Sliding to predict: vision-based beating heart motion estimation by modeling temporal interactions

Purpose: Technical advancements have been part of modern medical solutions as they promote better surgical alternatives that serve to the benefit of patients. Particularly with cardiovascular surgeries, robotic surgical systems enable surgeons to perform delicate procedures on a beating heart, avoiding the complications of cardiac arrest. This advantage comes with the price of having to deal with a dynamic target which presents technical challenges for the surgical system. In this work, we propose a solution for cardiac motion estimation. Methods: Our estimation approach uses a variational framework that guarantees preservation of the complex anatomy of the heart. An advantage of our approach is that it takes into account different disturbances, such as specular reflections and occlusion events. This is achieved by performing a preprocessing step that eliminates the specular highlights and a predicting step, based on a conditional restricted Boltzmann machine, that recovers missing information caused by partial occlusions. Results: We carried out exhaustive experimentations on two datasets, one from a phantom and the other from an in vivo procedure. The results show that our visual approach reaches an average minima in the order of magnitude of 10-7 while preserving the heart’s anatomical structure and providing stable values for the Jacobian determinant ranging from 0.917 to 1.015. We also show that our specular elimination approach reaches an accuracy of 99% compared to a ground truth. In terms of prediction, our approach compared favorably against two well-known predictors, NARX and EKF, giving the lowest average RMSE of 0.071. Conclusion: Our approach avoids the risks of using mechanical stabilizers and can also be effective for acquiring the motion of organs other than the heart, such as the lung or other deformable objects.Peer ReviewedPostprint (published version

Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

Bridge Simulation and Metric Estimation on Landmark Manifolds

We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional PDE with no closed-form solution in the nonlinear case. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood

Explainable Anatomical Shape Analysis through Deep Hierarchical Generative Models

Quantification of anatomical shape changes currently relies on scalar global indexes which are largely insensitive to regional or asymmetric modifications. Accurate assessment of pathology-driven anatomical remodeling is a crucial step for the diagnosis and treatment of many conditions. Deep learning approaches have recently achieved wide success in the analysis of medical images, but they lack interpretability in the feature extraction and decision processes. In this work, we propose a new interpretable deep learning model for shape analysis. In particular, we exploit deep generative networks to model a population of anatomical segmentations through a hierarchy of conditional latent variables. At the highest level of this hierarchy, a two-dimensional latent space is simultaneously optimised to discriminate distinct clinical conditions, enabling the direct visualisation of the classification space. Moreover, the anatomical variability encoded by this discriminative latent space can be visualised in the segmentation space thanks to the generative properties of the model, making the classification task transparent. This approach yielded high accuracy in the categorisation of healthy and remodelled left ventricles when tested on unseen segmentations from our own multi-centre dataset as well as in an external validation set, and on hippocampi from healthy controls and patients with Alzheimer's disease when tested on ADNI data. More importantly, it enabled the visualisation in three-dimensions of both global and regional anatomical features which better discriminate between the conditions under exam. The proposed approach scales effectively to large populations, facilitating high-throughput analysis of normal anatomy and pathology in large-scale studies of volumetric imaging

Deep Learning in Cardiology

The medical field is creating large amount of data that physicians are unable to decipher and use efficiently. Moreover, rule-based expert systems are inefficient in solving complicated medical tasks or for creating insights using big data. Deep learning has emerged as a more accurate and effective technology in a wide range of medical problems such as diagnosis, prediction and intervention. Deep learning is a representation learning method that consists of layers that transform the data non-linearly, thus, revealing hierarchical relationships and structures. In this review we survey deep learning application papers that use structured data, signal and imaging modalities from cardiology. We discuss the advantages and limitations of applying deep learning in cardiology that also apply in medicine in general, while proposing certain directions as the most viable for clinical use.Comment: 27 pages, 2 figures, 10 table

Posterior shape models

We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a "posterior shape model", which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness

Geometric and projection effects in Kramers-Moyal analysis

Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze stochastic time series, particularly nonlinear ones. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically-inspired examples, these effects are predicted and explored with a non-stochastic projection operator method, and compared with direct numerical simulation of the systems' Langevin equations. General features and characteristics are identified, and the utility of the Kramers-Moyal method discussed. Projections of a system are in general non-Markovian, but here the Kramers-Moyal method remains useful, and in any case the primary examples considered are found to be close to Markovian.Comment: Submitted to Phys. Rev.