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Ablation strategies remain poorly defined for persistent atrial fibrillation (AF) patients with recurrence despite intact pulmonary vein isolation (PVI). As the ability to perform durable PVI improves, the need for advanced mapping to identify extra-PV sources of AF becomes increasingly evident. Multiple mapping technologies attempt to localize these self-sustained triggers and/or drivers responsible for initiating and/or maintaining AF; however, current approaches suffer from technical limitations. Electrographic flow (EGF) mapping is a novel mapping method based on well-established principles of optical flow and fluid dynamics. It enables the full spatiotemporal reconstruction of organized wavefront propagation within the otherwise chaotic and disorganized electrical conduction of AF. Given the novelty of EGF mapping and relative unfamiliarity of most clinical electrophysiologists with the mathematical principles powering the EGF algorithm, this paper provides an in-depth explanation of the technical/mathematical foundations of EGF mapping and demonstrates clinical applications of EGF mapping data and analyses. Graphical abstract Starting with a 64-electrode basket catheter, unipolar EGMs are recorded and processed using an algorithm to visualize the electrographic flow and highlight the location of high prevalence AF “source” activity. The AF sources are agnostic to the specific mechanisms of source signal generation.

Emerging evidence indicates that activity flow over resting‐state network topology allows the prediction of task activations. However, previous studies have mainly adopted static, linear functional connectivity (FC) estimates as activity flow routes. It is unclear whether an intrinsic network topology that captures the dynamic nature of FC can be a better representation of activity flow routes. Moreover, the effects of between‐ versus within‐network connections and tight versus loose (using rest baseline) task contrasts on the prediction of task‐evoked activity across brain systems remain largely unknown. In this study, we first propose a probabilistic FC estimation derived from a dynamic framework as a new activity flow route. Subsequently, activity flow mapping was tested using between‐ and within‐network connections separately for each region as well as using a set of tight task contrasts. Our results showed that probabilistic FC routes substantially improved individual‐level activity flow prediction. Although it provided better group‐level prediction, the multiple regression approach was more dependent on the length of data points at the individual‐level prediction. Regardless of FC type, we consistently observed that between‐network connections showed a relatively higher prediction performance in higher‐order cognitive control than in primary sensorimotor systems. Furthermore, cognitive control systems exhibit a remarkable increase in prediction accuracy with tight task contrasts and a decrease in sensorimotor systems. This work demonstrates that probabilistic FC estimates are promising routes for activity flow mapping and also uncovers divergent influences of connectional topology and task contrasts on activity flow prediction across brain systems with different functional hierarchies. This study proposed a new probabilistic FC routes for activity flow mapping. Our results not only showed that probabilistic FC routes substantially improved individual‐level activity flow prediction but also uncovered divergent influences of connectional topology and task contrasts on activity flow prediction across brain systems with different functional hierarchies.

BackgroundThe optimal ablation approach for the treatment of persistent atrial fibrillation (AF) is still under debate; however, the identification and elimination of AF sources is thought to play a key role. Currently available technologies for the identification of AF sources are not able to differentiate between active rotors or focal impulse (FI) and passive circular turbulences as generated by the interaction of a wave front with a functional obstacle such as fibrotic tissue.ObjectivesThis study introduces electrographic flow (EGF) mapping as a novel technology for the identification and characterization of AF sources in humans.MethodsTwenty-five patients with AF (persistent: n = 24, long-standing persistent: n = 1; mean age 70.0 ± 8.3 years, male: n = 17) were included in this prospective study. Focal impulse and Rotor-Mapping (FIRM) was performed in addition to pulmonary vein isolation using radiofrequency in conjunction with a 3D-mapping-system. One-minute epochs were exported from the EP-recording-system and re-analyzed using EGF mapping after the procedure.Results44 potential AF sources (43 rotors and one FI) were identified with FIRM and 39 of these rotors were targeted for ablation. EGF mapping verified 40 of these patterns and identified 24/40 (60%) as active sources while 16/40 (40%) were classified as passive circular turbulences. Four rotors were not identified by EGF mapping.ConclusionEGF is the first method to identify active AF sources during AF ablation procedures in humans and discriminate them from passive rotational phenomena, which occur if the excitation wavefront passes conduction bariers. EGF mapping may allow improved guidance of AF ablation procedures.

Integration of multi-sensor, multi-platform remotely sensed data is an effective methodology for monitoring active volcanoes as it ensures a constant data flow, which is needed for repeated eruptive events in brief intervals. It allows broad observation of the eruptive scenario and quantification of the erupted products. We integrated remote sensing data, through GIS software, to map the lava flows of Etna, one of the most active volcanoes in the world. Between July 2019 and December 2023, Etna gave rise to seventy-five eruptive events, mainly from the summit craters, emplacing one hundred lava flows. We updated Etna's 1999-2019 map, with the most recent eruptive products, mapping ninety-three lava flows out of the one hundred-five. For cartographic simplicity, summit flows are grouped by year or eruptive cycle, while flank flows are distinguished by date. To better display the products and highlight the mapping process, we added twenty-one detailed maps to the main map.

In this paper, we survey the existence, uniqueness and interior regularity of solutions to the Dirichlet problem associated with various energy functionals in the setting of mappings between singular metric spaces. Based on known ideas and techniques, we separate the necessary analytical assumptions to axiomatizing the theory in the singular setting. More precisely, (1) we extend the existence result of Guo and Wenger (Comm Anal Geom 28(1):89–112, 2020) for solutions to the Dirichlet problem of Korevaar–Schoen energy functional to more general energy functionals in purely singular setting. (2) When Y has non-positive curvature in the sense of Alexandrov (NPC), we show that the ideas of Jost (Calc Var Partial Differ Equ 5(1):1–19, 1997) and Lin (Analysis on singular spaces, collection of papers on geometry, analysis and mathematical physics, World Science Publishers, River Edge, pp 114–126, 1997) can be adapted to the purely singular setting to yield local Hölder continuity of solutions of the Dirichlet problem of Korevaar–Schoen and Kuwae–Shioya. (3) We extend the Liouville theorem of Sturm (J Reine Angew Math 456:173–196, 1994) for harmonic functions to harmonic mappings between singular metric spaces. (4) We extend the theorem of Mayer (Comm Anal Geom 6:199–253, 1998) on the existence of the harmonic mapping flow and solve the corresponding initial boundary value problem. Combing these known ideas, with the more or less standard techniques from analysis on metric spaces based on upper gradients, leads to new results when we consider harmonic mappings from RCD(K,N) spaces into NPC spaces. Similar results for the Dirichlet problem associated with the Kuwae–Shioya energy functional and the upper gradient functional are also derived.

Mitral valve morphology after mitral valve surgery affects postoperative intraventricular flow patterns and long-term cardiac performance. We visualized ventricular flow by echocardiography vector flow mapping (VFM) to reveal the impact of different mitral valve procedures. Eleven cases of mechanical mitral valve replacement (nine in the anti-anatomical and two in the anatomical position), three bioprosthetic mitral valve replacements, and four mitral valve repairs were evaluated. The mean age at the procedure was 57.4 ± 17.8 year, and the echocardiography VFM in the apical long-axis view was performed 119.9 ± 126.7 months later. Flow energy loss (EL), kinetic pressure (KP), and the flow energy efficiency ratio (EL/KP) were measured. The cases with MVR in the anatomical position and with valve repair had normal vortex directionality (“Clockwise”; N  = 6), whereas those with MVR in the anti-anatomical position and with a bioprosthetic mitral valve had the vortex in the opposite direction (“Counterclockwise”; N  = 12). During diastole, vortex direction had no effect on EL (“Clockwise”: 0.080 ± 0.025 W/m; “Counterclockwise”: 0.083 ± 0.048 W/m; P  = 0.31) or KP (“Clockwise”: 0.117 ± 0.021 N; “Counterclockwise”: 0.099 ± 0.057 N; P  = 0.023). However, during systole, the EL/KP ratio was significantly higher in the “Counterclockwise” vortex than that in the “Clockwise” vortex (1.056 ± 0.463 vs. 0.617 ± 0.158; P  = 0.009). MVP and MVR with a mechanical valve in the anatomical position preserve the physiological vortex, whereas MVR with a mechanical valve in the anti-anatomical position and a bioprosthetic mitral valve generate inefficient vortex flow patterns, resulting in a potential increase in excessive cardiac workload.

Intraventricular velocity distribution reflects left ventricular (LV) diastolic function and can be measured non-invasively by flow mapping technologies. We designed our study to compare intraventricular velocities and gradients, obtained by vector flow mapping (VFM) technology during early diastole in consecutive patients diagnosed with mild and advanced diastolic dysfunction at echocardiography and a control group with a purpose to validate the hypothesis of relationship between new parameters and severity of diastolic dysfunction and conventional markers of elevated LV filling pressure. Two-dimensional streamline fields were obtained using VFM technology in 121 subjects (57 with normal diastolic function, 38 with mild diastolic dysfunction and 26 with advanced diastolic dysfunction). We measured several velocities and calculated a gradient along the selected streamline, which we compared between groups and correlated them with conventional echocardiographic parameters. Apical intraventricular velocity gradient (GrIV) was the lowest in control group, followed by mild and advanced diastolic dysfunction groups (5.3 ± 1.9 vs. 6.8 ± 2.5 vs. 13.6 ± 5.0/s, p < 0.001) and showed good correlation with E/e’ (r = 0.751, p < 000.1). GrIV/e’ ratio was the strongest single predictor of severity of diastolic dysfunction. Different degrees of diastolic dysfunction affect the Intraventricular velocity behavior during early diastole obtained by VFM. GrIV could discriminate between groups with different levels of diastolic dysfunction and was closely associated with classical echocardiographic indices of elevated LV filling pressure. GrIV/e’ ratio has a potential to become a single parameter needed to assess left ventricular diastolic function.

The aim of this study was to assess left ventricular (LV) summation of energy loss (EL-SUM), average energy loss (EL-AVE) and wall shear stress (WSS) using vector flow mapping (VFM) in patients with hypertrophic cardiomyopathy (HCM). Forty HCM patients, and 40 controls were evaluated by transthoracic echocardiography. Conventional echocardiographic parameters, summation and average of energy loss (EL-total, EL-base, EL-mid and EL-apex), and WSS in each segment were calculated at different phases. Compared with controls, conventional diastolic measurements were impaired in HCM patients. HCM patients also showed increased EL-SUM-total and EL-AVE-total at the peak of LV rapid ejection period as well as decreased EL-SUM-total and EL-AVE-total at the end of early diastole. In controls, EL-SUM and EL-AVE showed a gradual decrease from the basal segment to the apex, this regularity was not observed in HCM patients. Compared with controls, HCM patients showed increased WSS at the peak of the LV rapid ejection period and the atrial contraction period as well as decreased WSS at the end of early diastole (all p < 0.05). WSS was increased slightly at the peak of the LV rapid filling period in HCM patients (p = 0.055). EL and WSS values derived from VFM are novel flow dynamic parameters that can effectively evaluate systolic and diastolic hemodynamic function in HCM patients.

Regional scale debris flow susceptibility is widely evaluated by statistical methods. However, the initiation mechanism of debris flow is not considered, which leads to the neglect of the microtopographic characteristics. To address this problem, we established three novel combined models by introducing the physical model into statistical methods. The integrating models consists of two parts, the statistical models and the TRIGRS model. The eventual results obtained with the integrating model consider both the prediction result of the statistical method for debris flow susceptibility and the mechanism of debris flow initiation. To test the feasibility of the integrating model, three representative statistical models, the analytic hierarchy process (AHP), Shannon entropy (Entropy) and support vector machine (SVM) were selected to evaluate debris flow susceptibility in Yongji County of Jilin Province, China. The results demonstrate that the performance of the integrated models is significantly better than that of the single statistical model, especially in the local areas. The integrating models (AHP-TR, Entropy-TR, SVM-TR) can generate higher quality debris flow susceptibility maps (DFSMs) than the single model, which clearly reflect the scope and boundaries of the areas which are most prone to debris flow and identify the flat land and valleys between adjacent high-prone areas. It also reduces the overprediction generated by the physical model. In general, combining the statistical methods with the TRIGRS model can maximize the strengths of these models and avoid their weaknesses and obtain the effect of 1 + 1 > 2.

The aim of this study was to evaluate the diagnostic performance of the diastolic retrograde ratio in the descending aorta in patients with aortic regurgitation (AR) by vector flow mapping (VFM). Conventional Doppler echocardiography and VFM were performed in 73 patients with various degrees of AR and 40 controls. AR severity was assessed by an expert using the currently recommended integrative approach, including vena contracta width (VCW), jet width to left ventricular outflow tract (jet width/LVOT) ratio, and effective regurgitant orifice area (EROA). The retrograde ratio, derived as the quotient of backward flow volume (VFb) and forward flow volume (VFf) in the descending aorta, was measured using VFM. The diastolic retrograde ratio was found to increase across groups of subjects with absent (6.1 ± 4.0%), mild (21.3 ± 8.2%), moderate (43.6 ± 9.4%), and severe (70.5 ± 10.5%) AR. Furthermore, in a linear correction model, the retrograde ratio correlated strongly with the VCW (r = 0.930, P < 0.001), jet width/LVOT ratio (r = 0.884, P < 0.001), and EROA (r = 0.927, P < 0.001). In the receiver operating characteristic curve, the retrograde ratio had an area under the curve of 0.958 for a diagnosis of severe AR (SEM: 0.0205, P < 0.0001). A retrograde ratio > 56% indicated severe AR with a sensitivity of 93% and a specificity of 89%, whereas a value > 59% indicated severe AR with a sensitivity of 96% and a specificity of 82%. The retrograde ratio in the descending aorta is useful in identifying AR severity. This accurate and simple quantitative parameter should be incorporated in the comprehensive evaluation of AR.