arXiv subjects

Christian Canedo

Publications and source records attributed to Christian Canedo.

3 recordsLinked to original sources

arXiv2026

Unifying Adaptive Fourier and M\"obius-Based Models for Efficient and Interpretable Biomedical Signal Decomposition

Oscillatory biomedical signals such as electrocardiograms (ECG) and electroencephalograms (EEG) call for decompositions that are both computationally efficient and interpretable. This paper establishes a formal connection between two finite-order frameworks that have largely evolved independently: Adaptive Fourier Decomposition (AFD), based on orthonormal Takenaka-Malmquist expansions, and the Frequency-Modulated Mobius (FMM) model, a parametric decomposition built on Mobius transforms with morphologically meaningful parameters. We prove that finite-order AFD and FMM decompositions are mathematically equivalent. Under mild regularity assumptions, we further show that their associated estimation procedures solve the same underlying optimization problem when FMM is formulated with independent Gaussian noise. The results are extended to multi-channel signals, which are central in multilead bioelectric recordings. Practically, the equivalence clarifies how fast AFD approximations, including FFT-based implementations, relate to FMM-style parametrization and component interpretability. We illustrate these implications with an EEG example evaluating approximation behavior as the number of components increases, and with an ECG use case comparing five-component decompositions on representative beats, contrasting unlabeled AFD components with physiologically identified FMM components. Overall, the proposed equivalence provides a principled basis to leverage the computational advantages of AFD alongside the interpretability of FMM in biomedical signal analysis.

eess.SP↗

arXiv2022

A Unique Cardiac Electrophysiological 3D Model

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about the heart diagnostic. Even though it is one of the major problems in biomedical research, an efficient mathematical formulation for this modelling has still not been found. In this paper, we present an outstanding mathematical model. It relies on a five dipole representation of the cardiac electric source, each one associated with the well-known waves of the electrocardiogram signal. The mathematical formulation is simple enough to be easily parametrized and rich enough to provide realistic signals. Beyond the physical basis of the model, the parameters are physiologically interpretable as they characterize the wave shape, similar to what a physician would look for in signals, thus making them very useful in diagnosis. The model accurately reproduces the electrocardiogram and vectocardiogram signals of any diseased or healthy heart, bringing together different systems in a single model. Furthermore, a novel algorithm accurately identifies the model parameters. This new discovery represents a revolution in electrocardiography research, solving one of the main problems in this field. It is especially useful for the automatic diagnosis of cardiovascular diseases, patient follow-up or decision-making on new therapies.

physics.med-ph↗

arXiv2022

Compelling new electrocardiographic markers for automatic diagnosis

The automatic diagnosis of heart diseases from the electrocardiogram (ECG) signal is crucial in clinical decision-making. However, the use of computer-based decision rules in clinical practice is still deficient, mainly due to their complexity and a lack of medical interpretation. The objetive of this research is to address these issues by providing valuable diagnostic rules that can be easily implemented in clinical practice. In this research, efficient diagnostic rules friendly in clinical practice are provided. In this paper, interesting parameters obtained from the ECG signals analysis are presented and two simple rules for automatic diagnosis of Bundle Branch Blocks are defined using new markers derived from the so-called FMMecg delineator. The main advantages of these markers are the good statistical properties and their clear interpretation in clinically meaningful terms. High sensitivity and specificity values have been obtained using the proposed rules with data from more than 35000 patients from well known benchmarking databases. In particular, to identify Complete Left Bundle Branch Blocks and differentiate this condition from subjects without heart diseases, sensitivity and specificity values ranging from 93% to 99% and from 96% to 99%, respectively. The new markers and the automatic diagnosis are easily available at https://fmmmodel.shinyapps.io/fmmEcg/, an app specifically developed for any given ECG signal. The proposal is different from others in the literature and it is compelling for three main reasons. On the one hand, the markers have a concise electrophysiological interpretation. On the other hand, the diagnosis rules have a very high accuracy. Finally, the markers can be provided by any device that registers the ECG signal and the automatic diagnosis is made straightforwardly, in contrast to the black-box and deep learning algorithms.

physics.med-ph↗