NONINVASIVE METHOD AND SYSTEM FOR CHARACTERIZING CARDIOVASCULAR SYSTEMS

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First Claim
1. A method for localizing and characterizing both the architectural features and function of cardiovascular tissues, comprising the steps of obtaining ECG data for the heart;
 processing the ECG data to localize, image, and characterize architectural features and function of tissues without use of other measuring devices or invasive procedures; and
using phase information to determine a location of an architectural feature or function of the tissues to display an abnormality associated with the tissues in a 3D image.
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Abstract
The present disclosure uses physiological data, ECG signals as an example, to evaluate cardiac structure and function in mammals. Two approaches are presented, e.g., a modelbased analysis and a spacetime analysis. The first method uses a modified Matching Pursuit (MMP) algorithm to find a noiseless model of the ECG data that is sparse and does not assume periodicity of the signal. After the model is derived, various metrics and subspaces are extracted to image and characterize cardiovascular tissues using complexsubharmonicfrequencies (CSF) quasiperiodic and other mathematical methods. In the second method, spacetime domain is divided into a number of regions, the density of the ECG signal is computed in each region and inputted into a learning algorithm to image and characterize the tissues.
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1 Claim
 1. A method for localizing and characterizing both the architectural features and function of cardiovascular tissues, comprising the steps of obtaining ECG data for the heart;
processing the ECG data to localize, image, and characterize architectural features and function of tissues without use of other measuring devices or invasive procedures; and using phase information to determine a location of an architectural feature or function of the tissues to display an abnormality associated with the tissues in a 3D image.
1 Specification
This application claims priority to U.S. Provisional Patent Application No. 61/684,217, filed on Aug. 17, 2012, entitled “NONINVASIVE METHOD AND SYSTEM FOR CHARACTERIZING CARDIOVASCULAR SYSTEMS,” which is incorporated herein by reference in its entirety.
The current algorithms employed in signal processing of electrocardiographic (ECG) signals are rudimentary and have limited diagnostic accuracy. In fact, validated and accepted ECG scoring systems like the Selvester score have only a 71% accuracy in detecting a previous myocardial infarction when compared to cardiac magnetic resonance (CMR) imaging and the ECG is recognized as having significant limitations in ruling in or ruling out an acute myocardial infarction. The ability of the ECG to detect left ventricular hypertrophy and other conditions is also extremely limited. In fact, the ECG not recommended to be used to rule out left ventricular hypertrophy in patients with hypertension. We claim that analysis of ECG data can be improved upon using techniques to identify and quantify phase space changes to localize, image, and characterize architectural features and function of cardiovascular and other mammalian tissues.
There are various time domain and frequency domain signalprocessing techniques which are being used for the analysis of physiological signals to obtain more detailed information. While time domain techniques are often used, they alone are incapable of quantifying certain fluctuation characteristics of a number of pathologies related to physiological signals. For example, traditional methods for performing frequencydomain analysis of surface ECG signals, such as the Fourier transform, are limited since they do not address the aperiodic random nature of biological and electromagnetic noise. For example, complex ECG waveforms with large variation in their morphologies have been shown to occur with the development of arrhythmias. Dominant frequency analysis on ECG data can be problematic since nonlinear dynamic systems can appear to generate random noise. Discrete fast Fourier transforms and wavelet analysis have been shown experimentally to be incapable of detecting deterministic chaos in the presence of strong periodicity which tends to obscure the underlying nonlinear structures.
The present disclosure generally relates to noninvasive methods and techniques for characterizing mammalian cardiovascular systems. More specifically, the present disclosure relates to noninvasive methods that utilize electrocardiographic (ECG) phase space data to localize, image, and characterize architectural features and function of the myocardium and cardiovascular tissues.
The present disclosure uses physiological data, ECG signals as an example, to evaluate cardiac structure and function in mammals. However, it is also claimed that other physiological data can similarly be used to image and characterize other organ systems in mammals using a similar approach. The present disclosure provides an improved and efficient method to image and characterize the heart using a highresolution ECG data. It is claimed that these ECG data can be used to identify, localize, and characterize cardiovascular tissues. ECG waveforms possess highdimensional data with complex nonlinear variability that cannot be efficiently captured by traditional modeling techniques. Two approaches, namely modelbased analysis and spacetime analysis, are used to study the dynamical and geometrical properties of ECG data. The first method uses a modified Matching Pursuit (MMP) algorithm to find a noiseless model of the ECG data that is sparse and does not assume periodicity of the signal. After the model is derived, various metrics and subspaces are extracted to image and characterize cardiovascular tissues using complexsubharmonicfrequencies (CSF) quasiperiodic and other mathematical methods. In the second method, spacetime domain is divided into a number of regions (12 regions for ventricular tissue, see
As such, the present disclosure provides for a noninvasive system and method whereby ECG measurements can be taken and transformed to characterize and image architectural features of cardiovascular and other tissues. Further, the present disclosure provides a system and method to image (inverse ECG problem) and localize architectural features and function of cardiovascular tissues.
Exemplary embodiments of the present disclosure will hereinafter be described in conjunction with the following drawing figures, wherein like numerals denote like elements, and wherein:
Dynamical signal density can be computed using nonFourier or Fourier n dimensional fractional integral summation across all ECG leads on the derived model over the scan window. Typically the order of fractional integral could be −1.5 or −2.5 or any irrational, complex or real number.
Referring back to 106, the flow also proceeds to 112, where the modeled ECG is split into the low energy complex sub harmonic subspace (CSF). At 114, delayed phase space reconstruction is used to move the single or 3 lead or 12 lead CSF ECG into a 3 or higher dimensional space. At 116, the spacetime domain is divided into 12 Regions or higher and the density of the signal is computed for each region. At 118, the outputs of 110 and 116 are use to as 24 quantities (or higher) that are fed into a nested sinusoidal Gaussians to generate 17 segments model for the regional analysis of myocardial perfusion.
Referring to
Aspects of
where a, b, and c are some constants. For fixed values of a=b=0.1, Rossler system exhibits the following behavior for different values of c.
The ECG data is synchronized with Rossler system and then a semioptimal state is identified that magnifies dynamical features of the physiological signal under study,
In accordance with
Referring again to
Referring again to
Returning to
The last 20% of the selected atoms are used to form a “low energy subspace” signal corresponding to each of the leads. These low energy signals can be called x(t), y(t), and z(t) assuming 3 leads.
There are various time domain and frequency domain signal processing techniques used for the analysis of physiologic signals to obtain more detailed information. CSF exist in many physiological signals, not just the cardiac signals presented, and are likely indicative of other pathophysiological processes not otherwise detectable using prior art methods.
3D Visualization
The output obtained after applying the MMP algorithm on the ECG or other physiological signal, can be represented as a 3D phase space plot, as shown in
The 3D phase space plot localizes the presence of CSF related to altered tissue. For example, the CSF for the heart can be measured as a time delay and as a 3D trajectory in the atrial and ventricular subspaces. CSF trajectory is associated with those components of the ECG not captured by the dictionary, i.e. there is no linear combination of the atoms of the selected dictionaries that can represent the CSF trajectory.
Examples of the 3D phase space plot are shown in
The 3D phase space plot of the present disclosure may be displayed by any type of computing device, including, but not limited to, desktop computers, workstation computers, server computers, cloud computing devices, tablet devices, smart phones, and mobile computing devices.
A methodology will now be described below for producing output from an algorithm that correlates with clinical parameters describing tissue architecture, structure and function. Descriptive attributes in that class include left ventricular mass and fibrosis as measured using CMR LGE imaging. As indicated in
The algorithm utilizes spacetime densities computed using the spacetime analysis method to create a predominantly time agnostic feature set representative of the dynamics of the signal propagation through tissue. The spacetime metrics are then linked with clinical data sets, for example left ventricular mass, using a genetic learning algorithm. The subsequent result can then be used in independent data sets to reliably characterize the tissues of interest as shown in
 Estimate of percent fibrosis as measured using CMR LGE imaging =((cosh((gauss((SD1SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))+(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3{circumflex over ( )}2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))+(SD3+SD4+(SD6*(gauss((SD2*SD4))))+OD5*(gauss(USD7*SD3)/((SD2*SD6)−(SD3*SD6M)))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))−((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SDS))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))−((gauss((gauss(SD7))))/(SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3{circumflex over ( )}2)*SD7*(gauss(SD11))))/(SD1*SD2M))))))*gauss(((SD3+SD4+(SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6)))))){circumflex over ( )}2+((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5))))))))))){circumflex over ( )}2−((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3{circumflex over ( )}2)*SD7*(gauss(SD11))))/(SD1*SD2))))))))){circumflex over ( )}2)/(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3{circumflex over ( )}2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))+(SD3+SD4+(SD6*(gauss((SD2*SD4))))+OD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))+((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SDS))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))+(SD3+SD4+(SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6)))))){circumflex over ( )}2+((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SDS))))))))))){circumflex over ( )}2)))/cosh(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3{circumflex over ( )}2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))/cosh(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2))))))))){circumflex over ( )}2/((SD3+SD4+(SD6*(gauss((SD2*SD4))))+OD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))*((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))*gauss(((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SDS)))M*(gauss((cosh((gauss((SD6+(SD12/(SD6*SDS)))))))))))̂3*gauss(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(5D9))+(gauss((((SD10*SD8)+((SD3{circumflex over ( )}2)*SD7*(gauss(SD11))))/(SD1*5D2)))))))))+(SD3+SD4+SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((S D2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))+(cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5))))))))))))/((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3{circumflex over ( )}2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))−((cosh((gauss((SD1−D2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))))))) SD=signal density
 Estimation of left ventricular mass as measured using CMR=((SD9+(SD4*(cosh(SD5))))/((gauss(SD5))+(gauss(((SD1*5D10*SD7)/((((SD1*5D9*SD10*SD11*SD4)−SD11)−(SD9*SD10*SD12*SD7))−((SD1{circumflex over ( )}2)*SD10*SD5)))))))+((((SD4+(SD1*SD2)+(SD5*SD3)+(SD1*SD2*SD5))−SD8)/(cosh(((gauss((SD2+(SD4/SD1))))−(cosh((gauss((gauss(((SD1*SD3)+((−SD3)/SD5))))))))))))*(SD2+(SD1*5D2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2{circumflex over ( )}2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4))))))*((cosh(SD6))+(cosh((gauss((cosh(SD7))))))+(cosh((((cosh((gauss(SD6)))){circumflex over ( )}2)+((cosh((gauss(SD6))))*(cosh((gauss((gauss((gauss(SD6)))))))))+(cosh((gauss(SD9))))))))−((SD9+(SD3*(cosh(SD5)))))))/((gauss(SD5))+(gauss(((SD1*SD10*SD7)/((((SD1*SD9*SD10*SD11*SD4)−SD11)−(SD9*SD10*SD12*SD7))−((SD1{circumflex over ( )}2)*SD10*SD5))))))){circumflex over ( )}2*(((SD3+(SD1*SD2)+(SD5*SD3)+(SD1*SD2*SD5))−SD8)/(cosh(((gauss((SD2+(SD4/SD1))))−(cosh((gauss((gauss(((SD1*SD3)+((−SD3)/SD5))))))))))))))))/((SD2+(SD1*SD2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2{circumflex over ( )}2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4)))))){circumflex over ( )}2+(SD2+(SD1*SD2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2{circumflex over ( )}2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4)))))){circumflex over ( )}3*gauss((((SD3+(SD1*SD2)+(SD5*SD3)+(SD1*SD2*SD5))−SD8)/(cosh(((gauss((SD2+(SD4/SD1))))−(cosh((gauss((gauss(((SD1*SD3)+((−SD3)/SD5))))))))))))*(SD2+(SD1*SD2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2{circumflex over ( )}2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4))))))))/(((SD9+(SD3*(cosh(SD5))))/((gauss(SD5))+(gauss(((SD1*SD10*SD7)/((((SD1*SD9*SD10*SD11*SD4)−SD11)−(SD9*SD10*SD12*SD7))−((SD1{circumflex over ( )}2)*SD10*SD5))))))){circumflex over ( )}2))) SD=signal density
Ischemia of cardiac tissues is linked to the development of physiological changes that could alter complex subharmonics and results in variable and high dimensional changes.
In accordance with the present disclosure, physiological and pathophysiological features of tissues are modeled accurately and effectively using fractional derivatives. In contrast, classical integer derivativebased models capture these phenomena only approximately or not at all. Traditional integer order derivatives depend only on the local behavior of a function, while fractional derivatives depend on the whole history of the function. In this embodiment, there is utilized a method for detecting beat to beat complex subharmonic structures in the ECG based on digital differentiation and integration of fractional order. Since these signals are mathematically modeled as a linear combination of the selected atoms, they can be differentiated and integrated of fractional order. Let x′ (t), y′ (t), and z′ (t) be their integer order derivatives respectively, these derivatives and there ratios measure instability only at a local point of the signal and therefore are poor measures of stability for long complex ECG signals with significant beattobeat variability. An alternative to an integer derivative is the use of a fractional calculus to detect abnormal CSF signals in a physiological signal based on its past history.
There are two concepts regarding the lowenergy component subspace (made from the last 20% terms found by MMP) that are interesting and useful. First, the fractional derivative of this component can be noiselessly obtained, since it is a linear combination of selected atoms, and this fractional derivative can be useful to localize, image, and characterize architectural features of tissues. In addition, there are some useful fractional properties to consider. Thus suppose that x(t),y(t), and z(t) are respectively the X, Y, and Z coordinates of the lowenergy component and let x^{α}(t), y^{α}(t),and z^{α}(t) be their irrational fractional derivative of order a that can be any real(or complex) number. Then the magnitude of these irrational fractional derivatives can indicate instability when large and positive. Consider the regions when the irrational fractional derivatives are positive, in such regions, the low energy reentrant wavelets that signify alterations in tissue architecture and, or function.
The phase space plot information cannot be easily superimposed on a 3D representation of a given tissue since physiological function is variable across individuals. To overcome this problem, intrinsic phase space imaging does not use the interference in the phase plane of interest. Noiseless subspaces allow the recording of the phase of these waves. In cardiac tissues the amplitude resulting from this interference can be measured, however the phase of the orthogonal leads still carries the information about the structure and generates geometrical contrast in the image, thus the name phasecontrast imaging.
In phasebased imaging, phasecontrast takes advantage of the fact that different bioelectric structures have different impedances, and so spectral and nonspectral conduction delays and bend the trajectory of phase space orbit through the heart by different amounts. These small changes in trajectory can be normalized and quantified on a beattobeat basis and corrected for lead placement and the normalized phase space integrals can be mapped to a geometric mesh using a genetic algorithm to map 17 myocardial segments in the ventricle to various tomographic imaging modalities of the heart from retrospective data (exemplar formulas for 3 of the 17 regions below).
 basal anterior segment=cosh(SD10)−gauss(SD11*SD12*SDCSF1+0.005778*SDCSF2*SD6*SD10*SDCSF3−6.749*SDCSF4*(gauss((((0.0735+(0.3203*SDCSF5*(gauss((30.33*SD8*(gauss(((SD8+((61.1*SDCSF6*SDCSF7)/((SDCSF8*(gauss((9.666*SD1*SDCSF9*SDCSF10))))+(SDCSF11*(gauss((9.666*SD1*SDCSF9*SDCSF10))))+(SDCSF8*SDCSF12*SDCSF6*SDCSF7*(gauss((9.666*SD1*SDCSF9*SDCSF10)))))))−(gauss((gauss(SDCSF7))))))))))))−(2.994*SD10))−(17.03*(gauss((6.882*(gauss(((SD8+((61.1*SDCSF6*SDCSF7)/((SDCSF8*(gauss((9.666*SD1*SDCSF9*SDCSF10))))+(SDCSF11*(gauss((9.666*SD1*SDCSF9*SDCSF10))))+(SDCSF8*SDCSF12*SDCSF6*SDCSF7*(gauss((9.666*SD1*SDCSF9*SDCSF10)))))))−(gauss((gauss(SDCSF7))))))))))))/SD1)))*gauss(SD1))
 mid inferolateral segment=gauss(7.44069511*SD1+6*SD1*SD2+−2.51202217109399*SD3/SD4+SD5*SD6/(SD7*SD8)−SD3*SD8*SD9−0.8372177305*SD1*SD4)
 apical inferior segment=gauss((SD2*SD3−0.2868*SD3−0.2308*gauss(14.35*SD2−9.859*SD4))/(SD1{circumflex over ( )}2*((0.8889*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(5D6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8{circumflex over ( )}2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))+((SD1*((((gauss((aSD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8{circumflex over ( )}2))))))))/(gauss(SD8)))+(0.899.9*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1)−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD8)+((35.21*SDCSF2*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gaussa(SD1−(gaussa((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8{circumflex over ( )}2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD5)+((−5997000*SDCSF3*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSE10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8{circumflex over ( )}2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+5D11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393 SD5))))))/1.8))/SD11))+((0.8889*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8{circumflex over ( )}2))))))))/(gauss(SD8)))+(0.899.9*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSE1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))+*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gaussa(SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8̂2)))))))/(ss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393 SD5))))))/1.8))/SD8)+((35.21*SDCSF2*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8{circumflex over ( )}2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393 SD5))))))/1.8))/SD5)+((−5997000*SDCSF3*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(506/507))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8{circumflex over ( )}2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss(ODCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gaussa(SD1−(gauss((((SD3/(SD1+(SD1 *SD5)))+(1.764e−6*SD1*(SD5{circumflex over ( )}2)*(SD6/SD7))+(SD5*((−1*SD1){circumflex over ( )}2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8{circumflex over ( )}2))))))))/(gauss(SD8)))+(0.899.9*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD11)){circumflex over ( )}3))
 SD=signal density
 SDCSF =signal density complexsubharmonicfrequencies
In the second method, spacetime domain is divided into a number of regions (for example, 12 regions for ventricular and 6 regions for atrial tissues); the density of the baselineremoved ECG signal is computed in each region. These values contain specific information about the nonlinear variability of the physiological signal, specifically the ECG signal, that are linked to an alteration in tissue architecture and, or function. The calcium ion (Ca++) is a universal intracellular messenger. In muscle, Ca++ is central to contractile force activation. Ca++ is also important for temporal and spatial alterations in action potentials, modulation of contractile function due to systemic resistance (blood pressure), energy supplydemand balance (including mitochondrial function), cell death (apoptosis), and transcription regulation. It has been hypothesized that Ca++dependent ion pump variability occurs aperiodically in pathological cardiac myocytes, this creates significant microvolt beattobeat variations in the ECG signals and possibly other physiological signals (e.g., arterial pulse waveform). Variations in the ECG or other physiological signal can be measured and localized by linking the space time density structures to tissues of interest (for example, the 12 ventricular and 6 atrial regions). It should be noted a simple derivative or its ratios is not sufficient to characterize spacetime density structures over many cardiac cycles.
For the cardiac ventricle the 12 quantities are input to a genetic algorithm and are modeled to link 17 myocardial segments in the ventricle (see
Ectopic foci can produce dynamic spatial dispersion of repolarization and conduction block, initiating reentrant arrhythmias. Dynamic spatial dispersion of repolarization in atrial and ventricular tissues can be detected and localized using spacetime analysis on the described 6 atrial and 12 ventricular 6 regions. These quantities are then inputted into a genetic algorithm and are modeled to link regions of interest to various tomographic images from collected data.
Spatial changes in the phase space matrix can be can be computed using nonFourier or Fourier multidimensional fractional integral summation across all ECG leads on the derived model to generate the dynamical spacetime density metrics. For cardiac ventricular tissue these metrics are modeled using a genetic algorithm to link 17 nonlinear nested sinusoidal Gaussian equations previously described to the commonly used 17segment model shown in
Having thus described several embodiments of the present disclosure, 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 localization, imaging, and characterization of architectural features and function of tissues 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. These alterations, improvements, and modifications are intended to be suggested hereby, and are within the spirit and the scope of the present disclosure. 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 present disclosure is limited only by the following claims and equivalents thereto.