A comparison of machine learning methods for recovering noisy and missing 4D flow MRI data.

Experimental blood flow measurement techniques are invaluable for a better understanding of cardiovascular disease formation, progression, and treatment. One of the emerging methods is time-resolved three-dimensional phase-contrast magnetic resonance imaging (4D flow MRI), which enables noninvasive time-dependent velocity measurements within large vessels. However, several limitations hinder the usability of 4D flow MRI and other experimental methods for quantitative hemodynamics analysis. These mainly include measurement noise, corrupt or missing data, low spatiotemporal resolution, and other artifacts. Traditional filtering is routinely applied for denoising experimental blood flow data without any detailed discussion on why it is preferred over other methods. In this study, filtering is compared to different singular value decomposition (SVD)-based machine learning and autoencoder-type deep learning methods for denoising and filling in missing data (imputation). An artificially corrupted and voxelized computational fluid dynamics (CFD) simulation as well as in vitro 4D flow MRI data are used to test the methods. SVD-based algorithms achieve excellent results for the idealized case but severely struggle when applied to in vitro data. The autoencoders are shown to be versatile and applicable to all investigated cases. For denoising, the in vitro 4D flow MRI data, the denoising autoencoder (DAE), and the Noise2Noise (N2N) autoencoder produced better reconstructions than filtering both qualitatively and quantitatively. Deep learning methods such as N2N can result in noise-free velocity fields even though they did not use clean data during training. This work presents one of the first comprehensive assessments and comparisons of various classical and modern machine-learning methods for enhancing corrupt cardiovascular flow data in diseased arteries for both synthetic and experimental test cases.

Integrating multi-fidelity blood flow data with reduced-order data assimilation.

High-fidelity patient-specific modeling of cardiovascular flows and hemodynamics is challenging. Direct blood flow measurement inside the body with in-vivo measurement modalities such as 4D flow magnetic resonance imaging (4D flow MRI) suffer from low resolution and acquisition noise. In-vitro experimental modeling and patient-specific computational fluid dynamics (CFD) models are subject to uncertainty in patient-specific boundary conditions and model parameters. Furthermore, collecting blood flow data in the near-wall region (e.g., wall shear stress) with experimental measurement modalities poses additional challenges. In this study, a computationally efficient data assimilation method called reduced-order modeling Kalman filter (ROM-KF) was proposed, which combined a sequential Kalman filter with reduced-order modeling using a linear model provided by dynamic mode decomposition (DMD). The goal of ROM-KF was to overcome low resolution and noise in experimental and uncertainty in CFD modeling of cardiovascular flows. The accuracy of the method was assessed with 1D Womersley flow, 2D idealized aneurysm, and 3D patient-specific cerebral aneurysm models. Synthetic experimental data were used to enable direct quantification of errors using benchmark datasets. The accuracy of ROM-KF in reconstructing near-wall hemodynamics was assessed by applying the method to problems where near-wall blood flow data were missing in the experimental dataset. The ROM-KF method provided blood flow data that were more accurate than the computational and synthetic experimental datasets and improved near-wall hemodynamics quantification.

Modeling and Reducing the Effect of Geometric Uncertainties in Intracranial Aneurysms with Polynomial Chaos Expansion, Data Decomposition, and 4D-Flow MRI.

PURPOSE: Variations in the vessel radius of segmented surfaces of intracranial aneurysms significantly influence the fluid velocities given by computer simulations. It is important to generate models that capture the effect of these variations in order to have a better interpretation of the numerically predicted hemodynamics. Also, it is highly relevant to develop methods that combine experimental observations with uncertainty modeling to get a closer approximation to the blood flow behavior. METHODS: This work applies polynomial chaos expansion to model the effect of geometric uncertainties on the simulated fluid velocities of intracranial aneurysms. The radius of the vessel is defined as the uncertainty variable. Proper orthogonal decomposition is applied to characterize the solution space of fluid velocities. Next, a process of projecting the 4D-Flow MRI velocities on the basis vectors followed by coefficient mapping using generalized dynamic mode decomposition enables the merging of 4D-Flow MRI with the uncertainty propagated fluid velocities. RESULTS: Polynomial chaos expansion propagates the fluid velocities with an error of 2% in velocity magnitude relative to computer simulations. Also, the bifurcation region (or impingement location) shows a standard deviation of 0.17 m/s (since an available reported variance in the vessel radius is adopted to model the uncertainty, the expected standard deviation may be different). Numerical phantom experiments indicate that the proposed approach reconstructs the fluid velocities with 0.3% relative error in presence of geometric uncertainties. CONCLUSION: Polynomial chaos expansion is an effective approach to propagate the effect of the uncertainty variable in the blood flow velocities of intracranial aneurysms. Merging 4D-Flow MRI and uncertainty propagated fluid velocities leads to more realistic flow trends relative to ignoring the uncertainty in the vessel radius.

Super-resolution and denoising of 4D-Flow MRI using physics-Informed deep neural nets.

BACKGROUND AND OBJECTIVE: Time resolved three-dimensional phase contrast magnetic resonance imaging (4D-Flow MRI) has been used to non-invasively measure blood velocities in the human vascular system. However, issues such as low spatio-temporal resolution, acquisition noise, velocity aliasing, and phase-offset artifacts have hampered its clinical application. In this research, we developed a purely data-driven method for super-resolution and denoising of 4D-Flow MRI. METHODS: The flow velocities, pressure, and the MRI image magnitude are modeled as a patient-specific deep neural net (DNN). For training, 4D-Flow MRI images in the complex Cartesian space are used to impose data-fidelity. Physics of fluid flow is imposed through regularization. Creative loss function terms have been introduced to handle noise and super-resolution. The trained patient-specific DNN can be sampled to generate noise-free high-resolution flow images. The proposed method has been implemented using the TensorFlow DNN library and tested on numerical phantoms and validated in-vitro using high-resolution particle image velocitmetry (PIV) and 4D-Flow MRI experiments on transparent models subjected to pulsatile flow conditions. RESULTS: In case of numerical phantoms, we were able to increase spatial resolution by a factor of 100 and temporal resolution by a factor of 5 compared to the simulated 4D-Flow MRI. There is an order of magnitude reduction of velocity normalized root mean square error (vNRMSE). In case of the in-vitro validation tests with PIV as reference, there is similar improvement in spatio-temporal resolution. Although the vNRMSE is reduced by 50%, the method is unable to negate a systematic bias with respect to the reference PIV that is introduced by the 4D-Flow MRI measurement. CONCLUSIONS: This work has demonstrated the feasibility of using the readily available machinery of deep learning to enhance 4D-Flow MRI using a purely data-driven method. Unlike current state-of-the-art methods, the proposed method is agnostic to geometry and boundary conditions and therefore eliminates the need for tedious tasks such as accurate image segmentation for geometry, image registration, and estimation of boundary flow conditions. Arbitrary regions of interest can be selected for processing. This work will lead to user-friendly analysis tools that will enable quantitative hemodynamic analysis of vascular diseases in a clinical setting.

Towards multi-modal data fusion for super-resolution and denoising of 4D-Flow MRI.

4D-Flow magnetic resonance imaging (MRI) has enabled in vivo time-resolved measurement of three-dimensional blood flow velocities in the human vascular system. However, its clinical use has been hampered by two main issues, namely, low spatio-temporal resolution and acquisition noise. While patient-specific computational fluid dynamics (CFD) simulations can address the resolution and noise issues, its fidelity is impacted by accuracy of estimation of boundary conditions, model parameters, vascular geometry, and flow model assumptions. In this paper a scheme to address limitations of both modalities through data-fusion is presented. The solutions of the patient-specific CFD simulation are characterized using proper orthogonal decomposition (POD). Next, a process of projecting the 4D-Flow MRI data onto the POD basis and projection coefficient mapping using generalized dynamic mode decomposition (DMD) enables simultaneous super-resolution and denoising of 4D-Flow MRI. The method has been tested using numerical phantoms derived from patient-specific aneurysmal geometries and applied to in vivo 4D-Flow MRI data.

Denoising and spatial resolution enhancement of 4D flow MRI using proper orthogonal decomposition and lasso regularization.

4D-Flow MRI has emerged as a powerful tool to non-invasively image blood velocity profiles in the human cardio-vascular system. However, it is plagued by issues such as velocity aliasing, phase offsets, acquisition noise, and low spatial and temporal resolution. In imaging small blood vessel malformations such as intra-cranial aneurysms, the spatial resolution of 4D-Flow is often inadequate to resolve fine flow features. In this paper, we address the problem of low spatial resolution and noise by combining 4D-Flow MRI and patient specific computational fluid dynamics using Least Absolute Shrinkage and Selection Operator. Extensive experiments using numerical phantoms of two actual intra-cranial aneurysms geometries show the applicability of the proposed method in recovering the flow profile. Comparisons with the state-of-the-art denoising methods for 4D-Flow show lower error metrics. This method can enable more accurate computation of flow derived patho-physiological parameters such as wall shear stresses, pressure gradients, and viscous dissipation.

Curvelet Transform-based volume fusion for correcting signal loss artifacts in Time-of-Flight Magnetic Resonance Angiography data.

Flow fields in cerebral aneurysms can be measured in vivo with phase-contrast MRI (4D Flow MRI), providing 3D anatomical magnitude images as well as 3-directional velocities through the cardiac cycle. The low spatial resolution of the 4D Flow MRI data, however, requires the images to be co-registered with higher resolution angiographic data for better segmentation of the blood vessel geometries to adequately quantify relevant flow descriptors such as wall shear stress or flow residence time. Time-of-Flight Magnetic Resonance Angiography (TOF MRA) is a non-invasive technique for visualizing blood vessels without the need to administer contrast agent. Instead TOF uses the blood flow-related enhancement of unsaturated spins entering into an imaging slice as means to generate contrast between the stationary tissue and the moving blood. Because of the higher resolutions, TOF data are often used to assist with the segmentation process needed for the flow analysis and Computational Fluid Dynamics (CFD) modeling. However, presence of slow moving and recirculating blood flow such as in brain aneurysms, especially regions where the blood flow is not perpendicular to the image plane, causes signal loss in these regions. In this work a 3D Curvelet Transform-based image fusion approach is proposed for signal loss artifact reduction of TOF volume data. Experiments show the superiority of the proposed approach in comparison to other multi-resolution 3D Wavelet-based image fusion methodologies. The proposed approach can further facilitate model-based fluid analysis and pre/post-operative treatment of patients with brain aneurysms.

Multi-Modal Medical Image Registration with Full or Partial Data: A Manifold Learning Approach.

Multi-modal image registration is the primary step in integrating information stored in two or more images, which are captured using multiple imaging modalities. In addition to intensity variations and structural differences between images, they may have partial or full overlap, which adds an extra hurdle to the success of registration process. In this contribution, we propose a multi-modal to mono-modal transformation method that facilitates direct application of well-founded mono-modal registration methods in order to obtain accurate alignment of multi-modal images in both cases, with complete (full) and incomplete (partial) overlap. The proposed transformation facilitates recovering strong scales, rotations, and translations. We explain the method thoroughly and discuss the choice of parameters. For evaluation purposes, the effectiveness of the proposed method is examined and compared with widely used information theory-based techniques using simulated and clinical human brain images with full data. Using RIRE dataset, mean absolute error of 1.37, 1.00, and 1.41 mm are obtained for registering CT images with PD-, T1-, and T2-MRIs, respectively. In the end, we empirically investigate the efficacy of the proposed transformation in registering multi-modal partially overlapped images.

Slanted support window-based stereo matching for surface reconstruction of microscopic samples.

This work is to address the limitations of 2D Scanning Electron Microscopy (SEM) micrographs in providing 3D topographical information necessary for various types of analysis in biological and biomedical sciences as well as mechanical and material engineering by investigating modern stereo vision methodologies for 3D surface reconstruction of microscopic samples. To achieve this, micrograph pairs of the microscopic samples are acquired by utilizing an SEM equipped with motor controlled specimen stage capable of precise translational, rotational movements and tilting of the specimen stage. After pre-processing of the micrographs by SIFT feature detection/description followed by RANSAC for matching outlier removal and stereo rectification, a dense stereo matching methodology is utilized which takes advantage of slanted support window formulation for sub-pixel accuracy stereo matching of the input images. This results in a dense disparity map which is used to determine the true depth/elevation of individual surface points. This is a major improvement in comparison to previous matching methodologies which require additional post-processing refinement steps to reduce the negative effects of discrete disparity assignment or the blurring artifacts in near the edge regions. The provided results are great representatives of the superior performance of the slanted support window assumption employed here for surface reconstruction of microscopic samples.

Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression.

Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in vivo 4D Flow MRI data.

Three-dimensional reconstruction of highly complex microscopic samples using scanning electron microscopy and optical flow estimation.

Scanning Electron Microscope (SEM) as one of the major research and industrial equipment for imaging of micro-scale samples and surfaces has gained extensive attention from its emerge. However, the acquired micrographs still remain two-dimensional (2D). In the current work a novel and highly accurate approach is proposed to recover the hidden third-dimension by use of multi-view image acquisition of the microscopic samples combined with pre/post-processing steps including sparse feature-based stereo rectification, nonlocal-based optical flow estimation for dense matching and finally depth estimation. Employing the proposed approach, three-dimensional (3D) reconstructions of highly complex microscopic samples were achieved to facilitate the interpretation of topology and geometry of surface/shape attributes of the samples. As a byproduct of the proposed approach, high-definition 3D printed models of the samples can be generated as a tangible means of physical understanding. Extensive comparisons with the state-of-the-art reveal the strength and superiority of the proposed method in uncovering the details of the highly complex microscopic samples.

SD-SEM: sparse-dense correspondence for 3D reconstruction of microscopic samples.

Scanning electron microscopy (SEM) imaging has been a principal component of many studies in biomedical, mechanical, and materials sciences since its emergence. Despite the high resolution of captured images, they remain two-dimensional (2D). In this work, a novel framework using sparse-dense correspondence is introduced and investigated for 3D reconstruction of stereo SEM images. SEM micrographs from microscopic samples are captured by tilting the specimen stage by a known angle. The pair of SEM micrographs is then rectified using sparse scale invariant feature transform (SIFT) features/descriptors and a contrario RANSAC for matching outlier removal to ensure a gross horizontal displacement between corresponding points. This is followed by dense correspondence estimation using dense SIFT descriptors and employing a factor graph representation of the energy minimization functional and loopy belief propagation (LBP) as means of optimization. Given the pixel-by-pixel correspondence and the tilt angle of the specimen stage during the acquisition of micrographs, depth can be recovered. Extensive tests reveal the strength of the proposed method for high-quality reconstruction of microscopic samples.

Involuntary eye motion correction in retinal optical coherence tomography: Hardware or software solution?

In this paper, we review state-of-the-art techniques to correct eye motion artifacts in Optical Coherence Tomography (OCT) imaging. The methods for eye motion artifact reduction can be categorized into two major classes: (1) hardware-based techniques and (2) software-based techniques. In the first class, additional hardware is mounted onto the OCT scanner to gather information about the eye motion patterns during OCT data acquisition. This information is later processed and applied to the OCT data for creating an anatomically correct representation of the retina, either in an offline or online manner. In software based techniques, the motion patterns are approximated either by comparing the acquired data to a reference image, or by considering some prior assumptions about the nature of the eye motion. Careful investigations done on the most common methods in the field provides invaluable insight regarding future directions of the research in this area. The challenge in hardware-based techniques lies in the implementation aspects of particular devices. However, the results of these techniques are superior to those obtained from software-based techniques because they are capable of capturing secondary data related to eye motion during OCT acquisition. Software-based techniques on the other hand, achieve moderate success and their performance is highly dependent on the quality of the OCT data in terms of the amount of motion artifacts contained in them. However, they are still relevant to the field since they are the sole class of techniques with the ability to be applied to legacy data acquired using systems that do not have extra hardware to track eye motion.

Application of Independent Component Analysis Techniques in Speckle Noise Reduction of Retinal OCT Images.

Optical Coherence Tomography (OCT) is an emerging technique in the field of biomedical imaging, with applications in ophthalmology, dermatology, coronary imaging etc. OCT images usually suffer from a granular pattern, called speckle noise, which restricts the process of interpretation. Therefore the need for speckle noise reduction techniques is of high importance. To the best of our knowledge, use of Independent Component Analysis (ICA) techniques has never been explored for speckle reduction of OCT images. Here, a comparative study of several ICA techniques (InfoMax, JADE, FastICA and SOBI) is provided for noise reduction of retinal OCT images. Having multiple B-scans of the same location, the eye movements are compensated using a rigid registration technique. Then, different ICA techniques are applied to the aggregated set of B-scans for extracting the noise-free image. Signal-to-Noise-Ratio (SNR), Contrast-to-Noise-Ratio (CNR) and Equivalent-Number-of-Looks (ENL), as well as analysis on the computational complexity of the methods, are considered as metrics for comparison. The results show that use of ICA can be beneficial, especially in case of having fewer number of B-scans.

State-of-the-art in retinal optical coherence tomography image analysis.

Optical coherence tomography (OCT) is an emerging imaging modality that has been widely used in the field of biomedical imaging. In the recent past, it has found uses as a diagnostic tool in dermatology, cardiology, and ophthalmology. In this paper we focus on its applications in the field of ophthalmology and retinal imaging. OCT is able to non-invasively produce cross-sectional volumetric images of the tissues which can be used for analysis of tissue structure and properties. Due to the underlying physics, OCT images suffer from a granular pattern, called speckle noise, which restricts the process of interpretation. This requires specialized noise reduction techniques to eliminate the noise while preserving image details. Another major step in OCT image analysis involves the use of segmentation techniques for distinguishing between different structures, especially in retinal OCT volumes. The outcome of this step is usually thickness maps of different retinal layers which are very useful in study of normal/diseased subjects. Lastly, movements of the tissue under imaging as well as the progression of disease in the tissue affect the quality and the proper interpretation of the acquired images which require the use of different image registration techniques. This paper reviews various techniques that are currently used to process raw image data into a form that can be clearly interpreted by clinicians.

Fast k-NNG construction with GPU-based quick multi-select.

In this paper, we describe a new brute force algorithm for building the k-Nearest Neighbor Graph (k-NNG). The k-NNG algorithm has many applications in areas such as machine learning, bio-informatics, and clustering analysis. While there are very efficient algorithms for data of low dimensions, for high dimensional data the brute force search is the best algorithm. There are two main parts to the algorithm: the first part is finding the distances between the input vectors, which may be formulated as a matrix multiplication problem; the second is the selection of the k-NNs for each of the query vectors. For the second part, we describe a novel graphics processing unit (GPU)-based multi-select algorithm based on quick sort. Our optimization makes clever use of warp voting functions available on the latest GPUs along with user-controlled cache. Benchmarks show significant improvement over state-of-the-art implementations of the k-NN search on GPUs.

Efficient computation of k-Nearest Neighbour Graphs for large high-dimensional data sets on GPU clusters.

This paper presents an implementation of the brute-force exact k-Nearest Neighbor Graph (k-NNG) construction for ultra-large high-dimensional data cloud. The proposed method uses Graphics Processing Units (GPUs) and is scalable with multi-levels of parallelism (between nodes of a cluster, between different GPUs on a single node, and within a GPU). The method is applicable to homogeneous computing clusters with a varying number of nodes and GPUs per node. We achieve a 6-fold speedup in data processing as compared with an optimized method running on a cluster of CPUs and bring a hitherto impossible [Formula: see text]-NNG generation for a dataset of twenty million images with 15 k dimensionality into the realm of practical possibility.

Study of contact angle hysteresis using the Cellular Potts Model.

We use the Cellular Potts Model (CPM) to study the contact angle (CA) hysteresis in multiphase (solid-liquid-vapour) systems. We simulate a droplet over the tilted patterned surface, and a bubble placed under the surface immersed in liquid. The difference between bubbles and droplets was discussed through their CA hysteresis. Dependency of CA hysteresis on the surface structure and other parameters was also investigated. This analysis allows decoupling of the 1D (pinning of the triple line) and 2D (adhesion hysteresis in the contact area) effects and provides new insight into the nature of CA hysteresis.

Accelerating the Gillespie Exact Stochastic Simulation Algorithm using hybrid parallel execution on graphics processing units.

The Gillespie Stochastic Simulation Algorithm (GSSA) and its variants are cornerstone techniques to simulate reaction kinetics in situations where the concentration of the reactant is too low to allow deterministic techniques such as differential equations. The inherent limitations of the GSSA include the time required for executing a single run and the need for multiple runs for parameter sweep exercises due to the stochastic nature of the simulation. Even very efficient variants of GSSA are prohibitively expensive to compute and perform parameter sweeps. Here we present a novel variant of the exact GSSA that is amenable to acceleration by using graphics processing units (GPUs). We parallelize the execution of a single realization across threads in a warp (fine-grained parallelism). A warp is a collection of threads that are executed synchronously on a single multi-processor. Warps executing in parallel on different multi-processors (coarse-grained parallelism) simultaneously generate multiple trajectories. Novel data-structures and algorithms reduce memory traffic, which is the bottleneck in computing the GSSA. Our benchmarks show an 8×-120× performance gain over various state-of-the-art serial algorithms when simulating different types of models.

Accelerating the Gillespie τ-Leaping Method using graphics processing units.

The Gillespie τ-Leaping Method is an approximate algorithm that is faster than the exact Direct Method (DM) due to the progression of the simulation with larger time steps. However, the procedure to compute the time leap τ is quite expensive. In this paper, we explore the acceleration of the τ-Leaping Method using Graphics Processing Unit (GPUs) for ultra-large networks (>0.5e(6) reaction channels). We have developed data structures and algorithms that take advantage of the unique hardware architecture and available libraries. Our results show that we obtain a performance gain of over 60x when compared with the best conventional implementations.