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Nov 28

Segmentation and Vascular Vectorization for Coronary Artery by Geometry-based Cascaded Neural Network

Segmentation of the coronary artery is an important task for the quantitative analysis of coronary computed tomography angiography (CCTA) images and is being stimulated by the field of deep learning. However, the complex structures with tiny and narrow branches of the coronary artery bring it a great challenge. Coupled with the medical image limitations of low resolution and poor contrast, fragmentations of segmented vessels frequently occur in the prediction. Therefore, a geometry-based cascaded segmentation method is proposed for the coronary artery, which has the following innovations: 1) Integrating geometric deformation networks, we design a cascaded network for segmenting the coronary artery and vectorizing results. The generated meshes of the coronary artery are continuous and accurate for twisted and sophisticated coronary artery structures, without fragmentations. 2) Different from mesh annotations generated by the traditional marching cube method from voxel-based labels, a finer vectorized mesh of the coronary artery is reconstructed with the regularized morphology. The novel mesh annotation benefits the geometry-based segmentation network, avoiding bifurcation adhesion and point cloud dispersion in intricate branches. 3) A dataset named CCA-200 is collected, consisting of 200 CCTA images with coronary artery disease. The ground truths of 200 cases are coronary internal diameter annotations by professional radiologists. Extensive experiments verify our method on our collected dataset CCA-200 and public ASOCA dataset, with a Dice of 0.778 on CCA-200 and 0.895 on ASOCA, showing superior results. Especially, our geometry-based model generates an accurate, intact and smooth coronary artery, devoid of any fragmentations of segmented vessels.

  • 6 authors
·
May 7, 2023

XOCT: Enhancing OCT to OCTA Translation via Cross-Dimensional Supervised Multi-Scale Feature Learning

Optical Coherence Tomography Angiography (OCTA) and its derived en-face projections provide high-resolution visualization of the retinal and choroidal vasculature, which is critical for the rapid and accurate diagnosis of retinal diseases. However, acquiring high-quality OCTA images is challenging due to motion sensitivity and the high costs associated with software modifications for conventional OCT devices. Moreover, current deep learning methods for OCT-to-OCTA translation often overlook the vascular differences across retinal layers and struggle to reconstruct the intricate, dense vascular details necessary for reliable diagnosis. To overcome these limitations, we propose XOCT, a novel deep learning framework that integrates Cross-Dimensional Supervision (CDS) with a Multi-Scale Feature Fusion (MSFF) network for layer-aware vascular reconstruction. Our CDS module leverages 2D layer-wise en-face projections, generated via segmentation-weighted z-axis averaging, as supervisory signals to compel the network to learn distinct representations for each retinal layer through fine-grained, targeted guidance. Meanwhile, the MSFF module enhances vessel delineation through multi-scale feature extraction combined with a channel reweighting strategy, effectively capturing vascular details at multiple spatial scales. Our experiments on the OCTA-500 dataset demonstrate XOCT's improvements, especially for the en-face projections which are significant for clinical evaluation of retinal pathologies, underscoring its potential to enhance OCTA accessibility, reliability, and diagnostic value for ophthalmic disease detection and monitoring. The code is available at https://github.com/uci-cbcl/XOCT.

  • 6 authors
·
Sep 9

Benchmarking the CoW with the TopCoW Challenge: Topology-Aware Anatomical Segmentation of the Circle of Willis for CTA and MRA

The Circle of Willis (CoW) is an important network of arteries connecting major circulations of the brain. Its vascular architecture is believed to affect the risk, severity, and clinical outcome of serious neurovascular diseases. However, characterizing the highly variable CoW anatomy is still a manual and time-consuming expert task. The CoW is usually imaged by two non-invasive angiographic imaging modalities, magnetic resonance angiography (MRA) and computed tomography angiography (CTA), but there exist limited datasets with annotations on CoW anatomy, especially for CTA. Therefore, we organized the TopCoW challenge with the release of an annotated CoW dataset. The TopCoW dataset is the first public dataset with voxel-level annotations for 13 CoW vessel components, enabled by virtual reality technology. It is also the first large dataset using 200 pairs of MRA and CTA from the same patients. As part of the benchmark, we invited submissions worldwide and attracted over 250 registered participants from six continents. The submissions were evaluated on both internal and external test datasets of 226 scans from over five centers. The top performing teams achieved over 90% Dice scores at segmenting the CoW components, over 80% F1 scores at detecting key CoW components, and over 70% balanced accuracy at classifying CoW variants for nearly all test sets. The best algorithms also showed clinical potential in classifying fetal-type posterior cerebral artery and locating aneurysms with CoW anatomy. TopCoW demonstrated the utility and versatility of CoW segmentation algorithms for a wide range of downstream clinical applications with explainability. The annotated datasets and best performing algorithms have been released as public Zenodo records to foster further methodological development and clinical tool building.

  • 113 authors
·
Dec 29, 2023

Learning Tubule-Sensitive CNNs for Pulmonary Airway and Artery-Vein Segmentation in CT

Training convolutional neural networks (CNNs) for segmentation of pulmonary airway, artery, and vein is challenging due to sparse supervisory signals caused by the severe class imbalance between tubular targets and background. We present a CNNs-based method for accurate airway and artery-vein segmentation in non-contrast computed tomography. It enjoys superior sensitivity to tenuous peripheral bronchioles, arterioles, and venules. The method first uses a feature recalibration module to make the best use of features learned from the neural networks. Spatial information of features is properly integrated to retain relative priority of activated regions, which benefits the subsequent channel-wise recalibration. Then, attention distillation module is introduced to reinforce representation learning of tubular objects. Fine-grained details in high-resolution attention maps are passing down from one layer to its previous layer recursively to enrich context. Anatomy prior of lung context map and distance transform map is designed and incorporated for better artery-vein differentiation capacity. Extensive experiments demonstrated considerable performance gains brought by these components. Compared with state-of-the-art methods, our method extracted much more branches while maintaining competitive overall segmentation performance. Codes and models are available at http://www.pami.sjtu.edu.cn/News/56

  • 9 authors
·
Dec 10, 2020

From time-series to complex networks: Application to the cerebrovascular flow patterns in atrial fibrillation

A network-based approach is presented to investigate the cerebrovascular flow patterns during atrial fibrillation (AF) with respect to normal sinus rhythm (NSR). AF, the most common cardiac arrhythmia with faster and irregular beating, has been recently and independently associated with the increased risk of dementia. However, the underlying hemodynamic mechanisms relating the two pathologies remain mainly undetermined so far; thus the contribution of modeling and refined statistical tools is valuable. Pressure and flow rate temporal series in NSR and AF are here evaluated along representative cerebral sites (from carotid arteries to capillary brain circulation), exploiting reliable artificially built signals recently obtained from an in silico approach. The complex network analysis evidences, in a synthetic and original way, a dramatic signal variation towards the distal/capillary cerebral regions during AF, which has no counterpart in NSR conditions. At the large artery level, networks obtained from both AF and NSR hemodynamic signals exhibit elongated and chained features, which are typical of pseudo-periodic series. These aspects are almost completely lost towards the microcirculation during AF, where the networks are topologically more circular and present random-like characteristics. As a consequence, all the physiological phenomena at microcerebral level ruled by periodicity - such as regular perfusion, mean pressure per beat, and average nutrient supply at cellular level - can be strongly compromised, since the AF hemodynamic signals assume irregular behaviour and random-like features. Through a powerful approach which is complementary to the classical statistical tools, the present findings further strengthen the potential link between AF hemodynamic and cognitive decline.

  • 3 authors
·
Sep 26, 2017

Variationally Regularized Graph-based Representation Learning for Electronic Health Records

Electronic Health Records (EHR) are high-dimensional data with implicit connections among thousands of medical concepts. These connections, for instance, the co-occurrence of diseases and lab-disease correlations can be informative when only a subset of these variables is documented by the clinician. A feasible approach to improving the representation learning of EHR data is to associate relevant medical concepts and utilize these connections. Existing medical ontologies can be the reference for EHR structures, but they place numerous constraints on the data source. Recent progress on graph neural networks (GNN) enables end-to-end learning of topological structures for non-grid or non-sequential data. However, there are problems to be addressed on how to learn the medical graph adaptively and how to understand the effect of the medical graph on representation learning. In this paper, we propose a variationally regularized encoder-decoder graph network that achieves more robustness in graph structure learning by regularizing node representations. Our model outperforms the existing graph and non-graph based methods in various EHR predictive tasks based on both public data and real-world clinical data. Besides the improvements in empirical experiment performances, we provide an interpretation of the effect of variational regularization compared to standard graph neural network, using singular value analysis.

  • 2 authors
·
Dec 8, 2019

PVBM: A Python Vasculature Biomarker Toolbox Based On Retinal Blood Vessel Segmentation

Introduction: Blood vessels can be non-invasively visualized from a digital fundus image (DFI). Several studies have shown an association between cardiovascular risk and vascular features obtained from DFI. Recent advances in computer vision and image segmentation enable automatising DFI blood vessel segmentation. There is a need for a resource that can automatically compute digital vasculature biomarkers (VBM) from these segmented DFI. Methods: In this paper, we introduce a Python Vasculature BioMarker toolbox, denoted PVBM. A total of 11 VBMs were implemented. In particular, we introduce new algorithmic methods to estimate tortuosity and branching angles. Using PVBM, and as a proof of usability, we analyze geometric vascular differences between glaucomatous patients and healthy controls. Results: We built a fully automated vasculature biomarker toolbox based on DFI segmentations and provided a proof of usability to characterize the vascular changes in glaucoma. For arterioles and venules, all biomarkers were significant and lower in glaucoma patients compared to healthy controls except for tortuosity, venular singularity length and venular branching angles. Conclusion: We have automated the computation of 11 VBMs from retinal blood vessel segmentation. The PVBM toolbox is made open source under a GNU GPL 3 license and is available on physiozoo.com (following publication).

  • 6 authors
·
Jul 31, 2022

Artificial Intelligence-derived Vascular Age from Photoplethysmography: A Novel Digital Biomarker for Cardiovascular Health

With the increasing availability of wearable devices, photoplethysmography (PPG) has emerged as a promising non-invasive tool for monitoring human hemodynamics. We propose a deep learning framework to estimate vascular age (AI-vascular age) from PPG signals, incorporating a distribution-aware loss to address biases caused by imbalanced data. The model was developed using data from the UK Biobank (UKB), with 98,672 participants in the development cohort and 113,559 participants (144,683 data pairs) for clinical evaluation. After adjusting for key confounders, individuals with a vascular age gap (AI-vascular age minus calendar age) exceeding 9 years had a significantly higher risk of major adverse cardiovascular and cerebrovascular events (MACCE) (HR = 2.37, p < 0.005) and secondary outcomes, including diabetes (HR = 2.69, p < 0.005), hypertension (HR = 2.88, p < 0.005), coronary heart disease (HR = 2.20, p < 0.005), heart failure (HR = 2.15, p < 0.005), myocardial infarction (HR = 2.51, p < 0.005), stroke (HR = 2.55, p < 0.005), and all-cause mortality (HR = 2.51, p < 0.005). Conversely, participants with a vascular age gap below -9 years exhibited a significantly lower incidence of these outcomes. We further evaluated the longitudinal applicability of AI-vascular age using serial PPG data from the UKB, demonstrating its value in risk stratification by leveraging AI-vascular age at two distinct time points to predict future MACCE incidence. External validation was performed on a MIMIC-III-derived cohort (n = 2,343), where each one-year increase in vascular age gap was significantly associated with elevated in-hospital mortality risk (OR = 1.02, p < 0.005). In conclusion, our study establishes AI-vascular age as a novel, non-invasive digital biomarker for cardiovascular health assessment.

  • 5 authors
·
Feb 18

DS6, Deformation-aware Semi-supervised Learning: Application to Small Vessel Segmentation with Noisy Training Data

Blood vessels of the brain provide the human brain with the required nutrients and oxygen. As a vulnerable part of the cerebral blood supply, pathology of small vessels can cause serious problems such as Cerebral Small Vessel Diseases (CSVD). It has also been shown that CSVD is related to neurodegeneration, such as Alzheimer's disease. With the advancement of 7 Tesla MRI systems, higher spatial image resolution can be achieved, enabling the depiction of very small vessels in the brain. Non-Deep Learning-based approaches for vessel segmentation, e.g., Frangi's vessel enhancement with subsequent thresholding, are capable of segmenting medium to large vessels but often fail to segment small vessels. The sensitivity of these methods to small vessels can be increased by extensive parameter tuning or by manual corrections, albeit making them time-consuming, laborious, and not feasible for larger datasets. This paper proposes a deep learning architecture to automatically segment small vessels in 7 Tesla 3D Time-of-Flight (ToF) Magnetic Resonance Angiography (MRA) data. The algorithm was trained and evaluated on a small imperfect semi-automatically segmented dataset of only 11 subjects; using six for training, two for validation, and three for testing. The deep learning model based on U-Net Multi-Scale Supervision was trained using the training subset and was made equivariant to elastic deformations in a self-supervised manner using deformation-aware learning to improve the generalisation performance. The proposed technique was evaluated quantitatively and qualitatively against the test set and achieved a Dice score of 80.44 pm 0.83. Furthermore, the result of the proposed method was compared against a selected manually segmented region (62.07 resultant Dice) and has shown a considerable improvement (18.98\%) with deformation-aware learning.

  • 10 authors
·
Jun 18, 2020

Similarity-Based Self-Construct Graph Model for Predicting Patient Criticalness Using Graph Neural Networks and EHR Data

Accurately predicting the criticalness of ICU patients (such as in-ICU mortality risk) is vital for early intervention in critical care. However, conventional models often treat each patient in isolation and struggle to exploit the relational structure in Electronic Health Records (EHR). We propose a Similarity-Based Self-Construct Graph Model (SBSCGM) that dynamically builds a patient similarity graph from multi-modal EHR data, and a HybridGraphMedGNN architecture that operates on this graph to predict patient mortality and a continuous criticalness score. SBSCGM uses a hybrid similarity measure (combining feature-based and structural similarities) to connect patients with analogous clinical profiles in real-time. The HybridGraphMedGNN integrates Graph Convolutional Network (GCN), GraphSAGE, and Graph Attention Network (GAT) layers to learn robust patient representations, leveraging both local and global graph patterns. In experiments on 6,000 ICU stays from the MIMIC-III dataset, our model achieves state-of-the-art performance (AUC-ROC 0.94) outperforming baseline classifiers and single-type GNN models. We also demonstrate improved precision/recall and show that the attention mechanism provides interpretable insights into model predictions. Our framework offers a scalable and interpretable solution for critical care risk prediction, with potential to support clinicians in real-world ICU deployment.

  • 2 authors
·
Aug 1

RRWNet: Recursive Refinement Network for effective retinal artery/vein segmentation and classification

The caliber and configuration of retinal blood vessels serve as important biomarkers for various diseases and medical conditions. A thorough analysis of the retinal vasculature requires the segmentation of the blood vessels and their classification into arteries and veins, typically performed on color fundus images obtained by retinography. However, manually performing these tasks is labor-intensive and prone to human error. While several automated methods have been proposed to address this task, the current state of art faces challenges due to manifest classification errors affecting the topological consistency of segmentation maps. In this work, we introduce RRWNet, a novel end-to-end deep learning framework that addresses this limitation. The framework consists of a fully convolutional neural network that recursively refines semantic segmentation maps, correcting manifest classification errors and thus improving topological consistency. In particular, RRWNet is composed of two specialized subnetworks: a Base subnetwork that generates base segmentation maps from the input images, and a Recursive Refinement subnetwork that iteratively and recursively improves these maps. Evaluation on three different public datasets demonstrates the state-of-the-art performance of the proposed method, yielding more topologically consistent segmentation maps with fewer manifest classification errors than existing approaches. In addition, the Recursive Refinement module within RRWNet proves effective in post-processing segmentation maps from other methods, further demonstrating its potential. The model code, weights, and predictions will be publicly available at https://github.com/j-morano/rrwnet.

  • 3 authors
·
Feb 5, 2024

From Cities to Series: Complex Networks and Deep Learning for Improved Spatial and Temporal Analytics*

Graphs have often been used to answer questions about the interaction between real-world entities by taking advantage of their capacity to represent complex topologies. Complex networks are known to be graphs that capture such non-trivial topologies; they are able to represent human phenomena such as epidemic processes, the dynamics of populations, and the urbanization of cities. The investigation of complex networks has been extrapolated to many fields of science, with particular emphasis on computing techniques, including artificial intelligence. In such a case, the analysis of the interaction between entities of interest is transposed to the internal learning of algorithms, a paradigm whose investigation is able to expand the state of the art in Computer Science. By exploring this paradigm, this thesis puts together complex networks and machine learning techniques to improve the understanding of the human phenomena observed in pandemics, pendular migration, and street networks. Accordingly, we contribute with: (i) a new neural network architecture capable of modeling dynamic processes observed in spatial and temporal data with applications in epidemics propagation, weather forecasting, and patient monitoring in intensive care units; (ii) a machine-learning methodology for analyzing and predicting links in the scope of human mobility between all the cities of Brazil; and, (iii) techniques for identifying inconsistencies in the urban planning of cities while tracking the most influential vertices, with applications over Brazilian and worldwide cities. We obtained results sustained by sound evidence of advances to the state of the art in artificial intelligence, rigorous formalisms, and ample experimentation. Our findings rely upon real-world applications in a range of domains, demonstrating the applicability of our methodologies.

  • 2 authors
·
Jun 1, 2022

Understanding Graph Databases: A Comprehensive Tutorial and Survey

This tutorial serves as a comprehensive guide for understanding graph databases, focusing on the fundamentals of graph theory while showcasing practical applications across various fields. It starts by introducing foundational concepts and delves into the structure of graphs through nodes and edges, covering different types such as undirected, directed, weighted, and unweighted graphs. Key graph properties, terminologies, and essential algorithms for network analysis are outlined, including Dijkstras shortest path algorithm and methods for calculating node centrality and graph connectivity. The tutorial highlights the advantages of graph databases over traditional relational databases, particularly in efficiently managing complex, interconnected data. It examines leading graph database systems such as Neo4j, Amazon Neptune, and ArangoDB, emphasizing their unique features for handling large datasets. Practical instructions on graph operations using NetworkX and Neo4j are provided, covering node and edge creation, attribute assignment, and advanced queries with Cypher. Additionally, the tutorial explores common graph visualization techniques using tools like Plotly and Neo4j Bloom, which enhance the interpretation and usability of graph data. It also delves into community detection algorithms, including the Louvain method, which facilitates clustering in large networks. Finally, the paper concludes with recommendations for researchers interested in exploring the vast potential of graph technologies.

  • 3 authors
·
Nov 15, 2024

ParaTransCNN: Parallelized TransCNN Encoder for Medical Image Segmentation

The convolutional neural network-based methods have become more and more popular for medical image segmentation due to their outstanding performance. However, they struggle with capturing long-range dependencies, which are essential for accurately modeling global contextual correlations. Thanks to the ability to model long-range dependencies by expanding the receptive field, the transformer-based methods have gained prominence. Inspired by this, we propose an advanced 2D feature extraction method by combining the convolutional neural network and Transformer architectures. More specifically, we introduce a parallelized encoder structure, where one branch uses ResNet to extract local information from images, while the other branch uses Transformer to extract global information. Furthermore, we integrate pyramid structures into the Transformer to extract global information at varying resolutions, especially in intensive prediction tasks. To efficiently utilize the different information in the parallelized encoder at the decoder stage, we use a channel attention module to merge the features of the encoder and propagate them through skip connections and bottlenecks. Intensive numerical experiments are performed on both aortic vessel tree, cardiac, and multi-organ datasets. By comparing with state-of-the-art medical image segmentation methods, our method is shown with better segmentation accuracy, especially on small organs. The code is publicly available on https://github.com/HongkunSun/ParaTransCNN.

  • 3 authors
·
Jan 27, 2024

Hierarchical multi-class segmentation of glioma images using networks with multi-level activation function

For many segmentation tasks, especially for the biomedical image, the topological prior is vital information which is useful to exploit. The containment/nesting is a typical inter-class geometric relationship. In the MICCAI Brain tumor segmentation challenge, with its three hierarchically nested classes 'whole tumor', 'tumor core', 'active tumor', the nested classes relationship is introduced into the 3D-residual-Unet architecture. The network comprises a context aggregation pathway and a localization pathway, which encodes increasingly abstract representation of the input as going deeper into the network, and then recombines these representations with shallower features to precisely localize the interest domain via a localization path. The nested-class-prior is combined by proposing the multi-class activation function and its corresponding loss function. The model is trained on the training dataset of Brats2018, and 20% of the dataset is regarded as the validation dataset to determine parameters. When the parameters are fixed, we retrain the model on the whole training dataset. The performance achieved on the validation leaderboard is 86%, 77% and 72% Dice scores for the whole tumor, enhancing tumor and tumor core classes without relying on ensembles or complicated post-processing steps. Based on the same start-of-the-art network architecture, the accuracy of nested-class (enhancing tumor) is reasonably improved from 69% to 72% compared with the traditional Softmax-based method which blind to topological prior.

  • 6 authors
·
Oct 22, 2018

SPOCKMIP: Segmentation of Vessels in MRAs with Enhanced Continuity using Maximum Intensity Projection as Loss

Identification of vessel structures of different sizes in biomedical images is crucial in the diagnosis of many neurodegenerative diseases. However, the sparsity of good-quality annotations of such images makes the task of vessel segmentation challenging. Deep learning offers an efficient way to segment vessels of different sizes by learning their high-level feature representations and the spatial continuity of such features across dimensions. Semi-supervised patch-based approaches have been effective in identifying small vessels of one to two voxels in diameter. This study focuses on improving the segmentation quality by considering the spatial correlation of the features using the Maximum Intensity Projection~(MIP) as an additional loss criterion. Two methods are proposed with the incorporation of MIPs of label segmentation on the single~(z-axis) and multiple perceivable axes of the 3D volume. The proposed MIP-based methods produce segmentations with improved vessel continuity, which is evident in visual examinations of ROIs. Patch-based training is improved by introducing an additional loss term, MIP loss, to penalise the predicted discontinuity of vessels. A training set of 14 volumes is selected from the StudyForrest dataset comprising of 18 7-Tesla 3D Time-of-Flight~(ToF) Magnetic Resonance Angiography (MRA) images. The generalisation performance of the method is evaluated using the other unseen volumes in the dataset. It is observed that the proposed method with multi-axes MIP loss produces better quality segmentations with a median Dice of 80.245 pm 0.129. Also, the method with single-axis MIP loss produces segmentations with a median Dice of 79.749 pm 0.109. Furthermore, a visual comparison of the ROIs in the predicted segmentation reveals a significant improvement in the continuity of the vessels when MIP loss is incorporated into training.

  • 8 authors
·
Jul 11, 2024

Generating Drug Repurposing Hypotheses through the Combination of Disease-Specific Hypergraphs

The drug development pipeline for a new compound can last 10-20 years and cost over 10 billion. Drug repurposing offers a more time- and cost-effective alternative. Computational approaches based on biomedical knowledge graph representations have recently yielded new drug repurposing hypotheses. In this study, we present a novel, disease-specific hypergraph representation learning technique to derive contextual embeddings of biological pathways of various lengths but that all start at any given drug and all end at the disease of interest. Further, we extend this method to multi-disease hypergraphs. To determine the repurposing potential of each of the 1,522 drugs, we derive drug-specific distributions of cosine similarity values and ultimately consider the median for ranking. Cosine similarity values are computed between (1) all biological pathways starting at the considered drug and ending at the disease of interest and (2) all biological pathways starting at drugs currently prescribed against that disease and ending at the disease of interest. We illustrate our approach with Alzheimer's disease (AD) and two of its risk factors: hypertension (HTN) and type 2 diabetes (T2D). We compare each drug's rank across four hypergraph settings (single- or multi-disease): AD only, AD + HTN, AD + T2D, and AD + HTN + T2D. Notably, our framework led to the identification of two promising drugs whose repurposing potential was significantly higher in hypergraphs combining two diseases: dapagliflozin (antidiabetic; moved up, from top 32% to top 7%, across all considered drugs) and debrisoquine (antihypertensive; moved up, from top 76% to top 23%). Our approach serves as a hypothesis generation tool, to be paired with a validation pipeline relying on laboratory experiments and semi-automated parsing of the biomedical literature.

  • 5 authors
·
Nov 16, 2023

Neuro-inspired Ensemble-to-Ensemble Communication Primitives for Sparse and Efficient ANNs

The structure of biological neural circuits-modular, hierarchical, and sparsely interconnected-reflects an efficient trade-off between wiring cost, functional specialization, and robustness. These principles offer valuable insights for artificial neural network (ANN) design, especially as networks grow in depth and scale. Sparsity, in particular, has been widely explored for reducing memory and computation, improving speed, and enhancing generalization. Motivated by systems neuroscience findings, we explore how patterns of functional connectivity in the mouse visual cortex-specifically, ensemble-to-ensemble communication, can inform ANN design. We introduce G2GNet, a novel architecture that imposes sparse, modular connectivity across feedforward layers. Despite having significantly fewer parameters than fully connected models, G2GNet achieves superior accuracy on standard vision benchmarks. To our knowledge, this is the first architecture to incorporate biologically observed functional connectivity patterns as a structural bias in ANN design. We complement this static bias with a dynamic sparse training (DST) mechanism that prunes and regrows edges during training. We also propose a Hebbian-inspired rewiring rule based on activation correlations, drawing on principles of biological plasticity. G2GNet achieves up to 75% sparsity while improving accuracy by up to 4.3% on benchmarks, including Fashion-MNIST, CIFAR-10, and CIFAR-100, outperforming dense baselines with far fewer computations.

  • 3 authors
·
Aug 19

A Deep Learning Model for Coronary Artery Segmentation and Quantitative Stenosis Detection in Angiographic Images

Coronary artery disease (CAD) is a leading cause of cardiovascular-related mortality, and accurate stenosis detection is crucial for effective clinical decision-making. Coronary angiography remains the gold standard for diagnosing CAD, but manual analysis of angiograms is prone to errors and subjectivity. This study aims to develop a deep learning-based approach for the automatic segmentation of coronary arteries from angiographic images and the quantitative detection of stenosis, thereby improving the accuracy and efficiency of CAD diagnosis. We propose a novel deep learning-based method for the automatic segmentation of coronary arteries in angiographic images, coupled with a dynamic cohort method for stenosis detection. The segmentation model combines the MedSAM and VM-UNet architectures to achieve high-performance results. After segmentation, the vascular centerline is extracted, vessel diameter is computed, and the degree of stenosis is measured with high precision, enabling accurate identification of arterial stenosis. On the mixed dataset (including the ARCADE, DCA1, and GH datasets), the model achieved an average IoU of 0.6308, with sensitivity and specificity of 0.9772 and 0.9903, respectively. On the ARCADE dataset, the average IoU was 0.6303, with sensitivity of 0.9832 and specificity of 0.9933. Additionally, the stenosis detection algorithm achieved a true positive rate (TPR) of 0.5867 and a positive predictive value (PPV) of 0.5911, demonstrating the effectiveness of our model in analyzing coronary angiography images. SAM-VMNet offers a promising tool for the automated segmentation and detection of coronary artery stenosis. The model's high accuracy and robustness provide significant clinical value for the early diagnosis and treatment planning of CAD. The code and examples are available at https://github.com/qimingfan10/SAM-VMNet.

  • 6 authors
·
Jun 1, 2024

Homogenized C. elegans Neural Activity and Connectivity Data

There is renewed interest in modeling and understanding the nervous system of the nematode Caenorhabditis elegans (C. elegans), as this small model system provides a path to bridge the gap between nervous system structure (connectivity) and function (physiology). However, existing physiology datasets, whether involving passive recording or stimulation, are in distinct formats, and connectome datasets require preprocessing before analysis can commence. Here we compile and homogenize datasets of neural activity and connectivity. Our neural activity dataset is derived from 11 C. elegans neuroimaging experiments, while our connectivity dataset is compiled from 9 connectome annotations based on 3 primary electron microscopy studies and 1 signal propagation study. Physiology datasets, collected under varying protocols, measure calcium fluorescence in labeled subsets of the worm's 300 neurons. Our preprocessing pipeline standardizes these datasets by consistently ordering labeled neurons and resampling traces to a common sampling rate, yielding recordings from approximately 900 worms and 250 uniquely labeled neurons. The connectome datasets, collected from electron microscopy reconstructions, represent the entire nervous system as a graph of connections. Our collection is accessible on HuggingFace, facilitating analysis of the structure-function relationship in biology using modern neural network architectures and enabling cross-lab and cross-animal comparisons.

  • 4 authors
·
Nov 18, 2024

Improving anatomical plausibility in medical image segmentation via hybrid graph neural networks: applications to chest x-ray analysis

Anatomical segmentation is a fundamental task in medical image computing, generally tackled with fully convolutional neural networks which produce dense segmentation masks. These models are often trained with loss functions such as cross-entropy or Dice, which assume pixels to be independent of each other, thus ignoring topological errors and anatomical inconsistencies. We address this limitation by moving from pixel-level to graph representations, which allow to naturally incorporate anatomical constraints by construction. To this end, we introduce HybridGNet, an encoder-decoder neural architecture that leverages standard convolutions for image feature encoding and graph convolutional neural networks (GCNNs) to decode plausible representations of anatomical structures. We also propose a novel image-to-graph skip connection layer which allows localized features to flow from standard convolutional blocks to GCNN blocks, and show that it improves segmentation accuracy. The proposed architecture is extensively evaluated in a variety of domain shift and image occlusion scenarios, and audited considering different types of demographic domain shift. Our comprehensive experimental setup compares HybridGNet with other landmark and pixel-based models for anatomical segmentation in chest x-ray images, and shows that it produces anatomically plausible results in challenging scenarios where other models tend to fail.

  • 5 authors
·
Mar 21, 2022

Revisiting Graph Neural Networks on Graph-level Tasks: Comprehensive Experiments, Analysis, and Improvements

Graphs are essential data structures for modeling complex interactions in domains such as social networks, molecular structures, and biological systems. Graph-level tasks, which predict properties or classes for the entire graph, are critical for applications, such as molecular property prediction and subgraph counting. Graph Neural Networks (GNNs) have shown promise in these tasks, but their evaluations are often limited to narrow datasets, tasks, and inconsistent experimental setups, restricting their generalizability. To address these limitations, we propose a unified evaluation framework for graph-level GNNs. This framework provides a standardized setting to evaluate GNNs across diverse datasets, various graph tasks (e.g., graph classification and regression), and challenging scenarios, including noisy, imbalanced, and few-shot graphs. Additionally, we propose a novel GNN model with enhanced expressivity and generalization capabilities. Specifically, we enhance the expressivity of GNNs through a k-path rooted subgraph approach, enabling the model to effectively count subgraphs (e.g., paths and cycles). Moreover, we introduce a unified graph contrastive learning algorithm for graphs across diverse domains, which adaptively removes unimportant edges to augment graphs, thereby significantly improving generalization performance. Extensive experiments demonstrate that our model achieves superior performance against fourteen effective baselines across twenty-seven graph datasets, establishing it as a robust and generalizable model for graph-level tasks.

  • 6 authors
·
Jan 1

UMMAN: Unsupervised Multi-graph Merge Adversarial Network for Disease Prediction Based on Intestinal Flora

The abundance of intestinal flora is closely related to human diseases, but diseases are not caused by a single gut microbe. Instead, they result from the complex interplay of numerous microbial entities. This intricate and implicit connection among gut microbes poses a significant challenge for disease prediction using abundance information from OTU data. Recently, several methods have shown potential in predicting corresponding diseases. However, these methods fail to learn the inner association among gut microbes from different hosts, leading to unsatisfactory performance. In this paper, we present a novel architecture, Unsupervised Multi-graph Merge Adversarial Network (UMMAN). UMMAN can obtain the embeddings of nodes in the Multi-Graph in an unsupervised scenario, so that it helps learn the multiplex association. Our method is the first to combine Graph Neural Network with the task of intestinal flora disease prediction. We employ complex relation-types to construct the Original-Graph and disrupt the relationships among nodes to generate corresponding Shuffled-Graph. We introduce the Node Feature Global Integration (NFGI) module to represent the global features of the graph. Furthermore, we design a joint loss comprising adversarial loss and hybrid attention loss to ensure that the real graph embedding aligns closely with the Original-Graph and diverges from the Shuffled-Graph. Comprehensive experiments on five classical OTU gut microbiome datasets demonstrate the effectiveness and stability of our method. (We will release our code soon.)

  • 5 authors
·
Jul 31, 2024

Virtual Nodes Improve Long-term Traffic Prediction

Effective traffic prediction is a cornerstone of intelligent transportation systems, enabling precise forecasts of traffic flow, speed, and congestion. While traditional spatio-temporal graph neural networks (ST-GNNs) have achieved notable success in short-term traffic forecasting, their performance in long-term predictions remains limited. This challenge arises from over-squashing problem, where bottlenecks and limited receptive fields restrict information flow and hinder the modeling of global dependencies. To address these challenges, this study introduces a novel framework that incorporates virtual nodes, which are additional nodes added to the graph and connected to existing nodes, in order to aggregate information across the entire graph within a single GNN layer. Our proposed model incorporates virtual nodes by constructing a semi-adaptive adjacency matrix. This matrix integrates distance-based and adaptive adjacency matrices, allowing the model to leverage geographical information while also learning task-specific features from data. Experimental results demonstrate that the inclusion of virtual nodes significantly enhances long-term prediction accuracy while also improving layer-wise sensitivity to mitigate the over-squashing problem. Virtual nodes also offer enhanced explainability by focusing on key intersections and high-traffic areas, as shown by the visualization of their adjacency matrix weights on road network heat maps. Our advanced approach enhances the understanding and management of urban traffic systems, making it particularly well-suited for real-world applications.

  • 4 authors
·
Jan 17

BioGraphFusion: Graph Knowledge Embedding for Biological Completion and Reasoning

Motivation: Biomedical knowledge graphs (KGs) are crucial for drug discovery and disease understanding, yet their completion and reasoning are challenging. Knowledge Embedding (KE) methods capture global semantics but struggle with dynamic structural integration, while Graph Neural Networks (GNNs) excel locally but often lack semantic understanding. Even ensemble approaches, including those leveraging language models, often fail to achieve a deep, adaptive, and synergistic co-evolution between semantic comprehension and structural learning. Addressing this critical gap in fostering continuous, reciprocal refinement between these two aspects in complex biomedical KGs is paramount. Results: We introduce BioGraphFusion, a novel framework for deeply synergistic semantic and structural learning. BioGraphFusion establishes a global semantic foundation via tensor decomposition, guiding an LSTM-driven mechanism to dynamically refine relation embeddings during graph propagation. This fosters adaptive interplay between semantic understanding and structural learning, further enhanced by query-guided subgraph construction and a hybrid scoring mechanism. Experiments across three key biomedical tasks demonstrate BioGraphFusion's superior performance over state-of-the-art KE, GNN, and ensemble models. A case study on Cutaneous Malignant Melanoma 1 (CMM1) highlights its ability to unveil biologically meaningful pathways. Availability and Implementation: Source code and all training data are freely available for download at https://github.com/Y-TARL/BioGraphFusion. Supplementary information: Supplementary data are available at Bioinformatics online.

  • 6 authors
·
Jul 19

OCTA-500: A Retinal Dataset for Optical Coherence Tomography Angiography Study

Optical coherence tomography angiography (OCTA) is a novel imaging modality that has been widely utilized in ophthalmology and neuroscience studies to observe retinal vessels and microvascular systems. However, publicly available OCTA datasets remain scarce. In this paper, we introduce the largest and most comprehensive OCTA dataset dubbed OCTA-500, which contains OCTA imaging under two fields of view (FOVs) from 500 subjects. The dataset provides rich images and annotations including two modalities (OCT/OCTA volumes), six types of projections, four types of text labels (age / gender / eye / disease) and seven types of segmentation labels (large vessel/capillary/artery/vein/2D FAZ/3D FAZ/retinal layers). Then, we propose a multi-object segmentation task called CAVF, which integrates capillary segmentation, artery segmentation, vein segmentation, and FAZ segmentation under a unified framework. In addition, we optimize the 3D-to-2D image projection network (IPN) to IPN-V2 to serve as one of the segmentation baselines. Experimental results demonstrate that IPN-V2 achieves an ~10% mIoU improvement over IPN on CAVF task. Finally, we further study the impact of several dataset characteristics: the training set size, the model input (OCT/OCTA, 3D volume/2D projection), the baseline networks, and the diseases. The dataset and code are publicly available at: https://ieee-dataport.org/open-access/octa-500.

  • 10 authors
·
Dec 14, 2020

Forward Learning of Graph Neural Networks

Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is the de facto standard for training deep neural networks (NNs). However, despite its effectiveness, BP imposes several constraints, which are not only biologically implausible, but also limit the scalability, parallelism, and flexibility in learning NNs. Examples of such constraints include storage of neural activities computed in the forward pass for use in the subsequent backward pass, and the dependence of parameter updates on non-local signals. To address these limitations, the forward-forward algorithm (FF) was recently proposed as an alternative to BP in the image classification domain, which trains NNs by performing two forward passes over positive and negative data. Inspired by this advance, we propose ForwardGNN in this work, a new forward learning procedure for GNNs, which avoids the constraints imposed by BP via an effective layer-wise local forward training. ForwardGNN extends the original FF to deal with graph data and GNNs, and makes it possible to operate without generating negative inputs (hence no longer forward-forward). Further, ForwardGNN enables each layer to learn from both the bottom-up and top-down signals without relying on the backpropagation of errors. Extensive experiments on real-world datasets show the effectiveness and generality of the proposed forward graph learning framework. We release our code at https://github.com/facebookresearch/forwardgnn.

  • 8 authors
·
Mar 16, 2024

Motion simulation of radio-labeled cells in whole-body positron emission tomography

Cell tracking is a subject of active research gathering great interest in medicine and biology. Positron emission tomography (PET) is well suited for tracking radio-labeled cells in vivo due to its exceptional sensitivity and whole-body capability. For validation, ground-truth data are desirable that realistically mimic the flow of cells in a clinical situation. This study develops a workflow (CeFloPS) for simulating moving radio-labeled cells in a human phantom. From the XCAT phantom, the blood vessels are reduced to nodal networks along which cells can move and distribute to organs and tissues. The movement is directed by the blood flow, which is calculated in each node using the Hagen-Pooiseuille equation and Kirchhoff's laws assuming laminar flow. Organs are voxelized and movement of cells from artery entry to vein exit is generated via a biased 3D random walk. The probabilities of cells moving or remaining in tissues are derived from rate constants of tracer kinetic-based compartment modeling. PET listmode data is generated using the Monte-Carlo simulation framework GATE based on the definition of a large-body PET scanner with cell paths as moving radioactive sources and the XCAT phantom providing attenuation data. From the flow simulation of 100,000 cells, 100 sample cells were further processed by GATE and listmode data was reconstructed into images for comparison. As demonstrated by comparisons of simulated and reconstructed cell distributions, CeFloPS is capable of simulating cell behavior in whole-body PET. It achieves this simulation in a way that is anatomically and physiologically reasonable, thereby providing valuable data for the development and validation of cell tracking algorithms.

  • 5 authors
·
Jul 10, 2024

A Topological Perspective on Demystifying GNN-Based Link Prediction Performance

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across different nodes and its underlying reasons. To this end, we aim to demystify which nodes will perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit poorer LP performance, our empirical findings provide nuances to this viewpoint and prompt us to propose a better metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC has a higher correlation with LP performance than other node-level topological metrics like degree and subgraph density, offering a better way to identify low-performing nodes than using cold-start. With TC, we discover a novel topological distribution shift issue in which newly joined neighbors of a node tend to become less interactive with that node's existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and theoretically/empirically justify its efficacy in approximating TC and reducing the computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

  • 7 authors
·
Oct 6, 2023

Boosting EfficientNets Ensemble Performance via Pseudo-Labels and Synthetic Images by pix2pixHD for Infection and Ischaemia Classification in Diabetic Foot Ulcers

Diabetic foot ulcers are a common manifestation of lesions on the diabetic foot, a syndrome acquired as a long-term complication of diabetes mellitus. Accompanying neuropathy and vascular damage promote acquisition of pressure injuries and tissue death due to ischaemia. Affected areas are prone to infections, hindering the healing progress. The research at hand investigates an approach on classification of infection and ischaemia, conducted as part of the Diabetic Foot Ulcer Challenge (DFUC) 2021. Different models of the EfficientNet family are utilized in ensembles. An extension strategy for the training data is applied, involving pseudo-labeling for unlabeled images, and extensive generation of synthetic images via pix2pixHD to cope with severe class imbalances. The resulting extended training dataset features 8.68 times the size of the baseline and shows a real to synthetic image ratio of 1:3. Performances of models and ensembles trained on the baseline and extended training dataset are compared. Synthetic images featured a broad qualitative variety. Results show that models trained on the extended training dataset as well as their ensemble benefit from the large extension. F1-Scores for rare classes receive outstanding boosts, while those for common classes are either not harmed or boosted moderately. A critical discussion concretizes benefits and identifies limitations, suggesting improvements. The work concludes that classification performance of individual models as well as that of ensembles can be boosted utilizing synthetic images. Especially performance for rare classes benefits notably.

  • 3 authors
·
Nov 30, 2021

Graphlets correct for the topological information missed by random walks

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

  • 3 authors
·
May 23, 2024

Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

  • 8 authors
·
Aug 26, 2024 2

Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion

Hypergraphs are widely being employed to represent complex higher-order relations in real-world applications. Most existing research on hypergraph learning focuses on node-level or edge-level tasks. A practically relevant and more challenging task, edge-dependent node classification (ENC), is still under-explored. In ENC, a node can have different labels across different hyperedges, which requires the modeling of node features unique to each hyperedge. The state-of-the-art ENC solution, WHATsNet, only outputs single node and edge representations, leading to the limitations of entangled edge-specific features and non-adaptive representation sizes when applied to ENC. Additionally, WHATsNet suffers from the common oversmoothing issue in most HGNNs. To address these limitations, we propose CoNHD, a novel HGNN architecture specifically designed to model edge-specific features for ENC. Instead of learning separate representations for nodes and edges, CoNHD reformulates within-edge and within-node interactions as a hypergraph diffusion process over node-edge co-representations. We develop a neural implementation of the proposed diffusion process, leveraging equivariant networks as diffusion operators to effectively learn the diffusion dynamics from data. Extensive experiments demonstrate that CoNHD achieves the best performance across all benchmark ENC datasets and several downstream tasks without sacrificing efficiency. Our implementation is available at https://github.com/zhengyijia/CoNHD.

  • 2 authors
·
May 23, 2024

AeroPath: An airway segmentation benchmark dataset with challenging pathology

To improve the prognosis of patients suffering from pulmonary diseases, such as lung cancer, early diagnosis and treatment are crucial. The analysis of CT images is invaluable for diagnosis, whereas high quality segmentation of the airway tree are required for intervention planning and live guidance during bronchoscopy. Recently, the Multi-domain Airway Tree Modeling (ATM'22) challenge released a large dataset, both enabling training of deep-learning based models and bringing substantial improvement of the state-of-the-art for the airway segmentation task. However, the ATM'22 dataset includes few patients with severe pathologies affecting the airway tree anatomy. In this study, we introduce a new public benchmark dataset (AeroPath), consisting of 27 CT images from patients with pathologies ranging from emphysema to large tumors, with corresponding trachea and bronchi annotations. Second, we present a multiscale fusion design for automatic airway segmentation. Models were trained on the ATM'22 dataset, tested on the AeroPath dataset, and further evaluated against competitive open-source methods. The same performance metrics as used in the ATM'22 challenge were used to benchmark the different considered approaches. Lastly, an open web application is developed, to easily test the proposed model on new data. The results demonstrated that our proposed architecture predicted topologically correct segmentations for all the patients included in the AeroPath dataset. The proposed method is robust and able to handle various anomalies, down to at least the fifth airway generation. In addition, the AeroPath dataset, featuring patients with challenging pathologies, will contribute to development of new state-of-the-art methods. The AeroPath dataset and the web application are made openly available.

  • 6 authors
·
Nov 2, 2023 2

Phase-shifted remote photoplethysmography for estimating heart rate and blood pressure from facial video

Human health can be critically affected by cardiovascular diseases, such as hypertension, arrhythmias, and stroke. Heart rate and blood pressure are important biometric information for the monitoring of cardiovascular system and early diagnosis of cardiovascular diseases. Existing methods for estimating the heart rate are based on electrocardiography and photoplethyomography, which require contacting the sensor to the skin surface. Moreover, catheter and cuff-based methods for measuring blood pressure cause inconvenience and have limited applicability. Therefore, in this thesis, we propose a vision-based method for estimating the heart rate and blood pressure. This thesis proposes a 2-stage deep learning framework consisting of a dual remote photoplethysmography network (DRP-Net) and bounded blood pressure network (BBP-Net). In the first stage, DRP-Net infers remote photoplethysmography (rPPG) signals for the acral and facial regions, and these phase-shifted rPPG signals are utilized to estimate the heart rate. In the second stage, BBP-Net integrates temporal features and analyzes phase discrepancy between the acral and facial rPPG signals to estimate SBP and DBP values. To improve the accuracy of estimating the heart rate, we employed a data augmentation method based on a frame interpolation model. Moreover, we designed BBP-Net to infer blood pressure within a predefined range by incorporating a scaled sigmoid function. Our method resulted in estimating the heart rate with the mean absolute error (MAE) of 1.78 BPM, reducing the MAE by 34.31 % compared to the recent method, on the MMSE-HR dataset. The MAE for estimating the systolic blood pressure (SBP) and diastolic blood pressure (DBP) were 10.19 mmHg and 7.09 mmHg. On the V4V dataset, the MAE for the heart rate, SBP, and DBP were 3.83 BPM, 13.64 mmHg, and 9.4 mmHg, respectively.

  • 2 authors
·
Jan 9, 2024