NONINVASIVE METHOD AND SYSTEM FOR ESTIMATING MAMMALIAN CARDIAC CHAMBER SIZE AND MECHANICAL FUNCTION

Abstract

The present disclosure generally relates to systems and methods and systems of a noninvasive technique for characterizing cardiac chamber size and cardiac mechanical function. A mathematical analysis of three-dimensional (3D) high resolution data may be used to estimate chamber size and cardiac mechanical function. For example, high-resolution mammalian signals are analyzed across multiple leads, as 3D orthogonal (X,Y,Z), or 10-channel data, for 30 to 800 seconds, to derive estimates of cardiac chamber size and cardiac mechanical function. Multiple mathematical approaches may be used to analyze the dynamical and geometrical properties of the data.

Claims

1.-19. (canceled)

20. A system to noninvasively estimate a subject's cardiac chamber size and cardiac mechanical function, including left ventricular ejection fraction, the system comprising: a processor; and a memory having instructions stored thereon that when executed by the processor cause the processor to: obtain orthogonal data from an acquired measurement of one more surface electrical signals of the subject, wherein the orthogonal data have been obtained from measurements acquired via noninvasive equipment configured to measure electrical properties of the subject's heart; determine, via a numerical integral operation of one or more vectorcardiogram components associated with a vectorcardiogram of the orthogonal data, at least one value of one or more first parameters selected from the group consisting of a sum QRST integral parameter, a 3D volume integral parameter, a spatial QRST angle parameter, a 3D QRS loop volume parameter, a 3D T-loop volume parameter, a spatial ventricular gradient parameter, a spatial ventricular gradient azimuth parameter, and a spatial ventricular gradient elevation parameter; determine at least one value of an estimated cardiac chamber size parameter by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more first models associated with the cardiac chamber size; and determine at least one value of one or more cardiac chamber mechanical function parameters by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more second models associated with each of the cardiac chamber mechanical function parameters.

21. The system of claim 20, wherein the vectorcardiogram comprises a 12- or N-dimensional phase space transformation of the orthogonal data.

22. The system of claim 20, wherein the orthogonal data are acquired via ECG measurement equipment that includes a surface ECG instrument.

23. The system of claim 20, wherein the one or more cardiac chamber mechanical function parameters is selected from the group consisting of a cardiac output parameter, a stroke volume parameter, an end-diastolic volume parameter, an end-systolic volume parameter, and an ejection fraction parameter.

24. The system of claim 22, wherein the orthogonal data are obtained via the ECG measurement equipment over a time period of about 30 seconds to about 800 seconds.

25. The system of claim 20, wherein the at least one value of the one or more cardiac chamber mechanical function parameters is subsequently used to screen patients for structural heart disease.

26. The system of claim 20, wherein the at least one determined value of the one or more cardiac chamber mechanical function parameters comprises ventricular mechanical cardiac function values, the method further comprising using a variability of the ventricular mechanical cardiac function values among a plurality of heart beats in the orthogonal data to determine presence of a decline in cardiac function to assess risk of clinical events.

27. The system of claim 26, wherein the ventricular mechanical cardiac function values include cardiac output, stroke volume, end-diastolic volume, end-systolic volume and ejection fraction.

28. The system of claim 20, wherein the at least one determined value of the one or more cardiac chamber mechanical function parameters comprises atrial mechanical cardiac function values, the method further comprising using a variability of the atrial mechanical cardiac function values among a plurality of heart beats in the orthogonal data to determine presence of a reduced atrial cardiac function and to assess risk of clinical events.

29. The system of claim 20, wherein the at least one value of the Sum QRST integral parameter is determined by: ${\int }_{t_1}^{t_2}.Math..Math.V_x.Math.+{\int }_{t_1}^{t_2}.Math..Math.V_y.Math.+{\int }_{t_1}^{t_2}.Math..Math.V_z.Math.$ wherein V.sub.x, V.sub.y, and V.sub.z are the one or more vectorcardiogram components, and wherein t.sub.2-t.sub.1 comprises a measurement time window for the orthogonal data.

30. The system of claim 20, wherein the at least one value of the 3D QRS loop volume parameter, the 3D T-loop volume parameter, and the 3D volume integral parameter is determined by: ${\int }_{t_1}^{t_2}.Math..Math.V_x.Math.*{\int }_{t_1}^{t_2}.Math..Math.V_y.Math.*{\int }_{t_1}^{t_2}.Math..Math.V_z.Math.$ wherein V.sub.x, V.sub.y, and V.sub.z are the one or more vectorcardiogram components, and wherein t.sub.2-t.sub.1 comprises a measurement time window for the orthogonal data.

31. The system of claim 20, wherein the at least one value of the spatial ventricular gradient (SVG) parameter is determined by: $\sqrt{{\left({\int }_{t_1}^{t_2}.Math.V_x\right)}^2+{\left({\int }_{t_1}^{t_2}.Math.V_y\right)}^2+{\left({\int }_{t_1}^{t_2}.Math.V_z\right)}^2}$ wherein V.sub.x, V.sub.y, and V.sub.z are the one or more vectorcardiogram components, and wherein t.sub.2-t.sub.1 comprises a measurement time window for the orthogonal data.

32. The system of claim 20, wherein the at least one value of the spatial ventricular gradient azimuth parameter is determined by: $\arctan .Math.\frac{{\int }_{t_1}^{t_2}.Math.V_z}{t_1.Math.t_2.Math.V_x.Math.\mathrm{dt}}$ wherein V.sub.x and V.sub.z are the one or more vectorcardiogram components, and wherein t.sub.2-t.sub.1 comprises a measurement time window for the orthogonal data.

33. The system of claim 20, wherein the at least one value of the spatial ventricular gradient elevation parameter is determined by: $\arccos .Math.\frac{{\int }_{t_1}^{t_2}.Math.V_y}{\sqrt{{\left({\int }_{t_1}^{t_2}.Math.V_x\right)}^2+{\left({\int }_{t_1}^{t_2}.Math.V_y\right)}^2+{\left({\int }_{t_1}^{t_2}.Math.V_z\right)}^2}}$ wherein V.sub.x, V.sub.y, and V.sub.z are the one or more vectorcardiogram components, and wherein t.sub.2-t.sub.1 comprises a measurement time window for the orthogonal data.

34. The system of claim 20, wherein the at least one value of the one or more first parameters comprises spatial gradient parameters selected from the group consisting of a peak amplitude of the vectorcardiogram, a size of a QRS vector loop of the vectorcardiogram, an angle of depolarization, an angle of repolarization, and a voltage spatial gradient.

35. The system of claim 20, wherein the orthogonal data comprise high resolution orthogonal data having a resolution of at least 1000 Hz.

36. The system of claim 20, wherein the orthogonal data comprise three-dimensional orthogonal data.

37. The system of claim 20, wherein the memory comprises instructions stored thereon that when executed by the processor further cause the processor to: cause the at least one value of the estimated cardiac chamber size parameter and the at least one value of the one or more cardiac chamber mechanical function parameters to be presented in a graphical user interface.

38. The system of claim 20, wherein the memory comprises instructions stored thereon that when executed by the processor further cause the processor to: determine, via a numerical integral operation of the one or more vectorcardiogram components associated with the vectorcardiogram of the orthogonal data, at least one value of one or more second parameters associated with a heart-beat-to-heart-beat variability of the one or more first parameters.

39. A system for acquiring one or more signals of a subject's heart to be used to noninvasively estimate the subject's cardiac chamber size and cardiac mechanical function, including left ventricular ejection fraction, the system comprising: a component configured to noninvasively acquire one or more surface electrical signals of the subject, wherein the one or more signals is used to derive orthogonal data for estimating at least one value of a cardiac chamber size parameter and one or more cardiac chamber mechanical function parameters of the subject; wherein the estimating comprises: determining, by a processor, via a numerical integral operation of one or more vectorcardiogram components associated with a vectorcardiogram of the orthogonal data, at least one value of one or more first parameters selected from the group consisting of a sum QRST integral parameter, a 3D volume integral parameter, a spatial QRST angle parameter, a 3D QRS loop volume parameter, a 3D T-loop volume parameter, a spatial ventricular gradient parameter, a spatial ventricular gradient azimuth parameter, and a spatial ventricular gradient elevation parameter; determining, by the processor, at least one value of an estimated cardiac chamber size parameter by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more first models associated with the cardiac chamber size; and determining, by the processor, at least one value of one or more cardiac chamber mechanical function parameters by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more second models associated with each cardiac chamber mechanical function.

40. A non-transitory computer readable medium for acquiring one or more signals of a subject's heart to noninvasively estimate the subject's cardiac chamber size and cardiac mechanical function, including left ventricular ejection fraction, the computer-readable medium having instructions stored thereon that when executed by a processor cause the processor to: direct a component configured to noninvasively acquire one or more surface electrical signals of the subject, wherein the one or more signals is used to derive orthogonal data for estimating at least one value of a cardiac chamber size parameter and one or more cardiac chamber mechanical function parameters of the subject; wherein the estimating comprises: determining, by a processor, via a numerical integral operation of one or more vectorcardiogram components associated with a vectorcardiogram of the orthogonal data, at least one value of one or more first parameters selected from the group consisting of a sum QRST integral parameter, a 3D volume integral parameter, a spatial QRST angle parameter, a 3D QRS loop volume parameter, a 3D T-loop volume parameter, a spatial ventricular gradient parameter, a spatial ventricular gradient azimuth parameter, and a spatial ventricular gradient elevation parameter; determining, by the processor, at least one value of an estimated cardiac chamber size parameter by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more first models associated with the cardiac chamber size; and determining, by the processor, at least one value of one or more cardiac chamber mechanical function parameters by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more second models associated with each cardiac chamber mechanical function.

41. A non-transitory computer-readable medium to noninvasively estimate a subject's cardiac chamber size and cardiac mechanical function, including left ventricular ejection fraction, the computer-readable medium having instructions stored thereon that when executed by a processor cause the processor to: obtain orthogonal data that have been derived from one or more acquired surface electrical signals of the subject, wherein the one or more signals has been noninvasively acquired via a component configured to measure electrical properties of the subject's heart; determine, via a numerical integral operation of one or more vectorcardiogram components associated with a vectorcardiogram of the orthogonal data, at least one value of one or more first parameters selected from the group consisting of a sum QRST integral parameter, a 3D volume integral parameter, a spatial QRST angle parameter, a 3D QRS loop volume parameter, a 3D T-loop volume parameter, a spatial ventricular gradient parameter, a spatial ventricular gradient azimuth parameter, and a spatial ventricular gradient elevation parameter; determine at least one value of an estimated cardiac chamber size parameter by applying the one or more first parameters and the one or more second parameters in one or more first models associated with the cardiac chamber size; and determine at least one value of one or more cardiac chamber mechanical function parameters by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more second models associated with each cardiac chamber mechanical function.

42. A system to noninvasively estimate a subject's cardiac chamber size and cardiac mechanical function, including left ventricular ejection fraction, the system comprising: a component configured to noninvasively acquire a measurement of one or more surface electrical signals of the subject, wherein the one or more signals is used to derive orthogonal data for estimating at least one value of a cardiac chamber size parameter and the one or more cardiac chamber mechanical function parameters; a processor; and a memory having instructions stored thereon that when executed of the instructions by the processor cause the processor to: determine, via a numerical integral operation of one or more vectorcardiogram components associated with a vectorcardiogram of the orthogonal data, at least one value of one or more first parameters selected from the group consisting of a sum QRST integral parameter, a 3D volume integral parameter, a spatial QRST angle parameter, a 3D QRS loop volume parameter, a 3D T-loop volume parameter, a spatial ventricular gradient parameter, a spatial ventricular gradient azimuth parameter, and a spatial ventricular gradient elevation parameter; determine at least one value of an estimated cardiac chamber size parameter by applying the at least one value of the one or more first parameters and the at least one value of the one or more second parameters in one or more first models associated with the cardiac chamber size; and determine at least one value of one or more cardiac chamber mechanical function parameters by applying the at least one value of one or more first parameters and the at least one value of the one or more second parameters in one or more second models associated with each of the cardiac chamber mechanical function parameters.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The components in the drawings are not necessarily to scale relative to each other. Like reference numerals designate corresponding parts throughout the several views.

[0013] FIG. 1 illustrates exemplar vectorcardiograms and three dimensional integrals that may be computed and used in estimating cardiac chamber size and mechanical function;

[0014] FIG. 2 illustrates, in the vectorcardiograms of FIG. 1, a spatial QRST angle that may be used as a metric for evaluating cardiac chamber size and mechanical function;

[0015] FIG. 3 illustrates a workflow to generate a model that is predictive of ejection fraction, diastolic volume, systolic volume, cardiac chamber volumes and masses;

[0016] FIG. 4 illustrates a correlation plot of predicted LVEF from the ECG against the MUGA measured ejection fraction; and

[0017] FIG. 5 illustrates a Bland-Altman plot of predicted LVEF from an ECG-measured assessment and a MUGA-measured assessment.

DETAILED DESCRIPTION

[0018] The present disclosure has been designed to assess cardiac chamber size and cardiac mechanical function by evaluating the electrical activity of the heart. With reference to the equations that follow the written description below, the present disclosure provides a method whereby high-resolution mammalian ECG signals are analyzed across multiple leads, as 3D orthogonal (X,Y,Z) or 10-channel data, for 30 to 800 seconds (Eq. 1), to derive estimates of cardiac chamber size and cardiac mechanical function. Multiple mathematical approaches are used to analyze the dynamical and geometrical properties of the ECG data under study.

[0019] FIG. 1 illustrates exemplar vectorcardiograms and three dimensional integrals that may be computed and used in estimating cardiac chamber size and mechanical function. The first method uses vectorcardiography and topology to characterize the ECG manifestations of the cardiac repolarization and depolarization process. The vectorcardiogram (VCG) is a method that records, in the three planes of space, the electrical potential of the heart during the cardiac cycle. Chamber activation manifests as the P loop (atrial depolarization), a dominant high amplitude QRS loop (ventricular depolarization), and the T loop (ventricular depolarization (Eq. 10), which result from the spatial temporal summation of multiple vectors of bioelectric potentials that originate in the heart during the cardiac cycle. The entirety of the cycle is known as the PQRST, and can be referenced in sub-cycles. The spatial electrical gradients (Eq. 4) embedded in the electrical properties relate to the volume and the local properties of the chamber of interest. This includes bioelectric inhomogeneities and the physics of cardiac mechanical function.

[0020] FIG. 2 illustrates a spatial QRST angle that may be used as a metric for evaluating cardiac chamber size and mechanical function. The spatial gradients obtained by the VCG can be measured in a variety of ways including the QRST integral (Eq. 2), which captures the peak amplitudes, the size of the QRS vector loop (Eq. 9), and the angles of depolarization and repolarization (Eqs. 5,6). The depolarization of the heart moves from the endocardium to the epicardium, and this is captured in the QRS vector loop volume (Eq. 9) morphology. This rapid myocardial activation, in early ventricular systole, develops perfusion pressure. Maximal right and left pressure is reached before the beginning of the T wave. These pressure gradients embed cardiac function information in the voltage spatial gradients (Eq. 4). The pressure in the endocardium is higher than in the epicardium; this forces ventricular myocytes to repolarize in the epicardium first. The unequal distribution of endocardial pressure throughout the ventricles delays the time the endocardium begins to repolarize and this delay is correlated to cardiac output. These delays can be quantified with the volume QRST integral (Eq. 3) over an ECG signal across each of the three leads (X, Y, Z) in a given time period (typically 30-800 seconds). The magnitude of this integral is predictive when extracting LV chamber size and estimating LVEF from the ECG.

[0021] Other features required to reliably assess LVEF include, but are not limited to, the morphology of the VCG loop, conduction velocity over the initial 50% of the QRS VCG (Eq. 7), and spatial alterations in the QRST angle.

[0022] Corrections for body size (body mass index), gender, cardioactive medications, and variations in ECG lead placement are required to reliably assess LVEF.

[0023] The aforementioned techniques and approaches can also be used to assess the size and function of other chambers, including the right and left atria, and to quantify myocardial relaxation, commonly referred to as diastolic function.

[0024] FIG. 3 illustrates a workflow to generate a model that is predictive of ejection fraction, diastolic volume, systolic volume, cardiac chamber volumes and mass. This includes left ventricular (I-V) and right ventricular (RV) end-systolic (ES) and end-diastolic (ED) linear dimensions and volumes; LV and RV ejection fraction (EF), and LV mass (LVM); and left atrial (LA) and right atrial (RA) end-systolic volumes.

[0025] At 302, 30 to 100 (or more) consecutive seconds of ECG data are gathered at each of a single 12-lead, or 3-lead, orthogonal lead(s). At 304, DC components and baseline wander are removed. This may be performed by using a modified moving average filter created for each lead. At 306, the single or 12-lead ECG data is moved into three-dimensional space. This may be performed, for example, using delayed phase space reconstruction or techniques using the Inverse Dower matrix (11). At 308, the space-time domain is divided into PQRST regions, and spatial gradients, angles, volumes, etc., and loop areas are numerically computed. At 310, 12 quantities are mathematically modelled to cardiac output. Alternatively or additionally, at 312, the 12 quantities are mathematically modelled to ejection fraction, and diastolic and systolic volume. Thus, the workflow of FIG. 3 provides a method to model cardiac output, ejection fraction, and diastolic and systolic volume.

[0026] FIG. 4 is a correlation plot of predicted LVEF (left ventricular ejection fraction) from the ECG of the present disclosure against the MUGA-measured ejection fraction (multiple gated acquisition measured ejection fraction are also referred to as radionuclide angiography LV ejection fraction). The techniques described herein were applied to a dataset of 213 orthogonal high-resolution (1000 Hz) ECGs (ECG-EF) with paired MUGA-evaluated left ventricular ejection fraction values. A statistically significant linear correlation in LVEF values was found (r=0.7, p<0.001). 3D-High Resolution ECG-computed LVEF and MUGA-measured LVEF had similar prognostic utility. For each 10% increase in LVEF, the risk of death was 40% lower with the MUGA (p<0.01) and 54% lower with ECG-estimated (p<0.01) LVEF.

[0027] FIG. 5 is a Bland-Altman plot used here to examine the disparity between the two measurements (ECG-EF vs MUGA EF) described and shown in connection with FIG. 4. The mean ECG-estimated LVEF was, on average, 2.5% (95% confidence interval 0.7% to 4.3%) lower than the MUGA-estimated LVEF. The range of the MUGA-calculated ejection fraction values was 15% to 75%. Together, the results described by FIGS. 4 and 5 demonstrate that the LVEF computed from the ECG signal using the methods disclosed is clinically equivalent to that measured by the gold standard method of MUGA. The equation that combined the different characterization methods, discussed to create these results, is below. This exemplar is not limiting and there are other solutions in this family with similar diagnostic ability, two of which are also provided.

[0028] Ejection Fraction Exemplar One=spatial VentricularGradientAzimuth+TWaveLoopVolumê2+36.63895238712*erf(1.29854235984933+spatialVentricularGradientAzimuth*QRVelocity−TWaveLoopVolume)+(3.73595220608718*spatialConductionVelocityGradient−4.95485967820254*spatialVentricularGradientElevation)/(TWaveLoop Volumê2+erf(spatialVentricularGradient̂4/(3.73595220608718*spatialConduction Velocity Gradient−4.95485967820254*spatialVentricularGradientElevation)))+CF

[0029] Ejection Fraction Exemplar Two=−0.381568077439472/(spatialVentricularGradientElevation*erf(spatialVentricularGradientAzimuth))+41.2156652358613*gauss(gauss(6.56930578402457+−2/spatialVentricularGradientAzimuth))+0.930158852689193*spatialConductionVelocityGradient̂2*erfc(erf(spatialVentricularGradient))/(spatialVentricularGradientElevation*TWaveLoopVolume)+CF

[0030] Ejection Fraction Exemplar Three=17.3495543240011+1.25836680957487*spatialConductionVelocityGradient+0.380736486799911/spatialVentricularGradient+0.310999364860442*spatialVentricularGradientElevation*spatialVentricularGradientAzimuth*erf(gauss(−2)*xyQRSLoopArea)+0.310999364860442*spatialVentricularGradientElevation*TWaveLoop Volumê2*erf(gauss(−2)*xyQRSLoopArea)+29.6734283926203*gauss(6.707623776*spatialVentricularGradient*spatialVentricularGradientElevation+−6.746230385*spatialVentricularGradientAzimuth*spatialVentricularGradientElevation̂3/spatialVentricularGradient)+11.394690922442*spatialVentricularGradientElevation*erf(gauss(−2)*xyQRSLoopArea)*erf(1.29854236+spatialVentricularGradientAzimuth*QRVelocity−TWaveLoopVolume)+0.310999364860442*spatial VentricularGradientAzimuth*erf(gauss(−2)*xyQRSLoopArea)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)*gauss(spatialVentricularGradient̂5/(erf(spatialVentricularGradientAzimutĥ2)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)))+0.310999364860442*TWaveLoopVolumê2*erf(gauss(−2)*xyQRSLoopArea)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)*gauss(spatialVentricularGradient̂5/(erf(spatialVentricularGradientAzimutĥ2)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)))+(23.0195707867421*spatialVentricularGradient*TWaveLoopVolume*spatialConductionVelocityGradient−30.5300327217556*spatialVentricularGradient*spatialVentricularGradientElevation*TWaveLoopVolume)/(xzQRSLoopArea*TWaveLoopVolumê2+xzQRSLoopArea*erf(spatialVentricularGradient̂4/(3.735952206*spatialConductionVelocityGradient−4.954859678*spatialVentricularGradientElevation)))+11.394690922442*erf(gauss(−2)*xyQRSLoopArea)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)*erf(1.29854236+spatialVentricularGradientAzimuth*QRVelocity−TWaveLoopVolume)*gauss(spatialVentricularGradient̂5/(erf(spatialVentricularGradientAzimutĥ2)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)))+1.16187876321497*spatialVentricularGradientElevation*spatialConductionVelocityGradient*erf(gauss(−2)*xyQRSLoopArea)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)*gauss(spatialVentricularGradient̂5/(erf(spatialVentricularGradientAzimutĥ2)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)))/(spatialVentricularGradientElevation*TWaveLoopVolumê2+spatialVentricularGradientElevation*erf(spatialVentricularGradient̂4/(3.735952206*spatialConductionVelocityGradient−4.954859678*spatialVentricularGradientElevation)))+(6.16163417448763*spatialVentricularGradient*spatialVentricularGradientAzimuth*TWaveLoopVolume+25.981797*TWaveLoopVolume*spatialVentricularGradient̂2+6.16163417448763*spatialVentricularGradient*TWaveLoopVolume*TWaveLoopVolumê2+1.863894357*TWaveLoopVolume*spatialConductionVelocityGradient*spatialVentricularGradient̂2+225.755821163649*spatialVentricularGradient*TWaveLoopVolume*erf(1.29854236+spatialVentricularGradientAzimuth*QRVelocity−TWaveLoopVolume)+43.95231606*TWaveLoopVolume*spatialVentricularGradient̂2*gauss(6.707623776*spatialVentricularGradient*spatialVentricularGradientElevation+−6.746230385*spatialVentricularGradientAzimuth*spatialVentricularGradientElevation̂3/spatialVentricularGradient))/xzQRSLoopArea+(1.16187876321497*spatialVentricularGradientElevation*spatialConductionVelocityGradient*erf(gauss(−2)*xyQRSLoopArea)−1.54095821283061*spatialVentricularGradientElevation̂2*erf(gauss(−2)*xyQRSLoopArea)−1.54095821283061*spatialVentricularGradientElevation*erf(gauss(−2)*xyQRSLoopArea)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea)*gauss(spatialVentricularGradient̂5/(erf(spatialVentricularGradientAzimutĥ2)*erf(2258*PQRSTIntegralProd/yzQRSLoopArea))))/(TWaveLoopVolumê2+erf(spatialVentricularGradient̂4/(3.735952206*spatialConductionVelocityGradient−4.954859678*spatialVentricularGradientElevation)))−spatialVentricularGradientElevation*TWaveLoopVolume*spatialConductionVelocityGradient+CF

[0031] As described herein, the following example formulae, equations and relationships may be used to estimate LVEF:

[00001]$1..Math..Math.\mathrm{ECG}.Math..Math.\mathrm{time}.Math..Math.\mathrm{window}=t.Math..Math.2-t.Math..Math.1$$2..Math..Math.\mathrm{SumQRST}={\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vx}.Math.+{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vy}.Math.+{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vz}.Math.$$3..Math..Math.\mathrm{DECG}.Math..Math.\mathrm{Volume}.Math..Math.\mathrm{Integral}=\mathrm{VPQRST}={\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vx}.Math.*{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vy}.Math.*{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vz}.Math.$$4..Math..Math.\mathrm{Spatial}.Math..Math.\mathrm{ventricular}.Math..Math.\mathrm{gradient}.Math..Math.\left(\mathrm{SVG}\right)=\sqrt{\left({\left({\int }_{t_1}^{t_2}.Math.\mathrm{Vx}\right)}^2+{\left({\int }_{t_1}^{t_2}.Math.\mathrm{Vy}\right)}^2+{\left({\int }_{t_1}^{t_2}.Math.\mathrm{Vz}\right)}^2\right)}$$5..Math..Math.\mathrm{Spatial}.Math..Math.\mathrm{ventricular}.Math..Math.\mathrm{gradient}.Math..Math.\mathrm{elevation}=\arccos \left(\left({\int }_{t_1}^{t_2}.Math.\mathrm{Vydt}\right)/\mathrm{SVG}\right)$$6..Math..Math.\mathrm{Spatial}.Math..Math.\mathrm{ventricular}.Math..Math.\mathrm{gradient}.Math..Math.\mathrm{azimuth}=\arctan \left((.Math.{\int }_{t_1}^{t_2}.Math.\mathrm{Vzdt})/{\int }_{t_1}^{t_2}.Math.\mathrm{Vxdt}\right)$$7..Math..Math.\mathrm{Spatial}.Math..Math.\mathrm{conduction}.Math..Math.\mathrm{velocity}.Math..Math.\mathrm{gradient}.Math..Math.\left(\mathrm{SCVG}\right)=\sqrt{\left({\left(\mathrm{dVx}/\mathrm{dt}\right)}^2+{\left(\mathrm{dVy}/\mathrm{dt}\right)}^2+{\left(\mathrm{dVz}/\mathrm{dt}\right)}^2\right)}$$8..Math..Math.\mathrm{Spatial}.Math..Math.\mathrm{conduction}.Math..Math.\mathrm{velocity}.Math..Math.\mathrm{elevation}=\arccos \left(\frac{\frac{\mathrm{dVy}}{\mathrm{dt}}}{\mathrm{SCVG}}\right)$$9..Math..Math.3.Math.\mathrm{DQRS}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume}=\mathrm{SumQRS}={\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vx}.Math.*{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vy}.Math.*{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vz}.Math.$$10..Math..Math.3.Math.\mathrm{DT}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume}=\mathrm{VT}={\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vx}.Math.*{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vy}.Math.*{\int }_{t_1}^{t_2}.Math..Math.\mathrm{Vz}.Math.$$11..Math..Math.\mathrm{Cardiac}.Math..Math.\mathrm{output}=f\left(3.Math.\mathrm{DT}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},3.Math.\mathrm{DQRS}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},\mathrm{Spatial}.Math..Math.\mathrm{ventricular}.Math..Math.\mathrm{gradient},3.Math.\mathrm{DECG}.Math..Math.\mathrm{Volume}.Math..Math.\mathrm{Integral},\mathrm{SumQRST}\right)$$12..Math..Math.\mathrm{Stroke}.Math..Math.\mathrm{volume}=f\left(3.Math.\mathrm{DECG}.Math..Math.\mathrm{Volume}.Math..Math.\mathrm{Integral},3.Math.\mathrm{DT}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},3.Math.\mathrm{DQRS}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},\mathrm{SumQRST},\mathrm{peak}.Math..Math.\mathrm{spatial}.Math..Math.\mathrm{QRST}.Math..Math.\mathrm{angle}\right)$$13..Math..Math.\mathrm{End}.Math.\text{-}.Math.\mathrm{systolic}.Math..Math.\mathrm{volume}=f\left(3.Math.\mathrm{DECG}.Math..Math.\mathrm{Volume}.Math..Math.\mathrm{Integral},3.Math.\mathrm{DT}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},3.Math.\mathrm{DQRS}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},\mathrm{SumQRST},\mathrm{peak}.Math..Math.\mathrm{spatial}.Math..Math.\mathrm{QRST}.Math..Math.\mathrm{angle},\mathrm{Spatial}.Math..Math.\mathrm{ventricular}.Math..Math.\mathrm{gradient}.Math..Math.\mathrm{elevation}\right)$$14..Math..Math.\mathrm{End}.Math.\text{-}.Math.\mathrm{diastolic}.Math..Math.\mathrm{volume}=f\left(3.Math.\mathrm{DECG}.Math..Math.\mathrm{Volume}.Math..Math.\mathrm{Integral},3.Math.\mathrm{DT}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},3.Math.\mathrm{DQRS}.Math..Math.\mathrm{loop}.Math..Math.\mathrm{volume},\mathrm{SumQRST},\mathrm{peak}.Math..Math.\mathrm{spatial}.Math..Math.\mathrm{QRST}.Math..Math.\mathrm{angle},\mathrm{Spatial}.Math..Math.\mathrm{ventricular}.Math..Math.\mathrm{gradient}.Math..Math.\mathrm{elevation}\right)$$15..Math..Math.\mathrm{CF}=\mathrm{Correction}.Math..Math.\mathrm{factors}.Math..Math.\mathrm{which}.Math..Math.\mathrm{include}.Math..Math.\mathrm{race},\mathrm{weight},\mathrm{age},\mathrm{gender},\mathrm{medication}$$16..Math..Math.\mathrm{Ejection}.Math..Math.\mathrm{Fraction}=\frac{\mathrm{End}.Math..Math.\mathrm{diastolic}.Math..Math.\mathrm{volume}-\mathrm{End}.Math..Math.\mathrm{systolic}.Math..Math.\mathrm{volume}}{\mathrm{End}.Math..Math.\mathrm{diastolic}.Math..Math.\mathrm{volume}}*100$

[0032] Having thus described implementations of the claimed invention, it will be rather apparent to those skilled in the art that the foregoing detailed disclosure is intended to be presented by way of example only, and is not limiting. Many advantages for noninvasive method and system for estimate cardiac chamber size and cardiac mechanical function have been discussed herein. Various alterations, improvements, and modifications will occur and are intended to those skilled in the art, though not expressly stated herein. Any alterations, improvements, and modifications are intended to be suggested hereby, and are within the spirit and the scope of the claimed invention. Additionally, the recited order of the processing elements or sequences, or the use of numbers, letters, or other designations therefore, is not intended to limit the claimed processes to any order except as may be specified in the claims. Accordingly, the claimed invention is limited only by the following claims and equivalents thereto.

REFERENCES

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[0044] All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference was individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.