A Persistent Homology-Based Topological Loss for CNN-Based Multiclass Segmentation of CMR.

Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a separation of data into anatomical components with known structure and configuration. The most popular CNN-based methods are optimised using pixel wise loss functions, ignorant of the spatially extended features that characterise anatomy. Therefore, whilst sharing a high spatial overlap with the ground truth, inferred CNN-based segmentations can lack coherence, including spurious connected components, holes and voids. Such results are implausible, violating anticipated anatomical topology. In response, (single-class) persistent homology-based loss functions have been proposed to capture global anatomical features. Our work extends these approaches to the task of multi-class segmentation. Building an enriched topological description of all class labels and class label pairs, our loss functions make predictable and statistically significant improvements in segmentation topology using a CNN-based post-processing framework. We also present (and make available) a highly efficient implementation based on cubical complexes and parallel execution, enabling practical application within high resolution 3D data for the first time. We demonstrate our approach on 2D short axis and 3D whole heart CMR segmentation, advancing a detailed and faithful analysis of performance on two publicly available datasets.

A Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology.

We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in topological data analysis, we can specify the desired topology of segmented objects in terms of their Betti numbers and then drive the proposed segmentations to contain the specified topological features. Importantly this process does not require any ground-truth labels, just prior knowledge of the topology of the structure being segmented. We demonstrate our approach in four experiments: one on MNIST image denoising and digit recognition, one on left ventricular myocardium segmentation from magnetic resonance imaging data from the UK Biobank, one on the ACDC public challenge dataset and one on placenta segmentation from 3-D ultrasound. We find that embedding explicit prior knowledge in neural network segmentation tasks is most beneficial when the segmentation task is especially challenging and that it can be used in either a semi-supervised or post-processing context to extract a useful training gradient from images without pixelwise labels.

Deep Learning-Based Detection and Correction of Cardiac MR Motion Artefacts During Reconstruction for High-Quality Segmentation.

Segmenting anatomical structures in medical images has been successfully addressed with deep learning methods for a range of applications. However, this success is heavily dependent on the quality of the image that is being segmented. A commonly neglected point in the medical image analysis community is the vast amount of clinical images that have severe image artefacts due to organ motion, movement of the patient and/or image acquisition related issues. In this paper, we discuss the implications of image motion artefacts on cardiac MR segmentation and compare a variety of approaches for jointly correcting for artefacts and segmenting the cardiac cavity. The method is based on our recently developed joint artefact detection and reconstruction method, which reconstructs high quality MR images from k-space using a joint loss function and essentially converts the artefact correction task to an under-sampled image reconstruction task by enforcing a data consistency term. In this paper, we propose to use a segmentation network coupled with this in an end-to-end framework. Our training optimises three different tasks: 1) image artefact detection, 2) artefact correction and 3) image segmentation. We train the reconstruction network to automatically correct for motion-related artefacts using synthetically corrupted cardiac MR k-space data and uncorrected reconstructed images. Using a test set of 500 2D+time cine MR acquisitions from the UK Biobank data set, we achieve demonstrably good image quality and high segmentation accuracy in the presence of synthetic motion artefacts. We showcase better performance compared to various image correction architectures.

Interpretable Deep Models for Cardiac Resynchronisation Therapy Response Prediction.

Advances in deep learning (DL) have resulted in impressive accuracy in some medical image classification tasks, but often deep models lack interpretability. The ability of these models to explain their decisions is important for fostering clinical trust and facilitating clinical translation. Furthermore, for many problems in medicine there is a wealth of existing clinical knowledge to draw upon, which may be useful in generating explanations, but it is not obvious how this knowledge can be encoded into DL models - most models are learnt either from scratch or using transfer learning from a different domain. In this paper we address both of these issues. We propose a novel DL framework for image-based classification based on a variational autoencoder (VAE). The framework allows prediction of the output of interest from the latent space of the autoencoder, as well as visualisation (in the image domain) of the effects of crossing the decision boundary, thus enhancing the interpretability of the classifier. Our key contribution is that the VAE disentangles the latent space based on 'explanations' drawn from existing clinical knowledge. The framework can predict outputs as well as explanations for these outputs, and also raises the possibility of discovering new biomarkers that are separate (or disentangled) from the existing knowledge. We demonstrate our framework on the problem of predicting response of patients with cardiomyopathy to cardiac resynchronization therapy (CRT) from cine cardiac magnetic resonance images. The sensitivity and specificity of the proposed model on the task of CRT response prediction are 88.43% and 84.39% respectively, and we showcase the potential of our model in enhancing understanding of the factors contributing to CRT response.

A Persistent Homology-Based Topological Loss Function for Multi-class CNN Segmentation of Cardiac MRI.

With respect to spatial overlap, CNN-based segmentation of short axis cardiovascular magnetic resonance (CMR) images has achieved a level of performance consistent with inter observer variation. However, conventional training procedures frequently depend on pixel-wise loss functions, limiting optimisation with respect to extended or global features. As a result, inferred segmentations can lack spatial coherence, including spurious connected components or holes. Such results are implausible, violating the anticipated topology of image segments, which is frequently known a priori. Addressing this challenge, published work has employed persistent homology, constructing topological loss functions for the evaluation of image segments against an explicit prior. Building a richer description of segmentation topology by considering all possible labels and label pairs, we extend these losses to the task of multi-class segmentation. These topological priors allow us to resolve all topological errors in a subset of 150 examples from the ACDC short axis CMR training data set, without sacrificing overlap performance.

Weighted Manifold Alignment using Wave Kernel Signatures for Aligning Medical Image Datasets.

Manifold alignment (MA) is a technique to map many high-dimensional datasets to one shared low-dimensional space. Here we develop a pipeline for using MA to reconstruct high-resolution medical images. We present two key contributions. First, we develop a novel MA scheme in which each high-dimensional dataset can be differently weighted preventing noisier or less informative data from corrupting the aligned embedding. We find that this generalisation improves performance in our experiments in both supervised and unsupervised MA problems. Second, we use the wave kernel signature as a graph descriptor for the unsupervised MA case finding that it significantly outperforms the current state-of-the-art methods and provides higher quality reconstructed magnetic resonance volumes than existing methods.

Automatic CNN-based detection of cardiac MR motion artefacts using k-space data augmentation and curriculum learning.

Good quality of medical images is a prerequisite for the success of subsequent image analysis pipelines. Quality assessment of medical images is therefore an essential activity and for large population studies such as the UK Biobank (UKBB), manual identification of artefacts such as those caused by unanticipated motion is tedious and time-consuming. Therefore, there is an urgent need for automatic image quality assessment techniques. In this paper, we propose a method to automatically detect the presence of motion-related artefacts in cardiac magnetic resonance (CMR) cine images. We compare two deep learning architectures to classify poor quality CMR images: 1) 3D spatio-temporal Convolutional Neural Networks (3D-CNN), 2) Long-term Recurrent Convolutional Network (LRCN). Though in real clinical setup motion artefacts are common, high-quality imaging of UKBB, which comprises cross-sectional population data of volunteers who do not necessarily have health problems creates a highly imbalanced classification problem. Due to the high number of good quality images compared to the relatively low number of images with motion artefacts, we propose a novel data augmentation scheme based on synthetic artefact creation in k-space. We also investigate a learning approach using a predetermined curriculum based on synthetic artefact severity. We evaluate our pipeline on a subset of the UK Biobank data set consisting of 3510 CMR images. The LRCN architecture outperformed the 3D-CNN architecture and was able to detect 2D+time short axis images with motion artefacts in less than 1ms with high recall. We compare our approach to a range of state-of-the-art quality assessment methods. The novel data augmentation and curriculum learning approaches both improved classification performance achieving overall area under the ROC curve of 0.89.

Mechanically Powered Motion Imaging Phantoms: Proof of Concept.

Motion imaging phantoms are expensive, bulky and difficult to transport and set-up. The purpose of this paper is to demonstrate a simple approach to the design of multi-modality motion imaging phantoms that use mechanically stored energy to produce motion.We propose two phantom designs that use mainsprings and elastic bands to store energy. A rectangular piece was attached to an axle at the end of the transmission chain of each phantom, and underwent a rotary motion upon release of the mechanical motor. The phantoms were imaged with MRI and US, and the image sequences were embedded in a 1D non linear manifold (Laplacian Eigenmap) and the spectrogram of the embedding was used to derive the angular velocity over time. The derived velocities were consistent and reproducible within a small error. The proposed motion phantom concept showed great potential for the construction of simple and affordable motion phantoms.

Embedding graphs in Lorentzian spacetime.

Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG) into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.