Changing views of time series waveforms

Abstract

The ventricular electrical depolarization may be represented with a vector heart diagram (QRS) ring present in the 3D space. By knowing that the QRS ring is typically a closed trajectory on a plane (2D), a single-channel QRS can be changed (e.g., by rotation, projection, etc.) to different viewing angles along the plane to provide a viewpoint that is more favorable for morphological interpretation. Any single-phase or dual-phase single-channel QRS (time series) waveform can be decomposed into the form x (alpha, t) = sin (alpha t) u (t), t spanning [0, 2pi], where u (t) is an invariant intrinsic component, typically upright and single-phase, and sin (alpha t) is a variable component of the waveform. In this way, x (alpha, t) may be changed by replacing one parameter of the original variable component sin (alpha t) with a second parameter (e.g., upright single phase sin (0.5 t)) associated with the target view of the waveform. Meanwhile, the inherent component remains unchanged in the changing process.

Description

Cross - reference

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 429,667, filed on December 3, 2022, which is hereby incorporated by reference in its entirety for all purposes. Technical Field

[0002] The present disclosure relates to changing views of time - series waveforms (e.g., by rotation, projection, and / or other techniques). Background Art

[0003] Single - channel electrocardiogram (ECG) devices are widely used in patches, watches, sports equipment, etc. For rhythm interpretation such as tachycardia or atrial fibrillation, single - channel ECG can provide consistent rhythm information. However, for the morphological interpretation of QRS waveforms, such as intraventricular conduction block or ST abnormalities, single - channel ECG can only provide an arbitrary shape, which depends on the position of its lead vector relative to the subject's QRS electrical axis vector. Summary of the Invention

[0004] The following is a non - exhaustive list of some aspects of the present technology. These and other aspects will be described in the following disclosure.

[0005] Ventricular electrical depolarization can be represented by its vectorcardiogram QRS loop existing in 3D space. By recognizing that the QRS loop is usually a closed trajectory on a plane (2D), a single - channel QRS can be changed (e.g., by rotation, projection, etc.) into different perspectives along this plane to provide viewpoints that are more conducive to morphological interpretation.

[0006] Any single - phase or biphasic single - channel QRS (time - series) waveform can be decomposed into the form x(α,t)=sin(αt)u(t), where t spans [0,2π], where u(t) is an invariant intrinsic component, usually upright and single - phase, and where sin(αt) is the variable component of the waveform. Thus, x(α,t) can be changed by replacing the parameter (e.g., α) of the original variable component sin(αt) with a second parameter (e.g., upright single - phase sin(0.5t)) associated with the target view of the waveform. Meanwhile, the intrinsic component remains unchanged.

[0007] Through this decomposition, for the same QRS loop, the projection of x(1.0,t) shows a completely biphasic (RS pattern) "QRS". The projection of x(0.75,t) shows a biphasic "QRS" with an R wave and a small S wave (Rs pattern). The projection of x(0.5,t) shows a completely single - phase "QRS" (R pattern).

[0008] By recognizing that any single - phase or biphasic QRS can be decomposed into an intrinsic component and a variable component, a single - channel ECG can be obtained and projections can be created along the planar QRS loop, which is more conducive to morphological interpretation.

[0009] Some aspects of the present technology include a method for changing a first view of a time - series waveform to a second view. The method includes separating the first view of the time - series waveform into an invariant intrinsic component and a variable parameterized component. The method includes replacing a first parameter associated with the first view of the variable parameterized component with a second parameter associated with the second view. The method includes changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter.

[0010] Some aspects of the present technology include a non - transitory computer - readable medium having instructions thereon. When executed by a computer, the instructions cause the computer to perform operations. The operations include separating a first view of a time - series waveform into an invariant intrinsic component and a variable parameterized component. The operations include replacing a first parameter associated with the first view of the variable parameterized component with a second parameter associated with a second view of the time - series waveform. The operations change the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter.

[0011] Some aspects of the present technology include a system for changing a first view of a time - series waveform to a second view. The system includes one or more processors and / or other components. The one or more processors are configured to separate a first view of the time - series waveform into an invariant intrinsic component and a variable parameterized component. The one or more processors are configured to replace a first parameter associated with the first view of the variable parameterized component with a second parameter associated with the second view. The one or more processors are configured to change the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter.

[0012] Note that while this disclosure focuses on changing the view of cardiac time series waveforms (e.g., by rotation, projection, and / or other techniques), the principles described herein can be applied to changing the view of other time series waveforms, including but not limited to time series waveforms associated with a cardioids microphone (e.g., to improve microphone pattern detection); point source (finite source) sensors for radiating loop antennas; single-source Hall effect sensors (magnetometers) for determining remote magnetic source field lines and / or determining the position and orientation of a resonant (contactless) charging device to improve charging coil alignment (dynamic electric vehicle charging (DEVC)); cameras (quality) sensors for crankshafts, camshafts, wind turbines, and / or any other object rotating in three-dimensional (3D) space; geolocation sensing of a personal smartphone traveling in a two-dimensional (2D) plane (e.g., the ground) from a point source (e.g., a Wi-Fi tower); orbital mechanics of a remote planetary system from a limited field of view; photoacoustic spectroscopy; and / or other applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The above and other aspects of the technology will be better understood when the present application is read in conjunction with the following drawings, in which like reference numerals represent like or identical elements:

[0014] Figure 1 Shows the QRS complex of an electrocardiogram (ECG) in three-dimensional (3D) space, and two different one-dimensional (1D) views (lead I and the cardiocentric axis) of this 3D waveform.

[0015] Figure 2 Illustrates examples of possible QRS ECG waveform patterns.

[0016] Figure 2 A shows an example of an ECG QRS complex with an R pattern: a single phase with an upward deflection.

[0017] Figure 2 B shows an example of an ECG QRS complex with an Rs pattern: a biphasic waveform with an upward deflection followed by a relatively small downward deflection.

[0018] Figure 2 C shows an example of an ECG QRS complex with an RS pattern: a biphasic waveform with an upward deflection followed by a downward deflection.

[0019] Figure 2 D shows an example of an ECG QRS complex with an rS pattern: a biphasic waveform with a relatively small upward deflection followed by a downward deflection.

[0020] Figure 2 E shows an example of an ECG QRS complex with a Q pattern: a single phase with a downward deflection.

[0021] Figure 2 F shows an example of an ECG QRS complex with a Qr pattern: a biphasic waveform starting with a downward deflection followed by a relatively small upward deflection.

[0022] Figure 2 G shows an example of an ECG QRS complex with a QR pattern: a biphasic waveform starting with a downward deflection followed by an upward deflection.

[0023] Figure 2 H shows an example of an ECG QRS complex with a qR pattern: a biphasic waveform starting with a relatively small downward deflection followed by an upward deflection.

[0024] Figure 3 A schematic diagram of a system configured to change a first view of a time - series waveform to a second view is provided.

[0025] Figure 4 Aspects of various waveforms are shown.

[0026] Figure 4 A shows an exemplary time - series waveform x(α0, t)=sn(α0t)u(t).

[0027] Figure 4 B shows the intrinsic component (u(t)) of x(α0, t).

[0028] Figure 4 C shows the parametric component (sin(α0t)) of x(α0,t).

[0029] Figure 4 D shows the product of the sine wave sin(α1t) and the same intrinsic component u(t) as in x(α0, t).

[0030] Figure 4 E shows the intrinsic component u(t) used in x(α0, t), which is the same as the intrinsic component u(t) in x(α0, t).

[0031] Figure 4 F shows the sine wave sin(α1t) with a frequency of α1.

[0032] Figure 5 Examples of the original waveform (α = 1.0) and the projected waveform (α = 0.5) are shown, and the two waveforms have the same intrinsic component u(t).

[0033] Figure 6Displays \(x(\alpha_0,t)=\sin(\alpha_0t)(1 - \cos t)\) for various frequencies \(\alpha_0\in[0.5,1.0]\) (which can be more generally written as \(x(\alpha,t)=A\sin(\alpha t)(1 - \cos\beta t)\)).

[0034] Figure 7A Displays \(\sin(0.8t)\) over \(t\in[0,2\pi]\) with 50 sampling times, where zero values within 0.1 are circled.

[0035] Figure 7B Displays the (e.g., original) time - series waveform The first view of the modified waveform (\(\alpha_1 = 0.5\)), where Figure 7A The corresponding part in

[0036] Figure 8 Displays the effect of the error in estimating the frequency in the first view of the projection.

[0037] Figure 8 A shows the transition from the original (first - view) waveform \(\alpha_0 = 0.8\) to the modified (e.g., projected) waveform (from the first view to the second view), but the projection is carried out at an incorrect assumed frequency is performed.

[0038] Figure 8 B shows the projected waveform of the original waveform \(\alpha_0 = 0.8\), but the projection is carried out at an incorrect assumed frequency is performed.

[0039] Figure 8 C shows the projected waveform of the original waveform \(\alpha_0 = 0.8\), but the projection is carried out at an incorrect assumed frequency is performed.

[0040] Figure 8 D shows the projected waveform of the original waveform \(\alpha_0 = 0.8\), but the projection is carried out at an incorrect assumed frequency is performed.

[0041] Figure 9 Displays Figure 8 The value of the continuity measure for searching \(\alpha_0\in(0.808+[-0.05,0.05])\) in the example shown in D m )

[0042] Figure 10 Displays waveforms with various patterns.

[0043] Figure 10 A shows the waveforms of the set of patterns \(\{R,Rs,RS\}\).

[0044] Figure 10B shows the waveforms of the {Q, Qr, QR} mode set.

[0045] Figure 10 C shows the waveforms of the {qR} mode set.

[0046] Figure 10 D shows the waveforms of the {rS} mode set.

[0047] Figure 11 Shows the change of the first view of the time series waveform to the second view.

[0048] Figure 11 A shows an example of the original (first view) ECG QRS complex time series waveform of the Rs mode.

[0049] Figure 11 B shows according to Figure 11 the corresponding sine wave with a sine frequency calculated from the original ECG QRS waveform shown in A.

[0050] Figure 11 C shows the projection of the ECG QRS complex in Figure 11 A as an R mode waveform.

[0051] Figure 12 Shows the measurement result of the pre-ejection period (PEP).

[0052] Figure 12 A shows the measurement result of the pre-ejection period (PEP) of ECG lead I.

[0053] Figure 12 B shows the PEP measurement result of ECG lead II.

[0054] Figure 12 C shows the PEO measurement result of ECG lead III.

[0055] Figure 12 D shows the same PEP measurement result as Figure 12 that shown in A for ECG lead I, with the QRS projection as a single-phase waveform.

[0056] Figure 12 E shows the same PEP measurement result as Figure 12 that shown in B for the ECG lead II, with the QRS projection as a single-phase waveform.

[0057] Figure 12 F shows the same PEP measurement result as Figure 12 that shown in C for the ECG lead III, with the QRS projection as a single-phase waveform.

[0058] Figure 13Shows another example of the waveform and its projection to reveal the presence of LBBB.

[0059] Figure 13 A shows the QRS of an ECG with left bundle branch block (LBBB).

[0060] Figure 13 B shows the same ECG as Figure 13 shown in A, with the QRS projected as a single-phase waveform.

[0061] Figure 14 Shows the QRS complex projected onto successive views of ±30°.

[0062] Figure 15 Illustrates the measurement results of the T to QRS amplitude ratio and the related projection.

[0063] Figure 15 A shows the conventional measurement results of the T to QRS amplitude ratio for ECG leads V2, V3, and V4.

[0064] Figure 15 B shows a single-lead ECG ( Figure 15 lead V2 of the same ECG as shown in A), with the QRS projected as a single-phase waveform and the T wave projected as a single-phase waveform.

[0065] Figure 15 C shows a single-lead ECG ( Figure 15 lead V2 of the same ECG as shown in A), with the QRS projected as a biphasic waveform and the T wave projected as a single-phase waveform.

[0066] Figure 16 Illustrates the difference between the conventional measurement of the QRS-T angle using an ECG in three-dimensional space and the determination of the QRS-T angle using a single-lead ECG view of the same ECG.

[0067] Figure 16 A shows the conventional measurement of the QRS-T angle using an ECG in three-dimensional space.

[0068] Figure 16 B shows the determination of the QRS-T angle using a single-lead ECG view of the same ECG as Figure 16 shown in A.

[0069] Figure 17 Is a diagram showing an exemplary computing device according to an embodiment of the present system.

[0070] Figure 18 Is a flowchart showing a method of changing a first view of a time series waveform to a second view.

[0071] Although the present invention may have various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will be described in detail herein. The drawings may not be drawn to scale. However, it should be understood that the drawings and their detailed description are not intended to limit the invention to the particular form disclosed, but on the contrary, are intended to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims. Detailed Description

[0072] To mitigate the problems described herein, the inventors had to invent solutions and, in some cases equally importantly, recognize problems that had been overlooked (or not yet foreseen) by others in the field of ECG time series waveforms. The inventors wish to emphasize that it is very difficult to identify those problems that are just emerging and that, if industry trends continue as the inventors expect, these problems will become more apparent in the future. Additionally, since many problems are solved, it should be understood that some embodiments are directed to specific problems and not all embodiments solve every problem of the traditional systems described herein or provide every benefit described herein. That being said, improvements in various permutations for solving these problems are described below.

[0073] A time series waveform provides a one-dimensional (1D) view of a trajectory. When a trajectory spans multiple dimensions of physical space or state space, multiple time series waveforms observed from various viewpoints of the trajectory can improve the observation of the trajectory. For example, the electrical activity of the heart can be described as a trajectory in three-dimensional (3D) space. To observe this 3D trajectory, a traditional 12-lead electrocardiogram (ECG) displays 12 separate 1D viewpoints of the trajectory in the form of 12 time series waveforms obtained from multiple electrodes arranged on the body surface. The most prominent feature of each heartbeat in an ECG is the QRS complex waveform (QRS). The QRS represents the rapid electrical depolarization of the ventricles, which causes myocardial contraction and thus provides the pumping action of the heart. Figure 1 An example of the trajectory 100 of an ECG QRS relative to the human torso 102 is shown, as represented by the loop 104 in the 3D space 106. Figure 1 Two different one-dimensional (1D) views (lead I and electrical axis) of this 3D waveform are also shown, as well as the right arm (RA) and left arm (LA) leads of the ECG.

[0074] The QRS waveform of an ECG typically appears as a deflection away from a relatively static baseline. The waveform can be a single deflection (monophasic), two deflections (biphasic), or multiple deflections (polyphasic). The waveform can start with an upward deflection or a downward deflection. For example, in the QRS of an ECG, the waveform can be described as belonging to various patterns. Figure 2 An example of possible QRS ECG waveform patterns is shown. Figure 2A shows an example of an ECG QRS complex with an R pattern: a single phase with an upward deflection 202. Figure 2 B shows an example of an ECG QRS complex with an Rs pattern: a biphasic waveform with an upward deflection 204 followed by a relatively smaller downward deflection 206. Figure 2 C shows an example of an ECG QRS complex with an RS pattern: a biphasic waveform with an upward deflection 208 followed by a downward deflection 210. Figure 2 D shows an example of an ECG QRS complex with an rS pattern: a biphasic waveform with a relatively smaller upward deflection 212 followed by a downward deflection 214. Figure 2 E shows an example of an ECG QRS complex with a Q pattern: a single - phase waveform with a downward deflection 216. Figure 2 F shows an example of an ECG QRS complex with a Qr pattern: a biphasic waveform starting with a downward deflection 218 followed by a relatively smaller upward deflection 220. Figure 2 G shows an example of an ECG QRS complex with a QR pattern: a biphasic waveform starting with a downward deflection 222 followed by an upward deflection 224. Figure 2 H shows an example of an ECG QRS complex with a qR pattern: a biphasic waveform starting with a relatively smaller downward deflection 226 followed by an upward deflection 228.

[0075] Figure 2 A - Figure 2 The waveforms shown in the examples of H are Figure 1 each different 1D projection of the same 3D trajectory of the QRS waveform of the ECG shown. These individual waveforms describe the same 3D trajectory from eight different viewpoints. If only one waveform or one viewpoint, such as an ECG provided by a smartwatch or other similar sensor, is given, then the Figure 1 observation of the 3D trajectory shown will be severely limited.

[0076] In multi - channel ECG interpretation, when multiple viewpoints of the 3D trajectory of a given QRS are available, certain heart diseases or conditions can be better observed. However, if only a single - channel viewpoint or waveform is provided, the observation of the 3D trajectory will be limited. Limited observation of the QRS in 3D may lead to missing the detection of ST elevation associated with myocardial infarction, deep Q waves associated with myocardial infarction, the QRS bimodal shape associated with bundle - branch block, etc. Therefore, it is necessary to project the time - series waveform from one viewpoint to other viewpoints to improve the observation of the multi - dimensional trajectory.

[0077] Advantageously, the present system and method change (e.g., project, rotate, and / or otherwise change) a first view of a time series waveform into a different view of the time series waveform by changing parametric components of the waveform. The change is based on the recognition that a time series waveform can be decomposed into invariant intrinsic components and variable parametric components with given parameters. The change from one view to another is achieved by replacing an original value of a given parameter of the parametric component with a different value associated with the second view while keeping the intrinsic components unchanged. The present system and method can acquire a single-channel ECG and create a projection along a planar QRS loop, which is more conducive to morphological interpretation.

[0078] As described in more detail below, the present system and method are configured to estimate or otherwise determine parameter values of parametric components from a first view of a time series waveform (e.g., by measuring the period of the first view of the waveform by finding the interval between the first zero crossings of the waveform). The present system and method are configured to reduce potential singularities (e.g., by identifying segments of near singularities and setting these segments of near singularities aside for later calculation using alternative computational methods, such as interpolating segments of the projected waveform that are not near singularities, function approximation near singularities, etc.). The present system and method are configured to reduce inaccurate parameter estimation (e.g., by perturbation, including testing waveforms with trial parameters in the neighborhood of the estimated parameters to find the parameter with the least amount of discontinuity in the resulting projected waveform, and measuring the discontinuity by finding the maximum third derivative throughout the projected waveform, measuring only the slope near singularities of the projected waveform, etc.). The present system and method are configured to expand an optimized changed waveform into other waveforms by converting the waveform into a waveform in an optimized mode, and after changing the waveform into the second view, reversing part of the conversion if needed to obtain the final second view of the waveform.

[0079] The operations described herein can be performed by a software program, a computer, an electrocardiograph, a wearable device, a circuit, a data acquisition module, a waveform converter, combinations thereof, and / or other components. The operations can be performed by a system that includes a signal amplifier for acquiring an original ECG from a subject, a data acquisition module for converting the original ECG into an original digital ECG, a waveform converter for projecting the ECG waveform, and / or other components. The operations can be performed by embedded software for traditional ECG devices (e.g., Holter ECG and 12-lead ECG) acting as a waveform converter for projecting the ECG waveform to provide more viewpoints of cardiac electrical activity and / or other components.

[0080] The systems and methods described herein can be configured to improve the automated or manual interpretation of ECG waveforms for the following observations and any associated heart diseases or disorders, including but not limited to: the arrival time of peak cardiac depolarization; the monophasic morphology of a biphasic QRS waveform; ST elevation associated with myocardial infarction; deep Q waves associated with myocardial infarction; QRS onset in QT interval measurements associated with arrhythmia risk; QRS onset and end in QRS interval measurements associated with bundle branch block or cardiac remodeling; abnormal QRS shape associated with bundle branch block, Wolff-Parkinson-White syndrome, abnormal serum electrolyte concentration, hypothermia, and / or supraventricular tachycardia; and / or other cardiovascular diseases and / or disorders.

[0081] For example, Figure 3 A schematic diagram of a system 300 configured to change a first view of a time series waveform to a second view is provided. Figure 3 An embodiment of the system 300 is shown, which includes an ECG system 302, one or more processors 304, one or more computing devices 306, external resources 308, a network 350, and / or other components. Each of these components will be described in turn below.

[0082] The ECG system 302 is configured to generate one or more output signals that convey ECG information of a subject. The ECG system 302 can include an electrocardiograph, a wearable device, circuitry, a data acquisition module, a computer, and / or other components. The ECG system 302 can include a signal amplifier for obtaining the raw ECG from the subject, a data acquisition module for converting the raw ECG into a raw digital ECG, and / or other components. The operation of the ECG system 302 can be performed by embedded software for traditional ECG devices. The ECG system 302 can include a Holter ECG, a 12-lead ECG, and / or other ECGs. The ECG system 302 can be deployed in, for example, patches, wristbands, watches, clothing, sports equipment, and / or other devices. For example, the ECG system 302 can be configured to be worn at or near the heart of the subject. In some embodiments, the ECG system 302 can be and / or include a necklace, a chest strap, a shirt, a vest, and / or any other wearable device configured such that the system 300 can operate as described herein.

[0083] One or more processors 304 are configured to provide information processing capabilities in system 300. The one or more processors 304 may include software programs or be controlled by software programs. For example, the one or more processors 304 may be included in a computer such as computing device 306. The one or more processors 304 may include a waveform converter for projecting an ECG (e.g., QRS) waveform to provide additional viewpoints of cardiac electrical activity; and / or other components.

[0084] The one or more processors 304 may include one or more of a digital processor, an analog processor, digital circuitry designed to process information, analog circuitry designed to process information, a state machine, and / or other components for electronically processing information. In some embodiments, processor 304 may be included in and / or otherwise operatively coupled with ECG system 302, computing device 306, and / or other components of system 300. Although Figure 3 the one or more processors 304 are shown as a single entity herein, this is for illustrative purposes only. In some implementations, processor 304 may include multiple processing units. These processing units may be physically located within the same device (e.g., ECG system 302, computing device 306, etc.), or processor 304 may represent the processing functions of multiple devices operating in coordination (e.g., a processor within ECG system 302 and a second processor within computing device 306). Processor 304 may be configured to execute one or more computer program components. Processor 304 may be configured to execute computer program components by: software; hardware; firmware; some combination of software, hardware, and / or firmware; and / or other components for configuring the processing capabilities on processor 304.

[0085] Processor 304 is configured to change a first view of a time series waveform to a second view. The change may include projection, rotation, and / or other operations. The first view of the time series waveform may be generated based on a single-channel electrocardiogram (ECG) signal from ECG system 302 and / or other sources. In some embodiments, the time series waveform includes a single-phase or biphasic single-channel QRS waveform associated with the ECG. In some embodiments, the time series waveform includes a projection of a QRS loop. The second view of the time series waveform may be a projection along a planar QRS loop, which is more conducive to morphological interpretation compared to the first view. Processor 304 is configured to change the first view to the second view based on invariant intrinsic components and variable parameterized components having a second parameter. In some embodiments, the separation, replacement, change, and / or other operations described herein are performed to determine the center of the QRS complex, determine the width of the QRS complex, and / or determine ST elevation / depression and / or other cardiovascular diseases and / or disorders.

[0086] The processor 304 is configured to separate a first view of a time series waveform into invariant intrinsic components and variable parametric components. For example, to allow different views of a single time series waveform, a time series waveform (x) over a time span (t) spanning 2π cycles can be separated (or decomposed) into two components: an invariant intrinsic component u(t), and a parametric component v(α,t) of a parameter that, if varied, can provide different viewpoints of the waveform. The general form of this time series waveform can be written as: x(α,t) = v(α,t)u(t).

[0087] In some embodiments, the invariant intrinsic component is upright and single - phase. In some embodiments, the parametric component includes a sine - like function, and the first and second parameters include different frequencies of the sine - like function. The sine - like function can be a sine function or a cosine function. For example, one way to represent the parametric component is with a sine - like function (such as a sine or cosine function), with the frequency of the sine - like function as the parameter α. In some embodiments, the parametric component includes a Taylor series expansion, and the first and second parameters (e.g., different αs) include different Taylor series.

[0088] One way to parameterize using a sine - like function is to use the sine function as the sine - like function: v(α,t)=sin(αt), with the time t spanning from 0 to 2π. Using the sine function, the waveform can be written as: x(α,t)=sin(αt)u(t), t ∈ [0,2π].

[0089] Figure 4 Aspects of various waveforms are shown. Figure 4 A shows an exemplary QRS waveform x(α0,t). Assuming the waveform is decomposable, u(t) (as shown in Figure 4 B) and sin(α0t), with frequency α0 (as shown in Figure 4 C) can be found such that for t ∈ [0,2π], x(α0,t)=sin(α0t)u(t), where u(t) represents the intrinsic component of this QRS that remains invariant throughout the projection, and sin(α0t) represents the parametric component of this QRS (time series waveform).

[0090] In Figure 4 the example of A, α0 = 0.78 and both x(α0,t) and sin(α0t) are in a biphasic mode. On the other hand, if the projected (e.g., varied) waveform is upright and single - phase, the desired sine - like can be chosen as sin(0.5t) (as shown in Figure 4as shown in F), which is upright and single-phase within the span t ∈ [0, 2π]. If the parametric component of the first view (e.g., the original) waveform sin(α0t) is replaced with sin(α1t) where α1 = 0.5, then the projected (e.g., altered) waveform sin(α1t)u(t) will continue to retain the intrinsic component u(t)( Figure 4 E), while providing an upright and single-phase projected waveform( Figure 4 D).

[0091] Another way to parameterize using the sine function is to use the cosine function as sine-like: v(α, t) = cos(αt), with the time span between -π and π. Using the cosine function, the waveform can be written as: x(α, t) = cos(αt)u(t), t ∈ [-π, π].

[0092] By separating the time series waveform into an invariant intrinsic component and a parametric component, the first view of the waveform can be changed to another (e.g., second) view of the waveform by replacing its parametric component. The processor 304 is configured to replace the first parameter associated with the first view of the variable parametric component with a second parameter associated with the second view. In some embodiments, replacing the first parameter with the second parameter includes parameterized component division. For example, for the first view of a time series waveform using the sine parametric form x(α0, t) = sin(α0t)u(t), the target second view of the waveform x(α1, t) = sin(α1t)u(t) can be estimated by scaling the ratio of two sine functions according to the following (where represents the estimated value of x):

[0093] Figure 5 Shows a projection example of dividing the original waveform sine with α0 = 1 by the projected waveform with α1 = 0.5, calculated as follows:

[0094] Figure 5 Shows x(1, t) and Sampled at 50 samples, t ∈ [0, 2π], without samples of t where |sin(t)| < 0.1, where sin(t) is close to zero. Depending on the sampling rate and the original (e.g., first view) frequency and the target (e.g., second view) frequency and / or other factors, changing the time series waveform by parametric component replacement may require further consideration, such as: (1) Waveform parameter estimation - The parametric components of the original waveform (e.g., the first view of a time series waveform) may have unknown parameters. Before replacing the parametric components, it may be necessary to estimate the parameter α0 of the parametric components. (2) Reducing singularities - Replacing the parameter values of the parametric components may cause singularities to appear in the sections where the parametric components approach zero. Such replacement may require reducing singularities. (3) Reducing inaccurate parameter estimation - Inaccurate estimation of the parameters of the original (first view) time series waveform may lead to unpredictable discontinuities near singularities. It may be necessary to reduce inaccurate parameter estimation to find more accurate parameters. (4) Extending the optimized projection to all waveforms - Replacing the parameter values of the parametric components may be optimal for the original waveforms with certain patterns of projection, but not for others. Given the original (first view) waveforms of other patterns, it may be necessary to convert these original waveforms into one of the optimal patterns before replacing the parametric components.

[0095] Parameter determination

[0096] Given a certain original (e.g., first view) time series waveform x(α0,t) (where the parameter α0 is unknown), it is necessary to find a certain to estimate α0 ( denotes the estimated value of α0, where α0 is the "true" alpha (parameter) of the original waveform and can never be truly accurately found, only estimated to a certain numerical accuracy, or estimated with sufficient accuracy to produce an error below a threshold (such as the threshold described below). Figure 6 shows the original waveform (e.g., the first view) in the sinusoidal parametric form x(α0,t) = sin(α0t)u(t) (which can be more generally considered as x(α,t) = A sin(αt)(1 - cosβt)), where the intrinsic component u(t) is the same but the parametric component sin(α0t) is different. Figure 6 shows that different values of α0 result in different periods of x(α0,t) over t ∈ [0, 2π]. The processor 304 is configured to estimate α0 using the period length of the original waveform and / or other information.

[0097] For example, in some embodiments, the processor 304 ( Figure 3) can be configured such that a first parameter of a variable parameterized component associated with a first (e.g., original) view of a time series waveform can be determined based on the first zero crossing of the time series waveform. In an example of sine function parameterization, the first view of the (e.g., original) waveform at the position of the first zero crossing after the start of the waveform is the midpoint of a full period (2π). Let δ be defined as the proportion of 2π at the first zero crossing of x(α0,t) after t = 0. If the original waveform spans t ∈ [0, 2π], then the first zero crossing occurs at t = δ(2π). The first zero crossing after the start of the sine wave also occurs at the position of Thus, the first zero crossing occurs at Or:

[0098] For example, for the Figure 6 sin(0.8t) curve, the first zero crossing after the start of the waveform occurs at t = 0.625(2π), so δ = 0.625. Using frequency estimation, where the estimate of the original (first view) α0 is 0.8.

[0099] Singularity reduction

[0100] When a parameterized component of the original (e.g., first view) time series waveform is at or near zero, dividing by that parameterized component may approach a numerical singularity. The processor 304 can be configured to reduce potential singularities or near-singularities caused by division by a parameterized component by identifying sections of a second view of the time series waveform that contain potential singularities or near-singularities, applying alternative calculations to change the first view to the second view at these potential singularities or near-singularities sections and / or other operations. For example, using sine parameterization, the processor 304 can be configured such that the following rules can be applied: · If a section is identified as a near-singularity, calculate and · If a section is not identified as a near-singularity, perform a projection using an alternative calculation.

[0101] The processor 304 can identify potential singularities or near-singularities based on a threshold of the frequency sine of the first view of the time series waveform and / or by other operations. For example, one method for the processor 304 to identify near-singularity sections in an original (e.g., first view) time series waveform section is to create a threshold (θ) such that, in an example of sine parameterization, if then that section is a near-singularity, otherwise it is not. Another method for identifying near-singularity sections in an original waveform section is to create a threshold (θ) such that, in an example of sine parameterization, if then the section is a near-singularity, otherwise it is not.

[0102] In some embodiments, the alternative calculation can be or include interpolating the identified segments using segments that are not close to zero determined by parametric component replacement in a second view of the time series waveform. For example, the processor 304 can be configured to interpolate these segments using the transformed waveform on segments that are not close to zero calculated by parametric component replacement. A variety of linear or non-linear methods can be employed to perform this interpolation. In an example of sine parameterization, cubic spline interpolation of the projected waveform segments at can be used to calculate, for example, the near-singularity segments at

[0103] To illustrate the interpolation method, assume that the first view of the waveform to be transformed includes x(α0,t), α0 = 0.8. Figure 7A The parametric component sin(0.8t) on t ∈ [0, 2π] is shown, sampled at 50 samples, where the near-singularity values are identified by |sin(α0t)| < θ, θ = 0.1 and are indicated by circles. Figure 7B Shows the original waveform, the projected waveform at α1 = 0.5, where Figure 7A the corresponding part in

[0104] is circled. For a projection with singularity reduction, the non-near-singularity points can first be determined by sine partitioning. Subsequently, for example, cubic spline interpolation of the points previously calculated by sine partitioning can be used to determine those near-singularity points (circled). Figure 3 In some embodiments, the processor 304 ( Figure 3 ) is configured such that when the parametric component with the second parameter is close to a singularity, function approximation is used to perform the alternative calculation. For example, various discontinuous smoothing schemes can be employed, including partition of unity, and analytical approximations by using small angle assumptions or by considering the limiting behavior of the parametric component, and / or other schemes.

[0105] Reducing Inaccurate Parameter Estimation

[0106] The time series waveform segments near singularities can be identified based on the (original) parametric component of the first view, which can be based on, for example, an estimate of its parameter . Inaccurate parameter estimation can shift the near-singularity segments, resulting in discontinuities. In an example of sine parameterization, a small inaccuracy in its frequency parameter when divided by can cause waveform discontinuities from the first view to the second view (projection). Inaccurate ε estimation (where ) can make it difficult to identify the t samples where sin((1 + ε)α0t) is close to zero to reduce discontinuities near the singularity.

[0107] Figure 8 Shows the influence of the first view estimated frequency error on the projection effect. Figure 8 A, Figure 8 B, Figure 8 C and Figure 8 D respectively show the time series waveform changes (e.g., projection) from the first view to the second view from x(0.8,t) to with inaccuracies of ε = 0, 0.001, 0.005, 0.01 added. The circled samples represent the samples where and interpolation processing is adopted. As the ε level increases, the projection waveform exhibits more obvious discontinuities near the singularities. Ideally, the waveforms before, during, and after the singularities should be continuous and have as similar first-order derivatives as possible.

[0108] In some embodiments, the processor 304 ( Figure 3 ) is configured to reduce inaccurate parameter determination through perturbation and / or other methods. Perturbation can include testing different parameter values to determine which parameter value provides the best changed time series waveform continuity (or minimum discontinuity). For example, perturbation can include, given the parameter estimation value of the first view of a given (e.g., original) waveform, finding the parameter that provides the best projection waveform continuity in the neighborhood of the parameter estimation value by: searching for various trial parameter values α in where ε is the neighborhood size; and at each trial α, determining the measured value of the discontinuity D m such that the trial α with the lowest discontinuity measurement value will become α0 for changing the first view to the second view (e.g., for projection).

[0109] In some embodiments, the processor 304 ( Figure 3 ) can be configured to determine the discontinuity by determining the slopes of the time series waveforms before, during, and after the singularity or near-singularity section. For example, for the Figure 8 time series waveform m1 of the change (e.g., projection) from the first view to the second view shown in D is the slope before the singularity, m2 is the slope during the singularity, and m2 is the slope after the singularity. The second-order derivative (e.g., acceleration) between the three slopes can be obtained at each of the following: m(α,k) = |(m3 - m2) - (m2 - m1)|, and the discontinuity measurement D m (α) for each trial α may be the maximum value m(α,k) in all near-singularity sections of the entire waveform.

[0110] Given the estimated frequency value The possibility that it may be close to α0 but not exactly the same can be found by testing values close to to obtain a better estimate to minimize m D of the frequency. For example, for the estimated value it is possible to search within the range of with a step size of 0.001 to find the minimum value of D m . In an example where the ideal α0 is 0.8 and the inaccuracy is ε = 0.01, the estimated values are

[0111] Figure 9 showing a search within the range of 0.808 ± 0.05 with a step size of 0.001, which finds the minimum value of D at 0.800 m . The figure also shows that D m has a unique minimum value within this search range.

[0112] In some embodiments, the processor 304( Figure 3 ) is configured such that the discontinuity can be determined by determining the maximum third derivative of the second view of the time series waveform at each trial parameter value. At each trial α, the maximum third derivative can be found from the change (e.g., projection) of the time series waveform from the first view to the second view. For example, given a discrete time waveform of length n, the magnitude of the third derivative can be written as: and the discontinuity measurement D m (α) for each trial α is the maximum magnitude of the third difference across the entire waveform: D m (α) = max{m(α,k), k = 4, 5, …, n}.

[0113] Extend the waveform of the optimized change (projection) from the first view to the second view to other waveforms

[0114] The processor 304( Figure 3 ) can be configured such that the above operations can be extended to other waveform patterns, and / or the time series waveform can be converted to other waveform patterns by flipping the time axis, flipping the waveform axis, changing the parameters, and / or introducing a shift to the parametric components of the first view of the time series waveform.

[0115] Waveform projection (e.g., a change from a first view to a second view) may be optimal only for certain patterns of the original (e.g., first view) waveform. For example, for an original waveform in the sinusoidal parametric form x(α0,t) = sin(α0t)u(t) where t ∈ [0,2π], only one singularity is expected at α0t = π after the waveform starts. If the first wave of the waveform is not dominant, or if its first zero crossing occurs at δ < 0.5, then more than one singularity will occur after the waveform starts. The sinusoidal segmentation with reduced singularities is optimized for the original waveform where the first zero crossing after the waveform starts occurs at or after the midpoint (δ ≥ 0.5), or where the first wave “dominates” the waveform. Additionally, if the parametric component is represented by a sine function, the first wave of the original waveform should be upright because for any non-zero α0 with t ≥ 0, the first wave of sin(α0t) is upright. Thus, waveform projection using sinusoidal segmentation as the projection method is optimized for the original waveform where the first wave is dominant and upright, belonging to waveforms of the {R, Rs, RS} patterns. Besides waveforms of the {R, Rs, RS} patterns, there are other waveforms that do not start with a dominant upright wave, such as the following set of patterns: · {Q, Qr, QR}, which starts with a dominant downward wave (e.g., Q wave); · {qR}, which has a dominant upright wave (e.g., R wave), but starts with a relatively small downward wave (e.g., Q wave); and · {rS}, which has a dominant downward wave, followed by an upward wave (e.g., S wave), but starts with a relatively small upright wave (e.g., R wave).

[0116] Through several examples, Figure 10 waveforms with various patterns are shown. Figure 10 A shows the waveform of the {R, Rs, RS} pattern set, Figure 10 B shows the waveform of the {Q, Qr, QR} pattern set, Figure 10 C shows the waveform of the {qR} pattern set, and Figure 10 D shows the waveform of the {rS} pattern set. The {Q, Qr, QR} pattern looks like the {R, Rs, RS} pattern mirrored in waveform amplitude. The qR pattern looks like the Rs pattern mirrored in time. And the rS pattern looks like the Rs pattern mirrored in both waveform amplitude and time.

[0117] One way to extend the change (e.g., projection) from the first view to the second view to other modal waveforms is to transform the original (first view) time series waveform (x) to create a transformed waveform (y) in an optimized mode. In the example of sinusoidal parameterization, the projection can be optimized for the original waveforms of the {R, Rs, RS} modes. For all waveform mode sets, the following two rules can be applied: · If δ ∈ [0, 0.5], flip the horizontal (time) axis and change α0 from to and · After any horizontal flip in the previous step, if the first wave of the waveform continues to be a downward wave, flip the vertical (waveform) axis.

[0118] By applying these two (and / or other) rules, the above waveform mode set can be transformed by the processor 304 ( Figure 3 ) by flipping the vertical (waveform) axis, flipping the horizontal (time) axis, flipping both axes, or not flipping either axis: If the original waveform is in the {R, Rs, RS} mode (as shown in Figure 10 A): δ ∈ [0.5, 1], so no horizontal axis flip is needed, and α0 remains 1 / (2δ); and without a horizontal axis flip, the first wave of the waveform remains upward, so no vertical axis flip is needed. If the original waveform is in the {Q, Qr, QR} mode (as shown in Figure 10 B): δ ∈ [0.5, 1], so no horizontal axis flip is needed, and α0 remains 1 / (2δ); and without a horizontal axis flip, the first wave of the waveform remains downward, so a vertical axis flip is needed. If the original waveform is in the {qR} mode (as shown in Figure 10 C): δ ∈ [0, 0.5), so a horizontal axis flip is needed, and α0 changes to 1 / (2(1 - δ)); and if a horizontal axis flip is performed, the first wave of the waveform becomes upward, so no vertical axis flip is needed. If the original waveform is in the {rS} mode (as shown in Figure 10 D): δ ∈ [0, 0.5), so a horizontal axis flip is needed, and α0 changes to 1 / (2(1 - δ)); and if a horizontal axis flip is performed, the first wave of the waveform becomes downward, so a vertical axis flip is needed.

[0119] One way for the processor 304 to transform the waveform into an optimized mode is to flip the vertical axis and / or the horizontal axis of the entire original waveform (x) so as to transform the original waveform into a waveform y in an optimized mode before projection.

[0120] Since a horizontal axis flip will reverse the time order of the waveform, the time order should be restored after projection. If the transformed waveform (y) has not been horizontally flipped, the original waveform The projection will be the same as the transformed waveform : If the transformed waveform (y) has been horizontally flipped, the projection of the original waveform will be the horizontal flip of the projection of the transformed waveform . Given a time span of t ∈ [0, 2π], the horizontal flip will be

[0121] Given the original waveform x and its zero-crossing rate (δ) on t ∈ [0, 2π], the vertical axis and / or the horizontal axis can be flipped as follows: · For the original waveform in the {R, Rs, RS} mode, do not flip ο α0 = 1 / (2δ) ο y0(α0, t) = x(α0, t) ο Project y0(α0, t) from the original frequency α0 to the target frequency α1 to find ο · For the original waveform in the {Q, Qr, QR} mode, flip the vertical (waveform) axis ο α0 = 1 / (2δ) ο y V (α0, t) = -x(α0, t) ο Project y V (α0, t) from the original frequency α0 to the target frequency α1 to find ο · For the original waveform in the {qR} mode, flip the horizontal (time) axis ο α0 = 1 / (2(1 - δ)) ο y H (α0, t) = x(α0, 2π - t) ο Project y H (α0, t) from the original frequency α0 to the target frequency α1 to find ο · For the original waveform in the {rS} mode, flip both the vertical axis and the horizontal axis ο α0 = 1 / (2(1 - δ)) ο y VH (α0, t) = -x(α0, 2π - t) ο Project y VH (α0, t) from the original frequency α0 to the target frequency α1 to find ο

[0122] Another way for the processor 304 to convert the waveform into the optimized mode can be to introduce a time shift (φ) to the parameterized component. In the example of sinusoidal parameterization, the time shift can be introduced in the form of y(α,t) = sin(α(t - φ))u(t).

[0123] Since this method uses a time shift instead of inverting the waveform time series for horizontal flipping, it is no longer necessary to restore the time series after projection. That is, regardless of whether the converted waveform (y) is horizontally flipped, the projection of the original waveform will be the same as the projection of the converted waveform :

[0124] Given the original waveform on t ∈ [0, 2π] and its zero crossing rate (δ), the method using the time shift can be performed as follows: · For the original waveform in the {R, Rs, RS} mode, without flipping ο α0 = 1 / (2δ) ο y0(α0,t) = x(α0,t) = sin(α0(t - 0))u(t) ο Project y0(α0,t) from the original frequency α0 to the target frequency α1 to find ο · For the original waveform in the {Q, Qr, QR} mode, flip the vertical axis ο α0 = 1 / (2δ) ο y V (α0,t) = -sin(αt)u(t) = sin(α0(t - π / α0))u(t) ο Project y V (α0,t) from the original frequency α0 to the target frequency α1 to find ο · For the original waveform in the {qR} mode, flip the horizontal axis ο α0 = 1 / (2(1 - δ)) ο y H (α0,t) = sin(α(2π - t))u(t) = sin(α(t - (π / α + 2π)))u(t) ο Project y H (α0,t) from the original frequency α0 to the target frequency α1 to find ο · For the original waveform in the {rS} mode, flip both the vertical and horizontal axes ο α0 = 1 / (2(1 - δ)) ο y H (α0, t) = -sin(α(2π - t))u(t) = sin(α(t - 2π))u(t) ο The y from the original frequency α0 to the target frequency α1 VH (α0, t) projection to find ο

[0125] Example 1 - Example of changing the first view of a waveform to the second view (waveform projection)

[0126] As an example, to change the first view of a time - series waveform to the second view (e.g., project the original waveform as the target or final waveform), the processor 304( Figure 3 ) can use the following methods in combination. A method representing parametric components can be applied, using a sine - like function as the parametric component as described above. A method of parameterizing using a sine function can be applied, using the sine function as the parametric component x(α0, t) = sin(α0t)u(t). The time of the first zero - crossing of the waveform can be determined as a proportion (δ) of the time - span of the waveform to be projected, and the method of estimating the parameter α0 described above can be applied, by using the first zero - crossing after the start of the waveform as the half - cycle interval:

[0127] If x(α0, t) is not in the {R, Rs, RS} mode, or if x(α0, t) does not start with a dominant upright wave, the method of extended projection described above can be applied by converting the waveform to the {R, Rs, RS} mode using a waveform conversion method that introduces a phase shift into the parametric component of the above - mentioned waveform.

[0128] A method of reducing inaccurate parameter estimation can be applied by searching a series of trial frequencies For each trial frequency α: The method of reducing singularities described above can be applied, by doing the following: Using a method of identifying near - singularity states to identify those points that are near singularities, including: if |sin(αt)|≥θ, the section is not considered a near - singularity; and using the method of replacing the parametric component by sine - splitting described above to determine the projected waveform: such that if |sin(αt)| < θ, the segment is considered a near singularity. The determination of this segment can be postponed. Subsequently, using the method described above, the near-singularity segment is calculated by substituting it with a cubic spline interpolation of the segments that are not considered near singularities. For example, the method of calculating the discontinuity measurement by finding the maximum third-order difference in the entire waveform can be used to generate a discontinuity metric for this trial α. The discontinuity measurement of this trial α can be compared with all existing discontinuity measurements of all other trial αs. The α with the lowest discontinuity measurement value can be a0, and the projected waveform can be the one associated with a0

[0129] Figure 11 An example of changing the first view of a time-series waveform to a second view is shown. Figure 11 A shows an example of the original (first view) ECG QRS complex time-series waveform in the Rs mode. Figure 11 B shows the corresponding sine wave, where Figure 11 the sine frequency is calculated from the original ECG QRS waveform shown in A. Figure 11 C shows the Figure 11 projection of the ECG QRS complex in A into an R-mode waveform. For example, for Figure 11 the QRS of the ECG time-series waveform in A, the original waveform is in the Rs mode. The purpose of changing the first view to the second view (e.g., projection) is to obtain the R mode (α1 = 0.5) of this QRS time-series waveform example. The span of this QRS waveform mapped on t ∈ [0, 2π] is over 59 samples (d0 = 58). The first zero crossing d1 after the waveform starting point (at t = 0) appears between the 33rd and 34th samples, as Figure 11 shown in B. The processor 304 can be configured to use δ = d1 / d0 to find d1 more precisely by interpolating the sub-sample zero crossing between the 33rd and 34th samples, which is d1 = 32.91 in this example. Therefore, for a certain frequency α close to : the processor 304 can be configured to determine when sin(αt) is not close to zero or if |sin(αt)| < 0.1, additionally use the determined sample pairs to perform interpolation; and search for the frequency value α ∈ [0.881 - 0.05, 0.881 + 0.05] that produces the minimum D m , i.e., α = 0.878. Figure 11 C shows that the first view of the ECG QRS waveform has been changed (e.g., projected) to a second view, including the R mode (α1 = 0.5).

[0130] Example 2 - Electrocardiogram Application

[0131] QRS Center

[0132] Viewed from the vectorcardiogram view of the ECG time series waveform, the center of the QRS complex may be located at the maximum point of ventricular depolarization. The center of the QRS complex can be used to determine the pulse transition time, pre-ejection period (PEP), or can be used to determine the left ventricular end-diastolic pressure (LVEDP) or other measurements indicating heart failure. The center of the QRS complex can also be used to determine the QT interval or QT dispersion, both of which can be used to evaluate the risk of fatal arrhythmias or determine plasma electrolyte imbalances, including metabolic disorders such as diabetes.

[0133] Figure 12 The measurement result of PEP is shown. Figure 12 Various measurement results of different ECG leads are shown. Figure 12 A, Figure 12 B and Figure 12 C respectively show the PEP measurement values p1, p2, and p3, which are measured from the QRS complex of ECG leads I, II, and III of the same ECG to the pulse origin. Among them, although the distance between the same QRS and the same pulse is measured, the variation of PEP is very large. As Figure 12 D, Figure 12 E and Figure 12 F respectively show that after projecting the QRS complexes of these ECG leads I, II, and III into single-phase waveforms, the variations of the three PEP measurement values p4, p5, and p6 are significantly smaller. Using the operations described above, the processor 304 ( Figure 3 ) can be configured to find the center of the QRS by projecting the QRS complex time series waveform of the ECG into a single-phase waveform (for example, changing the first view to the second view). For example, using the sine parameterization of (α,t) = sin(αt)u(t), t ∈ [0,2π], the processor 304 can be configured to project the original parameter (frequency) α0 into the parameter α1 = 0.5. To reduce the potential multiple peaks of the pulse bimodality or signal artifacts, the processor 304 can fit a Gaussian function with an approximate height and width to the projected waveform as the projected waveform. For example, the processor 304 can find the center of the QRS at the peak of the Gaussian function.

[0134] Width of QRS

[0135] The width of the QRS complex can be determined based on the width of ventricular depolarization according to the cardiocentric view of the ECG time series waveform. The assessment of wide QRS can indicate intraventricular conduction block, such as left bundle branch block (LBBB). The assessment of wide QRS can also indicate ventricular hypertrophy. The presence of LBBB is used in the conventional criteria for determining ST-elevation myocardial infarction (STEMI) in addition to being an indicator of heart disease.

[0136] Figure 13 Another waveform example and its projection are shown to reveal the presence of LBBB. Figure 13 A shows an exemplary QRS with a width of w1, which is not sufficient to indicate LBBB. However, when this QRS is projected onto its unipolar view (as Figure 13 shown in B), its width is w2, which is sufficient to indicate LBBB. Using the above operations, the processor 304 can determine the width of the QRS by projecting the QRS of the ECG (e.g., changing the first non-cardiocentric view) into a unipolar waveform (e.g., the second cardiocentric view of the time series waveform). For example, using the sinusoidal parameterization of x(α,t) = sin(αt)u(t), t ∈ [0,2π], a projection from the original parameter (frequency value) α0 to the parameter α1 = 0.5 can be performed. For example, the processor 304 can determine the cross-sectional width of the unipolar projection waveform at 50% of the total height of the projected QRS. This cross-sectional width can be used to indicate wide QRS. A similar method also applies to the assessment of the P-wave width of the ECG, and a wide P-wave can indicate atrial enlargement.

[0137] The shape of the QRS

[0138] The shape of the QRS complex can be determined based on the shape of ventricular depolarization according to the cardiocentric view of the ECG time series waveform. The assessment of double or multiple peaks of the unipolar QRS complex can indicate intraventricular conduction block, such as left bundle branch block (LBBB). The assessment of the QRS shape can also indicate Brugada syndrome or chronic obstructive pulmonary disease (COPD). The presence of LBBB is used in the conventional criteria for determining ST-elevation myocardial infarction (STEMI) in addition to being an indicator of heart disease. Figure 13 A shows an exemplary QRS complex with a single peak m1 that does not indicate LBBB. However, when this QRS complex is projected onto its unipolar view (as Figure 13When it is as shown in B, it is found that it has double-peak peaks m2 and m3 indicating LBBB. Using the above operations, the processor 304 can determine the width of the QRS by projecting the QRS of the ECG (for example, changing the first non-axis view) into a single-phase waveform (for example, the second axis view of the time-series waveform). For example, using the sinusoidal parameterization of x(α,t)=sin(αt)u(t), t∈[0,2π], the projection from the original parameter (frequency value) α0 to the parameter α1 = 0.5 can be performed. The processor 304 can determine the presence of double-peak or multi-peak peaks based on the projected waveform. A similar method can be applied to the flutter waves in the ECG to reveal the presence of atrial flutter.

[0139] ST elevation / depression

[0140] The indication of ST segment elevation or depression is located at the end of the QRS complex time-series waveform and is usually evaluated in millivolts. The evaluation of ST elevation / depression can indicate heart diseases and / or other conditions.

[0141] For multiple ECG leads, the conventional evaluation of ST elevation / depression is performed by finding ST elevation / depression above a certain voltage threshold in two or more consecutive ECG leads. Two traditional ECG leads can be defined as consecutive if they are adjacent leads and are separated by a certain angle in the plane spanned by the two leads (for example, 30° apart in the frontal plane). Two traditional ECG leads can also be defined as consecutive if they belong to the same adjacent tissue region (for example, leads I, aVL, V5, and V6, which all belong to the lateral wall of the left ventricle).

[0142] Figure 14Shows an exemplary QRS complex qrs0, which is projected onto qrs1 (a consecutive -30° view of qrs0), and onto qrs2 (a consecutive +30° view of qrs0), each having different ST values at the QRS offset (QrsOff) to provide an assessment of whether the ST elevation of two consecutive leads is above a voltage threshold. The processor 304 can be configured to facilitate approximate calculation of the ST elevation / depression of consecutive leads relative to any ECG lead. Then the presence of ST elevation / depression can be determined by evaluating a combination of the actual lead and the approximate consecutive leads, where the ST elevation / depression of two or more consecutive leads is above a certain voltage threshold. Additionally, ST elevation / depression, as an indicator of ischemia, infarction, or reinfarction, can alternatively be evaluated by its magnitude relative to the total QRS magnitude. Using the above operations, the processor 304 can evaluate ST elevation / depression by projecting the QRS time series waveform of the ECG onto a waveform adjacent to the ECG. For example, using the sinusoidal parameterization of x(α,t) = sin(αt)u(t), t ∈ [0,2π], a projection can be performed from the original parameter (frequency value) α0 to a parameter α1 that is +30° from α0 or -30° from α0. The ST of the projected waveform can be determined. If the ST elevation or depression exceeds a conventional threshold, such as 1 mm (0.1 mV), it can indicate the presence of ST elevation / depression for that threshold. The ST can also be determined as a fraction of the overall QRS magnitude of the projected waveform. If the fraction of the ST over the projected QRS magnitude is above a certain threshold, the presence of ST elevation / depression can be evaluated.

[0143] T-to-QRS amplitude ratio

[0144] The T-wave to QRS (T-to-QRS) amplitude ratio is the ratio of the T-wave amplitude to the QRS complex amplitude. Evaluation of a high T-to-QRS amplitude ratio or a range of high T-to-QRS amplitude ratios can suggest heart disease and / or other disorders. Additionally, the T-to-QRS amplitude ratio is commonly used in the case of hyperacute T waves to distinguish aneurysms and infarctions, indicate unstable angina, or determine plasma electrolyte imbalances, including metabolic disorders such as diabetes. For multiple ECG leads, the conventional measurement of the T-to-QRS amplitude ratio is done by examining multiple leads in a plane (usually leads V2, V3, and V4). For each lead examined, the individual T-to-QRS amplitude ratio is calculated by dividing the maximum T-wave displacement by the maximum QRS displacement. And the T-to-QRS amplitude ratio of a multilead ECG is the maximum of these individual T-to-QRS amplitude ratios.

[0145] Figure 15 Shows the measurement results of the T-wave to QRS amplitude ratio and related projections. Figure 15A shows an example of a conventional measurement of the T-to-QRS amplitude ratio of a multi-lead ECG by finding the individual T-to-QRS amplitude ratios of the largest T-wave deflections and the largest QRS deflections in its leads V2, V3, and V4, and finding the maximum value among them (the single ratio of V3 in this example). However, using a single or a limited number of ECG leads, the range of the T-to-QRS ratio can be estimated and / or otherwise determined by: finding the upper limit of its QRS amplitude as the "reference amplitude" by projecting the QRS of the ECG lead onto its single-phase view (α1 = 0.5), finding the lower limit of its QRS amplitude as the "reference amplitude" by projecting the QRS onto its two-phase view (α1 = 1.0), finding the maximum T-wave amplitude as the "characteristic amplitude" by projecting the T-wave of the ECG lead onto its single-phase view (α1 = 0.5), and finding the ratio range by dividing the characteristic amplitude by these reference amplitudes. Figure 15 B shows an example of a single-lead ECG ( Figure 15 lead V2 of the example in A), in which the QRS complex is projected as a single-phase waveform and the T-wave is projected as a single-phase waveform; and their respective amplitudes (a QRS,M and a T,M ), which are used to estimate the lower limit of the T-to-QRS amplitude ratio (R V2,M = a T,M / a QRS,M ). Figure 15 C shows an example of a single-lead ECG ( Figure 15 lead V2 of the example in A), in which the QRS complex is projected as a two-phase waveform and the T-wave is projected as a single-phase waveform; and their respective amplitudes (a QRS,B and a T,M ), which are used to estimate the upper limit of the T-to-QRS amplitude ratio (R V2,B = a T,M / a QRS,B ).

[0146] Using the above operations, the processor 304 ( Figure 3) can be configured to find the amplitude range of the QRS complex in a plane by projecting the time series waveform of the QRS complex of the ECG into a single-phase waveform and a biphasic waveform (e.g., changing the first view to the second view), and find their amplitudes as the "reference amplitudes". For example, using the sinusoidal parameterization of x(α,t) = sin(αt)u(t), t ∈ [0, 2π], the processor 304 can be configured to project from the original parameter (frequency) α0 to the parameters α1 = 0.5 and α1 = 1.0. The processor 304 can also be configured to find the maximum amplitude of the T wave in a plane by projecting the time series waveform of the T wave of the ECG into another single-phase waveform (e.g., changing the first view to the second view), and use its amplitude as the "characteristic amplitude". For example, using the sinusoidal parameterization of x(α,t) = sin(αt)u(t), t ∈ [0, 2π], the processor 304 can be configured to project from the original parameter (frequency) α0 to the parameter α1 = 0.5. To estimate the range of the T-to-QRS amplitude ratio, the processor 304 can also determine the ratio of the characteristic amplitude to the reference amplitude.

[0147] QRS-T angle

[0148] The QRS-T angle is the difference between the angles of the three-dimensional (3D) vector of the T wave axis and the QRS complex axis. The evaluation of the QRS-T angle can indicate heart diseases and / or other conditions. Using a multi-lead ECG spanning 3D space, the QRS-T can be routinely measured in 3D space in the form of a representation of the multi-lead ECG. In 3D space, the QRS complex and the T wave appear as loops (the QRS loop and the T loop respectively) starting from the 3D origin (0, 0, 0) and returning to the 3D origin. The routine measurement of the QRS-T angle is measured in 3D space by finding the vector from the origin to the maximum value of the QRS loop, finding the vector from the origin to the maximum value of the T loop, and finding the angular difference between these two vectors.

[0149] Figure 16 Shows the difference between the routine measurement of the QRS-T angle using an ECG in three-dimensional space and the determination of the QRS-T angle using a single-lead ECG view of the same ECG. Figure 16A shows the conventional measurement of QRS-T, i.e., the angular difference between the QRS loop vector and the T loop vector in 3D space. However, for an ECG with a single or limited number of leads that may not be sufficient to create an adequate representation in 3D space, the QRS-T angle can be estimated and / or alternatively determined by calculating the angle of the QRS loop vector relative to the single-lead ECG view point as the "reference angle", estimating the angle of the T loop vector relative to the single-lead ECG view point as the "characteristic angle", and finding the difference between these two angles relative to the single-lead ECG view point. The reference angle can be calculated by finding the original parameter (frequency value) of the QRS complex, e.g., by using the sinusoidal parameterization of x(α,t) = sin(αt)u(t), t ∈ [0,2π] to find α0 of the QRS complex. The characteristic angle representing the T wave angle can be provided or derived from the relative amplitude of the T wave relative to the single-phase QRS complex amplitude and the T wave shape.

[0150] Figure 16 B shows an example of calculating the QRS angle by finding the original parameter (α0) of the QRS and calculating the amplitude (a QRS,M ) of its single-phase waveform. Using the above operations, the processor 304 ( Figure 3 ) can be configured to find the QRS complex angle (reference angle). For example, using the sinusoidal parameterization of the QRS complex x(α,t) = sin(αt)u(t), t ∈ [0,2π], the processor 304 can be configured to calculate the original parameter (frequency) α0 of the QRS complex and also create a projection from the original parameter (frequency) α0 to the parameter α1 = 0.5. The processor 304 can be configured to calculate the reference angle of the QRS complex based on α0. The processor 304 can also be configured to derive the characteristic angle of the T wave based on the T wave amplitude relative to the QRS complex projection amplitude. The processor 304 can be configured to calculate the difference between the characteristic angle and the reference angle as an estimate of the QRS-T angle.

[0151] Combined use of electrocardiograms

[0152] The above electrocardiogram applications can also be used in combination with each other (in any combination). Some embodiments of the combined use of QRS width, QRS shape, ST elevation or depression, T wave to QRS amplitude ratio, and / or QRS-T angle can indicate heart diseases and / or other conditions. For example, the width and shape of the QRS can be used in combination to evaluate the presence of left bundle branch block (LBBB). For example, such an indication of the presence of LBBB can be used in combination with the presence of ST elevation or depression to evaluate the presence of ST elevation myocardial infarction. For example, the presence of ST elevation or depression can be used in combination with the T wave to QRS amplitude ratio or the QRS-T angle to evaluate the presence of infarction or aneurysm.

[0153] Return Figure 3, one or more computing devices 306 can be and / or include a laptop computer, a tablet computer, a desktop computer, a smartphone, a gaming device, and / or other networked or non-networked computing devices, which have a display, a user input device (e.g., buttons, keys, voice recognition, or single-point or multi-point touch touchscreens), a memory (e.g., tangible, machine-readable, non-transitory memory), a network interface, an energy source (e.g., a battery), and a processor coupled to each of these components, such as processor 304 (as used herein, the term includes one or more processors). Memories such as the electronic storage 338 of the computing device 306 can store instructions that, when executed by the relevant processor, can provide an operating system and various applications, including, for example, a browser or a native mobile application. Additionally, the computing device 306 can include a user interface 336, which can include a monitor, a keyboard, a mouse, a touchscreen, etc. The user interface 336 can operate to provide a graphical user interface associated with the system 300, which communicates with the ECG system 302 and / or the processor 304 and facilitates user interaction with the data from the ECG system 302.

[0154] The user interface 336 is configured to provide an interface between the system 300 and a user (e.g., a doctor, etc.), through which the user can provide information to the system 300 and receive information from the system. This enables data, results, and / or instructions, and any other communicable items (collectively referred to as "information") to be communicated between the user and one or more of the ECG system 302, the processor 304, the computing device 306, the external resource 308, and / or other components. Examples of interface devices suitable for inclusion in the user interface 336 include a keypad, buttons, switches, a keyboard, a knob, a joystick, a display screen, a touchscreen, a speaker, a microphone, an indicator light, a sound alarm, a printer, and / or other interface devices. In one embodiment, the user interface 336 includes multiple separate interfaces (e.g., an interface as part of the ECG system 302, an interface in the computing device 306, etc.). In one embodiment, the user interface 336 includes at least one interface provided integrally with the processor 304. It should be understood that the present disclosure contemplates a variety of communication technologies between one or more components of the system 300, whether hardwired or wireless. Other exemplary input devices and technologies suitable for use with the system 300 as the user interface 336 include, but are not limited to, RS-232 ports, RF links, IR links, modems (telephone, cable, or other). In short, the present disclosure contemplates any technology for communicating information with the system 300 as the user interface 336.

[0155] The electronic storage 338 includes an electronic storage medium that stores information electronically. The electronic storage medium of the electronic storage 338 may include one or both of a system storage that is provided integrally with the system 300 (i.e., substantially non-removable) and / or a removable storage. The removable memory may be removably connected to the system 300 via, for example, a port (such as a USB port, a FireWire port, etc.) or a drive (such as a disk drive, etc.). The electronic storage 338 may include one or more of an optically readable storage medium (such as an optical disc, etc.), a magnetically readable storage medium (such as a magnetic tape, a magnetic hard disk, a floppy disk drive, etc.), a charge-based storage medium (such as an EEPROM, a RAM, etc.), a solid-state storage medium (such as a flash drive, etc.), and / or other electronically readable storage media. The electronic storage 338 may store software algorithms, information determined by the processor 304, information received via the user interface 336, and / or other information that enables the system 300 to operate properly. The electronic storage 338 may be a separate component within the system 300 (in whole or in part), or the electronic storage 338 may be provided integrally (in whole or in part) with one or more other components of the system 300 (such as the computing device 306, the processor 304, etc.).

[0156] In some embodiments, the external resource 308 includes an information source, such as a database, a website, etc.; an external entity participating in the system 300 (such as a system or network associated with the system 300), one or more servers external to the system 300, a network (such as the Internet), an electronic storage, a device related to Wi-Fi TM technology, a device related to technology, a data input device, or other resources. In some implementations, some or all of the functions attributed to the external resource 308 herein may be provided by resources included in the system 300. The external resource 308 may be configured to communicate with one or more other components of the system 300 via a wired and / or wireless connection, via a network (such as a local area network and / or the Internet), via cellular technology, via Wi-Fi technology, and / or via other resources.

[0157] The network 350 may include the Internet, a Wi-Fi network, technology, and / or other wireless technologies. In some embodiments, the ECG system 302, one or more processors 304, the computing device 306, the external resource 308, and / or other components of the system 300 communicate via near-field communication, Bluetooth, and / or radio frequency; via the network 350 (such as a network such as a Wi-Fi network, a cellular network, and / or the Internet); and / or by other communication methods.

[0158] In Figure 3In [the figure], the ECG system 302, one or more processors 304, one or more computing devices 306, and / or other components of system 300 are shown as separate entities. This is not intended to be limiting. Some and / or all components of system 300 and / or other components may be grouped into one or more single devices. For example, one or more processors 304 and computing devices 306 may be included in the ECG system 302. The ECG system 302 and / or other components may be included in a wearable device worn by an ECG subject. The wearable device may be a watch, a wristband, one or more patches, clothing, a device, and / or other wearable devices. The wearable device may be configured to be worn, for example, at or near the subject's heart. In some embodiments, the wearable device may be and / or include a necklace, a chest strap, a shirt, a vest, and / or any other wearable device configured such that system 300 can operate as described herein.

[0159] The illustrated components of system 300 are depicted as discrete functional blocks, but the embodiments are not limited to systems that organize the functions described herein as Figure 3 shown. The functions provided by each component of system 300 may be provided by software or hardware modules that differ from the currently described organization. For example, such software or hardware may be mixed, decomposed, distributed (e.g., within a data center or geographically), or organized in other different ways. Some or all of the functions described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine-readable medium.

[0160] Figure 17 is a diagram showing an exemplary computing device 1700 (similar and / or identical to the computing device 306 described above) according to an embodiment of the present system. Various parts of the systems and methods described herein may be included in or executed on one or more computing devices that are the same as or similar to the computing device 1700. For example, the processor 304 of system 300 ( Figure 3 ) may be and / or included in one or more computing devices that are the same as or similar to the computing device 1700. In addition, the processes, modules, processor components, and / or other components of system 300 described herein may be executed by one or more processing systems that are similar and / or identical to the computing device 1700.

[0161] The computing device 1700 may include one or more processors (e.g., processors 1710a - 1710n, which may be similar and / or identical to processor 304), which are coupled via an input / output (I / O) interface 1750 to a system memory 1720 (which may be similar and / or identical to the electronic storage 338), an input / output I / O device interface 1730, and a network interface 1740. The processors may include a single processor or multiple processors (e.g., a distributed processor). The processor can be any suitable processor capable of executing or otherwise implementing instructions. The processor may include a central processing unit (CPU) that executes program instructions to perform arithmetic, logical, and input / output operations of the computing device 1700. The processor can execute code that creates an execution environment for the program instructions (e.g., processor firmware, protocol stack, database management system, operating system, or a combination thereof). The processor may include a programmable processor. The processor may include a general - purpose or a special - purpose microprocessor. The processor can receive instructions and data from the memory (e.g., the system memory 1720). The computing device 1700 can be a single - processor system that includes one processor (e.g., processor 1710a), or a multi - processor system that includes any number of suitable processors (e.g., 1710a - 1710n). Multiple processors can be employed to execute one or more portions of the techniques described herein in parallel or sequentially. The processes described herein (e.g., the logical flow) can be executed by one or more programmable processors that execute one or more computer programs to perform functions by operating on input data and generating corresponding outputs. The processes described herein can be executed by special - purpose logic circuitry such as an FPGA (field - programmable gate array) or an ASIC (application - specific integrated circuit), and the device can also be implemented as the special - purpose logic circuitry. The computing device 1700 may include multiple computing devices (e.g., a distributed computer system) to implement various processing functions.

[0162] The I / O device interface 1730 may provide an interface for connecting one or more I / O devices 1760 to the computer device 1700. The I / O devices may include devices that receive input (e.g., from a user) or output information (e.g., to a user). The I / O device 1760 may include, for example, a graphical user interface presented on a display (e.g., a cathode ray tube (CRT) or a liquid crystal display (LCD) monitor), a pointing device (e.g., a computer mouse or a trackball), a keyboard, a keypad, a touchpad, a scanning device, a voice recognition device, a gesture recognition device, a printer, an audio speaker, a microphone, a camera, etc. The I / O device 1760 may be connected to the computing device 1700 via a wired or wireless connection. The I / O device 1760 may be connected to the computing device 1700 from a remote location. For example, an I / O device 1760 located on a remote computer system may be connected to the computing device 1700 via a network and the network interface 1740.

[0163] The network interface 1740 may include a network adapter that provides a connection between the computing device 1700 and a network (e.g., the network 350 described above). The network interface 1740 may facilitate data exchange between the computing device 1700 and other devices connected to the network (e.g., Figure 3 the network 350 shown in). The network interface 1740 may support wired or wireless communication. The network may include an electronic communication network, such as the Internet, a local area network (LAN), a wide area network (WAN), a cellular communication network, etc.

[0164] The system memory 1720 can be configured to store program instructions 1770 (e.g., machine-readable instructions) or data 1780. The program instructions 1770 can be executed by a processor (e.g., one or more of processors 1710a - 1710n) to implement one or more embodiments of the present technology. The instructions 1770 can include modules and / or components of computer program instructions for implementing one or more of the techniques described herein with respect to the various processing modules and / or components. The program instructions can include a computer program (which in some forms is referred to as a program, software, software application, script, or code). The computer program can be written in a programming language, including a compiled or interpreted language, or a declarative or procedural language. The computer program can include units suitable for use in a computing environment, including stand-alone programs, modules, components, or subroutines. The computer program may or may not correspond to a file in a file system. The program can be stored as part of a file that contains other programs or data (e.g., one or more scripts in a markup language document), in a single file dedicated to the program, or in multiple coordinated files (e.g., files that store one or more modules, subroutines, or portions of code). The computer program can be deployed to execute on one or more computer processors located locally at a site, or distributed across multiple remote sites and interconnected via a communication network.

[0165] The system memory 1720 may include a tangible program carrier on which program instructions are stored. The tangible program carrier may include a non-transitory computer-readable storage medium. The non-transitory computer-readable storage medium may include a machine-readable storage device, a machine-readable storage substrate, a memory device, or any combination thereof. The non-transitory computer-readable storage medium may include non-volatile memory (e.g., flash memory, ROM, PROM, EPROM, EEPROM memory), volatile memory (e.g., random access memory (RAM), static random access memory (SRAM), synchronous dynamic RAM (SDRAM)), mass storage memory (e.g., CD-ROM and / or DVD-ROM, hard disk), etc. The system memory 1720 may include a non-transitory computer-readable storage medium on which program instructions may be stored and executed by a computer processor (e.g., one or more of processors 1710a - 1710n) to cause the subject matter and functional operations described herein. The memory (e.g., system memory 1720) may include a single memory device and / or multiple memory devices (e.g., distributed memory devices). Instructions or other program code that provide the functions described herein may be stored on a tangible, non-transitory computer-readable medium. In some cases, the entire set of instructions may be stored on the medium at the same time, or in some cases, different portions of the instructions may be stored on the same medium at different times, e.g., copies may be created by writing the program code into a first-in, first-out buffer in a network interface, where some instructions are pushed out of the buffer before other portions of the instructions are written into the buffer, and all instructions reside in the memory of the buffer, just not all at the same time.

[0166] The I / O interface 1750 may be configured to coordinate I / O traffic between the processors 1710a - 1710n, the system memory 1720, the network interface 1740, the I / O devices 1760, and / or other peripheral devices. The I / O interface 1750 may perform protocol, timing, or other data conversions to convert data signals from one component (e.g., the system memory 1720) into a format suitable for use by another component (e.g., the processors 1710a - 1710n). The I / O interface 1750 may include support for devices attached via various types of peripheral buses (e.g., variants of the Peripheral Component Interconnect (PCI) bus standard or the Universal Serial Bus (USB) standard).

[0167] Implementations of the techniques described herein may be implemented using a single instance of the computing device 1700 or multiple computing devices 1700 configured to host different portions or instances of the implementation. The multiple computing devices 1700 may provide parallel or sequential processing / execution of one or more portions of the techniques described herein.

[0168] Those skilled in the art will understand that computing device 1700 is merely illustrative and is not intended to limit the scope of the techniques described herein. Computing device 1700 can include any combination of devices or software that can execute or otherwise provide the performance of the techniques described herein. For example, computing device 1700 can include or be a combination of a cloud computing system, a data center, a server rack, a server, a virtual server, a desktop computer, a laptop computer, a tablet computer, a server device, a client device, a mobile phone, a smartphone, a personal digital assistant (PDA), a mobile audio or video player, a gaming console, an in-vehicle computer, or a global positioning system (GPS), etc. Computing device 1700 can also be connected to other devices not shown or can operate as a stand-alone system. Additionally, in some embodiments, the functions provided by the illustrated components can be combined in fewer components or distributed in additional components. Similarly, in some embodiments, the functions of some of the illustrated components may not be provided, or other additional functions may be provided.

[0169] Those skilled in the art will also understand that although various items are shown as being stored in memory or on storage when in use, these items or portions thereof can be transferred between memory and other storage devices for purposes of memory management and data integrity. Alternatively, in other embodiments, some or all of the software components can be executed in the memory of another device and communicate with the illustrated computer system via inter-computer communication. Portions or all of the system components or data structures can also be stored (e.g., as instructions or structured data) on a computer-accessible medium or portable article for reading by an appropriate drive, various examples of which were described above. In some embodiments, instructions stored on a computer-accessible medium separate from computing device 1700 can be transmitted to computing device 1700 via a transmission medium or signal (e.g., an electrical, electromagnetic, or digital signal) transmitted via a communication medium (e.g., a network or a wireless link). Various embodiments can also include receiving, sending, or storing instructions or data implemented in accordance with the foregoing description on a computer-accessible medium. Thus, the present invention can be practiced using other computer system configurations.

[0170] Figure 18 A method 1800 for changing a first view of a time series waveform to a second view is shown. The first view of the time series waveform can be generated based on a single-channel electrocardiogram (ECG) signal from an ECG system deployed in, for example, a patch, a watch, or a sports device. In some embodiments, the time series waveform includes a single-phase or biphasic single-channel QRS waveform associated with the ECG. In some embodiments, the time series waveform includes a projection of the QRS loop. The second view of the time series waveform can be a projection along the planar QRS loop, which is more conducive to morphological interpretation compared to the first view.

[0171] The operations of method 1800 described below are for illustrative purposes. In some embodiments, method 1800 may be accomplished with one or more additional operations not described and / or without one or more of the operations discussed. Additionally, Figure 18 the order of operations of method 1800 shown and described hereinbelow is not intended to be limiting.

[0172] In some embodiments, some or all of method 1800 may be implemented in one or more processing devices (e.g., a digital processor, an analog processor, a digital circuit designed to process information, an analog circuit designed to process information, a state machine, and / or other mechanisms for electronically processing information). One or more processing devices (e.g., processor 304, processor 1710a, etc. described herein) may include one or more devices that execute some or all of the operations of method 1800 in response to instructions stored electronically on an electronic storage medium (e.g., electronic storage 338, system memory 1720, etc.). One or more processing devices may include one or more devices configured by hardware, firmware, and / or software to be specifically designed to perform one or more operations of method 1800.

[0173] In operation 1802, a first view of a time series waveform is separated into an invariant intrinsic component and a variable parametric component. In some embodiments, the invariant intrinsic component is upright and single-phase. In some embodiments, the parametric component includes a sinusoid-like function, and the first and second parameters include different frequencies of the sinusoid-like function. The sinusoid-like function may be, for example, a sine function or a cosine function. In some embodiments, the parametric component includes a Taylor series expansion, and the first and second parameters include different Taylor series. In some embodiments, operation 1802 is performed by a processor similar and / or identical to processor 304, processor 1710a, etc. (as Figure 3 and Figure 17 shown and described herein).

[0174] In operation 1804, a first parameter associated with the first view of the variable parametric component is replaced with a second parameter associated with a second view. For example, the first parameter associated with the first view of the variable parametric component may be determined based on the first zero crossing of the time series waveform. In some embodiments, operation 1804 includes reducing inaccurate parameter determination through perturbation. Perturbation may include testing different parameter values to determine which parameter value provides the best change in the continuity of the time series waveform (or the least discontinuity). In some embodiments, discontinuity may be determined by determining the slope of the time series waveform before, during, and after a singular or near-singular section. In some embodiments, discontinuity may be determined by determining the maximum third derivative of the entire second view of the time series waveform at each trial parameter value.

[0175] In some embodiments, replacing the first parameter with the second parameter includes parametric component segmentation. Operation 1804 may include reducing potential singularities or near-singularities caused by parametric component segmentation by identifying segments of a second view of the time series waveform that include potential singularities or near-singularities, applying alternative calculations to change the first view to the second view at these potential singularities or near-singularity segments, and / or other operations. Potential singularities or near-singularities may be identified based on a threshold of the frequency sine of the first view of the time series waveform and / or by other operations.

[0176] In some embodiments, the alternative calculation may be or include interpolating the identified segments at segments that are not close to zero using the second view of the time series waveform, as determined by parametric component replacement. In some embodiments, when a parametric component with the second parameter is close to a singularity, function approximation is used to perform the alternative calculation. In some embodiments, operation 1804 is performed by a processor similar and / or identical to processor 304, processor 1710a, etc. (as Figure 3 and Figure 17 shown and described herein).

[0177] In operation 1806, the first view is changed to the second view based on invariant intrinsic components and variable parametric components with the second parameter. In some embodiments, operation 1806 is performed by a processor similar and / or identical to processor 304, processor 1710a, etc. (as Figure 3 and Figure 12 shown and described herein).

[0178] Method 1800 may be extended to other waveform patterns by flipping the time axis, flipping the waveform axis, changing parameters, and / or introducing a shift to the parametric components of the first view of the time series waveform, and / or the time series waveform may be converted to other waveform patterns. In some embodiments, method 1800 includes performing separation (operation 1802), replacement (operation 1804), and change (operation 1806) to determine the center of the QRS complex, determine the width of the QRS complex, and / or determine ST elevation / depression and / or other cardiovascular diseases and / or conditions.

[0179] In the block diagrams, the components shown are depicted as discrete functional blocks, but the implementation is not limited to a system where the functions described herein are organized as shown. The functions provided by each component can be provided by software or hardware modules organized differently from the current description. For example, such software or hardware can be mixed, combined, replicated, decomposed, distributed (e.g., within a data center or geographically), or organized in other different ways. The functions described herein can be provided by one or more processors of one or more computers that execute code stored on a tangible, non - transitory, machine - readable medium. In some cases, although the singular term "medium" is used, the instructions can be distributed on different storage devices associated with different computing devices, e.g., each computing device associated with a different subset of instructions, and such an implementation is consistent with the use of the singular term "medium" herein. In some cases, a third - party content delivery network may contain some or all of the information transmitted over a network, and in such cases, to the extent of providing or otherwise making available the information (e.g., content), the information can be provided by sending instructions to retrieve the information from the content delivery network.

[0180] As used herein, the use of the term "compute" or "estimate" can generally be interchanged with "determine" or similar terms.

[0181] Various embodiments of the system and method are disclosed in the numbered clauses that follow. Other features, characteristics, and exemplary aspects of the present disclosure will be described in terms of clauses that can be claimed in any combination: 1. A method for changing a first view of a time - series waveform to a second view, the method comprising: separating the first view of the time - series waveform into invariant intrinsic components and variable parameterized components; replacing a first parameter associated with the first view of the variable parameterized component with a second parameter associated with the second view; and changing the first view to the second view based on the invariant intrinsic components and the variable parameterized component having the second parameter. 2. The method according to clause 1, wherein the time - series waveform comprises a single - phase or two - phase single - channel QRS waveform associated with an electrocardiogram (ECG). 3. The method according to any of the preceding clauses, wherein the time - series waveform comprises a projection of a QRS loop. 4. The method according to any of the preceding clauses, wherein the invariant intrinsic component is upright and single - phase. 5. The method according to any of the preceding clauses, wherein the parameterized component comprises a sine - like function, and the first and second parameters comprise different frequencies of the sine - like function. 6. The method according to any of the preceding clauses, wherein the sine - like function is a sine function or a cosine function. 7. The method according to any one of the preceding clauses, wherein the parametric component comprises a Taylor series expansion, and the first and second parameters comprise different Taylor series. 8. The method according to any one of the preceding clauses, wherein replacing the first parameter with the second parameter comprises parametric component segmentation. 9. The method according to any one of the preceding clauses, further comprising reducing potential singularities or near-singularities caused by parametric component segmentation by: (a) identifying a section of the second view of the time series waveform that includes potential singularities or near-singularities; and (b) applying alternative calculations to change the first view to the second view at these potential singularities or near-singularity sections. 10. The method according to any one of the preceding clauses, wherein potential singularities or near-singularities are identified based on a threshold of the frequency sine of the first view of the time series waveform. 11. The method according to any one of the preceding clauses, wherein the alternative calculation comprises interpolating the identified section at sections determined not to be close to zero by the parametric component replacement using the second view of the time series waveform. 12. The method according to any one of the preceding clauses, wherein when the second parameter is close to a singularity, function approximation is used as the parametric component to perform the alternative calculation. 13. The method according to any one of the preceding clauses, wherein the first parameter associated with the first view of the variable parametric component is determined based on the first zero crossing of the time series waveform. 14. The method according to any one of the preceding clauses, further comprising reducing inaccurate parameter determination by perturbation, the perturbation including testing different parameter values to determine which parameter value provides the best changed time series waveform continuity (or minimum discontinuity). 15. The method according to any one of the preceding clauses, further comprising determining discontinuity by determining the slopes of the time series waveform before, during, and after the singularity or near-singularity section. 16. The method according to any one of the preceding clauses, further comprising determining discontinuity by determining the maximum third derivative of the entire second view of the time series waveform at each trial parameter value. 17. The method according to any one of the preceding clauses, further comprising extending the method to other waveform patterns or converting the time series waveform to other waveform patterns by flipping the time axis, flipping the waveform axis, changing parameters, and / or introducing a shift to the parametric component of the first view of the time series waveform. 18. The method according to any one of the preceding clauses, wherein the first view of the time series waveform is generated based on a single-channel ECG (ECG) signal from an ECG system deployed in a patch, a watch, or a sports equipment. 19. The method according to any one of the preceding clauses, wherein the second view of the time series waveform includes a projection along the plane QRS loop, which is more conducive to morphological interpretation compared to the first view. 20. The method according to any one of the preceding clauses, further comprising performing separation, replacement, and alteration to determine the center of the QRS complex, determine the width of the QRS complex, and / or determine ST elevation / depression or other cardiovascular diseases or disorders. 21. The method according to any one of the preceding clauses, wherein changing the first view to the second view based on invariant intrinsic components and variable parametric components with a second parameter includes rotation and / or projection techniques. 22. The method according to any one of the preceding clauses, wherein changing the first view to the second view based on invariant intrinsic components and variable parametric components with a second parameter includes finding the center of the QRS complex by projecting the time series waveform of the QRS complex of the ECG as a single-phase waveform, and the method further includes determining the left ventricular end-diastolic pressure (LVEDP). 23. The method according to any one of the preceding clauses, wherein changing the first view to the second view based on invariant intrinsic components and variable parametric components with a second parameter includes finding the width of the QRS complex and / or determining the shape of the QRS complex by projecting the time series waveform of the QRS complex of the ECG as a single-phase waveform, and the method further includes determining left bundle branch block (LBBB). 24. The method according to any one of the preceding clauses, wherein: the width of the QRS complex includes the cross-sectional width of the single-phase projection waveform at 50% of the total height of the projection waveform; and / or the shape of the QRS complex includes the double-peak peak of the single-phase projection waveform. 25. The method according to any one of the preceding clauses, wherein changing the first view to the second view based on invariant intrinsic components and variable parametric components with a second parameter includes determining ST elevation and / or depression by projecting the time series waveform of the QRS complex of the ECG as a waveform adjacent to the ECG waveform, and the method further includes determining myocardial infarction and / or ischemia based on ST elevation and / or depression. 26. The method according to any one of the preceding clauses, wherein changing the first view to the second view based on invariant intrinsic components and variable parametric components with a second parameter includes determining the T-to-QRS amplitude ratio, which is the ratio of the T-wave amplitude to the QRS complex amplitude, and the method further includes determining myocardial infarction and / or ischemia based on the T-to-QRS amplitude ratio. 27. The method according to any one of the preceding clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes determining the QRS-T angle as the difference between the angle of the 3D vector of the T wave axis and the axis of the QRS complex, and the method further includes determining myocardial infarction and / or ischemia based on the QRS-T angle. 28. The method according to any one of the preceding clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes determining the left ventricular end-diastolic pressure (LVEDP), left bundle branch block (LBBB), the width and / or shape of the QRS complex, ST elevation and / or depression, the T to QRS amplitude ratio, the QRS-T angle, and / or a combination thereof, and the method further includes determining myocardial infarction and / or ischemia based on the LVEDP, LBBB, the width and / or shape of the QRS complex, ST elevation and / or depression, the T to QRS amplitude ratio, the QRS-T angle, and / or a combination thereof. 29. A non-transitory computer-readable medium having instructions thereon that, when executed by a computer, cause the computer to perform operations including: Separating a first view of a time series waveform into an invariant intrinsic component and a variable parametric component; replacing a first parameter associated with the first view of the variable parametric component with a second parameter associated with a second view of the time series waveform; and changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having the second parameter. 30. The medium according to clause 29, wherein the time series waveform includes a single-phase or two-phase single-channel QRS waveform associated with an electrocardiogram (ECG). 31. The medium according to any one of the preceding clauses, wherein the time series waveform includes a projection of a QRS loop. 32. The medium according to any one of the preceding clauses, wherein the invariant intrinsic component is upright and single-phase. 33. The medium according to any one of the preceding clauses, wherein the parametric component includes a sine-like function, and the first and second parameters include different frequencies of the sine-like function. 34. The medium according to any one of the preceding clauses, wherein the sine-like function is a sine function or a cosine function. 35. The medium according to any one of the preceding clauses, wherein the parametric component includes a Taylor series expansion, and the first and second parameters include different Taylor series. 36. The medium according to any one of the preceding clauses, wherein replacing the first parameter with the second parameter includes parametric component segmentation. 37. The medium according to any one of the preceding clauses, the operation further includes reducing potential singularities or near-singularities caused by parametric component segmentation by: (a) identifying a section containing potential singularities or near-singularities in a second view of the time series waveform; and (b) applying an alternative calculation to change the first view to the second view at these potential singularities or near-singularity sections. 38. The medium according to any one of the preceding clauses, wherein potential singularities or near-singularities are identified based on a threshold of the frequency sine of the first view of the time series waveform. 39. The medium according to any one of the preceding clauses, wherein the alternative calculation includes using the second view of the time series waveform to interpolate the identified segments at sections not close to zero, as determined by parametric component replacement. 40. The medium according to any one of the preceding clauses, wherein when the second parameter is close to a singularity, function approximation is used as the parametric component to perform the alternative calculation. 41. The medium according to any one of the preceding clauses, wherein the first parameter associated with the first view of the variable parametric component is determined based on the first zero crossing of the time series waveform. 42. The medium according to any one of the preceding clauses, the operation further includes reducing inaccurate parameter determination by perturbation, which includes testing different parameter values to determine which parameter value provides the best changed time series waveform continuity (or minimum discontinuity). 43. The medium according to any one of the preceding clauses, the operation further includes determining discontinuity by determining the slopes of the time series waveform before, during, and after the singularity or near-singularity section. 44. The medium according to any one of the preceding clauses, the operation further includes determining discontinuity by determining the maximum third derivative of the entire second view of the time series waveform at each trial parameter value. 45. The medium according to any one of the preceding clauses, the operation further includes extending the method to other waveform patterns or converting the time series waveform to other waveform patterns by flipping the time axis, flipping the waveform axis, changing parameters, and / or introducing a shift to the parametric component of the first view of the time series waveform. 46. The medium according to any one of the preceding clauses, wherein the first view of the time series waveform is generated based on a single-channel ECG signal from an ECG system deployed in a patch, a watch, or a sports equipment. 47. The medium according to any one of the preceding clauses, wherein the second view of the time series waveform includes a projection along the plane QRS loop, which is more conducive to morphological interpretation compared to the first view. 48. The medium according to any one of the foregoing clauses, the operation further includes performing separation, replacement, and alteration to determine the center of the QRS complex, determine the width of the QRS complex, and / or determine ST elevation / depression or other cardiovascular diseases or conditions. 49. The medium according to any one of the foregoing clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes rotation and / or projection techniques. 50. The medium according to any one of the foregoing clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes finding the center of the QRS complex by projecting the time series waveform of the QRS complex of the ECG into a single-phase waveform, and the operation further includes determining the left ventricular end-diastolic pressure (LVEDP) based on the center of the QRS complex. 51. The medium according to any one of the foregoing clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes finding the width of the QRS complex and / or determining the shape of the QRS complex by projecting the time series waveform of the QRS complex of the ECG into a single-phase waveform, and the operation further includes determining left bundle branch block (LBBB) based on the width and / or shape of the QRS complex. 52. The medium according to any one of the foregoing clauses, wherein: the width of the QRS complex includes the cross-sectional width of the single-phase projection waveform at 50% of the total height of the projection waveform; and / or the shape of the QRS complex includes the double-peak peak of the single-phase projection waveform. 53. The medium according to any one of the foregoing clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes determining ST elevation and / or depression by projecting the time series waveform of the QRS complex of the ECG into a waveform adjacent to the ECG waveform, and the operation further includes determining myocardial infarction and / or ischemia based on the ST elevation and / or depression. 54. The medium according to any one of the foregoing clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes determining the T-to-QRS amplitude ratio, which is the ratio of the T-wave amplitude to the QRS complex amplitude, and the method further includes determining myocardial infarction and / or ischemia based on the T-to-QRS amplitude ratio. 55. The medium according to any one of the preceding clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having a second parameter includes determining the QRS-T angle as the difference between the angle of the 3D vector of the T-wave axis and the QRS complex axis, and the method further includes determining myocardial infarction and / or ischemia based on the QRS-T angle. 56. The medium according to any one of the preceding clauses, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having a second parameter includes determining the left ventricular end-diastolic pressure (LVEDP), left bundle branch block (LBBB), the width and / or shape of the QRS complex, ST elevation and / or depression, the T-to-QRS amplitude ratio, the QRS-T angle, and / or a combination thereof, and the method further includes determining myocardial infarction and / or ischemia based on the LVEDP, LBBB, the width and / or shape of the QRS complex, ST elevation and / or depression, the T-to-QRS amplitude ratio, the QRS-T angle, and / or a combination thereof. 57. A system for changing a first view of a time series waveform to a second view, the system comprising: one or more processors configured to: separate a first view of the time series waveform into an invariant intrinsic component and a variable parameterized component; replace a first parameter associated with the first view of the variable parameterized component with a second parameter associated with the second view; and change the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter. 58. The system according to clause 57, further comprising an electrocardiogram (ECG) system configured to generate one or more output signals conveying ECG information of a subject; wherein: the one or more processors are further configured to convert the one or more output signals into a first view of the time series waveform, the first view including a digital representation of the ECG information in the output signals; and the time series waveform includes a single-phase or biphasic single-channel QRS waveform associated with the ECG. 59. The system according to any one of the preceding clauses, wherein the time series waveform includes a projection of the QRS loop. 60. The system according to any one of the preceding clauses, wherein the invariant intrinsic component is upright and single-phase. 61. The system according to any one of the preceding clauses, wherein the parameterized component includes a sine-like function, and the first and second parameters include different frequencies of the sine-like function. 62. The system according to any one of the preceding clauses, wherein the sine-like function is a sine function or a cosine function. 63. The system according to any one of the preceding clauses, wherein the parameterized component includes a Taylor series expansion, and the first and second parameters include different Taylor series. 64. The system according to any one of the preceding clauses, wherein replacing the first parameter with the second parameter includes parametric component segmentation. 65. The system according to any one of the preceding clauses, wherein one or more processors are further configured to reduce potential singularities or near-singularities caused by parametric component segmentation by: (a) identifying a section containing potential singularities or near-singularities in a second view of the time series waveform; and (b) applying alternative calculations to change the first view to the second view at these potential singularities or near-singularity sections. 66. The system according to any one of the preceding clauses, wherein potential singularities or near-singularities are identified based on a threshold of the frequency sine of the first view of the time series waveform. 67. The system according to any one of the preceding clauses, wherein the alternative calculation includes interpolating the identified section at sections determined not to be close to zero by parametric component replacement using the second view of the time series waveform. 68. The system according to any one of the preceding clauses, wherein when the second parameter is close to a singularity, function approximation is used as the parametric component to perform the alternative calculation. 69. The system according to any one of the preceding clauses, wherein the first parameter associated with the first view of the variable parametric component is determined based on the first zero crossing of the time series waveform. 70. The system according to any one of the preceding clauses, wherein one or more processors are further configured to reduce inaccurate parameter determination by perturbation, the perturbation including testing different parameter values to determine which parameter value provides the best changed time series waveform continuity (or minimum discontinuity). 71. The system according to any one of the preceding clauses, wherein one or more processors are further configured to determine discontinuity by determining the slopes of the time series waveform before, during, and after the singularity or near-singularity section. 72. The system according to any one of the preceding clauses, wherein one or more processors are further configured to determine discontinuity by determining the maximum third derivative of the second view of the time series waveform at each trial parameter value. 73. The system according to any one of the preceding clauses, wherein one or more processors are further configured to flip the time axis, flip the waveform axis, change parameters, and / or introduce a shift to the parametric component of the first view of the time series waveform. 74. The system according to any one of the preceding clauses, wherein the first view of the time series waveform is generated based on a single-channel electrocardiogram (ECG) signal from an ECG system deployed in a patch, a watch, or a sports equipment. 75. The system according to any one of the preceding clauses, wherein the second view of the time series waveform includes a projection along the plane QRS loop, which is more conducive to morphological interpretation compared to the first view. 76. The system according to any one of the preceding clauses, wherein the one or more processors are further configured to perform separation, replacement, and alteration to determine the center of the QRS complex, determine the width of the QRS complex, and / or determine ST elevation / depression or other cardiovascular diseases or disorders. 77. The system according to any one of the preceding clauses, wherein the one or more processors are configured such that changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes rotation and / or projection techniques. 78. The system according to any one of the preceding clauses, wherein the one or more processors are configured such that changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes finding the center of the QRS complex by projecting the QRS complex time series waveform of the ECG as a single-phase waveform, and the one or more processors are further configured to determine the left ventricular end-diastolic pressure (LVEDP) based on the center of the QRS complex. 79. The system according to any one of the preceding clauses, wherein the one or more processors are configured such that changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes finding the width of the QRS complex and / or determining the shape of the QRS complex by projecting the QRS complex time series waveform of the ECG as a single-phase waveform, and the one or more processors are further configured to determine left bundle branch block (LBBB) based on the width and / or shape of the QRS complex. 80. The system according to any one of the preceding clauses, wherein: the width of the QRS complex includes the cross-sectional width of the single-phase projection waveform at 50% of the total height of the projection waveform; and / or the shape of the QRS complex includes the double-peak peak of the single-phase projection waveform. 81. The system according to any one of the preceding clauses, wherein the one or more processors are configured such that changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having a second parameter includes determining ST elevation and / or depression by projecting the QRS complex time series waveform of the ECG as a waveform adjacent to the ECG waveform, and the one or more processors are further configured to determine myocardial infarction and / or ischemia based on the ST elevation and / or depression. 82. The system according to any one of the preceding clauses, wherein one or more processors are configured such that changing a first view to a second view based on an invariant intrinsic component and a variable parametric component having a second parameter includes determining a T to QRS amplitude ratio, which is the ratio of the T wave amplitude to the QRS complex amplitude, and the method further includes determining myocardial infarction and / or ischemia based on the T to QRS amplitude ratio. 83. The system according to any one of the preceding clauses, wherein one or more processors are configured such that changing a first view to a second view based on an invariant intrinsic component and a variable parametric component having a second parameter includes determining the QRS-T angle as the difference between the three-dimensional (3D) vector of the T wave axis and the angle of the QRS complex axis, and the method further includes determining myocardial infarction and / or ischemia based on the QRS-T angle. 84. The system according to any one of the preceding clauses, wherein one or more processors are configured such that changing a first view to a second view based on an invariant intrinsic component and a variable parametric component having a second parameter includes determining the left ventricular end-diastolic pressure (LVEDP), left bundle branch block (LBBB), width and / or shape of the QRS complex, ST elevation and / or depression, T to QRS amplitude ratio, QRS-T angle, and / or a combination thereof, and the method further includes determining myocardial infarction and / or ischemia based on the LVEDP, LBBB, width and / or shape of the QRS complex, ST elevation and / or depression, T to QRS amplitude ratio, QRS-T angle, and / or a combination thereof.

[0182] The reader should understand that this application describes several inventions. The applicant has grouped these inventions into one document rather than filing them as separate patent applications because their related subject matter helps to save the application process. However, the unique advantages and aspects of these inventions should not be conflated. In some cases, an embodiment solves all of the deficiencies noted herein, but it should be understood that the invention is independently useful and that some embodiments only solve a portion of these problems or provide other benefits not mentioned, which will be apparent to those skilled in the art after reading this disclosure. Due to cost constraints, some of the inventions disclosed herein may not currently be claimed but may be claimed in a subsequent application, such as a continuation application or by amending the claims. Similarly, due to space limitations, neither the abstract nor the summary of the invention section of this document should be considered to contain a comprehensive list of all such inventions or all aspects of such inventions.

[0183] It should be understood that the description and the drawings are not intended to limit the invention to the particular forms disclosed, but on the contrary, are intended to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims. Further modifications and alternative embodiments of various aspects of the invention will be apparent to those skilled in the art in light of this specification. Accordingly, the specification and drawings are to be regarded only as illustrative, and are used to teach those skilled in the art the general manner of practicing the invention. It should be understood that the forms of the invention shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those shown and described herein, components and processes may be reversed or omitted, and certain features of the invention may be used independently, all of which will be apparent to those skilled in the art after reading the description of the invention. Changes may be made to the elements described herein without departing from the spirit and scope of the invention as described in the following claims. The headings used herein are for organizational purposes only and are not intended to limit the scope of the description.

[0184] As used throughout this application, the word "can" is used in a permissive sense (i.e., meaning possible), rather than a mandatory sense (i.e., meaning must). Words such as "comprising", "including", and "containing" mean including but not limited to. As used throughout this application, the singular forms "a", "an", and "the" include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to "an element" or "a element" includes combinations of two or more elements, even though other terms and phrases are used to denote one or more elements, such as "one or more". Unless otherwise stated, the term "or" is non-exclusive, i.e., covers both "and" and "or". Statements describing a conditional relationship, such as "in response to X, Y", "at X, Y", "if X, Y", "when X, Y", etc., all cover causal relationships where the antecedent is a necessary causal condition, the antecedent is a sufficient causal condition, or the antecedent is a contributing causal condition to the consequent. For example, "state X occurs when condition Y is reached" is applicable to both "X occurs only when Y" and "X occurs when Y and Z". Such conditional relationships are not limited to consequents that occur immediately after the antecedent is reached, as some consequents may be delayed, and in a conditional statement, the antecedent is associated with its consequent, e.g., the antecedent is related to the likelihood of the consequent occurring. Unless otherwise stated, a statement mapping multiple attributes or functions to multiple objects (e.g., one or more processors perform steps A, B, C, and D) covers both mapping all such attributes or functions to all such objects and mapping a subset of the attributes or functions to a subset of the attributes or functions (e.g., all processors each perform steps A - D, and the case where processor 1 performs step A, processor 2 performs steps B and part of step C, and processor 3 performs part of step C and step D). Additionally, unless otherwise stated, a statement that a value or action is "based on" another condition or value covers both the case where the condition or value is the sole factor and the case where the condition or value is one of multiple factors. Unless otherwise stated, a statement that "each" instance of a certain set has certain properties should not be construed as excluding the case where some identical or similar members of a larger set do not have that property, i.e., each does not necessarily mean every. Unless explicitly specified, limitations on the order of the recited steps should not be read into the claims, e.g., using the explicit language "after performing X, perform Y", as opposed to statements that might be inappropriately argued to imply an order limitation (e.g., "perform X on an item, perform Y on the item after X"), which are used for the purpose of making the claims more readable rather than specifying an order. A statement referring to "at least Z of A, B, and C" (e.g., "at least Z of A, B, or C") means that there are at least Z in the listed categories (A, B, and C), and does not require at least Z units in each category.Unless otherwise explicitly stated, it is evident from the discussion that throughout the specification, the use of terms such as "processing", "computing", "estimating", "determining", etc. refers to actions or processes of a specific device, such as a special-purpose computer or a similar special-purpose electronic processing / computing device.

Claims

1. A method for changing a first view of a time series waveform to a second view, the method comprising: Separating the first view of the time series waveform into invariant intrinsic components and variable parametric components; Replacing a first parameter of the variable parametric component associated with the first view with a second parameter associated with the second view; And Changing the first view to the second view based on the invariant intrinsic components and the variable parametric component having the second parameter.

2. The method according to claim 1, wherein the time series waveform comprises a single-phase or bi-phase single-channel QRS waveform associated with an electrocardiogram (ECG).

3. The method according to claim 2, wherein the time series waveform comprises a projection of a QRS loop.

4. The method according to claim 1, wherein the invariant intrinsic components are upright and single-phase.

5. The method according to claim 1, wherein the parametric component comprises a sine-like function, and the first parameter and the second parameter comprise different frequencies of the sine-like function.

6. The method according to claim 5, wherein the sine-like function is a sine function or a cosine function.

7. The method according to claim 1, wherein the parametric component comprises a Taylor series expansion, and the first parameter and the second parameter comprise different Taylor series.

8. The method according to claim 1, wherein replacing the first parameter with the second parameter comprises parametric component segmentation.

9. The method according to claim 1, further comprising reducing potential singularities or near-singularities caused by parametric component segmentation by: (a) identifying a section of the second view of the time series waveform that contains the potential singularity or near-singularity, and (b) applying alternative calculations to change the first view to the second view at these potential singularity or near-singularity sections.

10. The method according to claim 9, wherein the potential singularity or near-singularity is identified based on a threshold of the frequency sine of the first view of the time series waveform.

11. The method according to claim 9, wherein the alternative calculation comprises using the second view of the time series waveform to interpolate the identified section at sections determined not to be close to zero by parametric component replacement.

12. The method according to claim 9, wherein when the second parameter is close to a singularity, function approximation is used as the parametric component to perform the alternative calculation.

13. The method according to claim 1, wherein the first parameter of the variable parametric component associated with the first view is determined based on the first zero crossing of the time series waveform.

14. The method according to claim 1, further comprising reducing inaccurate parameter determination by perturbation, the perturbation comprising testing different parameter values to determine which parameter value provides the best continuity (or minimum discontinuity) of the changed time series waveform.

15. The method according to claim 14, further comprising determining a discontinuity by determining the slope of the time series waveform before, during, and after a singular or near-singular section.

16. The method according to claim 14, further comprising determining a discontinuity by determining the maximum third derivative of the entire second view of the time series waveform at each trial parameter value.

17. The method according to claim 1, further comprising extending the method to other waveform patterns or converting the time series waveform to other waveform patterns by flipping the time axis, flipping the waveform axis, changing a parameter, and / or introducing a shift to the parameterized component of the first view of the time series waveform.

18. The method according to claim 1, wherein the first view of the time series waveform is generated based on a single-channel ECG signal from an ECG system deployed in a patch, a watch, or a sports device.

19. The method according to claim 18, wherein the second view of the time series waveform includes a projection along a plane QRS loop, which is more conducive to morphological interpretation compared to the first view.

20. The method according to claim 19, further comprising performing the separation, replacement, and change to determine the center of the QRS complex, determine the width of the QRS complex, and / or determine ST elevation / depression or other cardiovascular diseases or conditions.

21. The method according to claim 1, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes rotation and / or projection techniques.

22. The method according to claim 1, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes finding the center of the QRS complex by projecting the QRS complex time series waveform of the ECG as a single-phase waveform, and the method further comprises determining the left ventricular end-diastolic pressure (LVEDP).

23. The method according to claim 1, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes finding the width of the QRS complex and / or determining the shape of the QRS complex by projecting the QRS complex time series waveform of the ECG as a single-phase waveform, and the method further comprises determining left bundle branch block (LBBB).

24. The method according to claim 23, wherein: the width of the QRS complex includes the cross-sectional width of the single-phase projection waveform at 50% of the total height of the projection waveform; and / or the shape of the QRS complex includes the double-peak peak of the single-phase projection waveform.

25. The method according to claim 1, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having the second parameter includes determining ST elevation and / or depression by projecting the time series waveform of the QRS complex of the ECG as a waveform adjacent to the ECG waveform, and the method further includes determining myocardial infarction and / or ischemia based on the ST elevation and / or depression.

26. The method according to claim 1, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having the second parameter includes determining the T to QRS amplitude ratio, which is the ratio of the T wave amplitude to the QRS complex amplitude, and the method further includes determining myocardial infarction and / or ischemia based on the T to QRS amplitude ratio.

27. The method according to claim 1, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having the second parameter includes determining the QRS-T angle as the difference between the three-dimensional (3D) vector of the T wave axis and the angle of the QRS complex axis, and the method further includes determining myocardial infarction and / or ischemia based on the QRS-T angle.

28. The method according to claim 1, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having the second parameter includes determining left ventricular end-diastolic pressure (LVEDP), left bundle branch block (LBBB), the width and / or shape of the QRS complex, ST elevation and / or depression, the T to QRS amplitude ratio, the QRS-T angle, and / or a combination thereof, and the method further includes determining myocardial infarction and / or ischemia based on the LVEDP, the LBBB, the width and / or shape of the QRS complex, the ST elevation and / or depression, the T to QRS amplitude ratio, the QRS-T angle, and / or the combination thereof.

29. A non-transitory computer-readable medium having instructions thereon that, when executed by a computer, cause the computer to perform operations including the following: Separating a first view of a time series waveform into an invariant intrinsic component and a variable parametric component; Replacing the first parameter associated with the first view of the variable parametric component with a second parameter associated with a second view of the time series waveform; and Changing the first view to the second view based on the invariant intrinsic component and the variable parametric component having the second parameter.

30. The medium according to claim 29, wherein the time series waveform includes a single-phase or biphasic single-channel QRS waveform associated with an electrocardiogram (ECG).

31. The medium according to claim 30, wherein the time series waveform includes a projection of a QRS loop.

32. The medium according to claim 29, wherein the invariant intrinsic component is upright and single-phase.

33. The medium according to claim 29, wherein the parameterized component comprises a sine-like function, and the first parameter and the second parameter comprise different frequencies of the sine-like function.

34. The medium according to claim 33, wherein the sine-like function is a sine function or a cosine function.

35. The medium according to claim 29, wherein the parameterized component comprises a Taylor series expansion, and the first parameter and the second parameter comprise different Taylor series.

36. The medium according to claim 29, wherein replacing the first parameter with the second parameter comprises parametric component segmentation.

37. The medium according to claim 29, the operation further comprising reducing potential singularities or near-singularities caused by parametric component segmentation by: (a) identifying a section of the second view of the time series waveform that includes the potential singularity or near-singularity, and (b) applying an alternative calculation to change the first view to the second view at these potential singularity or near-singularity sections.

38. The medium according to claim 37, wherein the potential singularity or near-singularity is identified based on a threshold of the frequency sine of the first view of the time series waveform.

39. The medium according to claim 37, wherein the alternative calculation comprises interpolating the identified section at sections determined not to be close to zero by the parametric component replacement using the second view of the time series waveform.

40. The medium according to claim 37, wherein when the second parameter is close to a singularity, the alternative calculation is performed using a function approximation as the parametric component.

41. The medium according to claim 29, wherein the first parameter associated with the first view of the variable parametric component is determined based on the first zero crossing of the time series waveform.

42. The medium according to claim 29, the operation further comprising reducing inaccurate parameter determination by perturbation, the perturbation including testing different parameter values to determine which parameter value provides the best changed time series waveform continuity (or minimum discontinuity).

43. The medium according to claim 42, the operation further comprising determining discontinuity by determining the slopes of the time series waveform before, during, and after the singularity or near-singularity section.

44. The medium according to claim 42, the operation further comprising determining discontinuity by determining the maximum third derivative of the entire second view of the time series waveform at each trial parameter value.

45. The medium according to claim 29, the operation further comprising extending the operation to other waveform modes or converting the time series waveform to other waveform modes by flipping the time axis, flipping the waveform axis, changing parameters, and / or introducing a shift to the parametric component of the first view of the time series waveform.

46. The medium according to claim 29, wherein the first view of the time series waveform is generated based on a single-channel ECG signal from an electrocardiogram (ECG) system deployed in a patch, a watch, or a sports equipment.

47. The medium according to claim 46, wherein the second view of the time series waveform includes a projection along a planar QRS loop, which is more conducive to morphological interpretation compared to the first view.

48. The medium according to claim 47, wherein the operation further includes performing the separation, replacement, and alteration to determine the center of the QRS complex, determine the width of the QRS complex, and / or determine ST elevation / depression or other cardiovascular diseases or disorders.

49. The medium according to claim 29, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes rotation and / or projection techniques.

50. The medium according to claim 29, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes finding the center of the QRS complex by projecting the QRS complex time series waveform of the ECG as a single-phase waveform, and the operation further includes determining the left ventricular end-diastolic pressure (LVEDP) based on the center of the QRS complex.

51. The medium according to claim 29, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes finding the width of the QRS complex and / or determining the shape of the QRS complex by projecting the QRS complex time series waveform of the ECG as a single-phase waveform, and the operation further includes determining left bundle branch block (LBBB) based on the width and / or the shape of the QRS complex.

52. The medium according to claim 51, wherein: the width of the QRS complex includes the cross-sectional width of the single-phase projection waveform at 50% of the total height of the projection waveform; and / or the shape of the QRS complex includes the double-peak peak of the single-phase projection waveform.

53. The medium according to claim 29, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes determining ST elevation and / or depression by projecting the QRS complex time series waveform of the ECG as a waveform adjacent to the ECG waveform, and the operation further includes determining myocardial infarction and / or ischemia based on the ST elevation and / or depression.

54. The medium according to claim 29, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes determining the T-to-QRS amplitude ratio, which is the ratio of the T-wave amplitude to the QRS complex amplitude, and the method further includes determining myocardial infarction and / or ischemia based on the T-to-QRS amplitude ratio.

55. The medium according to claim 29, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes determining the QRS-T angle as the difference between the angle of a three-dimensional (3D) vector of the T-wave axis and the axis of the QRS complex, the method further including determining myocardial infarction and / or ischemia based on the QRS-T angle.

56. The medium according to claim 29, wherein changing the first view to the second view based on the invariant intrinsic component and the variable parameterized component having the second parameter includes determining left ventricular end-diastolic pressure (LVEDP), left bundle branch block (LBBB), the width and / or shape of the QRS complex, ST elevation and / or depression, the T to QRS amplitude ratio, the QRS-T angle, and / or a combination thereof, the method further including determining myocardial infarction and / or ischemia based on the LVEDP, the LBBB, the width and / or shape of the QRS complex, the ST elevation and / or depression, the T to QRS amplitude ratio, the QRS-T angle, and / or the combination thereof.

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