Dan Benjamini

Use of marginal distributions constrained optimization (MADCO) for accelerated 2D MRI relaxometry and diffusometry.

Measuring multidimensional (e.g., 2D) relaxation spectra in NMR and MRI clinical applications is a holy grail of the porous media and biomedical MR communities. The main bottleneck is the inversion of Fredholm integrals of the first kind, an ill-conditioned problem requiring large amounts of data to stabilize a solution. We suggest a novel experimental design and processing framework to accelerate and improve the reconstruction of such 2D spectra that uses a priori information from the 1D projections of spectra, or marginal distributions. These 1D marginal distributions provide powerful constraints when 2D spectra are reconstructed, and their estimation requires an order of magnitude less data than a conventional 2D approach. This marginal distributions constrained optimization (MADCO) methodology is demonstrated here with a polyvinylpyrrolidone-water phantom that has 3 distinct peaks in the 2D D-T1 space. The stability, sensitivity to experimental parameters, and accuracy of this new approach are compared with conventional methods by serially subsampling the full data set. While the conventional, unconstrained approach performed poorly, the new method had proven to be highly accurate and robust, only requiring a fraction of the data. Additionally, synthetic T1-T2 data are presented to explore the effects of noise on the estimations, and the performance of the proposed method with a smooth and realistic 2D spectrum. The proposed framework is quite general and can also be used with a variety of 2D MRI experiments (D-T2,T1-T2,D-D, etc.), making these potentially feasible for preclinical and even clinical applications for the first time.

White matter microstructure from nonparametric axon diameter distribution mapping

We report the development of a double diffusion encoding (DDE) MRI method to estimate and map the axon diameter distribution (ADD) within an imaging volume. A variety of biological processes, ranging from development to disease and trauma, may lead to changes in the ADD in the central and peripheral nervous systems. Unlike previously proposed methods, this ADD experimental design and estimation framework employs a more general, nonparametric approach, without a priori assumptions about the underlying form of the ADD, making it suitable to analyze abnormal tissue. In the current study, this framework was used on an ex vivo ferret spinal cord, while emphasizing the way in which the ADD can be weighted by either the number or the volume of the axons. The different weightings, which result in different spatial contrasts, were considered throughout this work. DDE data were analyzed to derive spatially resolved maps of average axon diameter, ADD variance, and extra-axonal volume fraction, along with a novel sub-micron restricted structures map. The morphological information contained in these maps was then used to segment white matter into distinct domains by using a proposed k-means clustering algorithm with spatial contiguity and left-right symmetry constraints, resulting in identifiable white matter tracks. The method was validated by comparing histological measures to the estimated ADDs using a quantitative similarity metric, resulting in good agreement. With further acquisition acceleration and experimental parameters adjustments, this ADD estimation framework could be first used preclinically, and eventually clinically, enabling a wide range of neuroimaging applications for improved understanding of neurodegenerative pathologies and assessing microstructural changes resulting from trauma.

Estimation of pore size distribution using concentric double pulsed-field gradient NMR

Estimation of pore size distribution of well calibrated phantoms using NMR is demonstrated here for the first time. Porous materials are a central constituent in fields as diverse as biology, geology, and oil drilling. Noninvasive characterization of monodisperse porous samples using conventional pulsed-field gradient (PFG) NMR is a well-established method. However, estimation of pore size distribution of heterogeneous polydisperse systems, which comprise most of the materials found in nature, remains extremely challenging. Concentric double pulsed-field gradient (CDPFG) is a 2-D technique where both q (the amplitude of the diffusion gradient) and φ (the relative angle between the gradient pairs) are varied. A recent prediction indicates this method should produce a more accurate and robust estimation of pore size distribution than its conventional 1-D versions. Five well defined size distribution phantoms, consisting of 1-5 different pore sizes in the range of 5-25 μm were used. The estimated pore size distributions were all in good agreement with the known theoretical size distributions, and were obtained without any a priori assumption on the size distribution model. These findings support that in addition to its theoretical benefits, the CDPFG method is experimentally reliable. Furthermore, by adding the angle parameter, sensitivity to small compartment sizes is increased without the use of strong gradients, thus making CDPFG safe for biological applications.

A proposed 2D framework for estimation of pore size distribution by double pulsed field gradient NMR

Reconstructing a pore size distribution of porous materials is valuable for applications in materials sciences, oil well logging, biology, and medicine. The major drawback of NMR based methods is an intrinsic limitation in the reconstruction which arises from the ill-conditioned nature of the pore size distribution problem. Consequently, while estimation of the average pore size was already demonstrated experimentally, reliable evaluation of pore size distribution remains a challenging task. In this paper we address this problem by analyzing the mathematical characteristics that create the difficulty and by proposing an NMR methodology and a numerical analysis. We demonstrate analytically that an accurate reconstruction of pore size distribution is problematic with the current known strategies for conducting a single or a double pulsed field gradient (s-PFG, d-PFG) experiment. We then present a method for choosing the experimental parameters that would significantly improve the estimation of the size distribution. We show that experimental variation of both q (the amplitude of the diffusion gradient) and ϕ (the relative angle between the gradient pairs) is significantly favorable over single and double-PFG applied with variation of only one parameter. Finally, we suggest a unified methodology (termed Concentric d-PFG) that defines a multidimensional approach where each data point in the experiment is characterized by ϕ and q. The addition of the angle parameter makes the experiment sensitive to small compartment sizes without the need to use strong gradients, thus making it feasible for in-vivo biological applications.

Pore size distribution of bioresorbable films using a 3-D diffusion NMR method.

Pore size distribution (PSD) within porous biomaterials is an important microstructural feature for assessing their biocompatibility, longevity and drug release kinetics. Scanning electron microscopy (SEM) is the most common method used to obtain the PSD of soft biomaterials. The method is highly invasive and user dependent, since it requires fracturing of the sample and then considers only the small portion that the user had acquired in the image. In the current study we present a novel nuclear magnetic resonance (NMR) method as an alternative method for estimation of PSD in soft porous materials. This noninvasive 3-D diffusion NMR method considers the entire volume of the specimen and eliminates the users need to choose a specific field of view. Moreover, NMR does not involve exposure to ionizing radiation and can potentially have preclinical and clinical uses. The method was applied on four porous 50/50 poly(dl-lactic-co-glycolic acid) bioresorbable films with different porosities, which were created using the freeze-drying of inverted emulsions technique. We show that the proposed NMR method is able to address the main limitations associated with SEM-based PSD estimations by being non-destructive, depicting the full volume of the specimens and not being dependent on the magnification factor. Upon comparison, both methods yielded a similar PSD in the smaller pore size range (1-25μm), while the NMR-based method provided additional information on the larger pores (25-50μm).

Joint radius-length distribution as a measure of anisotropic pore eccentricity: An experimental and analytical framework

In this work, we present an experimental design and analytical framework to measure the nonparametric joint radius-length (R-L) distribution of an ensemble of parallel, finite cylindrical pores, and more generally, the eccentricity distribution of anisotropic pores. Employing a novel 3D double pulsed-field gradient acquisition scheme, we first obtain both the marginal radius and length distributions of a population of cylindrical pores and then use these to constrain and stabilize the estimate of the joint radius-length distribution. Using the marginal distributions as constraints allows the joint R-L distribution to be reconstructed from an underdetermined system (i.e., more variables than equations), which requires a relatively small and feasible number of MR acquisitions. Three simulated representative joint R-L distribution phantoms corrupted by different noise levels were reconstructed to demonstrate the process, using this new framework. As expected, the broader the peaks in the joint distribution, the less stable and more sensitive to noise the estimation of the marginal distributions. Nevertheless, the reconstruction of the joint distribution is remarkably robust to increases in noise level; we attribute this characteristic to the use of the marginal distributions as constraints. Axons are known to exhibit local compartment eccentricity variations upon injury; the extent of the variations depends on the severity of the injury. Nonparametric estimation of the eccentricity distribution of injured axonal tissue is of particular interest since generally one cannot assume a parametric distribution a priori. Reconstructing the eccentricity distribution may provide vital information about changes resulting from injury or that occurred during development.

Imaging Local Diffusive Dynamics Using Diffusion Exchange Spectroscopy MRI.

The movement of water between microenvironments presents a central challenge in the physics of soft matter and porous media. Diffusion exchange spectroscopy (DEXSY) is a powerful 2D nuclear magnetic resonance method for measuring such exchange, yet it is rarely used because of its long scan time requirements. Moreover, it has never been combined with magnetic resonance imaging (MRI). Using probability theory, we vastly reduce the required data, making DEXSY MRI feasible for the first time. Experiments are performed on a composite nerve tissue phantom with restricted and free water-exchanging compartments.

Anisotropic phantom to calibrate high-q diffusion MRI methods

A silicon oil-filled glass capillary array is proposed as an anisotropic diffusion MRI phantom. Together with a computational/theoretical pipeline these provide a gold standard for calibrating and validating high-q diffusion MRI experiments. The phantom was used to test high angular resolution diffusion imaging (HARDI) and double pulsed-field gradient (d-PFG) MRI acquisition schemes. MRI-based predictions of microcapillary diameter using both acquisition schemes were compared with results from optical microscopy. This phantom design can be used for quality control and quality assurance purposes and for testing and validating proposed microstructure imaging experiments and the processing pipelines used to analyze them.

Magnetic resonance microdynamic imaging reveals distinct tissue microenvironments

&NA; Magnetic resonance imaging (MRI) provides a powerful set of tools with which to investigate biological tissues noninvasively and in vivo. Tissues are heterogeneous in nature; an imaging voxel contains an ensemble of different cells and extracellular matrix components. A long‐standing challenge has been to infer the content of and interactions among these microscopic tissue components within a macroscopic imaging voxel. Spatially resolved multidimensional relaxation–diffusion correlation (REDCO) spectroscopy holds the potential to deliver such microdynamic information. However, to date, vast data requirements have mostly relegated these type of measurements to nuclear magnetic resonance applications and prevented them from being widely and successfully used in conjunction with imaging. By using a novel data acquisition and processing strategy in this study, spatially resolved REDCO could be performed in reasonable scanning times with excellent prospects for clinical applications. This new MR imaging framework—which we term “magnetic resonance microdynamic imaging (MRMI)”—permits the simultaneous noninvasive and model‐free quantification of multiple subcellular, cellular, and interstitial tissue microenvironments within a voxel. MRMI is demonstrated with a fixed spinal cord specimen, enabling the quantification of microscopic tissue components with unprecedented specificity. Tissue components, such as axons, neuronal and glial soma, and myelin were identified on the basis of their multispectral signature within individual imaging voxels. These tissue elements could then be composed into images and be correlated with immunohistochemistry findings. MRMI provides novel image contrasts of tissue components and a new family of microdynamic biomarkers that could lead to new diagnostic imaging approaches to probe biological tissue alterations accompanied by pathological or developmental changes. HighligtsAccelerated relaxation‐diffusion correlation spectroscopic imaging with MADCO.Multidimensional MRI framework that integrates physical and chemical information.Said framework is termed magnetic resonance microdynamic imaging (MRMI).Model‐free evaluation of subcellular, cellular, and interstitial microenvironments.Tissue microenvironments images correlated with immunohistochemistry findings.

Towards clinically feasible relaxation-diffusion correlation MRI using MADCO

Multidimensional relaxation-diffusion correlation (REDCO) NMR is an assumption-free method that measures how water is distributed within materials. Although highly informative, REDCO had never been used in clinical MRI applications because of the large amount of data it requires, leading to infeasible scan times. A recently suggested novel experimental design and processing framework, marginal distributions constrained optimization (MADCO), was used here to accelerate and improve the reconstruction of such MRI correlations. MADCO uses the 1D marginal distributions as a priori information, which provide powerful constraints when 2D spectra are reconstructed, while their estimation requires an order of magnitude less data than conventional 2D approaches. In this work we experimentally examined the impact the complexity of the correlation distribution has on the accuracy and robustness of the estimates. MADCO and a conventional method were compared using two T1-D phantoms that differ in the proximity of their peaks, leading to a relatively simple case as opposed to a more challenging one. The phantoms were used to vet the achievable data compression using MADCO under these conditions. MADCO required ~43 and ~30 less data than the conventional approach for the simple and complex spectra, respectively, making it potentially feasible for preclinical and even clinical applications.