Changing views of time series waveforms
Electrical ventricular depolarization may be represented by its vectorcardiographic QRS loop, which exists in 3D space. By recognizing that the QRS loop is often a closed trajectory on a plane (2D), it is possible to change (e.g., by rotation, projection, etc.) the single-channel QRS into a different view angle along that plane to provide a viewpoint more favorable for morphologic interpretation. Any monophasic or biphasic single-channel QRS (time series) waveform can be decomposed into the form x(α, t)=sin(αt) u(t), with t spanning [0, 2π], where u(t) is an unchanging intrinsic component that is generally upright and monophasic, and where sin(αt) is a changeable component of the waveform. This way, x(α, t) may be changed by replacing a parameter of the original changeable component sin(αt) with a second parameter associated with a target view of the waveform, such as the upright monophasic sin(0.5t). Meanwhile the intrinsic component remains unchanged during this change.
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 an unchanging intrinsic component and a changeable parameterized component;
replacing a first parameter of the changeable parameterized 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 unchanging intrinsic component and the changeable parameterized component with the second parameter.
2 . The method of claim 1 , wherein the time series waveform comprises a monophasic or biphasic single channel QRS waveform associated with an electrocardiogram (ECG).
3 . The method of claim 2 , wherein the time series waveform comprises a projection of a QRS loop.
4 . The method of claim 1 , wherein the unchanging intrinsic component is upright and monophasic.
5 . The method of claim 1 , wherein the parameterized component comprises a sinusoidal function and the first and second parameters comprise different frequencies of the sinusoidal function.
6 . The method of claim 5 , wherein the sinusoidal function is a sine function or a cosine function.
7 . The method of claim 1 , wherein the parameterized component comprises a Taylor series expansion and the first and second parameters comprise different Taylor series.
8 . The method of claim 1 , wherein replacing the first parameter with the second parameter comprises parameterized component division.
9 . The method of claim 1 , further comprising mitigating potential singularities or near-singularities caused by parameterized component division by (a) identifying segments of the second view of the time series waveform that comprise the potential singularities or near-singularities, and (b) applying an alternative computation to change the first view to the second view at these potential singularity or near-singularity segments.
10 . The method of claim 9 , wherein the potential singularities or near singularities are identified based on a threshold on sines of frequencies of the first view of the time series waveform.
11 . The method of claim 9 , wherein the alternative computation comprises interpolation of the identified segments using the second view of the time series waveform at segments that are not near-zero, as determined by parametrized component replacement.
12 . The method of claim 9 , wherein the alternative computation is performed using functional approximation, as a parametrized component when the second parameter approaches singularity.
13 . The method of claim 1 , wherein the first parameter of the changeable parameterized component associated with the first view is determined based on a first zero crossing of the time series waveform.
14 . The method of claim 1 , further comprising mitigating inexact parameter determinations by perturbation, the perturbation comprising testing different parameter values to determine which parameter value provides a best changed time series waveform continuity (or least discontinuity).
15 . The method of claim 14 , further comprising determining discontinuity by determining slopes of the time series waveform preceding, during, and following singularity or near-singularity segments.
16 . The method of claim 14 , further comprising determining discontinuity by determining a largest third derivative throughout the second view of the time series waveform at each trial parameter value.
17 . The method of claim 1 , further comprising extending the method to, or converting the time series waveform to, other waveform patterns by flipping a time axis, flipping a waveform axis, changing the parameter, and/or introducing a shift to the parameterized component of the first view of the time series waveform.
18 . The method of claim 1 , 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, watch, or exercise equipment.
19 . The method of claim 18 , wherein the second view of the time series waveform comprises a projection along a planar QRS loop that is more favorable for morphologic interpretation compared to the first view.
20 . The method of claim 19 , further comprising performing the separating, replacing, and changing to determine a center of a QRS complex, determine a width of the QRS complex, and/or determine ST elevation/depression or other cardiovascular diseases or conditions.
21 . The method of claim 1 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises rotation and/or projection techniques.
22 . The method of claim 1 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises finding a center of a QRS complex by projecting a QRS complex time series waveform of an ECG to a waveform that is monophasic, the method further comprising determining a left ventricular end diastolic pressure (LVEDP).
23 . The method of claim 1 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises finding a width of a QRS complex and/or determining a shape of the QRS complex by projecting a QRS complex time series waveform of an ECG to a waveform that is monophasic, the method further comprising determining a left bundle branch block (LBBB).
24 . The method of claim 23 , wherein:
the width of the QRS complex comprises a cross-section width of a monophasic projected waveform at 50% of an overall height of the projected waveform; and/or
the shape of the QRS complex comprises bi-modal peaks of the monophasic projected waveform.
25 . The method of claim 1 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining ST elevation and/or depression by projecting a QRS complex time series waveform of an ECG to a waveform that is contiguous to an ECG waveform, the method further comprising determining myocardial infarction and/or ischemia based on the ST elevation and/or depression.
26 . The method of claim 1 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining a T-to-QRS amplitude ratio that is an amplitude of a T-wave as a proportion of an amplitude of a QRS complex, the method further comprising determining myocardial infarction and/or ischemia based on the T-to-QRS amplitude ratio.
27 . The method of claim 1 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining a QRS-T angle as the difference between 3-dimensional (3D) vectors of a T-wave axis and an angle of a QRS complex axis, the method further comprising determining myocardial infarction and/or ischemia based on the QRS-T angle.
28 . The method of claim 1 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining a left ventricular end diastolic pressure (LVEDP), a left bundle branch block (LBBB), a width and or a shape of a QRS complex, an ST elevation and/or depression, a T-to-QRS amplitude ratio, a QRS-T angle, and/or a combination thereof, the method further comprising 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, the instructions when executed by a computer causing the computer to perform operations comprising:
separating a first view of a time series waveform into an unchanging intrinsic component and a changeable parameterized component;
replacing a first parameter of the changeable parameterized component associated with the first view 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 unchanging intrinsic component and the changeable parameterized component with the second parameter.
30 . The medium of claim 29 , wherein the time series waveform comprises a monophasic or biphasic single channel QRS waveform associated with an electrocardiogram (ECG).
31 . The medium of claim 30 , wherein the time series waveform comprises a projection of a QRS loop.
32 . The medium of claim 29 , wherein the unchanging intrinsic component is upright and monophasic.
33 . The medium of claim 29 , wherein the parameterized component comprises a sinusoidal function and the first and second parameters comprise different frequencies of the sinusoidal function.
34 . The medium of claim 33 , wherein the sinusoidal function is a sine function or a cosine function.
35 . The medium of claim 29 , wherein the parameterized component comprises a Taylor series expansion and the first and second parameters comprise different Taylor series.
36 . The medium of claim 29 , wherein replacing the first parameter with the second parameter comprises parameterized component division.
37 . The medium of claim 29 , the operations further comprising mitigating potential singularities or near-singularities caused by parameterized component division by (a) identifying segments of the second view of the time series waveform that comprise the potential singularities or near-singularities, and (b) applying an alternative computation to change the first view to the second view at these potential singularity or near-singularity segments.
38 . The medium of claim 37 , wherein the potential singularities or near singularities are identified based on a threshold on sines of frequencies of the first view of the time series waveform.
39 . The medium of claim 37 , wherein the alternative computation comprises interpolation of the identified segments using the second view of the time series waveform at segments that are not near-zero, as determined by parametrized component replacement.
40 . The medium of claim 37 , wherein the alternative computation is performed using functional approximation, as a parametrized component when the second parameter approaches singularity.
41 . The medium of claim 29 , wherein the first parameter of the changeable parameterized component associated with the first view is determined based on a first zero crossing of the time series waveform.
42 . The medium of claim 29 , the operations further comprising mitigating inexact parameter determinations by perturbation, the perturbation comprising testing different parameter values to determine which parameter value provides a best changed time series waveform continuity (or least discontinuity).
43 . The medium of claim 42 , the operations further comprising determining discontinuity by determining slopes of the time series waveform preceding, during, and following singularity or near-singularity segments.
44 . The medium of claim 42 , the operations further comprising determining discontinuity by determining a largest third derivative throughout the second view of the time series waveform at each trial parameter value.
45 . The medium of claim 29 , the operations further comprising extending the operations to, or converting the time series waveform to, other waveform patterns by flipping a time axis, flipping a waveform axis, changing the parameter, and/or introducing a shift to the parameterized component of the first view of the time series waveform.
46 . The medium of claim 29 , 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, watch, or exercise equipment.
47 . The medium of claim 46 , wherein the second view of the time series waveform comprises a projection along a planar QRS loop that is more favorable for morphologic interpretation compared to the first view.
48 . The medium of claim 47 , the operations further comprising performing the separating, replacing, and changing to determine a center of a QRS complex, determine a width of the QRS complex, and/or determine ST elevation/depression or other cardiovascular diseases or conditions.
49 . The medium of claim 29 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises rotation and/or projection techniques.
50 . The medium of claim 29 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises finding a center of a QRS complex by projecting a QRS complex time series waveform of an ECG to a waveform that is monophasic, the operations further comprising determining a left ventricular end diastolic pressure (LVEDP) based on the center of the QRS complex.
51 . The medium of claim 29 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises finding a width of a QRS complex and/or determining a shape of the QRS complex by projecting a QRS complex time series waveform of an ECG to a waveform that is monophasic, the operations further comprising determining a left bundle branch block (LBBB) based on the width and/or the shape of the QRS complex.
52 . The medium of claim 51 , wherein:
the width of the QRS complex comprises a cross-section width of the monophasic projected waveform at 50% of an overall height of the projected waveform; and/or
the shape of the QRS complex comprises bi-modal peaks of the monophasic projected waveform.
53 . The medium of claim 29 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining ST elevation and/or depression by projecting a QRS complex time series waveform of an ECG to a waveform that is contiguous to an ECG waveform, the operations further comprising determining myocardial infarction and/or ischemia based on the ST elevation and/or depression.
54 . The medium of claim 29 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining a T-to-QRS amplitude ratio that is an amplitude of a T-wave as a proportion of an amplitude of a QRS complex, the method further comprising determining myocardial infarction and/or ischemia based on the T-to-QRS amplitude ratio.
55 . The medium of claim 29 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining a QRS-T angle as the difference between 3-dimensional (3D) vectors of a T-wave axis and an angle of a QRS complex axis, the method further comprising determining myocardial infarction and/or ischemia based on the QRS-T angle.
56 . The medium of claim 29 , wherein changing the first view to the second view based on the unchanging intrinsic component and the changeable parameterized component with the second parameter comprises determining a left ventricular end diastolic pressure (LVEDP), a left bundle branch block (LBBB), a width and or a shape of a QRS complex, an ST elevation and/or depression, a T-to-QRS amplitude ratio, a QRS-T angle, and/or a combination thereof, the method further comprising 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.