Functional clustering of neuronal signals with FMM mixture models.

The identification of unlabeled neuronal electric signals is one of the most challenging open problems in neuroscience, widely known as Spike Sorting. Motivated to solve this problem, we propose a model-based approach within the mixture modeling framework for clustering oscillatory functional data called MixFMM. The core of the approach is the FMM (Frequency Modulated Möbius) waves, which are non-linear parametric time functions, flexible enough to describe different oscillatory patterns and simple enough to be estimated efficiently. In particular, specific model parameters describe the phase, amplitude and shape of the waveforms. A mixture model is defined using FMM waves as basic functions and gaussian errors, and an EM algorithm is proposed for estimating the parameters. Spike Sorting (SS) has received considerable attention in the literature, and different functional clustering approaches have been considered. We have conducted a fair comparative analysis of the MixFMM with three competitors. Two of them are traditional methods in functional clustering and widely used in Spike Sorting. The third is an approach that has proven superior to many others solving Spike Sorting problems. The datasets used for validation include benchmarking simulated and real cases. The internal and external validation indexes confirm a better performance of the MixFMM on real data sets against the three competitors and an outstanding performance in simulated data against traditional approaches.

Compelling new electrocardiographic markers for automatic diagnosis.

BACKGROUND AND OBJECTIVE: 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. METHODS: 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. RESULTS: High sensitivity and specificity values have been obtained using the proposed rules with data from more than 35,000 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. CONCLUSIONS: 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 electrocardiographic 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.

A unique cardiac electrocardiographic 3D model. Toward interpretable AI diagnosis.

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about heart diagnostics. In this paper, we present an efficient mathematical formulation for this modeling simple enough to be easily parameterized and rich enough to provide realistic signals. It relies on a five dipole representation of the cardiac electric source, each one associated with the well-known waves of the electrocardiogram signal. 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 signals of any diseased or healthy heart. This new discovery represents a significant advance in electrocardiography research. It is especially useful for diagnosis, patient follow-up or decision-making on new therapies; is also a promising tool for well-performing, transparent and interpretable AI approaches.

A simple parametric representation of the Hodgkin-Huxley model.

The Hodgkin-Huxley model, decades after its first presentation, is still a reference model in neuroscience as it has successfully reproduced the electrophysiological activity of many organisms. The primary signal in the model represents the membrane potential of a neuron. A simple representation of this signal is presented in this paper. The new proposal is an adapted Frequency Modulated Möbius multicomponent model defined as a signal plus error model in which the signal is decomposed as a sum of waves. The main strengths of the method are the simple parametric formulation, the interpretability and flexibility of the parameters that describe and discriminate the waveforms, the estimators' identifiability and accuracy, and the robustness against noise. The approach is validated with a broad simulation experiment of Hodgkin-Huxley signals and real data from squid giant axons. Interesting differences between simulated and real data emerge from the comparison of the parameter configurations. Furthermore, the potential of the FMM parameters to predict Hodgkin-Huxley model parameters is shown using different Machine Learning methods. Finally, promising contributions of the approach in Spike Sorting and cell-type classification are detailed.

Electrophysiological and Transcriptomic Features Reveal a Circular Taxonomy of Cortical Neurons.

The complete understanding of the mammalian brain requires exact knowledge of the function of each neuron subpopulation composing its parts. To achieve this goal, an exhaustive, precise, reproducible, and robust neuronal taxonomy should be defined. In this paper, a new circular taxonomy based on transcriptomic features and novel electrophysiological features is proposed. The approach is validated by analysing more than 1850 electrophysiological signals of different mouse visual cortex neurons proceeding from the Allen Cell Types database. The study is conducted on two different levels: neurons and their cell-type aggregation into Cre lines. At the neuronal level, electrophysiological features have been extracted with a promising model that has already proved its worth in neuronal dynamics. At the Cre line level, electrophysiological and transcriptomic features are joined on cell types with available genetic information. A taxonomy with a circular order is revealed by a simple transformation of the first two principal components that allow the characterization of the different Cre lines. Moreover, the proposed methodology locates other Cre lines in the taxonomy that do not have transcriptomic features available. Finally, the taxonomy is validated by Machine Learning methods which are able to discriminate the different neuron types with the proposed electrophysiological features.