac electrical instability (U.S. Pat. 5,560,370 at column 6, lines 4-15).
• Another application of the QT interval dispersion analysis for prediction of sudden cardiac death is developed by J. Sarma (U.S. Patent No. 5,419,338). He describes a method of an autonomic nervous system testing that is designed to evaluate the imbalances between both parasympathetic and sympathetic controls on the heart and, thus, to indicate a predisposition for sudden cardiac death.
• a conventional non-invasive method of assessing coronary artery diseases associated with cardiac ischemia is based on the observation of morphological changes in a surface electrocardiogram during physiological exercise (stress test).
• a change of the ECG morphology such as an inversion of the T-wave, is known to be a qualitative indication of ischemia.
• the dynamics of the ECG ST- segments are continuously monitored while the shape and slope, as well as ST-segment elevation or depression, measured relative to an average base line, are altering in response to exercise load. A comparison of any of these changes with average values of monitored ST segment data provides an indication of insufficient coronary blood circulation and developing ischemia.
• Relatively low sensitivity and low resolution which are fundamental disadvantages of the conventional ST-segment depression method, are inherent in such method's being based on measuring an amplitude of a body surface ECG signal, which signal by itself does not accurately reflect changes in an individual cardiac cell's electrical parameters normally changing during an ischemic cardiac event.
• a body surface ECG signal is a composite determined by action potentials aroused from discharge of hundred of thousands of individual excitable cardiac cells. When electrical activity of excitable cells slightly and locally alters during the development of exercise-induced local ischemia, its electrical image in the ECG signal on the body surface is significantly overshadowed by the aggregate signal from the rest of the heart.
• the present invention is based on the finding that, for all individuals (not just patients afflicted with coronary artery disease), if the patient's heart rate reaches a sufficiently high level (which level will vary from individual to individual), then slowly or rapidly diminishing or even discontinuing the exercise (or other load causing the increased heart rate) will not evoke a clear or substantial sympatho- adrenal response in the subject.
• the exercise can be considered to be quasi-stationary; data may be collected from such a patient; and cardiac ischemia and/or cardiovascular health may be assessed in the patient in accordance with the techniques described herein.
• Embodiments of the present invention may overcome deficiencies in the conventional ST-segment analysis.
• An RR- and/or QT-RR interval data set may be used to assess cardiovascular health in a subject under certain conditions.
• Embodiments of the present invention may be useful to assess cardiovascular health in patients with varying degrees of ischemia such as patients with coronary artery disease ("CAD"), patients with moderate levels of ischemia, as well as patients without detectable ischemia.
• An RR- and/or QT-RR interval data set can be collected during stages of varying workloads and heart rates. The data collected during a recovery period after a relatively high workload and/or heart rate period may be analyzed as an indication of cardiovascular health.
• the subject's heart rate at its peak during heavy workload may be sufficiently high such that a quasi-stationary increasing heart rate period and subsequent recovery period are observed.
• the recovery period can involve decreasing the subject's heart rate by reducing workload gradually or by abruptly stopping exercise workload.
• the reduction of workload may be preceded by a "cool down" stage of reduced workload.
• the RR- and/or QT-RR interval data sets collected during the stage of relatively high workload and heart rate and the subsequent recovery stage in which workload is decreased or eliminated may be analyzed to indicate the cardiovascular health of the patient.
• a first aspect of the present invention is a method of assessing cardiac ischemia in a subject to provide a measure of cardiovascular health in that subject. The method comprises the steps of:
• step (d) generating from said comparison of step (c) a measure of cardiac ischemia during stimulation in said subject, wherein a greater difference between said first and second data sets indicates greater cardiac ischemia and lesser cardiac or cardiovascular health in said subject.
• the computer program product includes a computer usable storage medium having computer readable program code embodied in the medium.
• the computer readable program code includes:
• Figure 1 is a schematic graphic representation of the action potential in cardiac muscle summed up over its volume and the induced electrocardiogram (ECG) recorded on a human's body surface.
• ECG electrocardiogram
• Figure 2A depicts the equations used in a simplified mathematical model of periodic excitation.
• Figure 2B depicts a periodic excitation wave (action potential, u, and instantaneous threshold, v, generated by computer using a simplified mathematical model, the equations of which are set forth in Figure 2A.
• Figure 2C depicts a family of four composite dispersion-restitution curves corresponding to four values of the medium excitation threshold.
• Figure 3 is a block diagram of an apparatus for carrying out the present method.
• Figure 4A is a block diagram of the processing steps for data acquisition and analysis of the present invention.
• Figure 4B is an alternative block diagram of the processing steps for data acquisition and analysis of the present invention.
• Figure 5 illustrates experimental QT-interval versus RR-interval hysteresis loops for two healthy male (23 year old, thick line and 47 year old, thin line) subjects plotted on the composite dispersion-restitution curve plane.
• Figure 6 provides examples of the QT-RR interval hysteresis for two male subjects, one with a conventional ECG ST-segment depression (thin line) and one with a history of a myocardial infarction 12 years prior to the test (thick line). The generation of the curves is explained in greater detail in the specification below.
• Figure 7 illustrates sensitivity of the present invention and shows two QT-RR interval hysteresis loops for a male subject, the first one (thick lines) corresponds to the initial test during which an ST-segment depression on a conventional ECG was observed, and the second one shown by thin lines measured after a period of regular exercise.
• Figure 8 illustrates a comparative cardiac ischemia analysis based on a particular example of a normalized measure of the hysteresis loop area.
• ⁇ CII> (CII -CIImin)/(CII ma ⁇ - Cllmin) ("CII” means "cardiac ischemia index").
• Oi, Xi, and Yi represent human subject data.
• Xi represents data collected from one subject (0.28 - 0.35) in a series of tests (day/night testing, run/walk, about two months between tests); exercise peak heart rate ranged from 120 to 135.
• Yi represents data collected from one subject (0.46 - 0.86) in a series of tests (run/walk, six weeks between tests before and after a period of regular exercise stage); exercise peak heart rate ranged from 122 to 146.
• Black bars indicate a zone ( ⁇ CII> less than 0.70) in which a conventional ST depression method does not detect cardiac ischemia.
• the conventional method may detect cardiac ischemia only in a significantly narrower range indicated by high white bars (Y , Y 3 , O 7 : ⁇ CII> greater than 0.70).
• Figure 9 illustrates a typical rapid peripheral nervous system and hormonal control adjustment of the QT and RR interval to an abrupt stop in exercise (that is, an abrupt initiation of a rest stage).
• Figure 10 illustrates a typical slow (quasi-stationary) QT and RR interval adjustment measured during gradually increasing and gradually decreasing cardiac stimulation.
• Figure 11 demonstrates a block-diagram of the data processing by the method of optimized consolidation of a moving average, exponential and polynomial fitting (Example 11, steps 1-8).
• FIG. 12 demonstrates results of the processing throughout steps 1 to 8 of
• Example 11 Upper panels show QT and RR data sets processed from steps 1 to 3
• step 3 The exponential fitting curves (step 3) are shown in gray in the first two panels. Low panels show the same smooth dependencies after processing from step 4 to a final step 8. Here the CII (see right low panel) is equal to a ratio examplelO, section 7).
• Figure 13 demonstrates a block-diagram of the data processing by the method of a sequential moving average (Example 12, steps 1-3)
• Figure 14 demonstrates results of the processing throughout steps 1 to 2 of
• Example 12 Upper panels show processed QT and RR data sets, and the QT/RR hysteresis loop after step 1 (from left to right respectively). Low panels show the same smooth dependencies after the second moving average processing and a final step 3.
• Figure 15 shows a general data flow chart for major steps in optimized nonlinear transformation method. The left-hand side and the right-hand side boxes describe similar processing stages for the RR and QT-intervals, respectively.
• Figure 16 shows a detailed data flow chart for one data subset
• stage 1 uses a combination of traditional data processing methods and includes: moving averaging (1), determination of a minimum region (2), fitting a quadratic parabola to the data in this region (3), checking consistency of the result (4), finding the minimum and centering data at the minimum (5) and (6), conditionally sorting the data (7).
• Stages (8) through (11) are based on the dual-nonlinear transformation method for the non-linear regression.
• Figure 17 displays the nonlinear transformation of a filtered RR-interval data set. Panel A shows the data on the original (t,y)-plane, the minimum is marked with an asterisk inside a circle.
• the image of the minimum is also marked with an encircled asterisk. Note that the transformed data sets concentrate around a monotonously growing (average) curve with a clearly linear portion in the middle.
• Figure 18 is similar to Figure 17 but for a QT-interval data set.
• Figure 20 shows an example of full processing of the RR and QT data sets for one patient. Panels A and C represent RR and QT data sets and their fit.
• Panel B shows the corresponding ascending and descending curves and closing line on the (7 R R,7 QT )- plane, on which the area of such a hysteresis loop has the dimension of time-squared.
• the total error-for Panel A is 2.2% and for Panel C is 0.8%.
• Figure 21 is an RR-interval data set for a 60-year-old coronary artery disease "CAD" patient with 4.5 minutes of work load before an abrupt stop of exercise with a peak work load of 28 W (watt).
• CAD coronary artery disease
• Figure 22 is an RR-interval data set for the first 1.5 minutes of recovery after the abrupt stop of exercise with 4.5 minutes of work load for the same CAD patient in Figure 21.
• the HR recovery occurs at a slow, quasi stationary rate of 9 beats/min.
• Figure 23 is an RR-interval data set for a 50-year-old individual after fourteen minutes of work load before an almost abrupt stop of exercise preceded by two minutes of low, 20 W recovery work load after a peak work load of 130 W.
• Figure 24 is an RR-interval data set for the first 1.5 minutes of recovery after the almost abrupt stop of exercise preceded by two minutes of low, 20 W recovery work load after a peak work load of 130 W for the same 50-year-old individual in Figure 23.
• Figures 25-26 are RR- and QT- interval data sets and a calculated hysteresis loop for the coronary artery disease patient and the patient without coronary artery disease, respectively.
• Computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer- readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart block or blocks.
• Computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks.
• Cardiac ischemia refers to a lack of or insufficient blood supply to an area of cardiac muscle. Cardiac ischemia usually occurs in the presence of arteriosclerotic occlusion of a single or a group of coronary arteries. Arteriosclerosis is a product of a lipid deposition process resulting in fibro-fatty accumulations, or plaques, which grow on the internal walls of coronary arteries. Such an occlusion compromises blood flow through the artery, which reduction then impairs oxygen supply to the surrounding tissues during increased physiological need ⁇ for instance, during increased exercise loads.
• ischemia that may be detected by the present invention includes episodic, chronic and acute ischemia.
• "Exercise” as used herein refers to voluntary skeletal muscle activity of a subject that increases heart rate above that found at a sustained stationary resting state.
• Examples of exercise include, but are not limited to, cycling, rowing, weight-lifting, walking, running, stair-stepping, etc., which may be implemented on a stationary device such as a treadmill or in a non-stationary environment.
• “Exercise load” or “load level” refers to the relative strenuousness of a particular exercise, with greater loads or load levels for a given exercise producing a greater heart rate in a subject. For example, load may be increased in weight-lifting by increasing the amount of weight; load may be increased in walking or running by increasing the speed and/or increasing the slope or incline of the walking or running surface; etc.
• “Gradually increasing” and “gradually decreasing” an exercise load refers to exercise in which the subject is caused to perform an exercise under a plurality of different sequentially increasing or sequentially decreasing loads.
• the number of steps in the sequence can be infinite so the terms gradually increasing and gradually decreasing loads include continuous load increase and decrease, respectively.
• Hysteresis refers to a lagging of the physiological effect when the external conditions are changed.
• Hysteresis curves refer to a pair of curves in which one curve reflects the response of a system to a first sequence of conditions, such as gradually increasing heart rate, and the other curve reflects the response of a system to a second sequence of conditions, such as gradually decreasing heart rate.
• both sets of conditions are essentially the same ⁇ /.e., consist of the same (or approximately the same) steps—but are passed in different order in the course of time.
• a “hysteresis loop” refers to a loop formed by the two contiguous curves of the pair.
• ECG Electrocardiogram
• ECG refers to a continuous or sequential record (or a set of such records) of a local electrical potential field obtained from one or more locations outside the cardiac muscle. This field is generated by the combined electrical activity (action potential generation) of multiple cardiac cells.
• the recording electrodes may be either subcutaneously implanted or may be temporarily attached to the surface of the skin of the subject, usually in the thoracic region.
• An ECG record typically includes the single-lead ECG signal that represents a potential difference between any two of the recording sites including the site with a zero or ground potential.
• Non-quasi-stationary intervening rest when used to refer to a stage following increased cardiac stimulation, refers to a stage of time initiated by a sufficiently abrupt decrease in heart stimulation (e.g., an abrupt decrease in exercise load) so that it evokes a clear sympatho-adrenal response.
• a non-quasi- stationary intervening rest stage is characterized by a rapid sympatho-adrenal adjustment (as further described in Example 8 below), and the inclusion of an intervening rest stage precludes the use of a quasi-stationary exercise (or stimulation) protocol (as further described in Example 9 below).
• quasi- stationary intervening rest refers to a stage of time initiated by a decrease in heart stimulation that does not evoke a clear sympatho-adrenal response.
• Examples of conditions under which a quasi-stationary intervening rest occurs includes a stage of increasing heart rate up to a predetermined threshold that is sufficiently high such that subsequent intervening rest is quasi-stationary.
• a "predetermined threshold heart rate” refers to a range of heart rates that are sufficiently high such that a subsequent reduction in heart rate, e.g., due to decreased exercise load or the elimination of exercise load, is quasi-stationary.
• the predetermined threshold heart rate can be at least 130, 140, 150, 160 or more beats per minute.
• the predetermined threshold heart rate can be defined by the following formula:
• PT (220 ⁇ V bpm) - age ;
• PT is the predetermined threshold heart rate
• V is 10, 15, 20, 25, or 30, bpm is beats per minute
• age is the age of said subject.
• the threshold heart rate may correspond to a work load of between about 5, 10 or 20 W and about 30, 40, or 60 W for a coronary artery disease patient and a work load of between about 80, 90 or 100W to about 130, 150 or 170W for a non- coronary artery disease patient.
• the threshold heart rate may also be determined by observing the amount of stress that a patient experiences during exercise such that the threshold heart rate coincides with a degree of stress that is close to the maximum safe degree of stress.
• Quadrature-stationary conditions refer to any situation in which a gradual change in the external conditions and/or the physiological response it causes occurs slower than any corresponding adjustment due to sympathetic/parasympathetic and hormonal control. If the representative time of the external conditions variation is denoted by T e x t , and Ti nt is a representative time of the fastest of the internal, sympathetic/parasympathetic and hormonal control, then "quasi-stationary conditions” indicates ⁇ ext » ⁇ icott (e.g., ⁇ ex t is at least about two, three, four or five times greater than tj nt ). Abrupt changes in exercise load may be either quasi-stationary or non-quasi-stationary.
• a non-quasi-stationary abrupt change refers to a situation opposite quasi-stationary conditions corresponding to a sufficiently fast change in the external conditions as compared with the rate sympathetic/parasympathetic and hormonal control — that is, it requires that ⁇ ext « Tj n t (e.g., ⁇ ex t is at least about two, three, for our five times less than Ti court t ).
• ⁇ ext « Tj n t e.g., ⁇ ex t is at least about two, three, for our five times less than Ti context t .
• a quasi-stationary abrupt change refers to a relatively fast change in exercise load that is nonetheless quasi-stationary-, for example, because the change is preceded by a sufficiently high exercise load such that a slower, quasi-stationary recovery period is observed.
• QRS- and RR- data set refers to a record of the time course of an electrical signal comprising action potentials spreading through cardiac muscle.
• Any single lead ECG record incorporates a group of three consecutive sharp deflections usually called a QRS complex and generated by the propagation of the action potential's front through the ventricles.
• the electrical recovery of ventricular tissue is seen on the ECG as a relatively small deflection known as the T wave.
• the time interval between the cardiac cycles i.e., between the maxima of the consecutive R- waves
• action potential duration i.e., the time between the beginning of a QRS complex and the end of the ensuing T-wave
• an RR-interval can be defined as the time between any two similar points, such as the similar inflection points, on two consecutive R-waves, or any other way to measure cardiac cycle length.
• a QT- interval can be defined as the time interval between the peak of the Q-wave and the peak of the T wave. It can also be defined as the time interval between the beginning (or the center) of the Q-wave and the end of the ensuing T-wave defined as the point on the time axis (the base line) at which it intersects with the linear extrapolation of the T-wave's falling branch and started from its inflection point, or any other way to measure action potential duration.
• a QT- and RR- interval data set will contain two QT-interval related sequences ⁇ TQT,I,TQT,2,...,TQT, ⁇ , ⁇ and ⁇ t ⁇ ,t ,...,t n ⁇ , and will also contain two RR-interval related sequences ⁇ T RR ⁇ T RR ⁇ V .- J T RR ,,,, ⁇ and ⁇ t].,t 2 ,...,tn ⁇ (the sequence ⁇ t ⁇ ,t 2 ,...,t n ⁇ may or may not exactly coincide with the similar sequence in the QT data set).
• C[a,b] shall denote a set of continuous functions ⁇ f) on a segment [a,b].
• the quantities are treated as column vectors.
• E ⁇ shall denote a N-dimensional metric space with the metric R ⁇ (x,y), x,y E ⁇ . (R ⁇ (x,y) is said to be a distance between points and y.)
• a b (total) variation y [F] is defined for any absolutely continuous function F from a
• V ⁇ ( ] ⁇ I R(*,)-R(*, + .) l- (D.2)
• fe C [a,b] is called the (best) fit (or the best fitting) function of class
• E is implied to be an Euclidean space with an Euclidean metric.
• R then becomes the familiar mean-root-square error. The fit is performed
• a smoother function (comparison of smoothness): Let fit) and g(t) be functions from C[a,b] that have absolutely continuous derivatives on this segment. The function/ft) is smoother than the function g(t) if
• the prime denotes a time derivative, and a strict inequality holds in at least one ofrelations (D.4) and (D.5).
• a and B are Ni xNo matrices, is called a smoothing if the latter set is smoother than the former.
• a measure of a closed domain Let ⁇ be a singly connected domain on the plane ( ⁇ ,7) with the boundary formed by a simple (i.e., without self-intersections) continuous curve.
• a measure M of such a domain ⁇ on the plane ( ⁇ ,T) is defined as the Riemann integral
• ⁇ ( ⁇ ,7) is a nonnegative (weight) function on ⁇ .
• Figure 1 illustrates the correspondence between the temporal phases of the periodic action potential (AP, upper graph, 20) generated inside cardiac muscle and summed up over its entire volume and the electrical signal produced on the body surface and recorded as an electrocardiogram (ECG, lower graph, 21).
• the figure depicts two regular cardiac cycles.
• the QRS-complex is formed. It consists of three waves, Q, R, and S, which are marked on the lower panel.
• the recovery stage of the action potential is characterized by its fall off on the AP plot and by the T-wave on the ECG plot.
• the action potential duration is well represented by the time between Q and T waves and is conventionally defined as the QT interval, measured from the beginning of the Q wave to the end of the following T wave.
• the time between consecutive R- waves represents the duration of a cardiac cycle, while its reciprocal value represents the corresponding instantaneous heart rate.
• Figure 2 illustrates major aspects of the process of propagation of a periodic action potential through cardiac tissue and the formation of a corresponding composite dispersion-restitution curve.
• the tissue can be considered as a continuous medium and the propagation process as a repetition at each medium point of the consecutive phases of excitation and recovery.
• the former phase is characterized by a fast growth of the local membrane potential (depolarization), and the latter by its return to a negative resting value (repolarization).
• the excitation phase involves a very fast ( ⁇ 0.1ms) decrease in the excitation threshold and the following development of a fast inward sodium current that causes the upstroke of the action potential ( ⁇ lms).
• a fast inward sodium current that causes the upstroke of the action potential ( ⁇ lms).
• sodium current is inactivated; calcium and potassium currents are developing while the membrane is temporarily unexcitable (i.e., the threshold is high).
• a potassium current repolarizes the membrane so it again becomes excitable (the excitation threshold is lowered).
• the left-hand side of the first equation describes local accumulation of the electric charge on the membrane
• the first term in the right-hand side describes Ohmic coupling between neighboring points of the medium
• the term i(u,v) represents the transmembrane current as a function of the membrane potential and the varying excitation threshold ( ⁇ is a small constant, the ratio of the slow recovery rate to the fast excitation rate).
• ⁇ is a small constant, the ratio of the slow recovery rate to the fast excitation rate.
• the wave-train shown in panel B has been calculated for g(u,v)- ⁇ u+v r -v, where ⁇ and v r are appropriately chosen constants (v r has the meaning of the initial excitation threshold and is the main determinant of the medium excitability).
• the function i(u,v) was chosen to consist of two linear pieces, one for the sub-threshold region, u ⁇ v, and one for supra-threshold region, u>v.
• i(u,v) ⁇ r u when u ⁇ v
• i(u,v) ⁇ e ⁇ (u- " ex ) when u>v
• a medium with higher excitability corresponding to the tissue with better conduction, gives rise to a faster, more robust action potential with a longer Action Potential Duration (APD).
• APD Action Potential Duration
• This condition also means that a longer-lasting excitation propagates faster.
• a wave train with a higher frequency propagates slower since the medium has less time to recover from the preceding excitation and thus has a lower effective excitability.
• the restitution curve is 7 AP versus diastolic interval 7b ⁇ , which differently makes a quite similar physical statement.
• ⁇ T F (C)
• Such a curve (relation) shall be referred to as a composite dispersion-restitution curve (relation) and can be directly obtained from an experimental ECG recording by determining the QT-RR interval data set and plotting 7 QT versus 7 RR .
• a condition that the experimental ⁇ 7 QT ,7 RR ⁇ data set indeed represents the composite dispersion-restitution relation is the requirement that the data are collected under quasi-stationary conditions. Understanding this fact is a key discovery for the present invention. 3. Testing methods.
• the methods of the present invention are primarily intended for the testing of human subjects.
• Virtually any human subject can be tested by the methods of the present invention, including male, female, juvenile, adolescent, adult, and geriatric subjects.
• the methods may be carried out as an initial screening test on subjects for which no substantial previous history or record is available, or may be carried out on a repeated basis on the same subject (particularly where a comparative quantitative indicium of an individual's cardiac health over time is desired) to assess the effect or influence of intervening events and/or intervening therapy on that subject between testing sessions.
• the method of the present invention generally comprises (a) collecting a first RR- interval data set from said subject during a stage of gradually increasing heart rate up to a predetermined threshold of at least 130 beats per minute; (b) collecting a second RR- interval data set from said subject during a stage of gradually decreasing heart rate; (c) comparing said first RR- interval data set to said second RR- interval data set to determine the difference between said data sets; and (d) generating from said comparison of step (c) a measure of cardiac ischemia during stimulation in said subject, wherein a greater difference between said first and second data sets indicates greater cardiac ischemia and lesser cardiac or cardiovascular health in said subject.
• the stages of gradually increasing and gradually decreasing heart rate are carried out in a manner that maintains during both periods essentially or substantially the same stimulation of the heart by the peripheral nervous and hormonal control systems, so that it is the effect of cardiac ischemia rather than that of the external control which is measured by means of the present invention.
• This methodology can be carried out by a variety of techniques, including the technique of conducting two consecutive stages of gradually increasing and gradually decreasing exercise loads (or average heart rates).
• the stage of gradually increasing exercise load (or increased average heart rate) and the stage of gradually decreasing exercise load (or decreased average heart rate) may be the same in duration or may be different in duration.
• each stage is at least 3, 5, 8, or 10 minutes or more in duration.
• the duration of the two stages may be from about 6, 10, 16 or 20 minutes in duration to about 30, 40, or 60 minutes in duration or more.
• the two stages are preferably carried out sequentially in time — that is, with one stage following after the other substantially immediately, without an intervening rest stage. In the alternative, the two stages may be carried out separately in time, with an intervening "plateau" stage (e.g., of from 1 to 5 minutes) during which cardiac stimulation or exercise load is held substantially constant, before the stage of decreasing load is initiated.
• plateau e.g., of from 1 to 5 minutes
• a stage of decreasing exercise load may be considered to take place during the period following a quasi-stationary abrupt stop in exercise.
• the exercise protocol may include the same or different sets of load steps during the stages of increasing or decreasing heart rates.
• the peak load in each stage may be the same or different, and the minimum load in each stage may be the same or different.
• each stage consists of at least two or three different load levels, in ascending or descending order depending upon the stage. Relatively high load levels, which result in relatively high heart rates, can be used.
• the peak or predetermined threshold heart rate is sufficiently high such that subsequent resting or decreased exercise load periods are quasi-stationary.
• Embodiment of the present invention may be used to diagnose or test patients with varying levels of ischemia, including patients without detectable ischemia, patients with moderate ischemia, and patients with coronary artery disease.
• the predetermined threshold heart rate may correspond to varying workloads for different patients depending on overall fitness and cardiac health. For example, for an athletic or trained subject, for the first or ascending stage, a first load level may be selected to require a power output of 60 to 100 or 150 watts by the subject; an intermediate load level may be selected to require a power output of 100 to 150 or 200 watts by the subject; and a third load level may be selected to require a power output of 200 to 300 or 450 watts or more by the subject.
• a first load level may be selected to require a power output of 200 to 300 or 450 watts or more by the subject; an intermediate or second load level may be selected to require a power output of 100 to 150 or 200 watts by the subject; and a third load level may be selected to require a power output of 60 to 100 or 150 watts by the subject.
• Additional load levels may be included before, after, or between all of the foregoing load levels as desired, and adjustment between load levels can be carried out in any suitable manner, including step-wise or continuously.
• Increased heart rates up to the predetermined threshold heart rate may also be achieved by maintaining a single load level for a sustained period of time sufficient to reach the threshold heart rate.
• a first load level may be selected to require a power output of 20 to 40 to 75 or 100 watts by the subject; an intermediate load level may be selected to require a power output of 75 to 100 or 150 watts by the subject; and a third load level may be selected to require a power output of 125 to 200 or 300 watts or more by the subject.
• a first load level may be selected to require a power output of 125 to 200 or 300 watts or more by the subject; an intermediate or second load level may be selected to require a power output of 75 to 100 or 150 watts by the subject; and a third load level may be selected to require a power output of 40 to 75 or 100 watts by the subject.
• additional load levels may be included before, after, or between all of the foregoing load levels as desired, and adjustment between load levels can be carried out in any suitable manner, including step-wise or continuously.
• the predetermined threshold heart rate may also be achieved by sustained exercise at a single power output for a sufficient amount of time. The heart rate may be gradually increased and gradually decreased by subjecting the patient to a predetermined schedule of stimulation.
• the patient may be subjected to a gradually increasing exercise load and gradually decreasing exercise load, or gradually increasing electrical or pharmacological stimulation and gradually decreasing electrical or pharmacological stimulation, according to a predetermined program or schedule.
• a predetermined schedule is without feedback of actual heart rate from the patient.
• the heart rate of the patient may be gradually increased and gradually decreased in response to actual heart rate data collected from concurrent monitoring of said patient.
• Such a system is a feedback system.
• the heart rate of the patient may be monitored during the test and the exercise load (speed and/or incline, in the case of a treadmill) can be adjusted so that the heart rate varies in a prescribed way during both stages of the test.
• the monitoring and control of the load can be accomplished by a computer or other control system using a simple control program and an output panel connected to the control system and to the exercise device that generates an analog signal to the exercise device.
• a feedback system is that (if desired) the control system can insure that the heart rate increases substantially linearly during the first stage and decreases substantially linearly during the second stage.
• the generating step (d) may be carried out by any suitable means, such as by generating curves from the data sets (with or without actually displaying the curves), and then (i) directly or indirectly evaluating a measure (e.g., as defined in the integral theory) of the domain (e.g., area) between the hysteresis curves, a greater measure indicating greater cardiac ischemia in said subject, (ii) directly or indirectly comparing the shapes (e.g., slopes or derivatives thereof) of the curves, with a greater difference in shape indicating greater cardiac ischemia in the subject; or (iii) combinations of (i) and (ii). Specific examples are given in Example 4 below.
• the method of the invention may further comprise the steps of (e) comparing the measure of cardiac ischemia during exercise to at least one reference value (e.g., a mean, median or mode for the quantitative indicia from a population or subpopulation of individuals) and then (f) generating from the comparison of step (e) at least one quantitative indicium of cardiovascular health for said subject.
• at least one reference value e.g., a mean, median or mode for the quantitative indicia from a population or subpopulation of individuals
• any such quantitative indicium may be generated on a one-time basis (e.g., for assessing the likelihood that the subject is at risk to experience a future ischemia-related cardiac incident such as myocardial infarction or ventricular tachycardia), or may be generated to monitor the progress of the subject over time, either in response to a particular prescribed cardiovascular therapy, or simply as an ongoing monitoring of the physical condition of the subject for improvement or decline (again, specific examples are given in Example 4 below).
• steps (a) through (f) above are repeated on at least one separate occasion to assess the efficacy of the cardiovascular therapy or the progress of the subject.
• Any suitable cardiovascular therapy can be administered, including but not limited to, aerobic exercise, muscle strength building, change in diet, nutritional supplement, weight loss, smoking cessation, stress reduction, pharmaceutical treatment (including gene therapy), surgical treatment (including both open heart and closed heart procedures such as bypass, balloon angioplasty, catheter ablation, etc.) and combinations thereof.
• the therapy or therapeutic intervention may be one that is approved or one that is experimental. In the latter case, the present invention may be implemented in the context of a clinical trial of the experimental therapy, with testing being carried out before and after therapy (and/or during therapy) as an aid in determining the efficacy of the proposed therapy.
• FIG 3 provides an example of the apparatus for data acquisition, processing and analysis by the present invention. Electrocardiograms are recorded by an ECG recorder 30, via electrical leads placed on a subject's body.
• the ECG recorder may be, for example, a standard multi-lead Holter recorder or any other appropriate recorder.
• the analog/digital converter 31 digitizes the signals recorded by the ECG recorder and transfers them to a personal computer 32, or other computer or central processing unit, through a standard external input/output port. The digitized ECG data can then be processed by standard computer-based waveform analyzer software.
• Composite dispersion-restitution curves and a cardiac or cardiovascular health indicium or other quantitative measure of the presence, absence or degree of cardiac ischemia can then be calculated automatically in the computer through a program (e.g., Basic, Fortran, C++, etc.) implemented therein as software, hardware, or both hardware and software.
• a program e.g., Basic, Fortran, C++, etc.
• Figure 4A and Figure 4B illustrate the major steps of digitized data processing in order to generate an analysis of a QT-RR data set collected from a subject during there-and-back quasi-stationary changes in physiological conditions.
• the first four steps in Figure 4A and Figure 4B are substantially the same.
• the digitized data collected from a multi-lead recorder are stored in a computer memory for each lead as a data array 40a, 40b.
• the size of each data array is determined by the durations of the ascending and descending heart rate stages and a sampling rate used by the waveform analyzer, which processes an incoming digitized ECG signal.
• the waveform analyzer software first detects major characteristic waves (Q,R,S and T waves) of the ECG signal in each particular lead 41a, 41b.
• each ECG lead determines the time intervals between consecutive R waves and the beginning of Q and the end of T waves 42a, 42b. Using these reference points it calculates heart rate and RR- and QT- intervals. Then, the application part of the software sorts the intervals for the ascending and descending heart rate stages 43a, 43b. The next two steps can be made in one of the two alternative ways shown in Figures 4A and 4B, respectively.
• the fifth step as shown in Figure 4A consists of displaying by the application part of software QT- intervals versus RR- intervals 44a, separately for the ascending and descending heart rate stages effected by there-and-back gradual changes in physiological conditions such as exercise, pharmacological/electrical stimulation, etc.
• An alternative for the last two steps shown in Figure 4B requires that the application part of the software first averages, and/or filters and/or fits, using exponential or any other suitable functions, the QT intervals as functions of time for both stages and similarly processes the RR-interval data set to produce two sufficiently smooth curves each including the ascending and descending heart rate branches 44b.
• the following steps shown in Figures 4A and Figure 4B are again substantially the same.
• the next step 46a, 46b performed by the application part of the software can be graphically presented as closing the two branch hysteresis loop with an appropriate interconnecting or partially connecting line, such as a vertical straight line or a line connecting the initial and final points, in order to produce a closed hysteresis loop on the (JHQ T , 7 RR )-plane.
• the application software evaluates for each ECG lead an appropriate measure of the domain inside the closed hysteresis loop.
• a measure as defined in mathematical integral theory, is a generalization of the concept of an area and may include appropriate weight functions increasing or decreasing the contribution of different portions of the domain into said measure.
• the final step 48a, 48b of the data processing for each ECG lead is that the application software calculates indexes by appropriately renormalizing the said measure or any monotonous functions of said measure.
• the measure itself along with the indexes may reflect both the severity of the exercise-induced ischemia, as well as a predisposition to local ischemia that can be reflected in some particularities of the shape of the measured composite dispersion- restitution curves.
• the results of all above-mentioned signal processing steps may be used to quantitatively assess cardiac ischemia and, as a simultaneous option, cardiovascular system health of a particular individual under test.
• a similar data processing procedure can equivalently be performed on any plane obtained by a non-degenerate transformation of the (7Q ⁇ ,7 R )-plane, such as (T QT / KR ) where is the heart rate or the like.
• Such a transformation can be partly or fully incorporated in the appropriate definition of the said measure.
• each stage of a gradually increasing or gradually decreasing quasi- stationary exercise protocol is at least 2, 5, 8, or 10 minutes in duration.
• Each stage's duration is usually an order of magnitude longer than the average duration ( ⁇ 1 minute) of heart rate adjustment during an abrupt stop of the exercise between average peak load rate (from about 120 or 130 to about 150 or 160 beats/min) and average rest (from about 50 or 60 to about 70 or 80 beats/min) heart rate value (from about 50 or 60 to about 70 or 80 beats/min).
• CAD coronary artery disease
• 75W 75W
• the threshold heart rate at which the adjustment period is increased and becomes quasi-stationary can be defined by the formula
• PT (220 ⁇ V bpm) - age : where PT is the predetermined threshold heart rate, V is 15, 20, or 25, bpm is beats per minute, and age is the age of said subject.
• the threshold heart rate may be referred to as a rate close to the maximum predetermined heart rate. In these cases the heart rate deviations (described in the example 9 below) are small and indicate that the individual remains under significant physical stress even after an abrupt stop of exercise, without further exercise load exposure, or with a low load, e.g., less than 25 W load, during the first one or two minutes after exercise.
• the recovery portion of the QT/RR hysteresis loop, as well as the whole loop eventually formed after an abrupt stop of exercise, can be considered as the quasi-stationary loop. Indeed, a slow recovery of the heart rate to its initial, prior-to-exercise, level 2, 5, 8, 10 or more minutes in duration with small heart rate deviations and, therefore, still satisfies the underlying definition of a gradual exercise protocol (see example 9, below).
• a testing apparatus consistent with Figure 3 was assembled.
• the electrocardiograms are recorded by an RZ 152PM 12 Digital ECG Holter Recorder (ROZINN ELECTRONICS, INC.; 71-22 Myrtle Av., Glendale, New York, USA 11385-7254), via 12 electrical leads with Lead-Lok Holter/Stress Test Electrodes LL510 (LEAD-LOK, INC.; 500 Airport Way, P.O.Box L, Sandpoint, ID, USA 83864) placed on a subject's body in accordance with the manufacturer's instructions.
• Digital ECG data are transferred to a personal computer (Dell Dimension XPS T500MHz/Windows 98) using a 40 MB flash card (RZFC40) with a PC 700 flash card reader, both from Rozinn Electronics, Inc. Holter for Windows (4.0.25) waveform analysis software is installed in the computer, which is used to process data by a standard computer based waveform analyzer software.
• Composite dispersion- restitution curves and an indicium that provides a quantitative characteristic of the extent of cardiac ischemia are then calculated manually or automatically in the computer through a program implemented in Fortran 90.
• EXAMPLES 2-6 Human Hysteresis Curve Studies These examples illustrate quasi-stationary ischemia-induced QT-RR interval hystereses in a variety of different human subjects. These data demonstrate a high sensitivity and the high resolution of the method. EXAMPLES 2-3
• the method of the present invention allows one to observe ischemia-induced hystereses that provide a satisfactory resolution within a conventionally sub-threshold range of ischemic events and allows one to quantitatively differentiate between the hystereses of the two subjects.
• Figure 6 illustrates quasi- stationary QT-RR interval hystereses for the male subjects.
• the curves fitted to the squares and empty circles relate to the first individual and illustrate a case of cardiac ischemia also detectable by the conventional ECG - ST segment depression technique.
• the curves fitted to the diamonds and triangles relate to the other subject, an individual who previously had experienced a myocardial infarction.
• Figure 7 provides examples of quasi-stationary hystereses for a 55 year-old male subject before and after he engaged in a practice of regular aerobic exercise. Both experiments were performed according to the same quasi-stationary 20-minute protocol with a gradually increasing and gradually decreasing exercise load. Fitting curves are obtained using third-order polynomial functions.
• the first test shows a pronounced exercise-induced cardiac ischemic event developed near the peak level of exercise load, detected by both the method of the present invention and a conventional ECG-ST depression method. The maximum heart rate reached during the first test (before a regular exercise regimen was undertaken) was equal to 146.
• the subject After a course of regular exercise the subject improved his cardiovascular health, which can be conventionally roughly, qualitatively, estimated by a comparison of peak heart rates. Indeed, the maximum heart rate at the peak exercise load from the first experiment to the second decreased by 16.4%, declining from 146 to 122.
• a conventional ST segment method also indicates the absence of ST depression, but did not provide any quantification of such an improvement since this ischemic range is sub-threshold for the method. Unlike such a conventional method, the method of the present invention did provide such quantification.
• the curves in Figure 7 developed from the second experiment show that the area of a quasi-stationary, QT-RR interval hysteresis decreased significantly from the first experiment, and such hysteresis loop indicated that some level of exercise-induced ischemia still remained.
• Figure 7 demonstrates that, due to its high sensitivity and high resolution, the methods can be used in the assessment of delicate alterations in levels of cardiac ischemia, indicating changes of cardiovascular health when treated by a conventional cardiovascular intervention.
• FIG. 8 illustrates a comparative cardiovascular health analysis based on ischemia assessment by the method of the present invention.
• an indicium of cardiovascular health here designated the cardiac ischemia index and abbreviated "CII”
• CCI cardiac ischemia index
• S quasi-stationary QT-RR interval hysteresis loop area
• ⁇ CII> (CII - CII m in)/(CII ma ⁇ - CII m i n ) varying from 0 to 1.
• Alterations of ⁇ CII> in different subjects show that the method of the present invention allows one to resolve and quantitatively characterize different levels of cardiac and cardiovascular health in a region in which the conventional ST depression method is sub-threshold and is unable to detect any exercise-induced ischemia.
• the method of the present invention offers much more accurate assessing and monitoring of small variations of cardiac ischemia and associated changes of cardiac or cardiovascular health.
• Figure 9 illustrates a typical rapid sympathetic/parasympathetic nervous and hormonal adjustment of the QT (panels A, C) and RR (panels B,D) intervals to a non- quasi-stationary abrupt stop after 10 minutes of exercise with increasing exercise load.
• a human subject (a 47 year-old male) was at rest the first 10 minutes and then began to exercise with gradually (during 10 minutes) increasing exercise load (Panels A, B - to the left from the RR, QT minima). Then at the peak of the exercise load (heart rate about 120 beat/min) the subject stepped off the treadmill in order to initialize the fastest RR and QT interval's adaptation to a complete abrupt stop of the exercise load.
• Panels C and D demonstrate that the fastest rate of change of QT and RR intervals occurred immediately after the abrupt stop of the exercise load. These rates are about 0.015 s/min for QT intervals while they vary from 0.28s to 0.295s and about 0.15s/min for RR intervals while they grow from 0.45s to 0.6s. Based on the above-described experiment, a definition for "rapid sympatho-adrenal and hormonal transients" or “rapid autonomic nervous system and hormonal transients” may be given.
• the peak exercise load in Example 8 is not sufficient to cause a quasi-stationary abrupt stop in the subject. That is, the exercise load does not cause sufficient stress to require a lengthened recovery period as observed in Examples 9 and 10.
• Rapid transients due to autonomic nervous system and hormonal control refer to the transients with the rate of 0.15s/min for RR intervals, which corresponds to the heart rate's rate of change of about 25 beat/min, and 0.02s/min for QT intervals or faster rates of change in RR/QT intervals in response to a significant abrupt change (stop or increase) in exercise load (or other cardiac stimulus).
• the significant abrupt changes in exercise load are defined here as the load variations which cause rapid variations in RR/QT intervals, comparable in size with the entire range from the exercise peak to the stationary average rest values.
• Figure 10 illustrates a typical slow (quasi-stationary) QT (panel A) and RR
• panel B interval adjustment measured during gradually increasing and gradually decreasing exercise load in a right pre-cordial V3 lead of the 12 lead electrocardiogram recording.
• the sampling was 15 QT and RR intervals per minute.
• the ranges for the QT-RR interval, there-and-back, time variations were 0.34s - 0.27s - 0.33s (an average rate of change ⁇ 0.005s/min) and 0.79s - 0.47s - 0.67s (an average rate of change ⁇ 0.032s/min or ⁇ 6 beat/min) for QT and RR intervals, respectively.
• the standard root-mean-square deviation, ⁇ , of the observed QT and RR intervals, shown by black dots in both panels, from their exponential fits were on an order of magnitude smaller than the average difference between the corresponding peak and rest values during the entire test. These deviations were ⁇ 0.003s for QT and ⁇ 0.03s for RR intervals, respectively.
• FIGS 21-24 are the RR- interval data sets for a coronary artery disease patient and a patient without coronary artery disease.
• Figures 25-26 illustrate the formation of a hysteresis loop for the coronary artery disease patient and the patient without coronary artery disease.
• QT- and RR- interval data was collected from each subject during a stage of gradually increasing heart rate up to a predetermined threshold heart rate and during a stage of gradually decreasing heart rate. The stage of gradually decreasing heart rate may be preceded by a stage of reduced exercise load, as indicated.
• Figure 21 is an RR-interval data set for a 60-year-old coronary artery disease patient with 4.5 minutes of work load before a quasi-stationary abrupt stop of exercise with a peak work load of 28 W (watt).
• Figure 22 is an RR-interval data set for the first 1.5 minutes of recovery after the quasi-stationary abrupt stop of exercise with 4.5 minutes of work load for the same coronary artery disease patient in Figure 21. The heart rate recovery occurs at a slow, quasi-stationary rate of 9 beats/min.
• Figure 25 shows the formation of the hysteresis loop for the same patient using QT- and RR- data. The upper and lower panels show raw and smoothed data, respectively.
• Figure 23 is an RR-interval data set for a 50-year-old individual without coronary artery disease after fourteen minutes of work load before an almost abrupt stop of exercise preceded by two minutes of low, 20 W recovery work load after a peak work load of 130 W.
• Figure 24 is an RR-interval data set for the first 1.5 minutes of recovery after the almost abrupt stop of exercise preceded by two minutes of low, 20 W recovery work load after a peak work load of 130 W for the same 50- year-old individual in Figure 23.
• the heart rate recovery is characterized by a quasi- stationary rate of 14 beats/min.
• Figure 26 shows the formation of the hysteresis loop for the same patient using QT- and RR- data.
• the upper and lower panels show raw and smoothed data, respectively.
• a quasi-stationary exercise (or stimulation) protocol refers to two contiguous stages (each stage 3, 5, 8 or 10 minutes or longer in duration) of increasing and decreasing heart rates or stimulation, such as:
• Each stage's duration is approximately an order of magnitude (e.g., at least about two, three, five, eight or ten times) longer than the average duration (about 1 minute) of a heart rate adjustment during an abrupt stop of the exercise between average peak load rate (about 120 or 130 to about 150 or 160 beat/min) and average rest (about 50 or 60 to about 70 or 80 beat/min) heart rate values.
• the standard root-mean-square deviations of the original QT/RR interval data set from their smooth and monotonic (for each stage) fits are of an order of magnitude (e.g., at least about two, three, five, ten times) smaller than the average differences between peak and rest QT/RR interval values measured during the entire exercise under the quasi-stationary protocol.
• Example 11 A Method of Optimized Consolidation of a Moving Average, Exponential and Polynomial Fitting 1.
• Raw data averaging/filtering (box 1 in Figure 11).
• the raw data set consists of two subsets ⁇ ⁇ I-1,2,.. V RR -1 , and ⁇ ? QT , T QT ⁇ , where t x ' and T x ' denote the z-th sampling time instant and the respective, RR or QT, interval duration (subsript x stands for RR or QT).
• t x stands for RR or QT
• the filtering procedure in this example comprises a moving averaging of neighboring data points.
• a moving overage over a set of adjacent points by angular brackets with a subscript indicating the number of points included in the averaging operator.
• the sub step consists of preliminary estimation of the time instants, t ⁇ and t g J.of the minima of the initially averaged RR-interval and QT-interval-data sets, respectively.
• the algorithm averages all M pairs and calculates the average minimum time coordinate t defined as
• the algorithm determines the sampling time instant t' m , which is nearest to t .
• t ⁇ and tg J T for RR and QT data sets, respectively.
• the first correction of the coordinates of the preliminary minima (box 3 in Figure 11).
• the first correction to the minimum coordinates tj' ⁇ and t ⁇ r is found.
• the fitting is done separately for the descending (t ⁇ f) and ascending (t>f) branches of u(t) with the same value of constants A and f and different values of ⁇ for both branches.
• new values of constants A and ⁇ are determined for each branch.
• a constant A is taken from the previous step and the value of ⁇ is numerically adjusted to minimize the deviation value, ⁇ .
• the algorithm outputs the corrected values A and ⁇ and the respective values of ⁇ TM and ⁇ n ⁇ u ⁇ n .
• the preliminary smooth curves (box 4 in Figure 11).
• the sub step consists of calculating a series of moving averages over p consecutive points for each data subset ⁇ « ⁇ as follows
• N m N-m+l
• N the number of data points after the initial filtering at sub step 1.
• This the final set ⁇ w, ⁇ can be presented as
• the algorithm determines the final minimum values of QT and RR interval and the corresponding time instants.
• the algorithm sorts the smoothed data sets (10.8) and determines Mmm ⁇ (tmm,Tmm ) corresponding to the minimum value of T, . This can be written as
• each data set ⁇ u, ⁇ is split into two subsets ⁇ u' ⁇ and ⁇ u + ' ⁇ corresponding to the descending (t, ⁇ t, m ) and ascending (t, > t, m ) branch, respectively.
• the algorithm adds to the curves a set of points representing a closing line, which connects the end point of the lower (descending) branch with the initial point on the of the upper (ascending) branch and, thus, generates a closed QT/RR hysteresis loop.
• a measure of the domain bounded by the QT/RR hysteresis loop (box 8 in Figure 11).
• a measure of the domain inside the QT/RR hysteresis loop is computed by numerically evaluating the following integral (see definition above):
• ⁇ . is the domain on the (7 RR ,7 Q ⁇ )-plane with the boundary formed by the closed hysteresis loop
• P(7 RR ,7 QT ) is a nonnegative (weight) function.
• P(7 RR ,7 QT ) 1 so that S coincides with the area of domain ⁇
• EXAMPLE 12 A method of a sequential moving average 1.
• the sub step (similar to 10.1) consists of raw data averaging (filtering) according to formula (10.4). This is performed for a preliminary set of values of the averaging window width, p. 2.
• the sub step includes subsequent final smoothing of the preliminary smoothed data represented by the set ⁇ u ⁇ found at the previous step: as follows.
• the window width m t is varied numerically to achieve optimum smoothness and accuracy of the fit.
• the optimally averaged data points form smooth curves on the corresponding planes ( Figure 12,14).
• Figure 15 illustrates major steps in the data processing procedure involving our nonlinear transformations method.
• the first three similar stages are the preliminary stage, the secondary, nonlinear-transformation stage, and the computational stage. A more detailed data flow chart for these stages is shown in Figure 16.
• the preliminary stage is a combination of traditional data processing methods and includes: smoothing (averaging) the data sets (1), determination of a region near the minimum (2), and fitting a quadratic parabola to the data in this region (3), checking consistency of the result (4), renormalizing and centering the data at the minimum (5), cutting off the data segments outside the exercise region and separating the ascending and descending branches (6), and finally filtering off a data segment in near the minimum (7).
• Box 1 in Figure 16 indicates the moving averaging and itself consists of two steps.
• the subscript m will be omitted below if m is fixed and no ambiguity can arise.
• the next step in our algorithm is the initial determination of a time interval on which the parabolic fit will be performed, (the parabolic fit interval). This step is represented in Figure 16 by Box 2.
• this data subset can be redefined at a later stage if a certain condition is not satisfied. In the current realization of our algorithm this region defined differently for ⁇ t b T ⁇ and ⁇ t,,T ®T ⁇ data sets. For the data set
• ⁇ ti,r * ⁇ the initial parabolic fit segment is defined as the data segment ⁇ t TTM ⁇ with all sequential values of i between and the integer parameters n m ⁇ n and Am are defined as follows.
• the number « m j n determines the time instant t n among the original set of time instants which is the closest to the minimum on the averaged data set ⁇ tj>, ⁇ rj> ⁇ .
• t is the nearest to the average time instant ⁇ t M > which corresponds to the minimum value of the average RR-interval ⁇ T ⁇ R >, that is, the time instant with the subscript value M defined by the condition
• the link between An and m arises from the requirement that the algorithm is stable and consistent.
• the consistency is the requirement that the positions of the minimum of the curve obtained by moving averaging and by quadratic fitting were approximately the same.
• the initial parabolic fit segment is defined as the data subset that consists of all consecutive points belonging to the lower portion of the non-averaged ⁇ r, QT ⁇ data set.
• i ⁇ as the first (minimum) number such that
• R is a parameter, 0 ⁇ R ⁇ 1, that determines the portion of the data to be fitted with the quadratic parabola.
• the subscript • is the first (smallest) value of / such that condition (12.4) is satisfied.
• / is the last (greatest) value of / ' such that condition (12.4) is satisfied.
• This method can also be used for determining an initial data segment for the quadratic polynomial fitting of the RR-data set.
• box 3 in Figure 12.2 we fit the data in this region (for each data set) by a parabola so that the data are approximately represented by the equation
• the parabolic fit defines two important parameters of the data processing procedure, the position (t m i n ⁇ m i n ) of the minimum on the (t,7)-plane as follows
• the final step of the preliminary data processing is the conditional sorting (Box 7).
• the conditional sorting removes all consecutive points such that at least one of them falls below the minimum of the parabola.
• the preliminary data processing results in two data sets corresponding to the descending and ascending load stages.
• ⁇ (w) grows monotonously when u ⁇ 1 and decreases monotonously when u ⁇ 0.
• the subscript y represents a set of discrete or continuous parameters and indicates a particular choice of such a function.
• the functions g * (y) and f + (u) are monotonously increasing, while the functions g ⁇ (y) and ⁇ ⁇ (w) are monotonously decreasing.
• ⁇ t t , y ⁇ represent the data for the descending segment of the data set, i.e. t i ⁇ t a ⁇ B
• ⁇ t t , y ⁇ represent the data for the ascending segment of the data set i.e. for t t > t min .
• the average slope of the original data set is decreasing as tj approaches t m j n and eventually vanishing at the minimum.
• I ⁇ and J * are the number of data points on the descending and ascending branches, respectively.
• the (formerly) descending branch can be treated in exactly the same way as the ascending one if simultaneously with the time inversion given by the first line in Eq. (12.19) we perform an additional transformation of the descending branch ordinates as follows
• a family of functions ⁇ ( ⁇ , ⁇ , ⁇ ) is shown in Figure 19 for fifteen values of parameter ⁇ .
• the parameter ⁇ is completely scaled out by plotting the function on the plane ( ⁇ / ⁇ , ⁇ / ⁇ ).
• ⁇ M(K,a$) ⁇ [ k - K ⁇ a, , T k )] 2 (12.24) k ⁇ K,
• T s T m Y ⁇ + K ⁇ a ⁇ , ⁇ m ; ⁇ a mn , > mm ,t s -t m ⁇ n )) (12.28)
• a similar dense representation of the descending branch can be calculated in exactly the same way.
• the resulting bird-like curves are illustrated in panels A and C of Figure 20.
• the actual absolute and relative errors are indicated in the captions.
• the right hand side panels B and D represent hysteresis curves in two different representations and each resulting from the curves shown in Panels A and C.
• the following computations of the hysteresis loop and its measure given by Eq. (10.17) is then performed as described in Example 11.
• a separate hysteresis of the duration of RR-interval versus exercise work load which gradually varies, there-and-back, during the ascending and descending exercise stages.
• the RR-hysteresis can be displayed as loops on different planes based on just a single RR data set ⁇ ,7 ⁇ j analysis.
• the RR loop can also be introduced on the ( ⁇ ( ⁇ ) ,7 ⁇ ) or ( ⁇ ' , ( ⁇ ) ⁇ ) planes.
• W(t M ' ) is a work load that varies versus exercise stages, i.e. time and

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