PURPOSE:To develop a method for detecting respiratory phases and their onset during intra-arrest ventilation with ongoing chest compressions based on explicit definitions for respiratory phase onsets, enabling automated processing at scale. METHODS:An algorithm was developed that uses the product of airflow and airway pressure, and the product of flow and airway pressure slope. For experimental validation of the algorithm, ventilatory recordings from 13 pigs with mechanical ventilation were used. For each animal, 20 ventilations before induction of cardiac arrest (regular ventilation) and 20 ventilations during ongoing chest compressions with asynchronous ventilation (intra-arrest ventilation) were selected. Algorithm performance was analysed against investigator-validated annotations of respiratory phase onsets. RESULTS:The proposed algorithm yielded perfect classification of inspiratory and expiratory phases during regular and intra-arrest ventilation. For the determination of the exact timestamp of respiratory phase onsets, the algorithm had an F1-score of 1 in regular ventilation and 0.971 during intra-arrest ventilation. CONCLUSIONS:We propose an algorithm to detect respiratory phases and their exact onsets robust to chest compressions, which exhibits excellent results on a validation dataset. The concept incorporates the inherent relationship of airflow and airway pressure to differentiate between airflow due to artificial ventilations and airflow due to chest compressions.

Artificial intelligence offers great opportunities in critical care, particularly when a vast amount of continuously acquired physiological data is incorporated. High-quality, reliably labelled data are paramount for developing and training artificial intelligence methods. However, routinely recorded data in critical care are often noisy, and the sheer volume of high-resolution data is challenging to manage. Generalizable solutions for these problems are lacking, restricting progress. To address these barriers, we developed Vitabel, an open-source Python framework for post hoc loading, visualizing, aligning, and annotating medical time series. The framework provides sensible defaults and interactive components for efficient use in preconfigured workflows, while remaining flexible and extendable for custom analysis and annotation pipelines. It integrates seamlessly into Jupyter Notebooks, providing an interactive, customizable interface for visual interaction with the data. In this publication, we demonstrate its utility across three use cases. The code and exemplary data are provided as browser-based demos. Vitabel is freely available and published under the MIT license accompanying this publication.

AIM:To evaluate the accuracy of the EOlife X, a ventilation feedback device for training, during regular ventilation and during intra-arrest ventilation with ongoing chest compressions. METHODS:In this prospective experimental method-comparison study in a porcine cardiac arrest model, EOlife X-derived inspiratory tidal volume (Vti), expiratory tidal volume (Vte), and respiratory rate (f) were compared with sensor-based reference computations. Data were extracted by optical character recognition from screen recording of the EOlife X. Reference metrics were computed from continuous airflow and airway pressure measurements. For each animal, a two-minute-long period before cardiac arrest and a two-minute-long period of cardiopulmonary resuscitation (CPR) were analysed. The animals were mechanically ventilated via an endotracheal tube. Agreement was assessed using Bland-Altman analysis with linear mixed model derived bias and limits of agreement to account for repeated measures. Clinically acceptable differences were prespecified as ±50 mL for tidal volumes and ±3 /min for respiratory rate. RESULTS:Data from 11 animals, yielding 821 paired ventilations (581 regular, 240 intra-arrest), were analysed. During regular ventilation, EOlife X measurements were within the prespecified clinically acceptable difference for all metrics, while exceeding it for all metrics during intra-arrest ventilation: Bias for Vtiwas -26 mL with limits of agreement (LoA) ranging from -355 to 304 mL, for Vtebias was -281 mL (LoA -599 to 37 mL), and for f23.8 /min (LoA -50.2 to 97.8 /min). The proportions of measurements outside the prespecified clinically acceptable difference during intra-arrest ventilation were 37.1% for Vti, 86.2% for Vte, and 60.4% for f. Waveform inspection suggested that chest compression-induced reverse airflow affects airflow-based measurements. CONCLUSION:EOlife X showed agreement within predefined clinically acceptable limits during regular ventilation, but not during intra-arrest ventilation with ongoing chest compressions. Chest compression-induced reverse airflow appears to compromise airflow-based calculation of tidal volume and respiratory rate. Devices for ventilatory monitoring should be validated specifically under CPR conditions.

Models based on partial differential equations (PDEs) are powerful for describing a wide range of complex relationships in the natural sciences. Accurately identifying the PDE model, which represents the underlying physical law, is essential for a proper understanding of the problem. This reconstruction typically relies on indirect and noisy measurements of the system's state and, without specifically tailored methods, rarely yields symbolic expressions, thereby hindering interpretability. In this work, we address this issue by considering existing neural network architectures based on rational functions for the symbolic representation of physical laws. These networks leverage the approximation power of rational functions while also benefiting from their flexibility in representing arithmetic operations. Our main contribution is an identifiability result, showing that, in the limit of noiseless, complete measurements, such symbolic networks can uniquely reconstruct the simplest physical law within the PDE model. Specifically, reconstructed laws remain expressible within the symbolic network architecture, with regularization-minimizing parameterizations promoting interpretability and sparsity in case of L^1-regularization. In addition, we provide regularity results for symbolic networks. Empirical validation using the ParFam architecture supports these theoretical findings, providing evidence for the practical reconstructibility of physical laws.

INTRODUCTION:Cardiopulmonary bypass has been used to perform complex cardiac surgery for over 70 years. Advances in bypass techniques and perioperative medicine have increased the safety of cardiac procedures, leading to reduced morbidity and mortality. Nevertheless, cardiopulmonary bypass still carries risks, including systemic inflammation and dysfunction of various organs. To date, optimal blood pressure management during cardiopulmonary bypass remains a subject of ongoing debate. Conflicting evidence exists regarding negative outcomes associated with both low and high mean arterial pressures. Current clinical guidelines recommend a broad target range for mean arterial pressure during cardiopulmonary bypass, which underscores the existing gap in knowledge. In non-cardiac surgery, the time-weighted average of mean arterial pressure has been used to determine minimum safe thresholds, with greater deviation from 65 mm Hg associated with an increased risk of adverse outcomes. However, the definition and reporting of low blood pressure during cardiopulmonary bypass varies between studies, and the use of time-weighted averages below the threshold is still uncommon. Details on pump flow during extracorporeal circulation are seldom reported. METHODS AND ANALYSIS:We plan to conduct a retrospective, single-centre data analysis to investigate the effects of both arterial blood pressure and extracorporeal pump flow, including their time-weighted averages and areas under defined thresholds, during cardiopulmonary bypass on neurological outcomes in adult patients undergoing cardiac surgery between 2014 and 2023. The study will include both elective and emergency procedures, with separate analyses conducted based on the urgency and complexity of the operations. Digitally recorded anaesthesia and perfusion records will be imported and validated to extract information on haemodynamic parameters, neurological monitoring and extracorporeal circulation. Ischaemic and haemorrhagic strokes will be identified by screening postoperative brain imaging records for keywords indicating neurological events. Diagnostic data and additional patient and procedural information will be extracted from the local cardiac surgery database and hospital information system. Information about incidence and course of postoperative delirium will be extracted from the patient data management system used in intensive care. We expect to include approximately 500-700 cases per year in the final analysis. ETHICS AND DISSEMINATION:The local ethics committee approved our study (Ethics Committee of the Medical University of Graz, IRB00002556, 36-296 ex 23/24). We aim to publish the results of our study preferably in an open access format. TRIAL REGISTRATION NUMBER:The study protocol was registered at the Center for Open Science (https://doi.org/10.17605/OSF.IO/FAMV3).

In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via Gibbs densities p(x) ∝exp-E(x) with an appropriate energy functional E. Within this chapter we present a rigorous theoretical introduction to Bayesian inverse problems that includes results on well-posedness and stability in the finite-dimensional and infinite-dimensional setting. Afterwards we discuss the use of EBMs for Bayesian inverse problems and explain the most relevant techniques for learning EBMs from data. As a crucial part of Bayesian inverse problems, we cover several popular algorithms for sampling from EBMs, namely the Metropolis-Hastings algorithm, Gibbs sampling, Langevin Monte Carlo, and Hamiltonian Monte Carlo. Moreover, we present numerical results for the resolution of several inverse imaging problems obtained by leveraging an EBM that allows for the explicit verification of those properties that are needed for valid energy-based modeling.

This paper addresses the problem of recovering tracer kinetic parameters from multi-region measurement data in quantitative positron emission tomography (PET) imaging using the reversible two tissue compartment model. Its main result is an extension of our previous work on the irreversible two tissue compartment model. In analogy to our previous work, we show that also in the practically highly relevant reversible case, most tracer kinetic parameters can be uniquely identified from standard PET measurements without additional full blood sample analysis that is usually performed in practice, and under reasonable assumptions. In addition, unique identifiability of all parameters is shown, provided that additional measurements from the uncorrected total arterial blood tracer concentration are available. These can be obtained from standard PET measurements or from a simple blood sample analysis.

Artificial intelligence offers a great opportunity in critical care, particularly when a vast amount of continuously acquired physiological data is incorporated. High-quality, reliably labelled data are paramount for developing and training artificial intelligence methods. However, routinely recorded data in critical care are often noisy, and the sheer volume of high-resolution data is challenging to manage. Generalizable solutions for these problems are lacking, restricting progress.To address these barriers, we developed \vitabel{}, an open-source \python{} package for loading, visualising, aligning, and annotating medical time series with minimal coding. The tool integrates seamlessly into \jupyter{-notebooks}, providing an interactive, customizable interface to interact with the data visually. In this publication, we demonstrate its utility across three use cases. The code and exemplary data are provided as browser-based demos. \vitabel{} is freely available and published under the MIT license accompanying this publication.

This paper addresses the problem of learning reaction-diffusion (RD) systems from data while ensuring physical consistency and well-posedness of the learned models. Building on a regularization-based framework for structured model learning, we focus on learning parameterized reaction terms and investigate how to incorporate key physical properties, such as mass conservation and quasipositivity, directly into the learning process. Our main contributions are twofold: First, we propose techniques to systematically modify a given class of parameterized reaction terms such that the resulting terms inherently satisfy mass conservation and quasipositivity, ensuring that the learned RD systems preserve non-negativity and adhere to physical principles. These modifications also guarantee well-posedness of the resulting PDEs under additional regularity and growth conditions. Second, we extend existing theoretical results on regularization-based model learning to RD systems using these physically consistent reaction terms. Specifically, we prove that solutions to the learning problem converge to a unique, regularization-minimizing solution of a limit system even when conservation laws and quasipositivity are enforced. In addition, we provide approximation results for quasipositive functions, essential for constructing physically consistent parameterizations. These results advance the development of interpretable and reliable data-driven models for RD systems that align with fundamental physical laws.

Segmentation of cardiac magnetic resonance images (MRI) is crucial for the analysis and assessment of cardiac function, helping to diagnose and treat various cardiovascular diseases. Most recent techniques rely on deep learning and usually require an extensive amount of labeled data. To overcome this problem, few-shot learning has the capability of reducing data dependency on labeled data. In this work, we introduce a new method that merges few-shot learning with a U-Net architecture and Gaussian Process Emulators (GPEs), enhancing data integration from a support set for improved performance. GPEs are trained to learn the relation between the support images and the corresponding masks in latent space, facilitating the segmentation of unseen query images given only a small labeled support set at inference. We test our model with the M Ms-2 public dataset to assess its ability to segment the heart in cardiac magnetic resonance imaging from different orientations, and compare it with state-of-the-art unsupervised and few-shot methods. Our architecture shows higher DICE coefficients compared to these methods, especially in the more challenging setups where the size of the support set is considerably small.

We show that suitably regular functions can be approximated in the 𝒞^1-norm both with rational functions and rational neural networks, including approximation rates with respect to width and depth of the network, and degree of the rational functions. As consequence of our results, we further obtain 𝒞^1-approximation results for rational neural networks with the EQL^÷ and ParFam architecture, both of which are important in particular in the context of symbolic regression for physical law learning.

It is a common practice to evaluate the reproducibility of fMRI at the group level. However, for clinical applications of fMRI, where the focus is on reproducibility of single individuals, the high test-retest reliability that is sometimes reported for group-based measures can be misleading. On the level of single subjects, reproducibility of fMRI is still far too low for clinical applications, not even meeting the standards to use fMRI for scientific purposes. The goal of this work is to enhance the poor single-subject time course reproducibility of fMRI. For this purpose, we have developed a framework for post-processing fMRI signals using Savitzky-Golay (SG) filters in conjunction with general linear model (GLM) based data cleaning. The parameters of these filters were trained to be the optimal ones based on a dataset of working memory relevant signals. By employing our data-driven filtering framework, we successfully improve the average reproducibility correlation of a single fMRI time course from r = 0.26 (as obtained with a conventional statistical parametric mapping (SPM) data cleaning pipeline) to a fair level of r = 0.41. Additionally, we are able to enhance the average connectivity correlation from r = 0.44 to r = 0.54. Our conclusion is that signal post-processing with a data-driven SG filter framework may substantially improve time course reproducibility compared to conventional denoising pipelines. As a conservative estimate, we conjecture that roughly 10-30% of the population may benefit from optimized fMRI pipelines in a clinical setting depending on the measure of interest while this number was nihil for conventional fMRI pipelines.

In this work, a method for unsupervised energy disaggregation in private households equipped with smart meters is proposed. The method aims to classify power consumption as active or passive, granting the ability to report on the residents’ activity and presence without direct interaction. This lays the foundation for applications like non-intrusive health monitoring of private homes. The proposed method is based on minimizing a suitable energy functional, for which the iPALM (inertial proximal alternating linearized minimization) algorithm is employed, demonstrating that various conditions guaranteeing convergence are satisfied. In order to confirm feasibility of the proposed method, experiments on semi-synthetic test data sets and a comparison to existing methods are provided.

Research question The detection of single chest compressions (CCs) in defibrillator records is crucial to evaluate CPR quality parameters like longest pause duration.1 Currently, defibrillators detect CCs automatically and provide performance feedback via their proprietary software. While some manufacturers (e.g. Stryker) report the accuracy of their CC detection algorithm and allow to manually revise the automatically detected CCs to improve accuracy, others (e.g. ZOLL) do not offer this option.2 Recent works further suggest that using automatically detected CCs without revision or other open source methods is sufficient to compute quality markers.3,4 We aim to compare the accuracy of the automatic CC detection of two defibrillators. Methodology 131 defibrillator recordings from ZOLL’s X-Series devices with an applied feedback sensor and 70 recordings of Stryker’s LIFEPAK 15 devices were exported. ZOLL detects CC based on accelerometry data from its CC feedback sensor, while Stryker uses the thoracic impedance signal. Each set of recordings was annotated by a single annotator by adding missing CCs and deleting excess CCs, forming a ground truth. The results are reported as median, (10th percentile, 90th percentile) and were tested on statistical significance with a Mann-Whitney U test. Results Per case, the device by ZOLL detects in median 99.6, (97.8,99.9) % of all CCs correctly. 0.4, (0.1,2.3) % are deleted and 0.4, (0.1,2.3) % are added during the annotation process. For Stryker’s LIFEPAK 15 the respective numbers are: correctly detected: 96.7, (81.5,99.2) %, deleted: 1.8, (0.2,10.9) %, added: 3.3, (.8,18.5) %. The difference between the correctly identified CCs is significant (p<0.0001). The distribution of missing and excess CCs for all cases is shown in Figure 1. Interpretation It appears that ZOLL’s CC detection via an accelerometry based feedback sensor is more accurate than Stryker’s method using thoracic impedance. However, Stryker’s accuracy exceeds 95% as well, providing a reasonably reliable basis for CPR quality marker calculations.

An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal consistency between the different measurement times. The strongest consistency can be achieved by reconstructing data directly in phase space, the space of positions and velocities. However, this space is usually too highdimensional for feasible computations. We introduce a novel dimension reduction technique, based on projections of phase space onto lower-dimensional subspaces, which provably circumvents this curse of dimensionality: Indeed, in the exemplary framework of superresolution we prove that known exact reconstruction results stay true after dimension reduction, and we additionally prove new error estimates of reconstructions from noisy data in optimal transport metrics which are of the same quality as one would obtain in the non-dimension-reduced case.

In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously parametrized family of convex, positively one-homogeneous functionals defined on a common Banach space $X$. We show that, under mild assumptions, this functional admits an equivalent convex lifting in the space of measures with values in $X$. This reformulation allows us to prove well-posedness of a Tikhonov regularized inverse problem and opens the door to a sparse analysis of the solutions. In the case of finite-dimensional measurements we prove a representer theorem, showing that there exists a solution of the inverse problem that is sparse, in the sense that it can be represented as a linear combination of the extremal points of the ball of the lifted infinite infimal convolution functional. Then, we design a generalized conditional gradient method for computing solutions of the inverse problem without relying on an a priori discretization of the parameter space and of the Banach space $X$. The iterates are constructed as linear combinations of the extremal points of the lifted infinite infimal convolution functional. We prove a sublinear rate of convergence for our algorithm and apply it to denoising of signals and images using, as regularizer, infinite infimal convolutions of fractional-Laplacian-type operators with adaptive orders of smoothness and anisotropies.

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, also a novel primal-dual Langevin algorithm for sampling from non-smooth distributions is introduced in this work.

This paper addresses the problem of uniqueness in learning physical laws for systems of partial differential equations (PDEs). Contrary to most existing approaches, it considers a framework of structured model learning, where existing, approximately correct physical models are augmented with components that are learned from data. The main result of the paper is a uniqueness result that covers a large class of PDEs and a suitable class of neural networks used for approximating the unknown model components. The uniqueness result shows that, in the idealized setting of full, noiseless measurements, a unique identification of the unknown model components is possible as regularization-minimizing solution of the PDE system. Furthermore, the paper provides a convergence result showing that model components learned on the basis of incomplete, noisy measurements approximate the regularization-minimizing solution of the PDE system in the limit. These results are possible under specific properties of the approximating neural networks and due to a dedicated choice of regularization. With this, a practical contribution of this analytic paper is to provide a class of model learning frameworks different to standard settings where uniqueness can be expected in the limit of full measurements.