Patent Publication Number: US-2023157619-A1

Title: System and method for mapping cardiac activity

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims benefit of U.S. Provisional Application No. 63/012,998, filed 21 Apr. 2020, which is hereby incorporated by reference as though fully set forth herein. 
    
    
     BACKGROUND 
     The present disclosure relates generally to electrophysiological visualization and mapping. More specifically, the present disclosure relates to a system, method, and apparatus for generating visualizations of cardiac activity. 
     Electrophysiological mapping, and more particularly electrocardiographic mapping, is a part of numerous cardiac diagnostic and therapeutic procedures. As the complexity of such procedures increases, however, the electrophysiology maps utilized must increase in quality, in density, and in the rapidity and ease with which they can be generated. 
     Electrophysiology studies can include the creation of a local activation time (LAT) map. LAT maps can, for example, provide insight to a practitioner as to how an arrhythmia is traveling throughout the cardiac chambers. Indeed, those of ordinary skill in the art will be familiar with the graphical presentation of LAT maps in electroanatomical mapping systems. 
     In general, however, only a single LAT can be computed for a given electrogram. This may not be desirable for complex electrograms with low amplitude and long and fractionated potentials, such as may be common in low-voltage myocardium. 
     BRIEF SUMMARY 
     Disclosed herein is a method of visualizing cardiac activity. The method includes: receiving a plurality of electrophysiology (EP) data points at an electroanatomical mapping system, wherein each EP data point of the plurality of EP data points includes an electrogram signal; the electroanatomical mapping system classifying a first subset of the plurality of EP data points as substrate EP data points and a second subset of the plurality of EP data points as healthy EP data points; the electroanatomical mapping system generating a cloud map of the first subset of the plurality of EP data points; and the electroanatomical mapping system outputting a graphical representation of the cloud map of the first subset of the plurality of EP data points in combination with a graphical representation of an electrophysiology map of the second subset of the plurality of EP data points. 
     In aspects of the disclosure, the electroanatomical mapping system classifies a given EP data point of the plurality of EP data points as a substrate EP data point when a QRS duration metric for the given EP data point exceeds a preset threshold and as a healthy EP data point otherwise. 
     The method can also include transforming the electrogram signal associated with the EP data point into the wavelet domain, thereby computing a scalogram, and computing a peak-frequency function of the scalogram. For instance, a continuous wavelet transformation can be applied to the electrogram signal to compute the scalogram. The continuous wavelet transformation can utilize a high time-resolution mother wavelet, such as a Paul wavelet. 
     According to aspects of the disclosure, the step of the electroanatomical mapping system generating a cloud map of the first subset of the plurality of EP data points includes the electroanatomical mapping system: applying a Gaussian splatting algorithm to the first subset of the plurality of EP data points to create a structured points dataset; and applying an iso-contouring algorithm to the structured points dataset. 
     Also disclosed herein is a method of visualizing cardiac activity. The method includes receiving a plurality of electrophysiology (EP) data points at an electroanatomical mapping system, wherein each EP data point of the plurality of EP data points includes an electrogram signal. The method also includes, for each EP data point of the plurality of EP data points, the electroanatomical mapping system: transforming the electrogram signal for the EP data point into the wavelet domain, thereby computing a scalogram; and computing a wave function of the scalogram, thereby computing a plurality of wave functions. The electroanatomical mapping system generates a propagation wave map from the plurality of wave functions and outputs graphical representation of the propagation wave map. 
     In embodiments of the disclosure, the step of transforming the electrogram signal for the EP data point into the wavelet domain comprises applying a continuous wavelet transformation to the electrogram signal to compute the scalogram. The continuous wavelet transformation can utilize a high time-resolution mother wavelet, such as a Paul wavelet. 
     The step of computing a wave function of the scalogram can include computing a peak-frequency function of the scalogram. In other embodiments, the step of computing a wave function of the scalogram can include computing a composite wave function of the scalogram. 
     The propagation wave map can include a propagation wave trail map and/or an interpolated propagation wave map. 
     Also disclosed herein is a system for visualizing cardiac activity including a visualization module configured to: receive a plurality of electrophysiology (EP) data points, wherein each EP data point of the plurality of EP data points includes an electrogram signal; classify a first subset of the plurality of EP data points as substrate EP data points and a second subset of the plurality of EP data points as healthy EP data points; generate a cloud map of the first subset of the plurality of EP data points; and output a graphical representation of the cloud map of the first subset of the plurality of EP data points in combination with a graphical representation of an electrophysiology map of the second subset of the plurality of EP data points. 
     The visualization module can be configured to generate the cloud map of the first subset of the plurality of EP data points by: applying a Gaussian splatting algorithm to the first subset of the plurality of EP data points to create a structured points dataset; and applying an iso-contouring algorithm to the structured points dataset. 
     The instant disclosure also provides a system for visualizing cardiac activity including a visualization module configured to: receive a plurality of electrophysiology (EP) data points, wherein each EP data point of the plurality of EP data points includes an electrogram signal; compute a plurality of wave functions from the plurality of EP data points; generate a propagation wave map from the plurality of wave functions; and output a graphical representation of the propagation wave map. 
     The visualization module can be configured to compute the plurality of wave functions from the plurality of EP data points by, for each EP data point of the plurality of EP data points: transforming the electrogram signal for the EP data point into the wavelet domain, thereby computing a scalogram; and computing a wave function of the scalogram. 
     The graphical representation of the propagation wave map can include at least one of a propagation wave trail map and an interpolated propagation wave map. 
     The foregoing and other aspects, features, details, utilities, and advantages of the present invention will be apparent from reading the following description and claims, and from reviewing the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic diagram of an exemplary electroanatomical mapping system. 
         FIG.  2    depicts an exemplary catheter that can be used in connection with aspects of the instant disclosure. 
         FIGS.  3 A and  3 B  provide alphanumeric labeling conventions for electrodes carried by a multi-electrode catheter and the bipoles associated therewith. 
         FIG.  4    is a flowchart of representative steps that can be carried out in generating a graphical representation of cardiac activity as cloud maps according to exemplary embodiments disclosed herein. 
         FIG.  5    illustrates the transformation of an electrogram signal into the wavelet domain and the computation of a peak-frequency function from the resulting scalogram. 
         FIG.  6    illustrates a graphical representation of cardiac activity as a static cloud map. 
         FIG.  7    illustrates a graphical representation of cardiac activity as a dynamic cloud map. 
         FIG.  8    is a flowchart of representative steps that can be carried out in generating a graphical representation of cardiac activity as a propagation wave according to exemplary embodiments disclosed herein. 
         FIG.  9    illustrates the transformation of an electrogram signal into the wavelet domain and the computation of a peak-frequency function from the resulting scalogram. 
         FIG.  10    represents a propagation wave trail map according to aspects disclosed herein. 
         FIG.  11    represents a propagation wave map according to aspects disclosed herein. 
         FIG.  12    depicts the data of  FIG.  11    as a propagation wave trail map. 
         FIG.  13    illustrates a propagation map of two cycles of a tachycardia. 
     
    
    
     While multiple embodiments are disclosed, still other embodiments of the present disclosure will become apparent to those skilled in the art from the following detailed description, which shows and describes illustrative embodiments. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not restrictive. 
     DETAILED DESCRIPTION 
     The present disclosure provides systems and methods for the visualization of electrophysiology maps (e.g., electrocardiographic maps). For purposes of illustration, several exemplary embodiments will be described in detail herein with reference to cardiac electrophysiology procedures. More specifically, aspects of the disclosure will be described in the context of the visualization of cardiac activity using electrophysiology (EP) data points collected using a high density (HD) grid catheter, such as the Advisor™ HD grid mapping catheter from Abbott Laboratories (Abbott Park, Illinois), in conjunction with an electroanatomical mapping system, such as the EnSite Precision™ cardiac mapping system, also from Abbott Laboratories. Those of ordinary skill in the art will understand, however, how to apply the teachings herein to good advantage in other contexts and/or with respect to other devices. 
       FIG.  1    shows a schematic diagram of an exemplary electroanatomical mapping system  8  for conducting cardiac electrophysiology studies by navigating a cardiac catheter and measuring electrical activity occurring in a heart  10  of a patient  11  and three-dimensionally mapping the electrical activity and/or information related to or representative of the electrical activity so measured. System  8  can be used, for example, to create an anatomical model of the patient’s heart  10  using one or more electrodes. System  8  can also be used to measure electrophysiology data at a plurality of points along a cardiac surface and store the measured data in association with location information for each measurement point at which the electrophysiology data was measured, for example to create a diagnostic data map of the patient’s heart  10 . 
     As one of ordinary skill in the art will recognize, system  8  determines the location, and in some aspects the orientation, of objects, typically within a three-dimensional space, and expresses those locations as position information determined relative to at least one reference. This is referred to herein as “localization.” 
     For simplicity of illustration, the patient  11  is depicted schematically as an oval. In the embodiment shown in  FIG.  1   , three sets of surface electrodes (e.g., patch electrodes) are shown applied to a surface of the patient  11 , defining three generally orthogonal axes, referred to herein as an x-axis, a y-axis, and a z-axis. In other embodiments the electrodes could be positioned in other arrangements, for example multiple electrodes on a particular body surface. As a further alternative, the electrodes do not need to be on the body surface, but could be positioned internally to the body. 
     In  FIG.  1   , the x-axis surface electrodes  12 ,  14  are applied to the patient along a first axis, such as on the lateral sides of the thorax region of the patient (e.g., applied to the patient’s skin underneath each arm) and may be referred to as the Left and Right electrodes. The y-axis electrodes  18 ,  19  are applied to the patient along a second axis generally orthogonal to the x-axis, such as along the inner thigh and neck regions of the patient, and may be referred to as the Left Leg and Neck electrodes. The z-axis electrodes  16 ,  22  are applied along a third axis generally orthogonal to both the x-axis and the y-axis, such as along the sternum and spine of the patient in the thorax region, and may be referred to as the Chest and Back electrodes. The heart  10  lies between these pairs of surface electrodes  12 / 14 ,  18 / 19 , and  16 / 22 . 
     An additional surface reference electrode (e.g., a “belly patch”)  21  provides a reference and/or ground electrode for the system  8 . The belly patch electrode  21  may be an alternative to a fixed intra-cardiac electrode  31 , described in further detail below. It should also be appreciated that, in addition, the patient  11  may have most or all of the conventional electrocardiogram (“ECG” or “EKG”) system leads in place. In certain embodiments, for example, a standard set of 12 ECG leads may be utilized for sensing electrocardiograms on the patient’s heart  10 . This ECG information is available to the system  8  (e.g., it can be provided as input to computer system  20 ). Insofar as ECG leads are well understood, and for the sake of clarity in the figures, only a single lead  6  and its connection to computer  20  is illustrated in  FIG.  1   . 
     A representative catheter  13  having at least one electrode  17  is also shown. This representative catheter electrode  17  is referred to as the “roving electrode,” “moving electrode,” or “measurement electrode” throughout the specification. Typically, multiple electrodes  17  on catheter  13 , or on multiple such catheters, will be used. In one embodiment, for example, the system  8  may comprise sixty-four electrodes on twelve catheters disposed within the heart and/or vasculature of the patient. In other embodiments, system  8  may utilize a single catheter that includes multiple (e.g., eight) splines, each of which in turn includes multiple (e.g., eight) electrodes. 
     The foregoing embodiments are merely exemplary, however, and any number of electrodes and/or catheters may be used. For example, for purposes of this disclosure, a segment of an exemplary multi-electrode catheter, and in particular an HD grid catheter, is shown in  FIG.  2   . HD grid catheter  13  includes a catheter body  200  coupled to a paddle  202 . Catheter body  200  can further include first and second body electrodes  204 ,  206 , respectively. Paddle  202  can include a first spline  208 , a second spline  210 , a third spline  212 , and a fourth spline  214 , which are coupled to catheter body  200  by a proximal coupler  216  and to each other by a distal coupler  218 . In one embodiment, first spline  208  and fourth spline  214  can be one continuous segment and second spline  210  and third spline  212  can be another continuous segment. In other embodiments, the various splines  208 ,  210 ,  212 ,  214  can be separate segments coupled to each other (e.g., by proximal and distal couplers  216 ,  218 , respectively). It should be understood that HD catheter  13  can include any number of splines; the four-spline arrangement shown in  FIG.  2    is merely exemplary. 
     As described above, splines  208 ,  210 ,  212 ,  214  can include any number of electrodes  17 ; in  FIG.  2   , sixteen electrodes  17  are shown arranged in a four-by-four array. It should also be understood that electrodes  17  can be evenly and/or unevenly spaced, as measured both along and between splines  208 ,  210 ,  212 ,  214 . For purposes of easy reference in this description,  FIG.  3 A  provides alphanumeric labels for electrodes  17 . 
     As those of ordinary skill in the art will recognize, any two neighboring electrodes  17  define a bipole. Thus, the  16  electrodes  17  on catheter  13  define a total of 42 bipoles -  12  along splines (e.g., between electrodes  17   a  and  17   b , or between electrodes  17   c  and  17   d ),  12  across splines (e.g., between electrodes  17   a  and  17   c , or between electrodes  17   b  and  17   d ), and  18  diagonally between splines (e.g., between electrodes  17   a  and  17   d , or between electrodes  17   b  and  17   c ). 
     For ease of reference in this description,  FIG.  3 B  provides alphanumeric labels for the along- and across-spline bipoles.  FIG.  3 B  omits alphanumeric labels for the diagonal bipoles, but this is only for the sake of clarity in the illustration. It is expressly contemplated that the teachings herein can also be applied with respect to the diagonal bipoles. 
     Any bipole can, in turn, be used to generate a bipolar electrogram according to techniques that will be familiar to those of ordinary skill in the art. Moreover, these bipolar electrograms can be combined (e.g., linearly combined) to generate electrograms, again including activation timing information, in any direction of the plane of catheter  13  by computing an E-field loop for a clique of electrodes. U.S. Application No. 15/953,155, which is hereby incorporated by reference as though fully set forth herein, discloses details of computing an E-field loop for a clique of electrodes on a HD grid catheter. 
     In any event, catheter  13  can be used to simultaneously collect a plurality of electrophysiology data points for the various bipoles defined by electrodes  17  thereon, with each such electrophysiology data point including both localization information (e.g., position and orientation of a selected bipole) and an electrogram signal for the selected bipole. For purposes of illustration, methods according to the instant disclosure will be described with reference to individual electrophysiology data points collected by catheter  13 . It should be understood, however, that the teachings herein can be applied, in serial and/or in parallel, to multiple electrophysiology data points collected by catheter  13 . 
     Catheter  13  (or multiple such catheters) are typically introduced into the heart and/or vasculature of the patient via one or more introducers and using familiar procedures. Indeed, various approaches to introduce catheter  13  into a patient’s heart, such as transseptal approaches, will be familiar to those of ordinary skill in the art, and therefore need not be further described herein. 
     Since each electrode  17  lies within the patient, location data may be collected simultaneously for each electrode  17  by system  8 . Similarly, each electrode  17  can be used to gather electrophysiological data from the cardiac surface (e.g., surface electrograms). The ordinarily skilled artisan will be familiar with various modalities for the acquisition and processing of electrophysiology data points (including, for example, both contact and noncontact electrophysiological mapping), such that further discussion thereof is not necessary to the understanding of the techniques disclosed herein. Likewise, various techniques familiar in the art can be used to generate a graphical representation of a cardiac geometry and/or of cardiac electrical activity from the plurality of electrophysiology data points. Moreover, insofar as the ordinarily skilled artisan will appreciate how to create electrophysiology maps from electrophysiology data points, the aspects thereof will only be described herein to the extent necessary to understand the present disclosure. 
     Returning now to  FIG.  1   , in some embodiments, an optional fixed reference electrode  31  (e.g., attached to a wall of the heart  10 ) is shown on a second catheter  29 . For calibration purposes, this electrode  31  may be stationary (e.g., attached to or near the wall of the heart) or disposed in a fixed spatial relationship with the roving electrodes (e.g., electrodes  17 ), and thus may be referred to as a “navigational reference” or “local reference.” The fixed reference electrode  31  may be used in addition or alternatively to the surface reference electrode  21  described above. In many instances, a coronary sinus electrode or other fixed electrode in the heart  10  can be used as a reference for measuring voltages and displacements; that is, as described below, fixed reference electrode  31  may define the origin of a coordinate system. 
     Each surface electrode is coupled to a multiplex switch  24 , and the pairs of surface electrodes are selected by software running on a computer  20 , which couples the surface electrodes to a signal generator  25 . Alternately, switch  24  may be eliminated and multiple (e.g., three) instances of signal generator  25  may be provided, one for each measurement axis (that is, each surface electrode pairing). 
     The computer  20  may comprise, for example, a conventional general-purpose computer, a special-purpose computer, a distributed computer, or any other type of computer. The computer  20  may comprise one or more processors  28 , such as a single central processing unit (“CPU”), or a plurality of processing units, commonly referred to as a parallel processing environment, which may execute instructions to practice the various aspects described herein. 
     Generally, three nominally orthogonal electric fields are generated by a series of driven and sensed electric dipoles (e.g., surface electrode pairs  12 / 14 ,  18 / 19 , and  16 / 22 ) in order to realize catheter navigation in a biological conductor. Alternatively, these orthogonal fields can be decomposed and any pairs of surface electrodes can be driven as dipoles to provide effective electrode triangulation. Likewise, the electrodes  12 ,  14 ,  18 ,  19 ,  16 , and  22  (or any number of electrodes) could be positioned in any other effective arrangement for driving a current to or sensing a current from an electrode in the heart. For example, multiple electrodes could be placed on the back, sides, and/or belly of patient  11 . Additionally, such non-orthogonal methodologies add to the flexibility of the system. For any desired axis, the potentials measured across the roving electrodes resulting from a predetermined set of drive (source-sink) configurations may be combined algebraically to yield the same effective potential as would be obtained by simply driving a uniform current along the orthogonal axes. 
     Thus, any two of the surface electrodes  12 ,  14 ,  16 ,  18 ,  19 ,  22  may be selected as a dipole source and drain with respect to a ground reference, such as belly patch  21 , while the unexcited electrodes measure voltage with respect to the ground reference. The roving electrodes  17  placed in the heart  10  are exposed to the field from a current pulse and are measured with respect to ground, such as belly patch  21 . In practice the catheters within the heart  10  may contain more or fewer electrodes than the sixteen shown, and each electrode potential may be measured. As previously noted, at least one electrode may be fixed to the interior surface of the heart to form a fixed reference electrode  31 , which is also measured with respect to ground, such as belly patch  21 , and which may be defined as the origin of the coordinate system relative to which system  8  measures positions. Data sets from each of the surface electrodes, the internal electrodes, and the virtual electrodes may all be used to determine the location of the roving electrodes  17  within heart  10 . 
     The measured voltages may be used by system  8  to determine the location in three-dimensional space of the electrodes inside the heart, such as roving electrodes  17  relative to a reference location, such as reference electrode  31 . That is, the voltages measured at reference electrode  31  may be used to define the origin of a coordinate system, while the voltages measured at roving electrodes  17  may be used to express the location of roving electrodes  17  relative to the origin. In some embodiments, the coordinate system is a three-dimensional (x, y, z) Cartesian coordinate system, although other coordinate systems, such as polar, spherical, and cylindrical coordinate systems, are contemplated. 
     As should be clear from the foregoing discussion, the data used to determine the location of the electrode(s) within the heart is measured while the surface electrode pairs impress an electric field on the heart. The electrode data may also be used to create a respiration compensation value used to improve the raw location data for the electrode locations as described, for example, in U.S. Pat. No. 7,263,397, which is hereby incorporated herein by reference in its entirety. The electrode data may also be used to compensate for changes in the impedance of the body of the patient as described, for example, in U.S. Pat. No. 7,885,707, which is also incorporated herein by reference in its entirety. 
     Therefore, in one representative embodiment, system  8  first selects a set of surface electrodes and then drives them with current pulses. While the current pulses are being delivered, electrical activity, such as the voltages measured with at least one of the remaining surface electrodes and in vivo electrodes, is measured and stored. Compensation for artifacts, such as respiration and/or impedance shifting, may be performed as indicated above. 
     In aspects of the disclosure, system  8  can be a hybrid system that incorporates both impedance-based (e.g., as described above) and magnetic-based localization capabilities. Thus, for example, system  8  can also include a magnetic source  30 , which is coupled to one or more magnetic field generators. In the interest of clarity, only two magnetic field generators  32  and  33  are depicted in  FIG.  1   , but it should be understood that additional magnetic field generators (e.g., a total of six magnetic field generators, defining three generally orthogonal axes analogous to those defined by patch electrodes  12 ,  14 ,  16 ,  18 ,  19 , and  22 ) can be used without departing from the scope of the present teachings. Likewise, those of ordinary skill in the art will appreciate that, for purposes of localizing catheter  13  within the magnetic fields so generated, catheter  13  can include one or more magnetic localization sensors (e.g., coils). 
     In some embodiments, system  8  is the EnSite™ Velocity™ or EnSite Precision™ cardiac mapping and visualization system of Abbott Laboratories. Other localization systems, however, may be used in connection with the present teachings, including for example the RHYTHMIA HDX™ mapping system of Boston Scientific Corporation (Marlborough, Massachusetts), the CARTO navigation and location system of Biosense Webster, Inc. (Irvine, California), the AURORA® system of Northern Digital Inc. (Waterloo, Ontario), Sterotaxis, Inc.’s NIOBE® Magnetic Navigation System (St. Louis, Missouri), as well as MediGuide™ Technology from Abbott Laboratories. 
     The localization and mapping systems described in the following patents (all of which are hereby incorporated by reference in their entireties) can also be used with the present invention: U.S. Pat. Nos. 6,990,370; 6,978,168; 6,947,785; 6,939,309; 6,728,562; 6,640,119; 5,983,126; and 5,697,377. 
     Aspects of the disclosure relate to electrophysiological mapping, and in particular to generating visualizations (that is, graphical representations) of cardiac activity. Such visualizations can be output, for example, on display  23 . System  8  can therefore include a visualization module  58  that can be used to generate various electrophysiology maps, as disclosed herein, and to output the same (e.g., on display  23 ). 
     One exemplary method according to the present teachings will be explained with reference to the flowchart  400  of representative steps presented as  FIG.  4   . In some embodiments, for example, flowchart  400  may represent several exemplary steps that can be carried out by electroanatomical mapping system  8  of  FIG.  1    (e.g., by processor  28  and/or visualization module  58 ). It should be understood that the representative steps described below can be either hardware- or software-implemented. For the sake of explanation, the term “signal processor” may be used herein to describe both hardware- and software-based implementations of the teachings herein. 
     In block  402 , system  8  receives a plurality of electrophysiology (EP) data points, each of which includes both localization information and an electrogram signal. For instance, in embodiments of the disclosure, the localization information corresponds to the median position of catheter  13  during collection of the corresponding electrogram signal. 
     In block  404 , system  8  classifies a first subset of the EP data points as substrate EP data points and a second subset of the EP data points as healthy EP data points. According to aspects of the disclosure, system  8  utilizes a QRS duration metric for the electrogram associated with a given EP data point in order to make the classification. For instance, system  8  can classify an EP data point as substrate if the QRS duration metric of its respective electrogram exceeds a preset (and, optionally, user-defined) threshold (e.g., about 100 ms), and as healthy otherwise. Additional details regarding the computation of QRS duration metrics for purposes of distinguishing substrate from healthy tissue can be found in U.S. Application No. 16/294,313, which is hereby incorporated by reference as though fully set forth herein. 
     In block  406 , system  8  generates a cloud map of the first subset of the plurality of EP data points (that is, the substrate EP data points). As described in further detail below, cloud maps can be either dynamic or static. 
     For dynamic cloud maps, system  8  can transform the electrogram signal associated with each substrate EP data point into the wavelet domain, thereby computing a scalogram G(ƒ, t) of each electrogram signal. In embodiments of the disclosure, system  8  applies a continuous wavelet transformation to the electrogram signal using a high time-resolution mother wavelet, such as a Paul wavelet.  FIG.  5    depicts transformation of an electrogram signal  500  into a wavelet domain scalogram  502 . 
     Once the electrograms have been so transformed, system  8  can compute a peak-frequency function of the scalogram. According to aspects of the disclosure, the peak-frequency function of the scalogram is a one-dimensional energy function L(t) = max(ƒ), if G(ƒ, t) &gt; Energy Threshold , where ƒ ranges from about 0 Hz to about 1000 Hz and Energy Threshold  is a preset (and optionally user-defined) noise threshold. In embodiments of the disclosure, the preset noise threshold is a normalized value of about 0.2. For purposes of illustration,  FIG.  5    shows the peak-frequency function  504  of scalogram  502 . 
     Whether for a static or dynamic cloud map, system  8  can generally execute two substeps to generate the cloud map in block  406 . First, system  8  applies a Gaussian splatting algorithm to the first subset of EP data points. For instance, system  8  can apply the vtkGaussianSplatter algorithm (https://vtk.org/doc/nightly/html/classvtkGaussianSplatter.html), which is hereby incorporated by reference as though fully set forth herein. The vtkGaussianSplatter algorithm is a filter that injects input substrate EP data points into a structured points dataset. As each point is injected, it “splats” - that is, it distributes values to neighboring voxels in the structured points dataset according to a Gaussian distribution function. The Gaussian distribution function can be modified using scalar values, which expands the distribution, and/or normal/vectors, which creates an ellipsoidal distribution rather than a spherical distribution. 
     Generally, the Gaussian distribution function ƒ around a given substrate EP data point p is of form  
     
       
         
           
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     , where x is the current voxel sample point, r is the absolute distance between x and p, ExponentFactor is less than or equal to zero, and ScaleFactor can be multiplied by the scalar value (e.g., the QRS duration) of p. This distribution is spherical. 
     If point normals are present, however, then the distribution becomes elliptical:  
     
       
         
           
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     , where E is a preset (and, optionally, user-defined) eccentricity factor that controls the elliptical shape of the splat; z is the distance from x to p along normal N, and rxy is the distance from x to p in the direction perpendicular to normal N. 
     Next, system  8  applies an iso-contouring algorithm to the structured points dataset output by the Gaussian splatting algorithm. For instance, system  8  can apply the vtkContourFilter algorithm (https://vtk.org/doc/nightly/html/classvtkContourFiler.html), which is hereby incorporated by reference as though fully set forth herein. The vtkContourFilter algorithm takes the structured points dataset as input and generates as output an isosurface at a preset (and, optionally, user-defined) substrate value (e.g., QRS duration of about 100 ms). The output isosurface is then rendered translucent, along with scalar map values derived from the substrate EP data points. This generates the cloud map; the intensity (e.g., the QRS duration) of the substrate can be represented using color, greyscale, or another suitable display convention. 
     In block  408 , system  8  outputs the graphical representation of the cloud map (e.g., from the iso-contouring algorithm) in combination with a graphical representation of an electrophysiology map of the second subset of EP data points (e.g., the healthy EP data points). 
       FIG.  6    depicts a graphical representation  600  of a static cloud map. Substrate EP data points can be rendered with cloud scalar values  602 , while healthy EP data points can be rendered more traditionally (e.g., black dots  604 ). 
       FIG.  7    depicts a graphical representation  700  of a dynamic cloud map (as a sequence of progressive static images  702   a - 702   h ). Substrate EP data points at any given time step of the sequence can be rendered with cloud scalar values (such as the peak frequency function value at the given time step), while healthy EP data points can be rendered as a familiar LAT map (e.g., as an activation wavefront). 
     Another exemplary method according to the present teachings will be explained with reference to the flowchart  800  of representative steps presented as  FIG.  8   . In some embodiments, for example, flowchart  800  may represent several exemplary steps that can be carried out by electroanatomical mapping system  8  of  FIG.  1    (e.g., by processor  28  and/or visualization module  58 ). Once again, it should be understood that the representative steps described below can be either hardware- or software-implemented. 
     Block  802  is analogous to block  402 , discussed above, and includes receipt by system  8  of a plurality of EP data points. 
     In block  804 , system  8  transforms the electrogram signal for each EP data point into the wavelet domain, thereby computing a scalogram for each electrogram signal. The transformation of electrogram signals into the wavelet domain is described above in connection with the creation of dynamic cloud maps; block  804  is analogous. 
     In block  806 , system  8  computes a wave function for each scalogram, thereby computing a plurality of wave functions. According to aspects of the disclosure, system  8  computes the wave function by computing a one-dimensional peak-frequency function of the scalogram as described above. In this regard,  FIG.  9    illustrates the transformation of an electrogram signal  900  into a scalogram  902  and the corresponding one-dimensional peak frequency function  904 . The wave function can correspond to the one-dimensional peak-frequency function. Alternatively, a composite wave function can be derived from the one-dimensional peak-frequency functions of neighboring electrograms (e.g., as the average such one-dimensional peak-frequency function, the maximum such one-dimensional peak-frequency function, the minimum such one-dimensional peak frequency function, or the sum of such one-dimensional peak-frequency functions). 
     In block  808 , system  8  generates a propagation wave map from the plurality of wave functions, a graphical representation of which can be output in block  810  (e.g., in combination with a local activation time map, a substrate map, or the like). The instant disclosure contemplates both propagation wave trail maps and propagation wave maps. 
     Propagation Wave Trail Maps 
     For a propagation wave trail map, the leading edge of the propagation wave (e.g., the cardiac activation wavefront) is determined as the time point t* at each EP data point at which the corresponding wave function first goes above zero. For each such time point t*, discrete spherical glyphs are rendered, with the radius r of the glyph scaled by a factor c and the peak-frequency function L(t), such as  
     
       
         
           
             r 
             = 
             c 
             ∗ 
             
               
                 L 
                 
                   t 
                 
               
               
                 1000 
               
             
             . 
           
         
       
     
     In embodiments of the disclosure, c = 5, which renders glyphs of radius 0 cm to 5 cm for frequency ranges of about 0 Hz to about 1 kHz. 
     So rendered, the initial appearance of a glyph indicates the propagation wavefront. Trailing activity regions can be identified as areas where glyphs are slow to decay/disappear, or as areas where glyphs re-appear behind the leading edge of the propagation wave (e.g., in previously-activated regions). 
       FIG.  10    illustrates a graphical representation  1000  of a propagation wave trail map, in combination with a substrate map (e.g., a peak-to-peak voltage map), as a sequence of progressive static images  1002   a - 1002   h . The leading edge  1004  of the propagation wave is annotated in images  1002   a - 1002   d , while regions of trailing activity  1006  (that is, glyph regions behind the propagation wavefront) are annotated in images  1002   e - 1002   h . 
     Propagation Wave Maps 
     For a propagation wave map, system  8  interpolates the wave function for each time point t* over the plurality of EP data points. Trailing activity regions can be identified as regions where the wave function yields more than one activation time. 
     For instance,  FIG.  11    depicts a series of sequential propagation wave maps  1100   a - 1100   d , as well as the corresponding electrogram traces  1102   a - 1102   d  from which propagation wave maps  1100   a - 1100   d  are derived. Point  1104 , corresponding to electrogram trace  1106 , exhibits trailing activity, showing a second activation in map  1100   d . 
     For the sake of comparative illustration,  FIG.  12    depicts the same data as  FIG.  11    rendered as a propagation wave trail map image series  1200   a - 1200   d . 
     Although several embodiments have been described above with a certain degree of particularity, those skilled in the art could make numerous alterations to the disclosed embodiments without departing from the spirit or scope of this invention. 
     For example, the teachings herein can be applied in real time (e.g., during an electrophysiology study) or during post-processing (e.g., to electrophysiology data points collected during an electrophysiology study performed at an earlier time). 
     As another example, QRS duration metrics can be computed as composite QRS duration metrics over a user-defined spatial neighborhood or catheter electrode neighborhood. Thus, suitable QRS duration metrics include, without limitation, average QRS duration over a neighborhood, maximum QRS duration over a neighborhood, minimum QRS duration over a neighborhood, and sum of QRS duration over a neighborhood. 
     As still another example, the teachings herein can be used to visualize multiple cycles for a tachycardia as shown in  FIG.  13   . In particular, the top row of  FIG.  13    shows a first cycle  1300   a ,  1300   b ,  1300   c ,  1300   d  moving left-to-right, while the bottom row of  FIG.  13    shows a second cycle  1300   e ,  1300   f ,  1300   g ,  1300   h  moving right-to-left. Also shown are corresponding wave function traces  1302   a - 1302   h  for three points on the cardiac surface; in each wave function trace, the x-axis is time and the y-axis is the value of the wave function at time t (e.g., L(t)). 
     As yet a further example, static cloud maps can include additional metrics, such as fractionation or signal components. 
     All directional references (e.g., upper, lower, upward, downward, left, right, leftward, rightward, top, bottom, above, below, vertical, horizontal, clockwise, and counterclockwise) are only used for identification purposes to aid the reader’s understanding of the present invention, and do not create limitations, particularly as to the position, orientation, or use of the invention. Joinder references (e.g., attached, coupled, connected, and the like) are to be construed broadly and may include intermediate members between a connection of elements and relative movement between elements. As such, joinder references do not necessarily infer that two elements are directly connected and in fixed relation to each other. 
     It is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative only and not limiting. Changes in detail or structure may be made without departing from the spirit of the invention as defined in the appended claims.