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Perfusion imaging (PI) is clinically used to assess strokes and brain tumors. Commonly used PI approaches based on magnetic resonance imaging (MRI) or computed tomography (CT) measure the effect of a contrast agent moving through blood vessels and into tissue. Contrast-agent free approaches, for example, based on intravoxel incoherent motion, also exist, but are so far not routinely used clinically. These methods rely on estimating on the arterial input function (AIF) to approximately model tissue perfusion, neglecting spatial dependencies, and reliably estimating the AIF is also non-trivial, leading to difficulties with standardizing perfusion measures. In this work we therefore propose a data-assimilation approach (PIANO) which estimates the velocity and diffusion fields of an advection-diffusion model that best explains the contrast dynamics. PIANO accounts for spatial dependencies and neither requires estimating the AIF nor relies on a particular contrast agent bolus shape. Specifically, we propose a convenient parameterization of the estimation problem, a numerical estimation approach, and extensively evaluate PIANO. We demonstrate that PIANO can successfully resolve velocity and diffusion field ambiguities and results in sensitive measures for the assessment of stroke, comparing favorably to conventional measures of perfusion.

Perfusion imaging (PI) is clinically used to assess strokes and brain tumors. Commonly used PI approaches based on magnetic resonance imaging (MRI) or computed tomography (CT) image the effect of a contrast agent moving through blood vessels and into tissue. Contrast-agent free approaches, for example, based on intravoxel incoherent motion, also exist, but are so far not routinely used clinically. MR or CT perfusion imaging based on contrast agents relies on the estimation of the arterial input function (AIF) to approximately model tissue perfusion, neglecting spatial dependencies. Reliably estimating the AIF is also non-trivial, leading to difficulties with standardizing perfusion measures. In this work we therefore propose a data-assimilation approach (PIANO) which estimates the velocity and diffusion fields of an advection-diffusion model best explaining the contrast dynamics. PIANO accounts for spatial dependencies and neither requires estimating the AIF nor relies on a particular contrast agent bolus shape. Specifically, we propose a convenient parameterization of the estimation problem, a numerical estimation approach, and extensively evaluate PIANO. We demonstrate that PIANO can successfully resolve velocity and diffusion field ambiguities and results in sensitive measures for the assessment of stroke, comparing favorably to conventional measures of perfusion.

Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the advantages of such continuous formulations, most current techniques are not truly continuous-depth as they assume identical layers. Indeed, existing works throw into relief the myriad difficulties presented by an infinite-dimensional parameter space in learning a continuous-depth neural ODE. To this end, we introduce a shooting formulation which shifts the perspective from parameterizing a network layer-by-layer to parameterizing over optimal networks described only by a set of initial conditions. For scalability, we propose a novel particle-ensemble parametrization which fully specifies the optimal weight trajectory of the continuous-depth neural network. Our experiments show that our particle-ensemble shooting formulation can achieve competitive performance, especially on long-range forecasting tasks. Finally, though the current work is inspired by continuous-depth neural networks, the particle-ensemble shooting formulation also applies to discrete-time networks and may lead to a new fertile area of research in deep learning parametrization.

Deep learning models have been successful in computer vision and medical image analysis. However, training these models frequently requires large labeled image sets whose creation is often very time and labor intensive, for example, in the context of 3D segmentations. Approaches capable of training deep segmentation networks with a limited number of labeled samples are therefore highly desirable. Data augmentation or semi-supervised approaches are commonly used to cope with limited labeled training data. However, the augmentation strategies for many existing approaches are either hand-engineered or require computationally demanding searches. To that end, we explore an augmentation strategy which builds statistical deformation models from unlabeled data via principal component analysis and uses the resulting statistical deformation space to augment the labeled training samples. Specifically, we obtain transformations via deep registration models. This allows for an intuitive control over plausible deformation magnitudes via the statistical model and, if combined with an appropriate deformation model, yields spatially regular transformations. To optimally augment a dataset we use an adversarial strategy integrated into our statistical deformation model. We demonstrate the effectiveness of our approach for the segmentation of knee cartilage from 3D magnetic resonance images. We show favorable performance to state-of-the-art augmentation approaches.

We introduce a fluid-based image augmentation method for medical image analysis. In contrast to existing methods, our framework generates anatomically meaningful images via interpolation from the geodesic subspace underlying given samples. Our approach consists of three steps: 1) given a source image and a set of target images, we construct a geodesic subspace using the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model; 2) we sample transformations from the resulting geodesic subspace; 3) we obtain deformed images and segmentations via interpolation. Experiments on brain (LPBA) and knee (OAI) data illustrate the performance of our approach on two tasks: 1) data augmentation during training and testing for image segmentation; 2) one-shot learning for single atlas image segmentation. We demonstrate that our approach generates anatomically meaningful data and improves performance on these tasks over competing approaches.