Method and system for identification and visualization of spatiotemporal patterns

Abstract

Primary repeating patterns in recorded spatiotemporal data are identified, extracted, and / or refined by converting the data into phase data, determining a global cycle length with discrete time points per cycle, determining onset times in the original recording, calculating the best global phase progression over 2π, and over the entire cycle length, using the time points and onset times, assigning a singular value to each spatial location and generating a visual display of the pattern. Variations of the method may be used to identify features of the pattern such as spatial movement, focal sites, drift, and stability.

Description

[0001] METHOD AND SYSTEM FOR IDENTIFICATION AND VISUALIZATION OF SPATIOTEMPORAL PATTERNS

[0002] RELATED APPLICATIONS

[0003] This application claims the benefit of the priority of U.S. Provisional Application No. 63 / 530,417, filed August 2, 2023, which is incorporated herein by reference in its entirety.

[0004] GOVERNMENT RIGHTS

[0005] This invention was made with government support under Grant HL 122384 awarded by the National Institutes of Health (NIH). The government has certain rights in the invention.

[0006] FIELD OF THE INVENTION

[0007] The present invention relates to a system and method for automated determination of spatiotemporal patterns using data from spatially-distributed locations, and more specifically, to automatically generating visual representations of patterns in spatiotemporal data.

[0008] BACKGROUND

[0009] In many biomedical, physical, or engineering systems, a repetitive spatiotemporal pattern needs to be identified. Examples on long time-scales (months) include seasonal flow patterns in oceans while examples on short time-scales (seconds) include activation patterns during cardiac arrhythmias. To determine these repetitive patterns is challenging for several reasons. First, they need to be deduced from a limited set of discrete measurement points. Second, measurements are subject to noise, making it difficult to determine patterns. Third, the cycle length of local patterns does not necessarily align with the cycle length of global patterns. And fourth, determining the fundamental or primary repeating pattern (PRP) typically requires visual identification using a video or sequence of images that span multiple periods of the pattern. This identification is problematic since the pattern is very often obscured by the aforementioned noise and due to the sparseness of the data. What is necessary is a fully automated method and system that can determine the PRP and can display it as a single image, containing all relevant information.

[0010] One area in which identification of repeating patterns is an important tool is the field of medical diagnostics. In one example, millions of people worldwide are affected by heart rhythm disorders, during which the heart no longer exhibits regular and coherent contractions. These diseases often lead to serious health effects, including heart-failure, stroke, and mortality. Two of the most common arrhythmias are ventricular fibrillation (VF) and atrial fibrillation (AF), during which the heart loses its regularity and begins to contract in a chaotic, quivering manner. Even though the exact mechanisms are still debated, clinical work has shown that localized sources of electrical activity, in the form of rotational waves or focal activity, play a key role in these arrhythmias. This role is highlighted by studies that show that ablation targeted to the sites of these sources are effective in restoring normal sinus rhythm. Most of these studies used multielectrode recording devices, such as basket catheters, consisting of multiple spatially-distributed electrodes, that can record the electrical activity occurring during episodes of arrhythmia in the form of clinical electrograms. The data from these electrograms was then used in an attempt to infer the underlying propagation of electrical waves which causes the contraction of the heart. The determination of the location of the sources was then carried out using visual interpretation of phase maps, as inferred from the electrograms.

[0011] In the context of heart rhythm disorders, some existing approaches attempt to visualize the activation pattern in a 4s video that is interpreted by a technician. This technician then relates this information to the clinician that subsequently attempts targeted ablation. This interpretation is subject to technician subjectivity and introduces an unnecessary link between apparatus and clinician. Determination and detection of rotors is prone to operator error in mismarking or missing rotor or focal activations. In addition, it is time consuming as the operator needs to interpret lengthy videos of reconstituted electrical activity. These videos are typically complex and difficult to interpret.

[0012] There remains a need for an approach that eliminates the link between the apparatus and clinician to identify sources that drive the disorders in an automated fashion. Such an approach should allow the clinician to identify targets for ablation without requiring interpretation of complex videos and automatically determine the most stable sources responsible for the heart rhythm disorder. The inventive approach provides such a method to enable computation of PRPs underlying the dynamics of repetitive systems using spatially distributed recordings. SUMMARY

[0013] In exemplary embodiments, the present invention provides a system and method for automated determination of spatiotemporal patterns using data from spatially-distributed locations through the automated identification of single or multiple primary repeating patterns, which patterns can be visualized as a single image or video, revealing the elementary propagation pattern and eliminating the need to interpret complex and lengthy videos or image sequences. When applied to electrophysiological data recorded during heart rhythm disorders in patients, this invention provides a concise and succinct visual interpretation of complex activation maps, which can be used to guide therapies designed to treat such disorders.

[0014] The present invention provides for determination of the primary repeating patterns of spatially extended systems, quantifies the spatiotemporal organization and stability of these patterns, their period, and determines sources that underlie their dynamics. The data can be in the form of one-, two-, or three-dimensional spatial recordings The work uses activation sequences, raw or filtered data, or phase information as input and performs computational algorithms that compute the level of repetition for each possible activation pattern or partial pattern. The work visualizes the spatial and temporal evolution of these patterns in short sequences and in single maps. These visualizations can be used to determine the location and the type (rotational or focal) of the driving sources of the patterns. In addition, it can determine whether sources are stable or moving, can identify regions of fast and slow conduction, order and sequence of spatial activation, and can pinpoint lines and areas of block, velocity profiles, and sinks of activation.

[0015] In one aspect, a method for identifying repeating patterns in a recorded sequence of spatiotemporal data includes: converting the recorded sequence into phase data; creating data segments of global cycle length Tglobal with M discrete time points per cycle; determining a correlation between the data segments within the recorded sequence, wherein the data segments having a highest correlation value throughout the recorded sequence are used to determine N onset times; determining a phase progression that matches a predetermined phase increase over the global cycle length; obtaining a singular value for each spatial point to determine a primary repeating pattern (PRP); and generating a visual display of the PRP.

[0016] In some embodiments, the step of converting includes applying one or more of a Hilbert transform, sinusoidal recomposition, frequency analysis, and correlation analysis. The pre-determined phase increase may be 2?r. The PRP may be displayed as one or more of an isochronal map, an encapsulation map, and streamlines.

[0017] In some embodiments, the spatiotemporal data comprises electrical events in the heart recorded with sensing electrodes. The spatiotemporal data may include spatial data obtained from one-, two- or three-dimensional recordings, and a temporal component.

[0018] The method may further include spatially interpolating or temporally interpolating the spatiotemporal data before or after the step of converting. In some implementations, the method may further include dividing the recorded sequence into a plurality of subsegments and computing a PRP for each sub-segment to identify a spatially moving pattern.

[0019] In some embodiments, the method may further include the steps of identifying one or more critical points within all or a portion of the data segments by: using a clustering algorithm to match movement of the one or more critical points over the recorded sequence; and determining whether the one or more critical points are spatially confined, wherein the visual display indicates spatial regions in which one or more critical points recur as a focal or rotational site. In some embodiments, The method may further include calculating a temporal confidence value to quantify temporal occurrence of one or more critical points within the recorded sequence.

[0020] In some embodiments, the method may further include: storing the PRP as a baseline; repeating the steps of converting, creating data segments, determining a correlation, determining a phase progression, and obtaining a singular value for at least one subsequent recorded sequence to generate at least one subsequent PRP; and comparing the at least one subsequent PRP to the PRP to determine whether the repeating patterns are stable or indicative of a gradual drift over time.

[0021] In some applications, the method may further include identifying a subset of data segments having a selected cycle length range by: assigning a predetermined global cycle length value or value range; identifying data segments that exhibit a 2TC increase over the predetermined global cycle length value or value range; and filtering out data segments that do not exhibit a 2TC increase over the predetermined global cycle length value or value range.

[0022] In another aspect, a method for identifying repeating patterns in spatiotemporal data includes: inputting a recorded sequence of spatiotemporal data into a computer processor programmed to execute instructions to: convert the recorded sequence into phase data; create data segments of global cycle length Tglobal with M discrete time points per cycle; determine a correlation between the data segments within the recorded sequence, wherein the data segments having a highest correlation value throughout the recorded sequence are used to determine N onset times; determine a phase progression that corresponds to a 2TC phase increase over the global cycle length; obtain a singular value for each spatial point to determine a primary repeating pattern (PRP); and generate on a display device a visual representation of the PRP.

[0023] In some embodiments, the step of converting includes applying one or more of a Hilbert transform, sinusoidal recomposition, frequency analysis, and correlation analysis. The PRP may be displayed as one or more of an isochronal map, an encapsulation map, and streamlines.

[0024] In some embodiments, the spatiotemporal data comprises electrical events in the heart recorded with sensing electrodes. The spatiotemporal data may include spatial data obtained from one-, two- or three-dimensional recordings, and a temporal component.

[0025] The method may further include spatially interpolating or temporally interpolating the spatiotemporal data before or after the step of converting. In some implementations, the method may further include dividing the recorded sequence into a plurality of subsegments and computing a PRP for each sub-segment to identify a spatially moving pattern.

[0026] In some embodiments, the method may further include the steps of identifying one or more critical points within all or a portion of the data segments by: using a clustering algorithm to match movement of the one or more critical points over the recorded sequence; and determining whether the one or more critical points are spatially confined, wherein the visual display indicates spatial regions in which one or more critical points recur as a focal or rotational site. In some embodiments, The method may further include calculating a temporal confidence value to quantify temporal occurrence of one or more critical points within the recorded sequence.

[0027] In some embodiments, the method may further include: storing the PRP as a baseline; repeating the steps of converting, creating data segments, determining a correlation, determining a phase progression, and obtaining a singular value for at least one subsequent recorded sequence to generate at least one subsequent PRP; and comparing the at least one subsequent PRP to the PRP to determine whether the repeating patterns are stable or indicative of a gradual drift over time.

[0028] In some applications, the method may further include identifying a subset of data segments having a selected cycle length range by: assigning a predetermined global cycle length value or value range; identifying data segments that exhibit a 2TI increase over the predetermined global cycle length value or value range; and fdtering out data segments that do not exhibit a 2TI increase over the predetermined global cycle length value or value range.

[0029] In some embodiments, the inventive approach provides an automated process for quantifying a primary spatiotemporal pattern. In an exemplary application, the method allows identification of patterns that underlie cardiac arrhythmias. The inventive scheme thus allows one to reduce recordings of any length to a single snapshot that summarizes the complex activation maps recorded during arrhythmias into a single image that reveals the elementary propagation pattern during the heart rhythm disorder. This single image, in the form of isochronal lines or streamlines, thus constitutes a visual guide to sources that drive the arrhythmia and can be used to guide ablation therapies that target rotor or focal activity by minimizing erroneous visual interpretations of complicated phase maps. As the inventive scheme is capable of processing signals of any length, changes or drifts in activation patterns visible only in longer recordings can be identified. Because the inventive approach is able to process longer recordings, it allows for a more precise evaluation of the heart rhythm disorder.

[0030] Determining activation patterns in spatially extended systems is challenging due to the sparseness of available data, the noise level of recordings, and the need to interpret lengthy image sequences. Heart rhythm disorders, including but not limited to atrial fibrillation and ventricular tachycardia, offer an exemplary application of the inventive approach. Determination of the primary repeating pattern in these disorders is essential when applying targeted ablation, a form of treatment that is increasingly used. Atrial fibrillation is the most common heart rhythm disorder, affects millions of Americans, and results in increased morbidity and mortality. Ventricular tachycardia can lead to sudden cardiac death, which causes more than 200,000 victims per year. To successfully apply targeted ablation, the clinician needs to know the activation patterns in the atria or ventricles of the patient. Determining these patterns, however, is complex, time consuming and subject to operator interpretation. A major obstacle in this determination is the lack of an automated method that determines repeating pattern and identifies the sources that drive the disorder using comprehensive and easy to understand images or sequence of images.

[0031] Existing art, such as the FIRM method, attempts to visualize the activation pattern in a 4 s video that is interpreted by a technician. This technician then relates this information to the clinician that subsequently attempts targeted ablation. This interpretation is subject to technician subjectivity and introduces an unnecessary link between apparatus and clinician. The inventive approach will not only eliminate this link but will also identify sources that drive the disorders in an automated fashion. This will allow the clinician to identify targets for ablation without having to interpret complex videos and will automatically determine the most stable sources responsible for the heart rhythm disorder. As the inventive method is capable of processing signals of any length, changes or drifts in activation patterns visible only in longer recordings can be identified. Lastly, the method is able to process longer recordings, which allows for a more precise evaluation of the heart rhythm disorder.

[0032] This disclosure incorporates by reference the disclosures of the following patents: US8,521,266, US8,838,222, and US8,838,233 of Narayan and Rappel, and US10,918,303 of Rappel and Vidmar, which disclose computational methods for analyzing physiological signals to evaluate cardiac rhythm disorders.

[0033] Ablation procedures for atrial fibrillation and ventricular tachycardia are widely used and represent a multi-billion dollar market. However, the long-term success rate for these ablation procedures is still sub-optimal (~50 %), at least in part due to inefficient and inaccurate mapping. Furthermore, existing mapping modalities add considerable and expensive procedure time as well as the need for additional personnel. The inventive approach will significantly improve the accuracy of the mapping, will be able to quickly guide clinician to sources and pathways that drive the heart rhythm disorder, and will eliminate the need for personnel that are required to interpret electrogram recordings. In addition, applications of the inventive PRP analysis are not limited to short recordings, which can miss fundamental activation patterns and cannot evaluate their stability. Instead, by analyzing recordings of any length, the inventive method will make it possible to rigorously establish the stability of activation patterns, further guiding ablation. Thus, the inventive approach should be applicable to any mapping guided ablation procedure.

[0034] Analyses that can be performed using variations of the inventive approach include but are not limited to:

[0035] 1. identification of repeating patterns

[0036] 2. refinement of repeating patterns

[0037] 3. identification of non-repeating patterns

[0038] 4. identification of global cycle length of system 5. Denoising of repeating phase data

[0039] 6. Interpretation of repetitive data

[0040] 7. Identification, extraction, and refinement of patterns from data matching an input pattern

[0041] 8. Identification, extraction, and refinement of patterns from data matching an input cycle length

[0042] 9. Identification, extraction, and refinement of patterns from data matching an input cycle length range

[0043] 10. Analyzing multiple recording and stitching them together

[0044] 11. Identification of secondary or other repeating patterns

[0045] 12. Identification of high and low fidelity regions in recording

[0046] 13. Identification of rotational spatial sources

[0047] 14. Identification of focal spatial sources

[0048] 15. Quantifying the presence / occurrence of each spatial source

[0049] 16. Quantifying the movement / meandering of each spatial source

[0050] 17. Determining if sources are sinks or sources (passive or active)

[0051] 18. Identifying the temporal occurrence(s) of a repeating pattern

[0052] 19. Identifying the temporal occurrence(s) of a non-repeating pattern

[0053] 20. Identifying the temporal occurrence(s) of a transient pattern

[0054] 21. Assign a weight to each pattern occurrence

[0055] 22. Re-analyze temporal patterns in individual recordings

[0056] 23. Identify spatio-temporal changes in patterns

[0057] 24. Calculate spatio-temporal properties of propagation pattern

[0058] 25. Calculate local speed of propagating patterns

[0059] In applications to heart rhythm disorders, the inventive approach can be used to:

[0060] 26. identify tissue heterogeneities

[0061] 27. identify fiber orientation

[0062] 28. identify ablation targets

[0063] 29. identify sources of activity (rotational and focal)

[0064] 30. identify conducting and non-conducting regions

[0065] 31. identify good and bad electrode contact regions

[0066] 32. analyze cardiac arrhythmia sources in terms of sources / sinks, occurrence, meandering / movement. 32. guide targeted ablation.

[0067] Other applications of the inventive scheme will become apparent to those of skill in the art based on the disclosure herein and accompanying drawings.

[0068] BRIEF DESCRIPTION OF THE DRAWINGS

[0069] FIG. 1 is a flow diagram for implementing an exemplary embodiment of the inventive scheme for computing a primary repeating pattern.

[0070] FIGS. 2A-2B are examples, respectively, of noise-free and noisy voltage data at one spatial grid point.

[0071] FIGs. 3A-3B are phase maps computed based on sample noisy and noise-free voltage recordings, respectively. Several random snapshots from the resulting video are shown.

[0072] FIGs. 4A-4B are snapshots of a sample video that were created from PRP analysis on the noise-free data and noisy data, respectively.

[0073] FIGs. 5A-5B are sample isochronal maps generated for noise-free and noisy data, respectively.

[0074] FIGs. 6A-6B are sample streamlines for noise-free and noisy data, respectively.

[0075] FIGs. 7A-7B illustrate examples of noise-free and noisy data, respectively, at one grid point.

[0076] FIG. 8 is an example of a largely incoherent and difficult to interpret propagation pattern, computed using noisy data.

[0077] FIGs. 9A-9B show sample isochronal lines obtained using the PRP for noise-free and noisy data, respectively.

[0078] FIGs. 10A-10E illustrates examples of RPA in in-silico data, where FIG. 10A shows phase maps of a stable counterclockwise rotating spiral wave in the presence of large amounts of noise; FIGs. 10B-10C provide RPA results to the data shown in FIG. 10 A. The RPA filters out the noise and displays the underlying repeating pattern in snapshots (FIG. 10B) and a single encapsulation map (EM) with corresponding isochronal lines and streamlines (white) (FIG. 10C); FIG. 10D provides an example of the EM obtained using RPA of a simulation with a fast (upper) and slow spiral wave present in the domain; FIG. 10E is an EM showing a clockwise rotating spiral with spatial 90% confidence region (white line) with quantification of its presence in the recording (visible in 92% of snapshots). FIG. 11 shows an encapsulation map (EM) generated using RPA from data for a clockwise rotating spiral with non-linear fiber orientation in the direction of the curved black arrow that increases the local propagation speed. Noise with SNR=1 was added. The spiral is clearly visible and the increased conduction velocity along the fiber orientation is also visible as the distance between the isochronal lines. The local phase gradients correlate with the ground truth conduction velocity.

[0079] FIG. 12 shows four consecutive in-silico recordings of a counterclockwise rotating spiral used to calculate independent EMs shown as quadrants in the upper panel. Local phase values and gradients for the four quadrants were used to generate the stitched image in the lower panel.

[0080] FIG. 13 shows an EM indicating outward flow of activation from the center of a simulated focal source around grid point 33 / 33 as repeated activation. This focal course is clearly visible using the RPA.

[0081] FIGs. 14A-14C illustrate the analysis of sources and sinks in simulated data, where FIGs. 14A and 14B show a single spiral and a figure-of-eight spiral, respectively; FIG. 14C shows a multi-spiral system generated from a anchored-unanchored figure-of-eight spiral with periodic boundary conditions.

[0082] FIG. 15 is a schematic showing the steps of the inventive RPA applied to a specific cardiac electrogram using phase maps. In step 1 (upper panel), segments of spatial size AxB and length T are correlated with the entire recording, resulting in an oscillatory trace. Time differences of minima are averaged over all electrodes to determine Tgiobai. In step 2 (lower panel), AxB segments of length Tgiobai are correlated with the entire recording . The segment with the largest peak-to-peak amplitude is selected to calculate the N onset times. The minima of its time trace define the onset times used to determine the encapsulation map.

[0083] FIG. 16 is a block diagram of an exemplary computing environment for implementation of embodiments of the inventive schemes.

[0084] DETAILED DESCRIPTION OF EMBODIMENTS

[0085] The inventive scheme, which can be referred to as the “Repeating Pattern Algorithm” or “RPA,” uses data acquired from different methods, in-silico sources, or in- vivo sources, including but not limited to biomedical data, mechanical data, voltage data, phase data, or activation sequences. The data can be either pre-processed, filtered, or raw, and can be of any temporal resolution. The data can be acquired from spatially distributed recording sites and can be single variate or multivariate in any spatial resolution and configuration. The data can be obtained from one-dimensional, two-dimensional, or three- dimensional spatial recording modalities and include a temporal component, e.g., ID, 2D, 3D, each plus time.). The data can be acquired from a single recording session or from multiple recording sessions. The inventive approach can optionally interpolate the data spatially and / or temporally before or after the analysis, as well as convert temporal data into phase data. The data can be obtained from recording modalities with different spatial dimensions that are used sequentially to record different spatial sites.

[0086] Referring to FIG. 1, the inventive sequence to determine a primary repeating pattern proceeds in several steps. First, after collecting the temporal data in step 102, it is converted into phase data (step 104), using any method available (e.g., Hilbert transform, sinusoidal recomposition, frequency analysis, correlation analysis) and, possibly, interpolate and filter the data. In step 106, a global cycle length, Tgiobai, which represents the periodicity of the recordings, is computed. For this, data segments with a chosen temporal measure, in this case length, are created. Although data segments of any length can be used to compute the global cycle length, it is most convenient to employ segments that are significantly longer than the mean period of the individual recording points, for example calculated by standard methods such as power spectrum analysis or autocorrelation analysis. These segments include sequentially staggered data with potentially overlapping intervals of all or most recording sites, with start times that run from the initial data point until the maximally available data point minus the segment length. These segments will then be correlated with the entire recording from the start of the recording until the end of the recording. Using standard methods such as finding the periodicity of the correlation signal(s), this correlation analysis is used to compute Tgiobai.

[0087] In step 106, data segments of length equal to Tgiobai are created, with start times that are staggered with potentially overlapping intervals that are at least one temporal unit At apart. The global cycle length Tgiobai will have M discrete time points, computed as Tgiobai / At, where At is the temporal resolution of the recording (time between two consecutive temporal recordings). The correlation between these segments and the entire recording will be computed. In step 108, the data segments that show high correlation values throughout the entire recording are used to determine the N onset times of the global pattern. For example, the onset times throughout the recording can be calculated by identifying the segment with the highest correlation and calculating its extreme points in the correlation. Another example would be for each segment to compare its correlation with each other segment to calculate a “score” for each segment. A segment containing a spatiotemporal pattern will generally assign a high score to all segments showing a similar pattern, but a low score to patterns containing noise or a different pattern. Noisy patterns will generally assign a low score to all other patterns. These scores can, for example, be used to filter out segments showing different or single / rare-occurrence patterns as well as noisy patterns. The remaining segments can be used to calculate a new virtual segment from all existing segments, for example with a weighted or un-weighted average from which the onset times can be re-calculated that only contain desired parts of the signal.

[0088] For each recording site or interpolated site, the phase should progress by 2K each Tgiobai. In step 110, the NxM phase values for each spatial site are used to determine the progression that best matches the required increase in phase over the global cycle length. In step 112, a singular value is obtained for each spatial point, from which the PRP (primary repeating pattern) can be determined. The uncertainty of the phase at each spatial site can also be calculated, which can then be used to identify spatial low and high-fidelity regions in the recording. The results may then be used in step 114 to generate a visualization of the PRP.

[0089] Different approaches can be used to display the PRP with its temporal and spatial evolution during the global cycle length, including isochronal lines and streamlines. In one example, the locations of isochronal lines can be calculated using standard methods such as determining all spatial locations in the PRP with the same or similar value. In another example, the locations of streamlines can be determined by calculating the gradients of the PRP using standard methods including particle tracking and phase gradients. In addition, the uncertainty of values at each spatial point can be represented using color scales. These uncertainties can be visualized with a color-scaled grid that is plotted as a background in the isochronal or streamline maps and represent high fidelity and low fidelity regions. It is not necessary to visualize the PRPs using 2D grids / images. In some embodiments, the PRP can be projected using specific or arbitrary multi-dimensional geometries that are relevant to the modality of the signals.

[0090] The PRP can be automatically analyzed to determine the nature of the propagation pattern. This includes, but is not limited to, rotational activities, focal activities, lines or areas of block, coherent wave propagation, sinks of activity, velocity profiles, gradient profiles, etc. It can also be automatically analyzed to pinpoint the location of sources, including focal and rotational sources, and possible anisotropy in propagation. Each source can be assigned a region with a confidence interval (spatial, e.g., meandering / movement) and the fidelity of each region can be quantified as well (e.g., occurrence in percent).

[0091] Variations of the inventive approach can also be used to determine the movement of sources including their trajectories, and patterns. One way to identify a spatially moving pattern (e.g., a moving spiral) is by computing PRPs for sub-segments of the entire recording. Using correlation analysis, these PRPs can be compared, from which trajectories and moving patterns can be computed.

[0092] The movement or meandering of focal and rotational sites can also be quantified by taking some or all generated segments of length Tgiobai and identifying critical points such as focal and rotational activities in each segment. A supervised or unsupervised clustering algorithm, such as DBSCAN (Scikit-learn), can be used to match the movement of critical points over the recording. For example, a display can show regions in which these critical points occur during the recording time with a user-set confidence. For example, a shaded region around a focal source can be displayed to show that if the focal source is present in the recording, its occurrence is spatially confined to the shaded area in X% of cases. Instead of, or in addition to, a spatial confidence quantification, we can quantify the temporal occurrence of a critical point or entire pattern and add this information to the display. For example, in addition to the 90% spatial confidence shown by a shaded area, we can also assign to each critical point a number that shows that it is temporally present in Y% of the entire recording.

[0093] The inventive method can be used to quantify the occurrence or presence of critical points, expressed, for example, in terms of percent of entire recording. For this, it will identify critical points throughout all or some all Tgiobai segments, cluster, and calculate the number of critical points over all selected segments divided by total number of segments used for this analysis.

[0094] The inventive method can also identify changes in fundamental patterns and / or nonsignificant transient patterns. For this, changes of amplitude in the correlation analysis are used to determine the global cycle length. In addition, changes in amplitude in the correlation analysis can be used to compute the onset times, where significant amplitude changes indicate a change in pattern. The recording can be separated into segments when a change of pattern is detected. These segments can then be matched to either an existing pattern or a new pattern. For each pattern, by repeating the analysis, the global cycle length can be calculated, followed by computing and displaying the PRP. PRPs with a short lifetime can be excluded, which helps in eliminating transient patterns. For example, the analysis may reveal two different patterns “A” and “B”, which may or may not be alternating, or may reveal more than two distinct patterns.

[0095] The inventive method can be used for out-of-baseline detection by storing in memory or a database all or a portion of a recording over time. The stored recording can be used as a baseline to determine the similarity of a new recording. If the new recording closely tracks the baseline, the similarity of the new recording will be high, indicating, for example, stability in a subject’s condition. On the other hand, if the new recording deviates from the baseline, the similarity score may be relatively low. A threshold may be set for an acceptable degree of variation from baseline, and an alert may be generated to indicate a possible change in the subject’s condition. In some embodiments, the baseline can be adjusted or updated by accumulating and combining a series of multiple “normal” recordings over time. In other embodiments, accumulation of multiple recordings over time may be used to detect a gradual drift that, while not exceeding the threshold, may still indicate a pattern that might warrant further tests.

[0096] Rather than using only N onset times in the pattern, the phase properties can be used to calculate more artificial onset times, for example, by identifying all points with maximum phase difference compared to a segment and then calculating the opposite phase. This can be advantageous, especially if the recording is very noisy.

[0097] The inventive approach is not only capable of determining the predominant repeating pattern, but it can also identify and refine other patterns. Examples include:

[0098] 1. Identify transient patterns and single-occurrence patterns. The segments containing these patterns show very low similarity with all other segments.

[0099] 2. Determine and refine patterns with a specific frequency / cycle length (range). By enforcing a value or range for the global cycle length Tgiobai, segments can be enforced to store patterns that show a 2TI increase over that cycle length (range). All other segments that do not adhere to the given cycle length (range) are identified by a low score and can be discarded if chosen. The pattern that matches the cycle length requirement and is present in the signal can be displayed.

[0100] 3. Search for and refine patterns with a specific pattern. When scoring segments, a reference pattern can be input into the computing device to compare and look for patterns that match the input patterns. Segments with a high similarity will receive a high score and segments with a low similarity will receive a low score and can be discarded. The pattern that is similar to the reference pattern and is present in the signal can be displayed.

[0101] 4. Search and refine a pattern with a certain cycle length (range) that displays a specified pattern. Using 2. and 3., one can look for the occurrence of a specific signal signature in the signal, extract and refine it, and display it.

[0102] When dealing with different spatiotemporal fields of view, for example, for data that was recorded sequentially or simultaneously, the approach can be applied to all datasets and then the data in the grid points (with or without overlap) can be used to combine the single datasets. For this, the datasets can be overlaid, if possible, or extrapolated phase values and gradients can be used.

[0103] The inventive method can be applied to generate the patterns in the original recording modality by applying a score to all segments and using these scores including the global / identified / input cycle length and the pattern onset times to get the time points in the original recording modality. Using the score assigned to each onset time in the recording modality, the primary pattern can be computed in the original recording modality, for example by detrending and the time points and calculating the weighted average over each of the N onset times, individually for each of the M points in the cycle length, Tgiobai or other.

[0104] The following discussion and non-limiting examples illustrate application of embodiments of the inventive approach for identifying repeating patterns in in-silico data representing and / or simulating heart rhythm disorders:

[0105] When applied to heart rhythm disorders, the inventive approach determines repeating activation patterns during heart rhythm disorders, quantifies the spatiotemporal organization and stability of these patterns, and determines the location and characteristics of sources for the heart rhythm disorder. These visualizations can be used to determine the location and the type (rotational or focal) of the driving sources of heart rhythm disorders, which can then be targeted for ablation. In addition, it can determine whether sources are stable or moving, can identify regions of fast and slow conduction, can pinpoint lines of block, and can reveal the fiber orientation within cardiac tissue. The inventive technique can determine and extract in a fully automated way the map that best represents repeating patterns. The Repeating Pattern Algorithm (RPA) first constructs phase maps for the entire spatially extended recording and then mathematically determines: (1) the global period Tgiobai, and (2) the sequences of length Tgiobai within the entire recording that have the largest correlation with all other sequences. Once these sequences have been determined, they can be combined and visualized as a single snapshot showing activation lines or streamlines, representing the flow of activation. In other words, the entire lengthy recording can be encapsulated into a single snapshot, revealing the most important activation pattern. Furthermore, when the RPA averages over an extended recording, e.g., in heart rhythm disorder recordings, it automatically suppresses noise artifacts. In addition, it uses raw electrogram signals as input, avoiding the need for filtering or QRS subtraction algorithms, and can identify and remove electrodes with poor signals.

[0106] Example 1 : Noisy and Noise Free Data

[0107] An example of the RPA pipeline for a noisy and noise-free case in two dimensions is provided in FIGs. 2A-6B. A repeating pattern was computer generated, using a generic model for excitable systems, with as output a quantity, referred to for this example as “voltage”. This pattern consisted of a wave that rotates counterclockwise in a quasi- stationary fashion 72 times close to the center of the domain. The period of the spiral wave was approximately 8 time units, which were chosen to be “milliseconds” (ms). The data was recorded in a 8x8 distributed grid and noise was added to these recordings (white gaussian noise, SNR=1). The data was interpolated to a 57x57 grid. FIGs. 2A-2B provide examples of both the noise-free (FIG. 2A) and the noisy (FIG. 2B) voltage data at one spatial grid point. A phase map was computed based on these recordings and several random snapshots from the resulting video are shown in FIG. 3A (noise-free) and FIG. 3B (noisy). Using these snapshots, especially for the noisy data, it can be challenging to determine the underlying PRP. For both the noise-free and the noisy data, the global cycle length of the pattern was determined and identified all onset times of the repeating segments that underlie the PRP calculation. For both the noise-free and the noisy data, the final result reveals a pattern that is highly similar to the underlying pattern, which is a counterclockwise rotating spiral pattern. FIG. 4A shows several snapshots of the video that was created from the PRP analysis on the noise-free data. The pattern appears smoothed and refined compared to the snapshots from the underlying data (FIG. 3A). FIG. 4B provides several snapshots of the video that were created from the PRP analysis using the noisy data. Even though the data was extremely noisy, as seen in FIG. 3B, the PRP analysis reveals a clear counterclockwise rotating spiral, very similar to the result in the noise-free case. Single images that recapitulate the PRP, and therefore the entire recording, are shown in FIGs. 5A-5B and 6A-6B. FIGs. 5A-5B display the isochronal maps obtained using the inventive approach for both the noise-free (5A) and the noisy (5B) data, using a color scale in which blue represents early activation and red represents late activation. Both FIGs. 5A and 5B show a clear counterclockwise rotating spiral with the center at the location where the isochrones meet. The compound line represents the beginning / end of a cycle. FIGs. 6A- 6B display the streamlines for the noise-free (6 A) and the noisy (6B) data, representing the propagation of the pattern, as lines with arrows that indicated the direction of propagation. The counterclockwise rotating spiral (indicated by the dashed arrow) is clearly visible. At the background of FIGs. 6A-6B is a shaded grid which represents the uncertainty of the PRP at each grid point, in which the lightly shaded regions represent low uncertainty and black area (the small rectangle seen in the center of the pattern in FIG. 6B) represents high uncertainty. Note that both FIGs. 5A and 6A condense the entire data sequence into a single, easy to interpret image. FIGs. 5B and 6B show the same PRP, even though the underlying data was extremely noisy.

[0108] Example 2: Noisy and Noise-Free Data

[0109] In a second example, a repeating pattern was computer generated, consisting of a wave that propagated clockwise around a line of block 18 times, originating from the upperleft of the domain. The data was recorded in an 8x8 distributed grid and noise was added to these recordings (white gaussian noise, SNR=1). The data was interpolated to a 57x57 grid. FIGs. 7A-7B illustrate an example of both the noise-free (7 A) and the noisy (7B) data at one grid point. Snapshots from the phase video from the noisy data are shown in FIG. 8, displaying a largely incoherent and difficult to interpret propagation pattern. FIGs. 9A- 9B show the isochronal lines obtained using the PRP for the noise-free (9 A) and the noisy (9B) data. In both FIGs. 9A and 9B, the line of block from the left center to the center of the domain is clearly visible (isochronal lines meet in a line) and the propagation pattern, from the upper-left corner clockwise around the line of block horizontal in the middle to the left-bottom, is clearly visible. Example 3: Noisy and Noise-Free Data

[0110] A different way of showing the encapsulation map and some more capabilities of the inventive scheme are shown in FIGs. 10A-10E. FIGs. 10A and 10B corresponds to the same noisy phase map and PRP shown in FIGs 3B and 4B. FIG. 10C shows the encapsulation map (EM) with more color and with white streamlines. The isochronal lines meet at the tip of the spiral wave while the streamlines, representing activation flow, start at the tip and move outwards, indicating a rotational source. Furthermore, even if there are two rotational sources with different frequencies, the RPA can still determine the repeating pattern. This is demonstrated in FIG. 10D, which shows the EM of a simulation in which spiral waves of different frequency are present. Even though the upper panel in FIG. 10D has a 30% lower frequency, it is still clearly present in the EM. In addition, the RPA can quantify the temporal stability of a source by computing the percentage of time it is present, as well as the spatial stability by tracing the source location. FIG. 10E quantifies the movement of the spiral core, here with a 90% confidence region, designated by the white lines, and provides information about the occurrence of the spiral in the original recording (here, present in 92% of the recording).

[0111] Example 5: Conduction Patterns

[0112] The inventive RPA is further capable of analyzing and identifying heterogeneities in conduction and, the speed of a conduction pattern, and properties like conduction anisotropy. An example of this is shown in FIG. 11, in which a clockwise rotating spiral was simulated in an area with conduction heterogeneity (black arrow). The spacing between isochronal lines correspond to the increase in local conduction velocity. An encapsulation map (EM) was generated using RPA from the data with non-linear fiber orientation in the direction of the curved black arrow that increases the local propagation speed. Noise with SNR=1 was added. The spiral is clearly visible and the increased conduction velocity along the fiber orientation is also visible as the distance between the isochronal lines. The local phase gradients correlate with the ground truth conduction velocity.

[0113] Example 6: Sequential Recordings

[0114] The inventive approach can be used to analyze recordings that were taken sequentially and match the individual recordings in an automated fashion. Referring to the upper panel in FIG. 12, four consecutive in-silico recordings of a counterclockwise rotating spiral were taken and the EMs were calculated independently. The 4 PRPs are placed next to each other. The local phase values and gradients can be used to identify the best match between the four patterns by applying a phase offset individually to the quadrants. The quadrants were used to generate a stitched image, an example of which is shown in the lower panel.

[0115] Example 7: Focal Source Identification

[0116] A focal source was simulated around grid point 33 / 33 as repeated activation. FIG. 13 shows the EM computed from virtual electrodes capturing repeated focal activity. The arrows represent an outward flow of activation from the center of the focal source, which can be detected by calculating the spatial site of origin of the activation. This focal source is clearly visible using the RPA.

[0117] Example 8: Source Characterization

[0118] Using the RPA and streamlines (or phase gradients), an identified focal or rotational site, e.g., the source shown in FIG. 13, can be classified as a “source” or “sink”. Referring to FIGs. 14A-C, a source will project streamlines (or positive phase gradients) radially outward while a sink will show streamlines moving radially inward toward the rotational or focal site. FIGs. 14A and 14B show a single spiral and a figure-of-eight spiral, respectively, while FIG. 14C shows a multi-spiral system generated from a anchored- unanchored figure-of-eight spiral with periodic boundary conditions. The one or more black dots in each figure represent rotational sources (outwards phase gradients / streamlines) while the white dot in FIG. 14C represents a rotational sink.

[0119] Example 9: Application to Heart Rhythm Disorders

[0120] When applied to heart rhythm disorders, the inventive RPA approach can be used to determine repeating activation patterns during heart rhythm disorders, to quantify the spatiotemporal organization and stability of these patterns and determine the location and characteristics of sources for the heart rhythm disorder. These visualizations can be used to determine the location and the type (rotational or focal) of the driving sources of heart rhythm disorders, which can then be targeted for ablation. In addition, it can do one or more of determining whether sources are stable or moving, identifying regions of fast and slow conduction, pinpointing lines of block, and revealing the fiber orientation within cardiac tissue. The inventive approach can be used to guide ablation by determining the electrical activation patterns in the heart including the electrical properties of the tissue and by identifying all sources including their characteristic (e.g. sources, sinks, occurrence, core movement, etc.).

[0121] FIG. 15 illustrates an example of the inventive RPA approach applied to a specific electrophysiological dataset with spatial grid size AxB and of length C. It should be noted that the data can have more or fewer dimensions and the data does not need to conform to a grid.

[0122] In step 1 of the RPA algorithm (upper panel of FIG. 15), the global cycle length, Tgiobai, is determined. This represents the periodicity of recurrent spatial activation patterns. For this step, data segments of length T are created for the entire field of view (i.e., AxB). Preferably, but not necessarily, the data segments will be longer than the anticipated Tgiobai and will be staggered with at least one time unit apart (upper panel). For each of these segments, the normalized, average phase difference between the AxBxT segment and the entire AxBxC recording are calculated. This results in a time trace that is oscillatory with values between 0 (the segment is completely in phase and identical with that part of the recording) or 1 (it is completely identical and out of phase). By computing, for example, the average time interval between minima of this trace (indicated by black dots in the right side of the upper panel of FIG. 15) the periodicity of each segment can be quantified. Tgiobai is then defined as the mean of the periodicity of all segments. In step 2, segments of length Tgiobai, corresponding to M ms are used to compute new oscillatory traces by computing the normalized, average phase difference between the AxBxM segment and the entire AxBxC recording. For each trace, the average peak-to-peak amplitude is computed and a best segment with the highest amplitude is selected. Finally, in this example N global onset times are defined as the minima of the oscillatory trace of this “master” segment. Other methods may be used to compute the onset times. These onset times are indicated in the lower panel as white dots in the lower panel.

[0123] Next, assume that in the ideal case when the pattern is perfectly periodic, each spatial point (i,j) should complete a full cycle during Tgiobai. Thus, the value of the phase at each point within the map should progress by 2K each Tgiobai. To determine the AxB phase map that encapsulates the entire recording, the final phase7- is computed for each spatial point separately. This is accomplished by computing (pl j(k~) = ([ j(k) — 2K( / C — 1) / M for each time point k=l, . . . ,M and for all N onset times. This will result in NxM data points and (p j is defined as the circular mean of this angular distribution.

[0124] After applying the RPA, an encapsulation map (EM) is created. A single AxB phase map summarizes the entire electrogram recording, where the phase of each spatial point (i,j) is given by (plj . Using this EM, the streamlines corresponding to the activation flow can be computed. Thus, the EM can be displayed in the form of an isochronal map, showing increments in phase and thus time (see, for example, FIGs. 10A-10E, or in the form of a flowmap with streamlines. Furthermore, the EM can be used to determine rotational sites, representing spiral tips. These tips correspond to singularities in the phase maps of the EM: at this point, all lines of equal phase converge and the phase is undefined. The singularities (rotation sites) can be calculated using an index I (the winding number), which computes the line integral of the gradient of the phase cp* along a closed loop, per the following equation:

[0125] Focal sites can be calculated as sites from which activation originates.

[0126] Using the entire recording, it is possible to determine the percentage of time this rotational or focal site is present as well as its movement (e.g., FIG. 10E). Also, using the flowmap, it can be determined whether a site is a source (streamlines flow from the site) or a sink (streamlines go into the site). Note that the inventive RPA algorithm also enables filtering (all or partial removal) of data segments of poor quality such as noise, transients or different patterns. This can be accomplished, for example, by removing all onset times derived from the master segment with a peak-to-peak amplitude that is below a predetermined threshold value.

[0127] To summarize, the inventive algorithm works to identify the primary repeating pattern of data in a spatiotemporal system by:

[0128] - converting data into phase data;

[0129] - determining a global cycle length with M discrete time points per cycle;

[0130] - determining N onset times in the original recording (with or without scoring);

[0131] - calculating the best global phase progression over 2TI and over the entire cycle length using the MxN data points;

[0132] - assigning a singular value to each spatial location, for example, the phase value at the onset time; and - generating a visual display of the pattern, for example, an encapsulation map.

[0133] It may be noted that each step can be expanded, or steps added, to obtain different desired results.

[0134] Example 10: Computer Implementation

[0135] FIG. 16 is a block diagram of an exemplary computer system 2300 for implementing the inventive method. The computer system 2300 can include a set of instructions that can be executed to cause the computer system 2300 to perform the methods or computer-based functions disclosed herein. The computer system 2300 or any portion thereof, may operate as a standalone device or may be connected (e.g., using a network 2324) to other computer systems or devices disclosed herein. For example, the computer system 2300 can include or be included within any one or more of the catheter, computing device, server, biological sensor, and / or any other devices or systems disclosed herein.

[0136] In a networked deployment, the computer system 2300 may operate in the capacity of a server or a client machine in a server-client network environment, or a peer machine in a peer-to-peer (or distributed) network environment. The computer system 2300 can also be implemented as or incorporated into various devices, such as a personal computer (PC), a tablet PC, a personal digital assistant (PDA), a web appliance, a communications device, a mobile device, a server, client or any other machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine.

[0137] Further, while a single computer system 2300 is illustrated, the term “system” shall also be taken to include any collection of systems or sub-systems that individually or jointly execute a set, or multiple sets, of instructions to perform one or more computer functions. The computer system 2300 can include a processor 2302, e.g., a central processing unit (CPU), a graphics-processing unit (GPU), or both. Moreover, the computer system 2300 can include a main memory 2304 and a static memory 2306 that can communicate with each other via a bus 2326. As shown, the computer system 2300 may further include a video display unit 2310, such as a liquid crystal display (LCD), a light emitting diode (LED), a flat panel display, a solid state display, or a cathode ray tube (CRT). Additionally, the computer system 2300 may include an input device 2312, such as a keyboard, and a cursor control device 2314, such as a mouse. The computer system 2300 can also include a disk drive unit 2316, a signal generation device 2322, such as a speaker or remote control, and a network interface device 2308. In a particular embodiment, the disk drive unit 2316 may include a machine or computer-readable medium 2318 in which one or more sets of instructions 2320 (e.g., software) can be embedded. Further, the instructions 2320 may embody one or more of the methods, functions or logic as described herein. The instructions 2320 may reside completely, or at least partially, within the main memory 2304, the static memory 2306, and / or within the processor 2302 during execution by the computer system 2300. The main memory 2304 and the processor 2302 may also include computer-readable media.

[0138] In an alternative embodiment, dedicated hardware implementations, such as application specific integrated circuits, programmable logic arrays and other hardware devices, can be constructed to implement one or more of the methods, functions or logic described herein. Applications that may include the apparatus and systems of various embodiments can broadly include a variety of electronic and computer systems. One or more embodiments described herein may implement functions using two or more specific interconnected hardware modules or devices with related control and data signals that can be communicated between and through the modules, or as portions of an applicationspecific integrated circuit. Accordingly, the present system encompasses software, firmware, and hardware implementations.

Claims

CLAIMS:

1. A method for identifying repeating patterns in a recorded sequence of spatiotemporal data, comprising: converting the recorded sequence into phase data; creating data segments of global cycle length Tgiobai with M discrete time points per cycle; determining a correlation between the data segments within the recorded sequence, wherein the data segments having a highest correlation value throughout the recorded sequence are used to determine N onset times; determining a phase progression that matches a pre-determined phase increase over the global cycle length; obtaining a singular value for each spatial point to determine a primary repeating pattern (PRP); and generating a visual display of the PRP.

2. The method of claim 1, wherein the step of converting comprises applying one or more of a Hilbert transform, sinusoidal recomposition, frequency analysis, and correlation analysis.

3. The method of claim 1, wherein the pre-determined phase increase is 2K.

4. The method of claim 1, wherein the PRP is displayed as one or more of an isochronal map, an encapsulation map, and streamlines.

5. The method of claim 1, wherein the spatiotemporal data comprises electrical events in the heart recorded with sensing electrodes.

6. The method of claim 1, wherein the spatiotemporal data comprises spatial data obtained from one-, two- or three-dimensional recordings, and a temporal component.

7. The method of claim 1, further comprising spatially interpolating or temporally interpolating the spatiotemporal data before or after the step of converting.

8. The method of claim 1, further comprising: dividing the recorded sequence into a plurality of sub-segments and computing a PRP for each sub-segment to identify a spatially moving pattern.

9. The method of claim 1, further comprising:identifying one or more critical points within all or a portion of the data segments by: using a clustering algorithm to match movement of the one or more critical points over the recorded sequence; and determining whether the one or more critical points are spatially confined, wherein the visual display indicates spatial regions in which one or more critical points recur as a focal or rotational site.

10. The method of claim 9, further comprising calculating a temporal confidence value to quantify temporal occurrence of one or more critical points within the recorded sequence.

11. The method of claim 1, further comprising: storing the PRP as a baseline; repeating the steps of converting, creating data segments, determining a correlation, determining a phase progression, and obtaining a singular value for at least one subsequent recorded sequence to generate at least one subsequent PRP; and comparing the at least one subsequent PRP to the PRP to determine whether the repeating patterns are stable or indicative of a gradual drift over time.

12. The method of claim 1, further comprising identifying a subset of data segments having a selected cycle length range by: assigning a predetermined global cycle length value or value range; identifying data segments that exhibit a 2K increase over the predetermined global cycle length value or value range; and filtering out data segments that do not exhibit a 2K increase over the predetermined global cycle length value or value range.

13. A method for identifying repeating patterns in spatiotemporal data, comprising: inputting a recorded sequence of spatiotemporal data into a computer processor programmed to execute instructions to: convert the recorded sequence into phase data; create data segments of global cycle length Tgiobai with M discrete time points per cycle;determine a correlation between the data segments within the recorded sequence, wherein the data segments having a highest correlation value throughout the recorded sequence are used to determine N onset times; determine a phase progression that corresponds to a 2K phase increase over the global cycle length; obtain a singular value for each spatial point to determine a primary repeating pattern (PRP); and generate on a display device a visual representation of the PRP.

14. The method of claim 13, wherein the step of converting comprises applying one or more of a Hilbert transform, sinusoidal recomposition, frequency analysis, and correlation analysis.

15. The method of claim 13, wherein the PRP is displayed as one or more of an isochronal map, an encapsulation map, and streamlines.

16. The method of claim 13, wherein the spatiotemporal data comprises electrical events in the heart recorded with sensing electrodes.

17. The method of claim 13, wherein the spatiotemporal data comprises spatial data obtained from one-, two- or three-dimensional recordings, and a temporal component.

18. The method of claim 13, further comprising spatially interpolating or temporally interpolating the spatiotemporal data before or after the step of converting.

19. The method of claim 13, further comprising: dividing the recorded sequence into a plurality of sub-segments and computing a PRP for each sub-segment to identify a spatially moving pattern.

20. The method of claim 13, further comprising: identifying one or more critical points within all or a portion of the data segments by: using a clustering algorithm to match movement of the one or more critical points over the recorded sequence; and determining whether the one or more critical points are spatially confined, wherein the visual display indicates spatial regions in which one or more critical points recur as a focal or rotational site.

21. The method of claim 20, further comprising calculating a temporal confidence value to quantify temporal occurrence of one or more critical points within the recorded sequence.

22. The method of claim 13, further comprising: storing the PRP in a memory device in communication with the computer as a baseline PRP; repeating the steps of converting, creating data segments, determining a correlation, determining a phase progression, and obtaining a singular value for at least one subsequent recorded sequence to generate at least one subsequent PRP; and comparing the at least one subsequent PRP to the baseline PRP to determine whether the repeating patterns are stable or indicative of a gradual drift over time.

23. The method of claim 13, further comprising identifying a subset of data segments having a selected cycle length range by: assigning a predetermined global cycle length value or value range; identifying data segments that exhibit a 2K increase over the predetermined global cycle length value or value range; and filtering out data segments that do not exhibit a 2K increase over the predetermined global cycle length value or value range.

Images