Enrico Kaden

Parametric spherical deconvolution: Inferring anatomical connectivity using diffusion MR imaging

The human brain forms a complex neural network with a connectional architecture that is still far from being known in full detail, even at the macroscopic level. The advent of diffusion MR imaging has enabled the exploration of the structural properties of white matter in vivo. In this article we propose a new forward model that maps the microscopic geometry of nervous tissue onto the water diffusion process and further onto the measured MR signals. Our spherical deconvolution approach completely parameterizes the fiber orientation density by a finite mixture of Bingham distributions. In addition, we define the term anatomical connectivity, taking the underlying image modality into account. This neurophysiological metric may represent the proportion of the nerve fibers originating in the source area which intersect a given target region. The specified inverse problem is solved by Bayesian statistics. Posterior probability maps denote the probability that the connectivity value exceeds a chosen threshold, conditional upon the noisy observations. These maps allow us to draw inferences about the structural organization of the cerebral cortex. Moreover, we will demonstrate the proposed approach with diffusion-weighted data sets featuring high angular resolution.

Multi-compartment microscopic diffusion imaging

This paper introduces a multi-compartment model for microscopic diffusion anisotropy imaging. The aim is to estimate microscopic features specific to the intra- and extra-neurite compartments in nervous tissue unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The proposed MRI method is based on the Spherical Mean Technique (SMT), which factors out the neurite orientation distribution and thus provides direct estimates of the microscopic tissue structure. This technique can be immediately used in the clinic for the assessment of various neurological conditions, as it requires only a widely available off-the-shelf sequence with two b-shells and high-angular gradient resolution achievable within clinically feasible scan times. To demonstrate the developed method, we use high-quality diffusion data acquired with a bespoke scanner system from the Human Connectome Project. This study establishes the normative values of the new biomarkers for a large cohort of healthy young adults, which may then support clinical diagnostics in patients. Moreover, we show that the microscopic diffusion indices offer direct sensitivity to pathological tissue alterations, exemplified in a preclinical animal model of Tuberous Sclerosis Complex (TSC), a genetic multi-organ disorder which impacts brain microstructure and hence may lead to neurological manifestations such as autism, epilepsy and developmental delay.

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study.

To identify optimal pulsed gradient spin‐echo (PGSE) and oscillating gradient spin‐echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions.

Quantitative mapping of the per‐axon diffusion coefficients in brain white matter

This article presents a simple method for estimating the effective diffusion coefficients parallel and perpendicular to the axons unconfounded by the intravoxel fiber orientation distribution. We also call these parameters the per‐axon or microscopic diffusion coefficients.

Variational inference of the fiber orientation density using diffusion MR imaging

Diffusion MR imaging has enabled the in vivo exploration of the connectional architecture in human brain. This method particularly reveals the complex system of long-range nerve fibers that integrate the functionally distinct areas of the cerebral cortex. Since the fibers are not directly observed but the diffusion process of water molecules in the underlying material, a forward model is established that maps the microgeometry of nervous tissue onto the diffusion-weighted signals. This article proposes the spherical deconvolution of the fiber orientation density in a reproducing kernel Hilbert space, thereby generalizing previous approaches that perform a truncated Fourier analysis on the sphere. The specified inverse problem is solved within a smoothing spline framework which preserves the characteristic properties of a density function, namely its normalization and non-negativity. A Gaussian process model allows the specification of confidence bands for the estimated fiber orientation density and the rigorous selection of the hyperparameters, here the high-frequency content in the density function and the noise variance of the MR observations. In addition, we weaken the constant diffusivity assumption frequently made in the spherical convolution methodology. The novel approach, which uncovers the fiber orientation field of white matter, is demonstrated with diffusion-weighted data sets featuring high angular resolution.

Image quality transfer and applications in diffusion MRI

ABSTRACT This paper introduces a new computational imaging technique called image quality transfer (IQT). IQT uses machine learning to transfer the rich information available from one‐off experimental medical imaging devices to the abundant but lower‐quality data from routine acquisitions. The procedure uses matched pairs to learn mappings from low‐quality to corresponding high‐quality images. Once learned, these mappings then augment unseen low quality images, for example by enhancing image resolution or information content. Here, we demonstrate IQT using a simple patch‐regression implementation and the uniquely rich diffusion MRI data set from the human connectome project (HCP). Results highlight potential benefits of IQT in both brain connectivity mapping and microstructure imaging. In brain connectivity mapping, IQT reveals, from standard data sets, thin connection pathways that tractography normally requires specialised data to reconstruct. In microstructure imaging, IQT shows potential in estimating, from standard “single‐shell” data (one non‐zero b‐value), maps of microstructural parameters that normally require specialised multi‐shell data. Further experiments show strong generalisability, highlighting IQTs benefits even when the training set does not directly represent the application domain. The concept extends naturally to many other imaging modalities and reconstruction problems. Graphical abstract Figure. No Caption available. HighlightsImage quality transfer propagates information from rare or expensive high quality images to abundant or cheap low quality images.Dramatically outperforms interpolation in resolution enhancement of diffusion MRI.Enables tractography to recover fine pathways normally only accessible at 1.25 mm resolution from 2.5 mm data sets.Provides plausible NODDI and SMT maps from single‐shell input data.Requires only off‐the‐shelf and computationally light machine learning and imaging tools and complementary to other sparse reconstruction and super‐resolution techniques.

Bayesian image quality transfer with CNNs: Exploring uncertainty in dMRI super-resolution

In this work, we investigate the value of uncertainty modelling in 3D super-resolution with convolutional neural networks (CNNs). Deep learning has shown success in a plethora of medical image transformation problems, such as super-resolution (SR) and image synthesis. However, the highly ill-posed nature of such problems results in inevitable ambiguity in the learning of networks. We propose to account for intrinsic uncertainty through a per-patch heteroscedastic noise model and for parameter uncertainty through approximate Bayesian inference in the form of variational dropout. We show that the combined benefits of both lead to the state-of-the-art performance SR of diffusion MR brain images in terms of errors compared to ground truth. We further show that the reduced error scores produce tangible benefits in downstream tractography. In addition, the probabilistic nature of the methods naturally confers a mechanism to quantify uncertainty over the super-resolved output. We demonstrate through experiments on both healthy and pathological brains the potential utility of such an uncertainty measure in the risk assessment of the super-resolved images for subsequent clinical use.

Bayesian Image Quality Transfer

Image quality transfer (IQT) aims to enhance clinical images of relatively low quality by learning and propagating high-quality structural information from expensive or rare data sets. However, the original framework gives no indication of confidence in its output, which is a significant barrier to adoption in clinical practice and downstream processing. In this article, we present a general Bayesian extension of IQT which enables efficient and accurate quantification of uncertainty, providing users with an essential prediction of the accuracy of enhanced images. We demonstrate the efficacy of the uncertainty quantification through super-resolution of diffusion tensor images of healthy and pathological brains. In addition, the new method displays improved performance over the original IQT and standard interpolation techniques in both reconstruction accuracy and robustness to anomalies in input images.

Can T 2 -spectroscopy resolve submicrometer axon diameters?

The microscopic geometry of white matter carries rich information about brain function in health and disease. A key challenge for medical imaging is to estimate microstructural features noninvasively. One important parameter is the axon diameter, which correlates with the conduction time delay of action potentials and is affected by various neurological disorders. Diffusion magnetic resonance (MR) experiments are the method of choice today when we aim to recover the axon diameter distribution, although the technique requires very high gradient strengths in order to assess nerve fibers with one micrometer or less in diameter. In practice in-vivo brain imaging is only sensitive to the largest axons, not least due to limitations in the human physiology which tolerates only moderate gradient strengths. This work studies, from a theoretical perspective, the feasibility of T2-spectroscopy to resolve submicrometer tissue structures. Exploiting the surface relaxation effect, we formulate a plausible biophysical model relating the axon diameter distribution to the T2-weighted signal, which is based on a surface-to-volume ratio approximation of the Bloch-Torrey equation. Under a certain regime of bulk and surface relaxation coefficients, our simulation results suggest that it might be possible to reveal axons smaller than one micrometer in diameter.

Relevance of time-dependence for clinically viable diffusion imaging of the spinal cord

Time‐dependence is a key feature of the diffusion‐weighted (DW) signal, knowledge of which informs biophysical modelling. Here, we study time‐dependence in the human spinal cord, as its axonal structure is specific and different from the brain.