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Is a single lethal electric field threshold sufficient to characterize the lesion size in computational modeling of cardiac pulsed-field ablation?

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Heart Rhythm O2 2025年第5期6卷 671-677页

作者： Petras, Argyrios Amoros Figueras, Gerard Moreno Weidmann, Zoraida García-Sánchez, Tomás Viladés Medel, David Ivorra, Antoni Guerra, Jose M. Gerardo-Giorda, Luca RICAM–Johann Radon Institute for Computational and Applied Mathematics Linz Austria Department of Cardiology Hospital de la Santa Creu i Sant Pau Universitat Autònoma de Barcelona CIBER CV Barcelona Spain Department of Information and Communication Technologies Universitat Pompeu Fabra Barcelona Spain Institute for Mathematical Methods in Medicine and Data-Based Modelling Johannes Kepler University Linz Austria

Background: Pulsed-field ablation (PFA) is a novel cardiac ablation technology based on irreversible electroporation (IRE). PFA computational models rely on identification of a lethal electric field threshold to predict the IRE area. However, the predicted lesion anisotropy ratios (width over depth) vary extensively among recent studies, and these discrepancies remain a subject of discussion. Objective: This work aims to evaluate the predicted lesion anisotropy ratios using a PFA computational model by applying it to an open-chest in vivo porcine model geometry. methods: Six domestic swine underwent epicardial PFA applications using a previously described waveform protocol. Animals were killed at least 3 hours after the last ablation, and lesions were assessed using triphenyltetrazolium chloride (TTC) staining. Numeric simulations were performed on a segmented and meshed porcine thoracic computed tomography (CT) scan, mimicking the open-chest experimental setup. Results: The maximum width of all simulated lesions was observed at the epicardial surface. The anisotropy ratios (AR) of the experimental lesions were smaller than the simulated ones (AR experimental vs simulated, 1.0–1.7 vs 2–2.7;Q1–Q3 quartiles). Increasing the peak voltage resulted in larger lesions;however, the computational model clearly underestimated the increase in lesion depth compared with the experimental data. Conclusion: Our computational model shows that a single lethal electric field threshold is insufficient to accurately predict both lesion depth and width in cardiac PFA. Our study suggests that for the given PFA waveforms, a threshold between 270 and 500 V/cm provides satisfactory lesion depth estimations, and a higher threshold between 790 and 1000 V/cm better captures the lesion width. © 2025 Heart Rhythm Society

关键词： Cardiac ablation Computer simulations Electric field threshold mathematical modeling Pulsed field ablation

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ONLINE LEARNING ALGORITHMS IN HILBERT SPACES WITH β− AND φ−MIXING SEQUENCES

arXiv

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arXiv 2025年

作者： Roy, Priyanka Saminger-Platz, Susanne Institute for Mathematical Methods in Medicine and Data-Based Modeling Johannes Kepler University Linz Altenberger Strasse 69 LinzA-4020 Austria

In this paper, we study an online algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes, called the mixing process. For such a process, the degree of dependence is measured by various mixing coefficients. As a representative example, we analyze a strictly stationary Markov chain, where the dependence structure is characterized by the β− and φ−mixing coefficients. For these dependent samples, we derive nearly optimal convergence rates. Our findings extend existing error bounds for i.i.d. observations, demonstrating that the i.i.d. case is a special instance of our framework. Moreover, we explicitly account for an additional factor introduced by the dependence structure in the Markov *** Codes 60J20, 68T05, 68Q32, 62L20 Copyright © 2025, The Authors. All rights reserved.

关键词： Markov chains

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Adjointable maps between linear orthosets

arXiv

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arXiv 2025年

作者： Paseka, Jan Vetterlein, Thomas Department of Mathematics and Statistics Masaryk University Kotlářská 2 Brno611 37 Czech Republic Institute for Mathematical Methods in Medicine and Data Based Modeling Johannes Kepler University Linz Altenberger Straße 69 Linz4040 Austria

Given an (anisotropic) Hermitian space H, the collection P (H) of at most one-dimensional subspaces of H, equipped with the orthogonal relation ⊥ and the zero linear subspace {0}, is a linear orthoset and up to orthoisomorphism any linear orthoset of rank ≥ 4 arises in this way. We investigate in this paper the correspondence of structure-preserving maps between Hermitian spaces on the one hand and between the associated linear orthosets on the other hand. Our particular focus is on adjointable maps. We show that, under a mild assumption, adjointable maps between linear orthosets are induced by quasilinear maps between Hermitian spaces and if the latter are linear, they are adjointable as well. Specialised versions of this correlation lead to Wigner-type theorems;we see, for instance, that orthoisomorphisms between the orthosets associated with at least 3-dimensional Hermitian spaces are induced by quasiunitary maps. In addition, we point out that orthomodular spaces of dimension ≥ 4 can be characterised as irreducible Fréchet orthosets such that the inclusion map of any subspace is adjointable. Together with a transitivity condition, we may in this way describe the infinite-dimensional classical Hilbert *** Codes 46C05, 06C15, 15A04, 51A10, 51F20 Copyright © 2025, The Authors. All rights reserved.

关键词： Hilbert spaces

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Categories of orthosets and adjointable maps

arXiv

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arXiv 2025年

An orthoset is a non-empty set together with a symmetric and irreflexive binary relation ⊥, called the orthogonality relation. An orthoset with 0 is an orthoset augmented with an additional element 0, called falsity, which is orthogonal to every element. The collection of subspaces of a Hilbert space that are spanned by a single vector provides a motivating example. We say that a map f: X → Y between orthosets with 0 possesses the adjoint g: Y → X if, for any x ∈ X and y ∈ Y, f (x) ⊥ y if and only if x ⊥ g(y). We call f in this case adjointable. For instance, any bounded linear map between Hilbert spaces induces a map with this property. We discuss in this paper adjointability from several perspectives and we put a particular focus on maps preserving the orthogonality relation. We moreover investigate the category OS of all orthosets with 0 and adjointable maps between them. We especially focus on the full subcategory iOS of irredundant orthosets with 0. iOS can be made into a dagger category, the dagger of a morphism being its unique adjoint. iOS contains dagger subcategories of various sorts and provides in particular a framework for the investigation of projective Hilbert *** Codes 81P10, 06C15, 46C05 Copyright © 2025, The Authors. All rights reserved.

关键词： Vector spaces

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An explainable evolving fuzzy neural network in position identification of basketball players 1

An explainable evolving fuzzy neural network in position ide...

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1st Workshop on Online Learning from Uncertain data Streams, OLUD 2022

作者： de Campos Souza, Paulo Vitor Lughofer, Edwin Johannes Kepler university Linz Institute for Mathematical Methods in Medicine and Data Based Modeling Altenberger Strasse 69 Linz4040 Austria

Evolving fuzzy neural networks have the adaptive capacity to solve complex problems. They can facilitate understanding the behavior of the analyzed problem as they can extract knowledge from an analyzed data set. Thus, this work proposes applying an evolving fuzzy neural network capable of solving pattern classification problems with considerable interpretability in the position identification of basketball players. The models used in these tests were compared to the state-of-the-art on the subject, and their results were superior (87.50 % of accuracy) and interpretable. In addition to being accurate in solving the problems, the model presented relevant information on data stream processing, allowing a complete evaluation of the data behavior during its evaluation. © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

关键词： Fuzzy neural networks

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Characterisation of quadratic spaces over the Hilbert field by means of the orthogonality relation

arXiv

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arXiv 2025年

作者： Korbelář, Miroslav Paseka, Jan Vetterlein, Thomas Department of Mathematics Faculty of Electrical Engineering Czech Technical University in Prague Technická 2 Praha166 27 Czech Republic Department of Mathematics and Statistics Masaryk University Kotlářská 2 Brno611 37 Czech Republic Institute for Mathematical Methods in Medicine and Data Based Modeling Johannes Kepler University Altenberger Straße 69 Linz4040 Austria

An orthoset is a set equipped with a symmetric, irreflexive binary relation. With any (anisotropic) Hermitian space H, we may associate the orthoset (P (H), ⊥), consisting of the set of one-dimensional subspaces of H and the usual orthogonality relation. (P (H), ⊥) determines H essentially uniquely. We characterise in this paper certain kinds of Hermitian spaces by imposing transitivity and minimality conditions on their associated orthosets. By gradually considering stricter conditions, we restrict the discussion to a more and more narrow class of Hermitian spaces. We are eventually interested in quadratic spaces over countable subfields of R. A line of an orthoset is the orthoclosure of two distinct element. For an orthoset to be line-symmetric means roughly that its automorphism group acts transitively both on the collection of all lines as well as on each single line. Line-symmetric orthosets turn out to be in correspondence with transitive Hermitian spaces. Furthermore, quadratic orthosets are defined similarly, but are required to possess, for each line , a group of automorphisms acting on transitively and commutatively. We show the correspondence of quadratic orthosets with transitive quadratic spaces over ordered fields. We finally specify those quadratic orthosets that are, in a natural sense, minimal: for a finite n > 4, the orthoset (P (Rn), ⊥), where R is the Hilbert field, has the property of being embeddable into any other quadratic orthoset of rank n. Copyright © 2025, The Authors. All rights reserved.

关键词： Hilbert spaces

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Evolving Multi-Label Fuzzy Classifier

arXiv

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arXiv 2022年

作者： Lughofer, Edwin Institute for Mathematical Methods in Medicine and Data Based Modeling Johannes Kepler University Linz Austria

Multi-label classification has attracted much attention in the machine learning community to address the problem of assigning single samples to more than one (not necessarily non-overlapping) class at the same time. We propose an evolving multi-label fuzzy classifier (EFC-ML) which is able to self-adapt and self-evolve its structure with new incoming multi-label samples in an incremental, single-pass manner. It is based on a multi-output Takagi-Sugeno type architecture, where for each class a separate consequent hyper-plane is defined, which yields flexibility for partially approximating the respective classes in a binary [0,1]-regression context. The learning procedure embeds a locally weighted incremental correlation-based algorithm combined with (conventional) recursive fuzzily weighted least squares and Lasso-based regularization. Locality is important to avoid the out-masking effect of single class labels in one or more rules;the correlation-based part ensures that the interrelations between class labels, a specific well-known property in multi-label classification for improved performance, are preserved properly;the Lasso-based regularization reduces the curse of dimensionality effects in the case of a higher number of inputs. Antecedent learning is achieved by product-space clustering and conducted for all class labels together, which yields a single rule base (opposed to related techniques such as one-versus-rest or classifier chaining, achieving multiple different rule bases, one per class), allowing a compact knowledge view and thus enabling better interpretable insights. Furthermore, our approach comes with an online active learning (AL) strategy for updating the classifier on just a (smaller) number of selected samples, which in turn makes the approach applicable for scarcely labelled streams in applications, where the annotation effort is typically expensive. It is based on three essential concepts: novelty content in the antecedent space, uncertainty d

关键词： Fuzzy sets

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In Silico Assessment of a Multipore Electrode Design for High Power Short Duration Ablation

In Silico Assessment of a Multipore Electrode Design for Hig...

引用

2022 Computing in Cardiology, CinC 2022

作者： Petras, Argyrios Leoni, Massimiliano Weidmann, Zoraida Moreno Guerra, Jose M Gerardo-Giorda, Luca Austrian Academy of Sciences Linz Austria Hospital de la Santa Creu i Sant Pau Iib Sant Pau Universitat Autònoma de Barcelona Ciber Cv Department of Cardiology Barcelona Spain Institute for Mathematical Methods in Medicine and Data-Based Modelling Johannes Kepler University Linz Austria

ISBN: (纸本)9798350300970

High Power Short Duration (HPSD) ablation is an emerging approach to the radiofrequency catheter ablation for the treatment of cardiac arrhythmias. New catheter technologies have been introduced accommodating HPSD protocols, featuring multiple pores distributed around the electrode tip among others. Our previous in-silico assessment considered 6-pores electrodes, which were proven to not provide adequate cooling of the blood during the ablation. In this work, we explore the impact of a better electrode cooling system on the HPSD procedure using our previously validated computational model. A new electrode design is considered that consists of 66 irrigation pores based on state-of-the-art catheters used for HPSD. Ablations of 90W applied power for a duration of 4s for different contact forces show improved cooling of the electrode, without any steam pop complications. Yet, multiple pores around the electrode tip are not sufficient for effective blood cooling at low flows. © 2022 Creative Commons.

关键词： Cooling

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Should I Tilt or Should I Push? Effect of Contact Force and Catheter Inclination in Cardiac RF Ablation 50

Should I Tilt or Should I Push? Effect of Contact Force and ...

引用

50th Computing in Cardiology, CinC 2023

作者： Leoni, Massimiliano Petras, Argyrios Weidmann, Zoraida Moreno Guerra, Jose M Gerardo-Giorda, Luca Hospital de la Santa Creu i Sant Pau Iib Sant Pau Universitat Autònoma de Barcelona Ciber Cv Department of Cardiology Barcelona Spain Austrian Academy of Sciences Linz Austria Institute for Mathematical Methods in Medicine and Data-Based Modelling Johannes Kepler University Linz Austria

ISBN: (纸本)9798350382525

Radiofrequency ablation is a minimally invasive treatment for cardiac arrhythmias. During the procedure, the catheter is placed at the arrhythmogenic site to deliver electric current. There is uncertainty in the contact force and the catheter orientation, which can be affected by many factors, including the cardiac anatomy and the heartbeat. In this work we explore the impact of the contact force and different catheter inclinations on the resulting lesion. An improved electrical model allows to properly account for the current that flows to the tissue through the blood, a relevant aspect when the catheter is not per-pendicular. The lesion size consistently increases with the catheter inclination, regardless of the contact force. © 2023 CinC.

关键词： Catheters

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UPPER BOUNDS FOR LEARNING IN REPRODUCING KERNEL HILBERT SPACES FOR NON IID SAMPLES

arXiv

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arXiv 2024年

作者： Roy, Priyanka Saminger-Platz, Susanne Institute for Mathematical Methods in Medicine and Data-Based Modeling Johannes Kepler University Linz Altenberger Strasse 69 LinzA-4020 Austria

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming to approximate the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We further extend these results to an online regularized learning algorithm in reproducing kernel Hilbert spaces, where the samples are drawn along a Markov chain trajectory hence the samples are of the non i.i.d. *** Codes 60J20, 68T05, 68Q32, 62L20 Copyright © 2024, The Authors. All rights reserved.

关键词： Markov chains

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