Simulation and experimental verification of the diffusion in an anisotropic fiber phantom

Influence of Diffusion Time and Temperature on Restricted Diffusion Signal: A Phantom Study

PURPOSE

Diffusion MRI is a physical measurement method that quantitatively indicates the displacement of water molecules diffusing in voxels. However, there are insufficient data to characterize the diffusion process physically in a uniform structure such as a phantom. This study investigated the transitional relationship between structure scale, temperature, and diffusion time for simple restricted diffusion using a capillary phantom.

METHODS

We performed diffusion-weighted pulsed-gradient stimulated-echo acquisition mode (STEAM) MRI with a 9.4 Tesla MRI system (Bruker BioSpin, Ettlingen, Germany) and a quadrature coil with an inner diameter of 86 mm (Bruker BioSpin). We measured the diffusion coefficients (radial diffusivity [RD]) of capillary plates (pore sizes 6, 12, 25, 50, and 100 μm) with uniformly restricted structures at various temperatures (10ºC, 20ºC, 30ºC, and 40ºC) and multiple diffusion times (12-800 ms). We evaluated the characteristics of scale, temperature, and diffusion time for restricted diffusion.

RESULTS

The RD decayed and became constant depending on the structural scale. Diffusion coefficient fluctuations with temperature occurred mostly under conditions of a large structural scale and short diffusion time. We obtained data suggesting that temperature-dependent changes in the diffusion coefficients follow physical laws.

CONCLUSION

No water molecules were observed outside the glass tubes in the capillary plates, and the capillary plates only reflected a restricted diffusion process within the structure.We experimentally evaluated the characteristics of simple restricted diffusion to reveal the transitional relationship of the diffusion coefficient with diffusion time, structure scale, and temperature through composite measurement.

Assessment of Mechanically Induced Changes in Helical Fiber Microstructure Using Diffusion Tensor Imaging

Noninvasive methods to detect microstructural changes in collagen-based fibrous tissues are necessary to differentiate healthy from damaged tissues in vivo but are sparse. Diffusion Tensor Imaging (DTI) is a noninvasive imaging technique used to quantitatively infer tissue microstructure with previous work primarily focused in neuroimaging applications. Yet, it is still unclear how DTI metrics relate to fiber microstructure and function in musculoskeletal tissues such as ligament and tendon, in part because of the high heterogeneity inherent to such tissues. To address this limitation, we assessed the ability of DTI to detect microstructural changes caused by mechanical loading in tissue-mimicking helical fiber constructs of known structure. Using high-resolution optical and micro-computed tomography imaging, we found that static and fatigue loading resulted in decreased sample diameter and a re-alignment of the macro-scale fiber twist angle similar with the direction of loading. However, DTI and micro-computed tomography measurements suggest microstructural differences in the effect of static versus fatigue loading that were not apparent at the bulk level. Specifically, static load resulted in an increase in diffusion anisotropy and a decrease in radial diffusivity suggesting radially uniform fiber compaction. In contrast, fatigue loads resulted in increased diffusivity in all directions and a change in the alignment of the principal diffusion direction away from the constructs' main axis suggesting fiber compaction and microstructural disruptions in fiber architecture. These results provide quantitative evidence of the ability of DTI to detect mechanically induced changes in tissue microstructure that are not apparent at the bulk level, thus confirming its potential as a noninvasive measure of microstructure in helically architected collagen-based tissues, such as ligaments and tendons.

CACTUS: a computational framework for generating realistic white matter microstructure substrates

Monte-Carlo diffusion simulations are a powerful tool for validating tissue microstructure models by generating synthetic diffusion-weighted magnetic resonance images (DW-MRI) in controlled environments. This is fundamental for understanding the link between micrometre-scale tissue properties and DW-MRI signals measured at the millimetre-scale, optimizing acquisition protocols to target microstructure properties of interest, and exploring the robustness and accuracy of estimation methods. However, accurate simulations require substrates that reflect the main microstructural features of the studied tissue. To address this challenge, we introduce a novel computational workflow, CACTUS (Computational Axonal Configurator for Tailored and Ultradense Substrates), for generating synthetic white matter substrates. Our approach allows constructing substrates with higher packing density than existing methods, up to 95% intra-axonal volume fraction, and larger voxel sizes of up to 500μm3 with rich fibre complexity. CACTUS generates bundles with angular dispersion, bundle crossings, and variations along the fibres of their inner and outer radii and g-ratio. We achieve this by introducing a novel global cost function and a fibre radial growth approach that allows substrates to match predefined targeted characteristics and mirror those reported in histological studies. CACTUS improves the development of complex synthetic substrates, paving the way for future applications in microstructure imaging.

Insights into Infusion-Based Targeted Drug Delivery in the Brain: Perspectives, Challenges and Opportunities

Targeted drug delivery in the brain is instrumental in the treatment of lethal brain diseases, such as glioblastoma multiforme, the most aggressive primary central nervous system tumour in adults. Infusion-based drug delivery techniques, which directly administer to the tissue for local treatment, as in convection-enhanced delivery (CED), provide an important opportunity; however, poor understanding of the pressure-driven drug transport mechanisms in the brain has hindered its ultimate success in clinical applications. In this review, we focus on the biomechanical and biochemical aspects of infusion-based targeted drug delivery in the brain and look into the underlying molecular level mechanisms. We discuss recent advances and challenges in the complementary field of medical robotics and its use in targeted drug delivery in the brain. A critical overview of current research in these areas and their clinical implications is provided. This review delivers new ideas and perspectives for further studies of targeted drug delivery in the brain.

A multi-modality medical imaging head and neck phantom: Part 2. Medical imaging

The head and neck phantom discussed in an accompanying paper (part 1), is imaged with MRI, X-ray CT, PET and ultrasound. MRI scans show a distinct image contrast between the brain compartment and other anatomical regions of the head. The silicone matrix that was used to create a porous brain compartment has a relatively high proton density and a spin-spin relaxation time (T₂) that is long enough to provide an MRI signal. While the longitudinal magnetization was found to recover according to a mono-exponential, a bi-exponential decay was observed for the transverse relaxation with a slow T₂ relaxation component corresponding to the perfusate and a fast T₂ relaxation component corresponding to the silicone. The fraction of the slow T₂ relaxation component increases upon perfusion. A dynamic contrast enhanced (DCE) MRI experiment is conducted in which the injection rate of the contrast agent is varied. Parametric DCE maps are created and reveal regional differences in contrast agent kinetics as a result of differences in porosity. The skull, vertebra and the brain compartment are clearly visible on X-ray CT. Dynamic PET scanning has been performed while the carotic arterial input function is monitored by use of a Geiger-Müller counter. Similar regions of perfusion are found in the PET study as in the DCE MRI study. By doping the perfusate with a lipid micelle emulsion, the phantom is applicable for carotic Doppler ultrasound demonstration and validation.

Physical and digital phantoms for validating tractography and assessing artifacts

Fiber tractography is widely used to non-invasively map white-matter bundles in vivo using diffusion-weighted magnetic resonance imaging (dMRI). As it is the case for all scientific methods, proper validation is a key prerequisite for the successful application of fiber tractography, be it in the area of basic neuroscience or in a clinical setting. It is well-known that the indirect estimation of the fiber tracts from the local diffusion signal is highly ambiguous and extremely challenging. Furthermore, the validation of fiber tractography methods is hampered by the lack of a real ground truth, which is caused by the extremely complex brain microstructure that is not directly observable non-invasively and that is the basis of the huge network of long-range fiber connections in the brain that are the actual target of fiber tractography methods. As a substitute for in vivo data with a real ground truth that could be used for validation, a widely and successfully employed approach is the use of synthetic phantoms. In this work, we are providing an overview of the state-of-the-art in the area of physical and digital phantoms, answering the following guiding questions: "What are dMRI phantoms and what are they good for?", "What would the ideal phantom for validation fiber tractography look like?" and "What phantoms, phantom datasets and tools used for their creation are available to the research community?". We will further discuss the limitations and opportunities that come with the use of dMRI phantoms, and what future direction this field of research might take.

Quantitative diffusion MRI of the abdomen and pelvis

Diffusion MRI has enormous potential and utility in the evaluation of various abdominal and pelvic disease processes including cancer and noncancer imaging of the liver, prostate, and other organs. Quantitative diffusion MRI is based on acquisitions with multiple diffusion encodings followed by quantitative mapping of diffusion parameters that are sensitive to tissue microstructure. Compared to qualitative diffusion-weighted MRI, quantitative diffusion MRI can improve standardization of tissue characterization as needed for disease detection, staging, and treatment monitoring. However, similar to many other quantitative MRI methods, diffusion MRI faces multiple challenges including acquisition artifacts, signal modeling limitations, and biological variability. In abdominal and pelvic diffusion MRI, technical acquisition challenges include physiologic motion (respiratory, peristaltic, and pulsatile), image distortions, and low signal-to-noise ratio. If unaddressed, these challenges lead to poor technical performance (bias and precision) and clinical outcomes of quantitative diffusion MRI. Emerging and novel technical developments seek to address these challenges and may enable reliable quantitative diffusion MRI of the abdomen and pelvis. Through systematic validation in phantoms, volunteers, and patients, including multicenter studies to assess reproducibility, these emerging techniques may finally demonstrate the potential of quantitative diffusion MRI for abdominal and pelvic imaging applications.

Design and characterization of a 3D-printed axon-mimetic phantom for diffusion MRI

PURPOSE

To introduce and characterize inexpensive and easily produced 3D-printed axon-mimetic diffusion MRI phantoms in terms of pore geometry and diffusion kurtosis imaging metrics.

METHODS

Phantoms were 3D-printed with a composite printing material that, after the dissolution of the polyvinyl alcohol, exhibits microscopic fibrous pores. Confocal microscopy and synchrotron phase-contrast micro-CT imaging were performed to visualize and assess the pore sizes. Diffusion MRI scans of four identical phantoms and phantoms with varying print parameters in water were performed at 9.4 T. Diffusion kurtosis imaging was fit to both data sets and used to assess the reproducibility between phantoms and effects of print parameters on diffusion kurtosis imaging metrics. Identical scans were performed 25 and 76 days later, to test their stability.

RESULTS

Segmentation of pores in three microscopy images yielded a mean, median, and SD of equivalent pore diameters of 7.57 μm, 3.51 μm, and 12.13 μm, respectively. Phantoms had T₁ /T₂ = 2 seconds/180 ms, and those with identical parameters showed a low coefficient of variation (~10%) in mean diffusivity (1.38 × 10^-3 mm² /s) and kurtosis (0.52) metrics and radial diffusivity (1.01 × 10^-3 mm² /s) and kurtosis (1.13) metrics. Printing temperature and speed had a small effect on diffusion kurtosis imaging metrics (< 16%), whereas infill density had a larger and more variable effect (> 16%). The stability analysis showed small changes over 2.5 months (< 7%).

CONCLUSION

Three-dimension-printed axon-mimetic phantoms can mimic the fibrous structure of axon bundles on a microscopic scale, serving as complex, anisotropic diffusion MRI phantoms.

MRI phantom for tissue simulation with respect to diffusion coefficient and kurtosis - Validation with injection of liposomal theranostics

This study presents gelatine-based and agar-based phantoms with an addition of glycerol, safflower oil, silicone oil and cellulose microcrystalline with a potential to cover the entire range of tissue diffusion coefficients and kurtosis values. Forty types of phantoms were prepared and examined for NMR relaxation times T₁ and T₂ and diffusional metrics D, K and ADC. Wide ranges of values of D (0.0003-0.0031 mm²s^-1), K (0.00-7.24) and ADC (0.0002-0.0031 mm²s^-1) were observed. Two of the phantoms closely mimic muscle and cortical gray matter with respect to water diffusion parameters. Although many of the presented phantoms display both D and K values within the range of human tissues, they match different tissues with respect to D and K. The imaging results for the gray matter simulating phantom injected with the liposomal solution, bear a resemblance to the particle size effect described in the literature. The phantoms presented in this work are simple in preparation and affordable tissue-simulating materials to be used primarily in development of diffusion kurtosis-based MRI methods and possibly in a preliminary assessment of MRI contrast agents. Further adjustments of the chemical compositions could potentially lead to development of new types of phantoms mimicking diffusional properties of more kinds of soft tissues.

Realistic Microstructure Simulator (RMS): Monte Carlo simulations of diffusion in three-dimensional cell segmentations of microscopy images

BACKGROUND

Monte Carlo simulations of diffusion are commonly used as a model validation tool as they are especially suitable for generating the diffusion MRI signal in complicated tissue microgeometries.

NEW METHOD

Here we describe the details of implementing Monte Carlo simulations in three-dimensional (3d) voxelized segmentations of cells in microscopy images. Using the concept of the corner reflector, we largely reduce the computational load of simulating diffusion within and exchange between multiple cells. Precision is further achieved by GPU-based parallel computations.

RESULTS

Our simulation of diffusion in white matter axons segmented from a mouse brain demonstrates its value in validating biophysical models. Furthermore, we provide the theoretical background for implementing a discretized diffusion process, and consider the finite-step effects of the particle-membrane reflection and permeation events, needed for efficient simulation of interactions with irregular boundaries, spatially variable diffusion coefficient, and exchange.

COMPARISON WITH EXISTING METHODS

To our knowledge, this is the first Monte Carlo pipeline for MR signal simulations in a substrate composed of numerous realistic cells, accounting for their permeable and irregularly-shaped membranes.

CONCLUSIONS

The proposed RMS pipeline makes it possible to achieve fast and accurate simulations of diffusion in realistic tissue microgeometry, as well as the interplay with other MR contrasts. Presently, RMS focuses on simulations of diffusion, exchange, and T₁ and T₂ NMR relaxation in static tissues, with a possibility to straightforwardly account for susceptibility-induced T₂^* effects and flow.

Challenges for biophysical modeling of microstructure

The biophysical modeling efforts in diffusion MRI have grown considerably over the past 25 years. In this review, we dwell on the various challenges along the journey of bringing a biophysical model from initial design to clinical implementation, identifying both hurdles that have been already overcome and outstanding issues. First, we describe the critical initial task of selecting which features of tissue microstructure can be estimated using a model and which acquisition protocol needs to be implemented to make the estimation possible. The model performance should necessarily be tested in realistic numerical simulations and in experimental data - adapting the fitting strategy accordingly, and parameter estimates should be validated against complementary techniques, when/if available. Secondly, the model performance and validity should be explored in pathological conditions, and, if appropriate, dedicated models for pathology should be developed. We build on examples from tumors, ischemia and demyelinating diseases. We then discuss the challenges associated with clinical translation and added value. Finally, we single out four major unresolved challenges that are related to: the availability of a microstructural ground truth, the validation of model parameters which cannot be accessed with complementary techniques, the development of a generalized standard model for any brain region and pathology, and the seamless communication between different parties involved in the development and application of biophysical models of diffusion.

Optimization and numerical evaluation of multi-compartment diffusion MRI using the spherical mean technique for practical multiple sclerosis imaging

BACKGROUND

The multi-compartment diffusion MRI using the spherical mean technique (SMT) has been suggested to enhance the pathological specificity to tissue injury in multiple sclerosis (MS) imaging, but its accuracy and precision have not been comprehensively evaluated.

METHODS

A Cramer-Rao Lower Bound method was used to optimize an SMT protocol for MS imaging. Finite difference computer simulations of spins in packed cylinders were then performed to evaluate the influences of five realistic pathological features in MS lesions: axon diameter, axon density, free water fraction, axonal crossing, dispersion, and undulation.

RESULTS

SMT derived metrics can be biased by some confounds of pathological variations, such as axon size and free water fraction. However, SMT in general provides valuable information to characterize pathological features in MS lesions with a clinically feasible protocol.

CONCLUSION

SMT may be used as a practical MS imaging method and should be further improved in clinical MS imaging.

Apparent diffusion coefficient measured by diffusion MRI of moving and deforming domains

The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torrey equation, describing the complex transverse magnetization due to diffusion-encoding magnetic field gradients, was developed to account for the motion and deformation. In that work, the motivation was to cancel the effect of the motion and deformation in the MRI image and the space scale of interest spans multiple voxels. In the present work, we adapt the mathematical equation to study the diffusion MRI signal at the much smaller scale of biological cells. We start with the Bloch-Torrey equation defined on a cell that is moving and deforming and linearize the equation around the magnitude of the diffusion-encoding gradient. The result is a second order signal model in which the linear term gives the imaginary part of the diffusion MRI signal and the quadratic term gives the apparent diffusion coefficient (ADC) attributable to the biological cell. We numerically validate this model for a variety of motions and deformations.

Dedicated diffusion phantoms for the investigation of free water elimination and mapping: insights into the influence of T2 relaxation properties

Conventional diffusion-weighted (DW) MRI suffers from free water contamination due to the finite voxel size. The most common case of free water contamination occurs with cerebrospinal fluid (CSF) in voxels located at the CSF-tissue interface, such as at the ventricles in the human brain. Another case refers to intra-tissue free water as in vasogenic oedema. In order to avoid the bias in diffusion metrics, several multi-compartment methods have been introduced, which explicitly model the presence of a free water compartment. However, fitting multi-compartment models in DW MRI represents a well known ill conditioned problem. Although during the last decade great effort has been devoted to mitigating this estimation problem, the research field remains active. The aim of this work is to introduce the design, characterise the NMR properties and demonstrate the use of two dedicated anisotropic diffusion fibre phantoms, useful for the study of free water elimination (FWE) and mapping models. In particular, we investigate the recently proposed FWE diffusion tensor imaging approach, which takes explicit account of differences in the transverse relaxation times between the free water and tissue compartments.

Robust Monte-Carlo Simulations in Diffusion-MRI: Effect of the Substrate Complexity and Parameter Choice on the Reproducibility of Results

Monte-Carlo Diffusion Simulations (MCDS) have been used extensively as a ground truth tool for the validation of microstructure models for Diffusion-Weighted MRI. However, methodological pitfalls in the design of the biomimicking geometrical configurations and the simulation parameters can lead to approximation biases. Such pitfalls affect the reliability of the estimated signal, as well as its validity and reproducibility as ground truth data. In this work, we first present a set of experiments in order to study three critical pitfalls encountered in the design of MCDS in the literature, namely, the number of simulated particles and time steps, simplifications in the intra-axonal substrate representation, and the impact of the substrate's size on the signal stemming from the extra-axonal space. The results obtained show important changes in the simulated signals and the recovered microstructure features when changes in those parameters are introduced. Thereupon, driven by our findings from the first studies, we outline a general framework able to generate complex substrates. We show the framework's capability to overcome the aforementioned simplifications by generating a complex crossing substrate, which preserves the volume in the crossing area and achieves a high packing density. The results presented in this work, along with the simulator developed, pave the way toward more realistic and reproducible Monte-Carlo simulations for Diffusion-Weighted MRI.

Single- and double-Diffusion encoding MRI for studying ex vivo apparent axon diameter distribution in spinal cord white matter

Mapping average axon diameter (AAD) and axon diameter distribution (ADD) in neuronal tissues non-invasively is a challenging task that may have a tremendous effect on our understanding of the normal and diseased central nervous system (CNS). Water diffusion is used to probe microstructure in neuronal tissues, however, the different water populations and barriers that are present in these tissues turn this into a complex task. Therefore, it is not surprising that recently we have witnessed a burst in the development of new approaches and models that attempt to obtain, non-invasively, detailed microstructural information in the CNS. In this work, we aim at challenging and comparing the microstructural information obtained from single diffusion encoding (SDE) with double diffusion encoding (DDE) MRI. We first applied SDE and DDE MR spectroscopy (MRS) on microcapillary phantoms and then applied SDE and DDE MRI on an ex vivo porcine spinal cord (SC), using similar experimental conditions. The obtained diffusion MRI data were fitted by the same theoretical model, assuming that the signal in every voxel can be approximated as the superposition of a Gaussian-diffusing component and a series of restricted components having infinite cylindrical geometries. The diffusion MRI results were then compared with histological findings. We found a good agreement between the fittings and the experimental data in white matter (WM) voxels of the SC in both diffusion MRI methods. The microstructural information and apparent AADs extracted from SDE MRI were found to be similar or somewhat larger than those extracted from DDE MRI especially when the diffusion time was set to 40 ms. The apparent ADDs extracted from SDE and DDE MRI show reasonable agreement but somewhat weaker correspondence was observed between the diffusion MRI results and histology. The apparent subtle differences between the microstructural information obtained from SDE and DDE MRI are briefly discussed.

The reproducibility of measurements using a standardization phantom for the evaluation of fractional anisotropy (FA) derived from diffusion tensor imaging (DTI)

OBJECTIVES

It is necessary to standardize the examination procedure and diagnostic criteria of diffusion tensor imaging (DTI). Thus, the purpose of this study was to examine the reproducibility of measurements using a standardization phantom composed of different fibre materials with different fibre densities (FDs) for the evaluation of fractional anisotropy (FA) derived from DTI.

MATERIALS AND METHODS

Two types of fibre materials wrapped in heat-shrinkable tubes were used as fibre phantoms. We designed fibre phantoms with three different FDs of each fibre material. The standardization phantom was examined using DTI protocol six times a day, and each examination session was repeated once a month for 7 consecutive months. Fibre tracking was performed by setting regions of interest in the FA map, and FA was measured in each fibre phantom. Coefficients of variation (CVs) were used to evaluate the inter-examination reproducibility of FA values. Furthermore, Bland-Altman plots were used to evaluate the intra-operator reproducibility of FA measurements.

RESULTS

All CVs for each fibre phantom were within 2% throughout the 7-month study of repeated DTI sessions. The high intra-operator reproducibility of the FA measurement was confirmed.

DISCUSSION

High reproducibility of measurements using a standardization phantom for the evaluation of FA was achieved.

Development of anisotropic phantoms using wood and fiber materials for diffusion tensor imaging and diffusion kurtosis imaging

Objective

Several studies have demonstrated that anisotropic phantoms can be utilized for diffusion magnetic resonance imaging. The purpose of our study was to examine whether wood is suitable as an anisotropic phantom material from the viewpoints of affordability and availability. In the current study, wood was used for restricted diffusion, and fibers were used for hindered diffusion.

Materials and methods

Wood and fiber phantoms were made. Diffusion kurtosis images were acquired with three magnetic resonance scanners. Fractional anisotropy, radial diffusivity, axial diffusivity, radial kurtosis and axial kurtosis values were measured. The wood phantom was imaged, and its durability was confirmed. The phantoms were imaged in varying orientations within the magnetic field. The wood was observed using an optical microscope.

Results

Ten kinds of wood and the fiber had a diffusion metrics. The wood diffusion metrics suggested low variation over a period of 9 months. Changing the orientation of the phantoms within the magnetic field resulted in changes in diffusion metrics. Observation of wood vessels and fibers was conducted.

Discussion

Wood and fibers have anisotropy and are promising as phantom materials. The development of anisotropic phantoms that anyone can use is useful for diffusion magnetic resonance imaging research and clinical applications.

Ex vivo diffusion MRI of the human brain: Technical challenges and recent advances

This review discusses ex vivo diffusion magnetic resonance imaging (dMRI) as an important research tool for neuroanatomical investigations and the validation of in vivo dMRI techniques, with a focus on the human brain. We review the challenges posed by the properties of post-mortem tissue, and discuss state-of-the-art tissue preparation methods and recent advances in pulse sequences and acquisition techniques to tackle these. We then review recent ex vivo dMRI studies of the human brain, highlighting the validation of white matter orientation estimates and the atlasing and mapping of large subcortical structures. We also give particular emphasis to the delineation of layered gray matter structure with ex vivo dMRI, as this application illustrates the strength of its mesoscale resolution over large fields of view. We end with a discussion and outlook on future and potential directions of the field.

Investigation of anisotropic fishing line-based phantom as tool in quality control of diffusion tensor imaging

This work proposes a low-cost, fishing line-based phantom for quality control of diffusion tensor imaging (DTI). The device was applied to investigate the relationship between DTI indexes (DTIi) and imaging acquisition parameters. A Dyneema^® fishing line phantom was built with fiber bundles of different thicknesses. DTI acquisitions were performed in a 3T magnetic resonance imaging scanner using an 8-channel and a 32-channel head coil. For each coil, the following acquisition parameters were changed, one at a time: diffusion sensitivity factor (b value), echo time, sensitivity encoding, voxel size, number of signal averages, and number of diffusion gradient directions (NDGD). DTIi including fractional anisotropy, relative anisotropy (RA), linear anisotropy (CL), and planar anisotropy (CP) were calculated for each image; the data were analyzed using the coefficient of variation (CV) and distributions of DTIi values. The 32-channel head coil presented higher CV values for the DTIi RA, CL, and CP when voxel size was changed. Using the phantom, dependences between diffusion-related parameters (b value and NDGD) and DTIi were also observed; the majority of these were for the smaller thickness fiber bundles. The device proved to be useful for the verification of the DTI performance over time.

Towards microstructure fingerprinting: Estimation of tissue properties from a dictionary of Monte Carlo diffusion MRI simulations

Many closed-form analytical models have been proposed to relate the diffusion-weighted magnetic resonance imaging (DW-MRI) signal to microstructural features of white matter tissues. These models generally make assumptions about the tissue and the diffusion processes which often depart from the biophysical reality, limiting their reliability and interpretability in practice. Monte Carlo simulations of the random walk of water molecules are widely recognized to provide near groundtruth for DW-MRI signals. However, they have mostly been limited to the validation of simpler models rather than used for the estimation of microstructural properties. This work proposes a general framework which leverages Monte Carlo simulations for the estimation of physically interpretable microstructural parameters, both in single and in crossing fascicles of axons. Monte Carlo simulations of DW-MRI signals, or fingerprints, are pre-computed for a large collection of microstructural configurations. At every voxel, the microstructural parameters are estimated by optimizing a sparse combination of these fingerprints. Extensive synthetic experiments showed that our approach achieves accurate and robust estimates in the presence of noise and uncertainties over fixed or input parameters. In an in vivo rat model of spinal cord injury, our approach provided microstructural parameters that showed better correspondence with histology than five closed-form models of the diffusion signal: MMWMD, NODDI, DIAMOND, WMTI and MAPL. On whole-brain in vivo data from the human connectome project (HCP), our method exhibited spatial distributions of apparent axonal radius and axonal density indices in keeping with ex vivo studies. This work paves the way for microstructure fingerprinting with Monte Carlo simulations used directly at the modeling stage and not only as a validation tool.

Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook

Phantoms, both numerical (software) and physical (hardware), can serve as a gold standard for the validation of MRI methods probing the brain microstructure. This review aims to provide guidelines on how to build, implement, or choose the right phantom for a particular application, along with an overview of the current state-of-the-art of phantoms dedicated to study brain microstructure with MRI. For physical phantoms, we discuss the essential requirements and relevant characteristics of both the (NMR visible) liquid and (NMR invisible) phantom materials that induce relevant microstructural features detectable via MRI, based on diffusion, intra-voxel incoherent motion, magnetization transfer or magnetic susceptibility weighted contrast. In particular, for diffusion MRI, many useful phantoms have been proposed, ranging from simple liquids to advanced biomimetic phantoms consisting of hollow or plain microfibers and capillaries. For numerical phantoms, the focus is on Monte Carlo simulations of random walk, for which the basic principles, along with useful criteria to check and potential pitfalls are reviewed, in addition to a literature overview highlighting recent advances. While many phantoms exist already, the current review aims to stimulate further research in the field and to address remaining needs.

Comparison of Glass Capillary Plates and Polyethylene Fiber Bundles as Phantoms to Assess the Quality of Diffusion Tensor Imaging

Purpose:

The purpose of this study was to evaluate the suitability of two phantoms, one made of capillary plates and the other polyethylene fibers, for assessing the quality of diffusion tensor imaging (DTI).

Methods:

The first phantom was a stack of glass capillary plates with many parallel micropores (CP). The second phantom was a bundle of polyethylene fiber Dyneema held together with a thermal shrinkage tube (Dy). High resolution multi-shot echo planar imaging (EPI) DTI acquisitions were performed at b-values of 0 and 1000 s/mm² and diffusion-times (T_diff) of 37.7 and 97.7 ms on a preclinical 7T MRI scanner. Thirty diffusion-encoding directions were used. The data were used to calculate the fractional anisotropy (FA), mean diffusivity (MD), and angular dispersion (AD). Further acquisitions were performed at b-values from 0 to 8000 s/mm² in 14 steps with the diffusion gradient applied parallel (axial) and perpendicular (radial) to the Z direction. On the other hand, the data acquired with a 3T MRI scanner were used to confirm that measurements on a clinical machine are consistent with the 7T MRI results.

Results:

The dependence of FA, MD and AD on T_diff was smaller for the Dy than for the CPs. The b-value-dependent signal attenuations in the axial direction at T_diff = 37.7 and 97.7 ms were similar for both phantoms. In the radial direction, Dy demonstrated similar b-value attenuation to that of in vivo tissue for both T_diffs, but the attenuation for the CPs was affected by the change in T_diff. Parameter estimates were similar for 3T and 7T MRI.

Conclusion:

The characteristics of the CP indicate that it can be used as a restricted-diffusion dominant phantom, while the characteristics of the Dy suggest that it can be used as a hindered-diffusion dominant phantom. Dy may be more suitable than CP for DTI quality control.

Liquid crystal phantom for validation of microscopic diffusion anisotropy measurements on clinical MRI systems

PURPOSE

To develop a phantom for validating MRI pulse sequences and data processing methods to quantify microscopic diffusion anisotropy in the human brain.

METHODS

Using a liquid crystal consisting of water, detergent, and hydrocarbon, we designed a 0.5-L spherical phantom showing the theoretically highest possible degree of microscopic anisotropy. Data were acquired on the Connectome scanner using echo-planar imaging signal readout and diffusion encoding with axisymmetric b-tensors of varying magnitude, anisotropy, and orientation. The mean diffusivity, fractional anisotropy (FA), and microscopic FA (µFA) parameters were estimated.

RESULTS

The phantom was observed to have values of mean diffusivity similar to brain tissue, and relaxation times compatible with echo-planar imaging echo times on the order of 100 ms. The estimated values of µFA were at the theoretical maximum of 1.0, whereas the values of FA spanned the interval from 0.0 to 0.8 as a result of varying orientational order of the anisotropic domains within each voxel.

CONCLUSIONS

The proposed phantom can be manufactured by mixing three widely available chemicals in volumes comparable to a human head. The acquired data are in excellent agreement with theoretical predictions, showing that the phantom is ideal for validating methods for measuring microscopic diffusion anisotropy on clinical MRI systems. Magn Reson Med 79:1817-1828, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

Neurite imaging reveals microstructural variations in human cerebral cortical gray matter

We present distinct patterns of neurite distribution in the human cerebral cortex using diffusion magnetic resonance imaging (MRI). We analyzed both high-resolution structural (T1w and T2w images) and diffusion MRI data in 505 subjects from the Human Connectome Project. Neurite distributions were evaluated using the neurite orientation dispersion and density imaging (NODDI) model, optimized for gray matter, and mapped onto the cortical surface using a method weighted towards the cortical mid-thickness to reduce partial volume effects. The estimated neurite density was high in both somatosensory and motor areas, early visual and auditory areas, and middle temporal area (MT), showing a strikingly similar distribution to myelin maps estimated from the T1w/T2w ratio. The estimated neurite orientation dispersion was particularly high in early sensory areas, which are known for dense tangential fibers and are classified as granular cortex by classical anatomists. Spatial gradients of these cortical neurite properties revealed transitions that colocalize with some areal boundaries in a recent multi-modal parcellation of the human cerebral cortex, providing mutually supportive evidence. Our findings indicate that analyzing the cortical gray matter neurite morphology using diffusion MRI and NODDI provides valuable information regarding cortical microstructure that is related to but complementary to myeloarchitecture.

Validation of diffusion MRI estimates of compartment size and volume fraction in a biomimetic brain phantom using a human MRI scanner with 300 mT/m maximum gradient strength

Diffusion microstructural imaging techniques have attracted great interest in the last decade due to their ability to quantify axon diameter and volume fraction in healthy and diseased human white matter. The estimates of compartment size and volume fraction continue to be debated, in part due to the lack of a gold standard for validation and quality control. In this work, we validate diffusion MRI estimates of compartment size and volume fraction using a novel textile axon ("taxon") phantom constructed from hollow polypropylene yarns with distinct intra- and extra-taxonal compartments to mimic white matter in the brain. We acquired a comprehensive set of diffusion MRI measurements in the phantom using multiple gradient directions, diffusion times and gradient strengths on a human MRI scanner equipped with maximum gradient strength (G_max) of 300 mT/m. We obtained estimates of compartment size and restricted volume fraction through a straightforward extension of the AxCaliber/ActiveAx frameworks that enables estimation of mean compartment size in fiber bundles of arbitrary orientation. The voxel-wise taxon diameter estimates of 12.2 ± 0.9 μm were close to the manufactured inner diameter of 11.8 ± 1.2 μm with G_max = 300 mT/m. The estimated restricted volume fraction demonstrated an expected decrease along the length of the fiber bundles in accordance with the known construction of the phantom. When G_max was restricted to 80 mT/m, the taxon diameter was overestimated, and the estimates for taxon diameter and packing density showed greater uncertainty compared to data with G_max = 300 mT/m. In conclusion, the compartment size and volume fraction estimates resulting from diffusion measurements on a human scanner were validated against ground truth in a phantom mimicking human white matter, providing confidence that this method can yield accurate estimates of parameters in simplified but realistic microstructural environments. Our work also demonstrates the importance of a biologically analogous phantom that can be applied to validate a variety of diffusion microstructural imaging methods in human scanners and be used for standardization of diffusion MRI protocols for neuroimaging research.

Assessing diffusion kurtosis tensor estimation methods using a digital brain phantom derived from human connectome project data

PURPOSE

Diffusion kurtosis imaging (DKI) has gained popularity in recent years as an advanced diffusion-weighted MRI technique. This work aims to quantitatively compare the performance and accuracy of four DKI processing algorithms. For this purpose, a digital DKI brain phantom is developed.

METHODS

Data from the Human Connectome Project database were used to generate a DKI digital phantom. In a Monte Carlo Rician noise simulation, four DKI processing algorithms were compared based on their mean squared error, squared bias, and variance.

RESULTS

Algorithm performance was region-dependent and differed for each diffusion metric and noise level. Crossover between variance and squared bias error occurred between signal-to-noise ratios of 30 and 40.

CONCLUSION

Through the framework presented here, DKI algorithms can be quantitatively compared via a ground truth data set. Error maps are critical as algorithm performance varies spatially. Bias-plus-variance decomposition provides a more complete picture than MSE alone. In combination with refinements in acquisition in future studies, the accuracy and efficiency of DKI will continue to improve promoting clinical adoption.

Increased rate of solvent diffusion in a prototypical supramolecular gel measured on the picosecond timescale

Solvent diffusion in a prototypical supramolecular gel probed by quasi-elastic neutron scattering on the picosecond timescale is faster than that in the respective bulk solvent.

Design and validation of diffusion MRI models of white matter

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the "biological accuracy" of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open questions and converge towards consensus.

Promise and pitfalls of g-ratio estimation with MRI

The fiber g-ratio is the ratio of the inner to the outer diameter of the myelin sheath of a myelinated axon. It has a limited dynamic range in healthy white matter, as it is optimized for speed of signal conduction, cellular energetics, and spatial constraints. In vivo imaging of the g-ratio in health and disease would greatly increase our knowledge of the nervous system and our ability to diagnose, monitor, and treat disease. MRI based g-ratio imaging was first conceived in 2011, and expanded to be feasible in full brain white matter with preliminary results in 2013. This manuscript reviews the growing g-ratio imaging literature and speculates on future applications. It details the methodology for imaging the g-ratio with MRI, and describes the known pitfalls and challenges in doing so.

Temperature and concentration calibration of aqueous polyvinylpyrrolidone (PVP) solutions for isotropic diffusion MRI phantoms

To use the "apparent diffusion coefficient" (Dapp) as a quantitative imaging parameter, well-suited test fluids are essential. In this study, the previously proposed aqueous solutions of polyvinylpyrrolidone (PVP) were examined and temperature calibrations were obtained. For example, at a temperature of 20°C, Dapp ranged from 1.594 (95% CI: 1.593, 1.595) μm2/ms to 0.3326 (95% CI: 0. 3304, 0.3348) μm2/ms for PVP-concentrations ranging from 10% (w/w) to 50% (w/w) using K30 polymer lengths. The temperature dependence of Dapp was found to be so strong that a negligence seems not advisable. The temperature dependence is descriptively modelled by an exponential function exp(c2 (T - 20°C)) and the determined c2 values are reported, which can be used for temperature calibration. For example, we find the value 0.02952 K-1 for 30% (w/w) PVP-concentration and K30 polymer length. In general, aqueous PVP solutions were found to be suitable to produce easily applicable and reliable Dapp-phantoms.

Presence of time-dependent diffusion in the brachial plexus

PURPOSE

This work describes the development of a method to measure the variation of apparent diffusion coefficient (ADC) with diffusion time (Δ) in the brachial plexus, as a potential method of probing microstructure.

METHODS

Diffusion-weighted MRI with body signal suppression was used to highlight the nerves from surrounding tissues, and sequence parameters were optimized for sensitivity to change with diffusion time. A porous media-restricted diffusion model based on the Latour-Mitra equation was fitted to the diffusion time-dependent ADC data from the brachial plexus nerves and cord.

RESULTS

The ADC was observed to reduce at long diffusion times, confirming that diffusion was restricted in the nerves and cord in healthy subjects. T2 of the nerves was measured to be 80 ± 5 ms, the diffusion coefficient was found to vary from (1.5 ± 0.1) × 10^-3 mm² /s at a diffusion time of 18.3 ms to (1.0 ± 0.2) × 10^-3 mm² /s at a diffusion time of 81.3 ms.

CONCLUSION

A novel method of probing restricted diffusion in the brachial plexus was developed. Resulting parameters were comparable with values obtained previously on biological systems. Magn Reson Med 79:789-795, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Monte Carlo Simulations of Diffusion Weighted MRI in Myocardium: Validation and Sensitivity Analysis

A model of cardiac microstructure and diffusion MRI is presented, and compared with experimental data from ex vivo rat hearts. The model includes a simplified representation of individual cells, with physiologically correct cell size and orientation, as well as intra- to extracellular volume ratio. Diffusion MRI is simulated using a Monte Carlo model and realistic MRI sequences. The results show good correspondence between the simulated and experimental MRI signals. Similar patterns are observed in the eigenvalues of the diffusion tensor, the mean diffusivity (MD), and the fractional anisotropy (FA). A sensitivity analysis shows that the diffusivity is the dominant influence on all three eigenvalues of the diffusion tensor, the MD, and the FA. The area and aspect ratio of the cell cross-section affect the secondary and tertiary eigenvalues, and hence the FA. Within biological norms, the cell length, volume fraction of cells, and rate of change of helix angle play a relatively small role in influencing tissue diffusion. Results suggest that the model could be used to improve understanding of the relationship between cardiac microstructure and diffusion MRI measurements, as well as in testing and refinement of cardiac diffusion MRI protocols.

Anisotropic diffusion phantoms based on microcapillaries

Diffusion MRI is an efficient and widely used technique for the investigation of tissue structure and organisation in vivo. Multiple phenomenological and biophysical diffusion models are intensively exploited for the analysis of the diffusion experiments. However, the verification of the applied diffusion models remains challenging. In order to provide a "gold standard" and to assess the accuracy of the derived parameters and the limitations of the diffusion models, anisotropic diffusion phantoms with well known architecture are demanded. In the present work we built four anisotropic diffusion phantoms consisting of hollow microcapillaries with very small inner diameters of 5, 10 and 20μm and outer diameters of 90 and 150μm. For testing the suitability of these phantoms, we performed diffusion measurements on all of them and evaluated the resulting data with a set of popular diffusion models, such as diffusion tensor and diffusion kurtosis imaging, a two compartment model with intra- and extra-capillary water spaces using bi-exponential fitting, and time-dependent diffusion coefficients in Mitra's limit. The perspectives and limitations of these diffusion phantoms are presented and discussed.

Concerning the matching of magnetic susceptibility differences for the compensation of background gradients in anisotropic diffusion fibre phantoms

Artificial, anisotropic fibre phantoms are nowadays increasingly used in the field of diffusion-weighted MRI. Such phantoms represent useful tools for, among others, the calibration of pulse sequences and validation of diffusion models since they can mimic well-known structural features of brain tissue on the one hand, but exhibit a reduced complexity, on the other. Among all materials, polyethylene fibres have been widely used due to their excellent properties regarding the restriction of water diffusion and surface relaxation properties. Yet the magnetic susceptibility of polyethylene can be distinctly lower than that of distilled water. This difference produces strong microscopic, background field gradients in the vicinity of fibre bundles which are not parallel to the static magnetic field. This, in turn, modulates the MRI signal behaviour. In the present work we investigate an approach to reduce the susceptibility-induced background gradients via reducing the heterogeneity in the internal magnetic susceptibility. An aqueous solution of magnesium chloride hexahydrate (MgCl₂·6H₂O) is used for this purpose. Its performance is demonstrated in dedicated anisotropic fibre phantoms with different geometrical configurations.

Validation of surface-to-volume ratio measurements derived from oscillating gradient spin echo on a clinical scanner using anisotropic fiber phantoms

A diffusion measurement in the short-time surface-to-volume ratio (S/V) limit (Mitra et al., Phys Rev Lett. 1992;68:3555) can disentangle the free diffusion coefficient from geometric restrictions to diffusion. Biophysical parameters, such as the S/V of tissue membranes, can be used to estimate microscopic length scales non-invasively. However, due to gradient strength limitations on clinical MRI scanners, pulsed gradient spin echo (PGSE) measurements are impractical for probing the S/V limit. To achieve this limit on clinical systems, an oscillating gradient spin echo (OGSE) sequence was developed. Two phantoms containing 10 fiber bundles, each consisting of impermeable aligned fibers with different packing densities, were constructed to achieve a range of S/V values. The frequency-dependent diffusion coefficient, D(ω), was measured in each fiber bundle using OGSE with different gradient waveforms (cosine, stretched cosine, and trapezoidal), while D(t) was measured from PGSE and stimulated-echo measurements. The S/V values derived from the universal high-frequency behavior of D(ω) were compared against those derived from quantitative proton density measurements using single spin echo (SE) with varying echo times, and from magnetic resonance fingerprinting (MRF). S/V estimates derived from different OGSE waveforms were similar and demonstrated excellent correlation with both SE- and MRF-derived S/V measures (ρ  ≥  0.99). Furthermore, there was a smoother transition between OGSE frequency f and PGSE diffusion time when using teffS/V=9/64f, rather than the commonly used t_eff  = 1/(4f), validating the specific frequency/diffusion time conversion for this regime. Our well-characterized fiber phantom can be used for the calibration of OGSE and diffusion modeling techniques, as the S/V ratio can be measured independently using other MR modalities. Moreover, our calibration experiment offers an exciting perspective of mapping tissue S/V on clinical systems.

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.

AxonPacking: An Open-Source Software to Simulate Arrangements of Axons in White Matter

HIGHLIGHTS

AxonPacking: Open-source software for simulating white matter microstructure.

Validation on a theoretical disk packing problem.

Reproducible and stable for various densities and diameter distributions.

Can be used to study interplay between myelin/fiber density and restricted fraction.

Quantitative Magnetic Resonance Imaging (MRI) can provide parameters that describe white matter microstructure, such as the fiber volume fraction (FVF), the myelin volume fraction (MVF) or the axon volume fraction (AVF) via the fraction of restricted water (fr). While already being used for clinical application, the complex interplay between these parameters requires thorough validation via simulations. These simulations required a realistic, controlled and adaptable model of the white matter axons with the surrounding myelin sheath. While there already exist useful algorithms to perform this task, none of them combine optimisation of axon packing, presence of myelin sheath and availability as free and open source software. Here, we introduce a novel disk packing algorithm that addresses these issues. The performance of the algorithm is tested in term of reproducibility over 50 runs, resulting density, and stability over iterations. This tool was then used to derive multiple values of FVF and to study the impact of this parameter on fr and MVF in light of the known microstructure based on histology sample. The standard deviation of the axon density over runs was lower than 10⁻³ and the expected hexagonal packing for monodisperse disks was obtained with a density close to the optimal density (obtained: 0.892, theoretical: 0.907). Using an FVF ranging within [0.58, 0.82] and a mean inter-axon gap ranging within [0.1, 1.1] μm, MVF ranged within [0.32, 0.44] and fr ranged within [0.39, 0.71], which is consistent with the histology. The proposed algorithm is implemented in the open-source software AxonPacking (https://github.com/neuropoly/axonpacking) and can be useful for validating diffusion models as well as for enabling researchers to study the interplay between microstructure parameters when evaluating qMRI methods.

Diffusion tensor imaging and histology of developing hearts

Diffusion tensor imaging (DTI) has emerged as a promising method for noninvasive quantification of myocardial microstructure. However, the origin and behavior of DTI measurements during myocardial normal development and remodeling remain poorly understood. In this work, conventional and bicompartmental DTI in addition to three-dimensional histological correlation were performed in a sheep model of myocardial development from third trimester to postnatal 5 months of age. Comparing the earliest time points in the third trimester with the postnatal 5 month group, the scalar transverse diffusivities preferentially increased in both left ventricle (LV) and right ventricle (RV): secondary eigenvalues D2 increased by 54% (LV) and 36% (RV), whereas tertiary eigenvalues D3 increased by 85% (LV) and 67% (RV). The longitudinal diffusivity D1 changes were small, which led to a decrease in fractional anisotropy by 41% (LV) and 33% (RV) in 5 month versus fetal hearts. Histological analysis suggested that myocardial development is associated with hyperplasia in the early stages of the third trimester followed by myocyte growth in the later stages up to 5 months of age (increased average myocyte width by 198%, myocyte length by 128%, and decreased nucleus density by 70% between preterm and postnatal 5 month hearts.) In a few histological samples (N = 6), correlations were observed between DTI longitudinal diffusivity and myocyte length (r = 0.86, P < 0.05), and transverse diffusivity and myocyte width (r = 0.96, P < 0.01). Linear regression analysis showed that transverse diffusivities are more affected by changes in myocyte size and nucleus density changes than longitudinal diffusivities, which is consistent with predictions of classical models of diffusion in porous media. Furthermore, primary and secondary DTI eigenvectors during development changed significantly. Collectively, the findings demonstrate a role for DTI to monitor and quantify myocardial development, and potentially cardiac disease. Copyright © 2016 John Wiley & Sons, Ltd.

NMR-based diffusion lattice imaging

Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g., about cell membranes. While it has been shown in recent articles that these experiments can be used to determine the shape of closed pores averaged over a volume of interest, it is still an open question how much information can be gained in open well-connected systems. In this theoretical work, it is shown that the full structure information of connected periodic systems is accessible. To this end, the so-called "SEquential Rephasing by Pulsed field-gradient Encoding N Time intervals" (SERPENT) sequence is used, which employs several diffusion encoding gradient pulses with different amplitudes. Two two-dimensional solid matrices that are surrounded by an NMR-visible medium are considered: a hexagonal lattice of cylinders and a rectangular lattice of isosceles triangles.

D-BRAIN: Anatomically Accurate Simulated Diffusion MRI Brain Data

Diffusion Weighted (DW) MRI allows for the non-invasive study of water diffusion inside living tissues. As such, it is useful for the investigation of human brain white matter (WM) connectivity in vivo through fiber tractography (FT) algorithms. Many DW-MRI tailored restoration techniques and FT algorithms have been developed. However, it is not clear how accurately these methods reproduce the WM bundle characteristics in real-world conditions, such as in the presence of noise, partial volume effect, and a limited spatial and angular resolution. The difficulty lies in the lack of a realistic brain phantom on the one hand, and a sufficiently accurate way of modeling the acquisition-related degradation on the other. This paper proposes a software phantom that approximates a human brain to a high degree of realism and that can incorporate complex brain-like structural features. We refer to it as a Diffusion BRAIN (D-BRAIN) phantom. Also, we propose an accurate model of a (DW) MRI acquisition protocol to allow for validation of methods in realistic conditions with data imperfections. The phantom model simulates anatomical and diffusion properties for multiple brain tissue components, and can serve as a ground-truth to evaluate FT algorithms, among others. The simulation of the acquisition process allows one to include noise, partial volume effects, and limited spatial and angular resolution in the images. In this way, the effect of image artifacts on, for instance, fiber tractography can be investigated with great detail. The proposed framework enables reliable and quantitative evaluation of DW-MR image processing and FT algorithms at the level of large-scale WM structures. The effect of noise levels and other data characteristics on cortico-cortical connectivity and tractography-based grey matter parcellation can be investigated as well.

Degeneracy in model parameter estimation for multi-compartmental diffusion in neuronal tissue

The ultimate promise of diffusion MRI (dMRI) models is specificity to neuronal microstructure, which may lead to distinct clinical biomarkers using noninvasive imaging. While multi-compartment models are a common approach to interpret water diffusion in the brain in vivo, the estimation of their parameters from the dMRI signal remains an unresolved problem. Practically, even when q space is highly oversampled, nonlinear fit outputs suffer from heavy bias and poor precision. So far, this has been alleviated by fixing some of the model parameters to a priori values, for improved precision at the expense of accuracy. Here we use a representative two-compartment model to show that fitting fails to determine the five model parameters from over 60 measurement points. For the first time, we identify the reasons for this poor performance. The first reason is the existence of two local minima in the parameter space for the objective function of the fitting procedure. These minima correspond to qualitatively different sets of parameters, yet they both lie within biophysically plausible ranges. We show that, at realistic signal-to-noise ratio values, choosing between the two minima based on the associated objective function values is essentially impossible. Second, there is an ensemble of very low objective function values around each of these minima in the form of a pipe. The existence of such a direction in parameter space, along which the objective function profile is very flat, explains the bias and large uncertainty in parameter estimation, and the spurious parameter correlations: in the presence of noise, the minimum can be randomly displaced by a very large amount along each pipe. Our results suggest that the biophysical interpretation of dMRI model parameters crucially depends on establishing which of the minima is closer to the biophysical reality and the size of the uncertainty associated with each parameter.

Innovative anisotropic phantoms for calibration of diffusion tensor imaging sequences

The paper describes a novel type of anisotropic phantoms designed for b-matrix spatial distribution diffusion tensor imaging (BSD-DTI). Cubic plate anisotropic phantom, cylinder capillary phantom and water reference phantom are described as a complete set necessary for calibration, validation and normalization of BSD-DTI. An innovative design of the phantoms basing on enclosing the anisotropic cores in glass balls filled with liquid made for the first time possible BSD calibration with usage of echo planar imaging (EPI) sequence. Susceptibility artifacts prone to occur in EPI sequences were visibly reduced in the central region of the phantoms. The phantoms were designed for usage in a clinical scanner's head coil, but can be scaled for other coil or scanner types. The phantoms can be also used for a pre-calibration of imaging of other types of phantoms having more specific applications.

Investigation of resolution effects using a specialized diffusion tensor phantom

PURPOSE

The clinical potential of the diffusion imaging-based analysis of fine brain structures such as fornix or cingulum is high due to the central role of these structures in psychiatric diseases. However, the quantification of diffusion parameters in fine structures is especially prone to partial volume effects (PVEs).

METHODS

In this study, a phantom for the investigation of PVEs and their influence on diffusion parameters in fine structures of different diameter is presented. The phantom is produced by winding wet polyester fibers onto a spindle. The resulting fiber strands have well defined square cross-sections of 1-25 mm(2) and provide a homogeneous and high fractional anisotropy (FA ≈ 0.9).

RESULTS

Several PVEs are demonstrated and analyzed. It is shown that inferred results such as the fiber geometry and diffusion parameters strongly depend on the relative position of the structure of interest to the voxel-grid. Several implications of PVEs on post-processing methods such as Tract-based Spatial Statistics and fiber tractography are demonstrated.

CONCLUSION

These results show that the handling of PVEs in common post-processing tasks can be problematic, and that the presented phantom provides a valuable tool for the improvement and evaluation of these effects.

Simulation of changes in diffusion related to different pathologies at cellular level after traumatic brain injury

PURPOSE

The goal of the current study was to investigate tissue pathology at the cellular level in traumatic brain injury (TBI) as revealed by Monte Carlo simulation of diffusion tensor imaging (DTI)-derived parameters and elucidate the possible sources of conflicting findings of DTI abnormalities as reported in the TBI literature.

METHODS

A model with three compartments separated by permeable membranes was employed to represent the diffusion environment of water molecules in brain white matter. The dynamic diffusion process was simulated with a Monte Carlo method using adjustable parameters of intra-axonal diffusivity, axon separation, glial cell volume fraction, and myelin sheath permeability. The effects of tissue pathology on DTI parameters were investigated by adjusting the parameters of the model corresponding to different stages of brain injury.

RESULTS

The results suggest that the model is appropriate and the DTI-derived parameters simulate the predominant cellular pathology after TBI. Our results further indicate that when edema is not prevalent, axial and radial diffusivity have better sensitivity to axonal injury and demyelination than other DTI parameters.

CONCLUSION

DTI is a promising biomarker to detect and stage tissue injury after TBI. The observed inconsistencies among previous studies are likely due to scanning at different stages of tissue injury after TBI. Magn Reson Med 76:290-300, 2016. © 2015 Wiley Periodicals, Inc.

Anisotropic phantoms in Magnetic Resonance Imaging

Even though Magnetic Resonance Imaging (MRI) gives possibility to obtain qualitatively very good images, most quantitative results obtained by means of MRI are biased with high dependence on particular hardware parameters, imaging sequence used, and properties of analysed sample. Thus to enable comparison between results obtained on different scanners a calibration is needed. In one of the approaches to Diffusion Tensor Imaging (DTI), a B-matrix Spatial Distribution DTI (BSD-DTI) anisotropic phantoms are crucial in precise determination of the diffusion tensor. Anisotropic phantoms can be also useful as a porosity models or rock models in geology. The paper focuses on characterization of several anisotropic phantoms and describes their applications in DTI, and other domains related to MRI.

Mesoscopic structure of neuronal tracts from time-dependent diffusion

Interpreting brain diffusion MRI measurements in terms of neuronal structure at a micrometer level is an exciting unresolved problem. Here we consider diffusion transverse to a bundle of fibers, and show theoretically, as well as using Monte Carlo simulations and measurements in a phantom made of parallel fibers mimicking axons, that the time dependent diffusion coefficient approaches its macroscopic limit slowly, in a (ln t)/t fashion. The logarithmic singularity arises due to short range disorder in the fiber packing. We identify short range disorder in axonal fibers based on histological data from the splenium, and argue that the time dependent contribution to the overall diffusion coefficient from the extra-axonal water dominates that of the intra-axonal water. This dominance may explain the bias in measuring axon diameters in clinical settings. The short range disorder is also reflected in the asymptotically linear frequency dependence of the diffusion coefficient measured with oscillating gradients, in agreement with recent experiments. Our results relate the measured diffusion to the mesoscopic structure of neuronal tissue, uncovering the sensitivity of diffusion metrics to axonal arrangement within a fiber tract, and providing an alternative interpretation of axonal diameter mapping techniques.