Deep vectorised operators for pulsatile hemodynamics estimation in coronary arteries from a steady-state prior

Cardiovascular hemodynamic fields provide valuable medical decision markers for coronary artery disease. Computational fluid dynamics (CFD) is the gold standard for accurate, non-invasive evaluation of these quantities in vivo. In this work, we propose a time-efficient surrogate model, powered by machine learning, for the estimation of pulsatile hemodynamics based on steady-state priors. We introduce deep vectorised operators, a modelling framework for discretisation independent learning on infinite-dimensional function spaces. The underlying neural architecture is a neural field conditioned on hemodynamic boundary conditions. Importantly, we show how relaxing the requirement of point-wise action to permutation-equivariance leads to a family of models that can be parametrised by message passing and self-attention layers. We evaluate our approach on a dataset of 74 stenotic coronary arteries extracted from coronary computed tomography angiography (CCTA) with patient-specific pulsatile CFD simulations as ground truth. We show that our model produces accurate estimates of the pulsatile velocity and pressure while being agnostic to re-sampling of the source domain (discretisation independence). This shows that deep vectorised operators are a powerful modelling tool for cardiovascular hemodynamics estimation in coronary arteries and beyond.

World of Forms: Deformable Geometric Templates for One-Shot Surface Meshing in Coronary CT Angiography

Deep learning-based medical image segmentation and surface mesh generation typically involve a sequential pipeline from image to segmentation to meshes, often requiring large training datasets while making limited use of prior geometric knowledge. This may lead to topological inconsistencies and suboptimal performance in low-data regimes. To address these challenges, we propose a data-efficient deep learning method for direct 3D anatomical object surface meshing using geometric priors. Our approach employs a multi-resolution graph neural network that operates on a prior geometric template which is deformed to fit object boundaries of interest. We show how different templates may be used for the different surface meshing targets, and introduce a novel masked autoencoder pretraining strategy for 3D spherical data. The proposed method outperforms nnUNet in a one-shot setting for segmentation of the pericardium, left ventricle (LV) cavity and the LV myocardium. Similarly, the method outperforms other lumen segmentation operating on multi-planar reformatted images. Results further indicate that mesh quality is on par with or improves upon marching cubes post-processing of voxel mask predictions, while remaining flexible in the choice of mesh triangulation prior, thus paving the way for more accurate and topologically consistent 3D medical object surface meshing.

Neural Fields for Continuous Periodic Motion Estimation in 4D Cardiovascular Imaging

Time-resolved three-dimensional flow MRI (4D flow MRI) provides a unique non-invasive solution to visualize and quantify hemodynamics in blood vessels such as the aortic arch. However, most current analysis methods for arterial 4D flow MRI use static artery walls because of the difficulty in obtaining a full cycle segmentation. To overcome this limitation, we propose a neural fields-based method that directly estimates continuous periodic wall deformations throughout the cardiac cycle. For a 3D + time imaging dataset, we optimize an implicit neural representation (INR) that represents a time-dependent velocity vector field (VVF). An ODE solver is used to integrate the VVF into a deformation vector field (DVF), that can deform images, segmentation masks, or meshes over time, thereby visualizing and quantifying local wall motion patterns. To properly reflect the periodic nature of 3D + time cardiovascular data, we impose periodicity in two ways. First, by periodically encoding the time input to the INR, and hence VVF. Second, by regularizing the DVF. We demonstrate the effectiveness of this approach on synthetic data with different periodic patterns, ECG-gated CT, and 4D flow MRI data. The obtained method could be used to improve 4D flow MRI analysis.

Vestibular schwannoma growth prediction from longitudinal MRI by time conditioned neural fields

Vestibular schwannomas (VS) are benign tumors that are generally managed by active surveillance with MRI examination. To further assist clinical decision-making and avoid overtreatment, an accurate prediction of tumor growth based on longitudinal imaging is highly desirable. In this paper, we introduce DeepGrowth, a deep learning method that incorporates neural fields and recurrent neural networks for prospective tumor growth prediction. In the proposed method, each tumor is represented as a signed distance function (SDF) conditioned on a low-dimensional latent code. Unlike previous studies that perform tumor shape prediction directly in the image space, we predict the latent codes instead and then reconstruct future shapes from it. To deal with irregular time intervals, we introduce a time-conditioned recurrent module based on a ConvLSTM and a novel temporal encoding strategy, which enables the proposed model to output varying tumor shapes over time. The experiments on an in-house longitudinal VS dataset showed that the proposed model significantly improved the performance ($\ge 1.6\%$ Dice score and $\ge0.20$ mm 95\% Hausdorff distance), in particular for top 20\% tumors that grow or shrink the most ($\ge 4.6\%$ Dice score and $\ge 0.73$ mm 95\% Hausdorff distance). Our code is available at ~\burl{https://github.com/cyjdswx/DeepGrowth}

Neural Fields for 3D Tracking of Anatomy and Surgical Instruments in Monocular Laparoscopic Video Clips

Laparoscopic video tracking primarily focuses on two target types: surgical instruments and anatomy. The former could be used for skill assessment, while the latter is necessary for the projection of virtual overlays. Where instrument and anatomy tracking have often been considered two separate problems, in this paper, we propose a method for joint tracking of all structures simultaneously. Based on a single 2D monocular video clip, we train a neural field to represent a continuous spatiotemporal scene, used to create 3D tracks of all surfaces visible in at least one frame. Due to the small size of instruments, they generally cover a small part of the image only, resulting in decreased tracking accuracy. Therefore, we propose enhanced class weighting to improve the instrument tracks. We evaluate tracking on video clips from laparoscopic cholecystectomies, where we find mean tracking accuracies of 92.4% for anatomical structures and 87.4% for instruments. Additionally, we assess the quality of depth maps obtained from the method's scene reconstructions. We show that these pseudo-depths have comparable quality to a state-of-the-art pre-trained depth estimator. On laparoscopic videos in the SCARED dataset, the method predicts depth with an MAE of 2.9 mm and a relative error of 9.2%. These results show the feasibility of using neural fields for monocular 3D reconstruction of laparoscopic scenes.

Brain-Shift: Unsupervised Pseudo-Healthy Brain Synthesis for Novel Biomarker Extraction in Chronic Subdural Hematoma

Chronic subdural hematoma (cSDH) is a common neurological condition characterized by the accumulation of blood between the brain and the dura mater. This accumulation of blood can exert pressure on the brain, potentially leading to fatal outcomes. Treatment options for cSDH are limited to invasive surgery or non-invasive management. Traditionally, the midline shift, hand-measured by experts from an ideal sagittal plane, and the hematoma volume have been the primary metrics for quantifying and analyzing cSDH. However, these approaches do not quantify the local 3D brain deformation caused by cSDH. We propose a novel method using anatomy-aware unsupervised diffeomorphic pseudo-healthy synthesis to generate brain deformation fields. The deformation fields derived from this process are utilized to extract biomarkers that quantify the shift in the brain due to cSDH. We use CT scans of 121 patients for training and validation of our method and find that our metrics allow the identification of patients who require surgery. Our results indicate that automatically obtained brain deformation fields might contain prognostic value for personalized cSDH treatment. Our implementation is available on: github.com/Barisimre/brain-morphing

Global Control for Local SO-Equivariant Scale-Invariant Vessel Segmentation

Personalized 3D vascular models can aid in a range of diagnostic, prognostic, and treatment-planning tasks relevant to cardiovascular disease management. Deep learning provides a means to automatically obtain such models. Ideally, a user should have control over the exact region of interest (ROI) to be included in a vascular model, and the model should be watertight and highly accurate. To this end, we propose a combination of a global controller leveraging voxel mask segmentations to provide boundary conditions for vessels of interest to a local, iterative vessel segmentation model. We introduce the preservation of scale- and rotational symmetries in the local segmentation model, leading to generalisation to vessels of unseen sizes and orientations. Combined with the global controller, this enables flexible 3D vascular model building, without additional retraining. We demonstrate the potential of our method on a dataset containing abdominal aortic aneurysms (AAAs). Our method performs on par with a state-of-the-art segmentation model in the segmentation of AAAs, iliac arteries and renal arteries, while providing a watertight, smooth surface segmentation. Moreover, we demonstrate that by adapting the global controller, we can easily extend vessel sections in the 3D model.

LaB-GATr: geometric algebra transformers for large biomedical surface and volume meshes

Many anatomical structures can be described by surface or volume meshes. Machine learning is a promising tool to extract information from these 3D models. However, high-fidelity meshes often contain hundreds of thousands of vertices, which creates unique challenges in building deep neural network architectures. Furthermore, patient-specific meshes may not be canonically aligned which limits the generalisation of machine learning algorithms. We propose LaB-GATr, a transfomer neural network with geometric tokenisation that can effectively learn with large-scale (bio-)medical surface and volume meshes through sequence compression and interpolation. Our method extends the recently proposed geometric algebra transformer (GATr) and thus respects all Euclidean symmetries, i.e. rotation, translation and reflection, effectively mitigating the problem of canonical alignment between patients. LaB-GATr achieves state-of-the-art results on three tasks in cardiovascular hemodynamics modelling and neurodevelopmental phenotype prediction, featuring meshes of up to 200,000 vertices. Our results demonstrate that LaB-GATr is a powerful architecture for learning with high-fidelity meshes which has the potential to enable interesting downstream applications. Our implementation is publicly available.

Quantifying white matter hyperintensity and brain volumes in heterogeneous clinical and low-field portable MRI

Brain atrophy and white matter hyperintensity (WMH) are critical neuroimaging features for ascertaining brain injury in cerebrovascular disease and multiple sclerosis. Automated segmentation and quantification is desirable but existing methods require high-resolution MRI with good signal-to-noise ratio (SNR). This precludes application to clinical and low-field portable MRI (pMRI) scans, thus hampering large-scale tracking of atrophy and WMH progression, especially in underserved areas where pMRI has huge potential. Here we present a method that segments white matter hyperintensity and 36 brain regions from scans of any resolution and contrast (including pMRI) without retraining. We show results on six public datasets and on a private dataset with paired high- and low-field scans (3T and 64mT), where we attain strong correlation between the WMH ($\rho$=.85) and hippocampal volumes (r=.89) estimated at both fields. Our method is publicly available as part of FreeSurfer, at: http://surfer.nmr.mgh.harvard.edu/fswiki/WMH-SynthSeg.

SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networks

Blood vessel orientation as visualized in 3D medical images is an important descriptor of its geometry that can be used for centerline extraction and subsequent segmentation and visualization. Arteries appear at many scales and levels of tortuosity, and determining their exact orientation is challenging. Recent works have used 3D convolutional neural networks (CNNs) for this purpose, but CNNs are sensitive to varying vessel sizes and orientations. We present SIRE: a scale-invariant, rotation-equivariant estimator for local vessel orientation. SIRE is modular and can generalise due to symmetry preservation. SIRE consists of a gauge equivariant mesh CNN (GEM-CNN) operating on multiple nested spherical meshes with different sizes in parallel. The features on each mesh are a projection of image intensities within the corresponding sphere. These features are intrinsic to the sphere and, in combination with the GEM-CNN, lead to SO(3)-equivariance. Approximate scale invariance is achieved by weight sharing and use of a symmetric maximum function to combine multi-scale predictions. Hence, SIRE can be trained with arbitrarily oriented vessels with varying radii to generalise to vessels with a wide range of calibres and tortuosity. We demonstrate the efficacy of SIRE using three datasets containing vessels of varying scales: the vascular model repository (VMR), the ASOCA coronary artery set, and a set of abdominal aortic aneurysms (AAAs). We embed SIRE in a centerline tracker which accurately tracks AAAs, regardless of the data SIRE is trained with. Moreover, SIRE can be used to track coronary arteries, even when trained only with AAAs. In conclusion, by incorporating SO(3) and scale symmetries, SIRE can determine the orientations of vessels outside of the training domain, forming a robust and data-efficient solution to geometric analysis of blood vessels in 3D medical images.