Mapping the parameter space of a T2-dependent model of water diffusion MR in brain tissue

We present a new model for describing the diffusion-weighted (DW) proton nuclear magnetic resonance signal obtained from normal grey matter. Our model is analytical and, in some respects, is an extension of earlier model schemes. We model tissue as composed of three separate compartments with individual properties of diffusion and transverse relaxation. Our study assumes slow exchange between compartments. We attempt to take cell morphology into account, along with its effect on water diffusion in tissues. Using this model, we simulate diffusion-sensitive MR signals and compare model output to experimental data from human grey matter. In doing this comparison, we perform a global search for good fits in the parameter space of the model. The characteristic nonmonoexponential behavior of the signal as a function of experimental b value is reproduced quite well, along with established values for tissue-specific parameters such as volume fraction, tortuosity and apparent diffusion coefficient. We believe that the presented approach to modeling diffusion in grey matter adds new aspects to the treatment of a longstanding problem.     

Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation

Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on diffusion-weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (mm(2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology.     

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.     

Investigation of laminar appearance of articular cartilage by means of magnetic resonance microscopy

Magnetic resonance (MR) images and relaxation and diffusion maps of articular cartilage were obtained to explain discrepancies in its MR appearance. Porcine specimens were studied only by MR microscopy. For human specimens a combination of MR microscopy and large-scale MR imaging was used. Common features in the laminar structures of human and porcine samples are described. It was found that the decay of transverse magnetization was nonexponential with a rapidly decaying component which prevented construction of reliable proton-density maps. Dependence of T₂ values on the orientation of specimens in the magnetic field as well as magnetization transfer experiments supported the previous suggestions about a significant role of dipolar interaction with protons of collagen in the laminar appearance of articular cartilage. The loss of the laminar structure induced by rotation of the human cartilage specimen around the axis normal to its surface demonstrated nonuniform angular distribution of the collagen fibers within the layer.     

Study of water diffusion in human dentin by optical coherent tomography

The diffusion of chemical agents in dental tissues is of interest for many problems of dental tissue physiology (diffusion of liquor and water), dental healing (diffusion of preparations), and cosmetic dental treatment (diffusion of whitening agents). The water diffusion in samples of human dentin was monitored using optical coherent tomography (OCT). This diffusion manifests itself as a change in the slope and amplitude of the OCT signal from the sample. It is shown that the average dentin permeability with respect to water is (15.11 ± 21.73) × 10⁻⁶ cm/s. These experimental results demonstrate the OCT efficiency for studying the diffusion in hard biological tissues.     

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.     

Numerical simulations of short-mixing-time double-wave-vector diffusion-weighting experiments with multiple concatenations on whole-body MR systems

Double- or two-wave-vector diffusion-weighting experiments with short mixing times in which two diffusion-weighting periods are applied in direct succession, are a promising tool to estimate cell sizes in the living tissue. However, the underlying effect, a signal difference between parallel and antiparallel wave vector orientations, is considerably reduced for the long gradient pulses required on whole-body MR systems. Recently, it has been shown that multiple concatenations of the two wave vectors in a single acquisition can double the modulation amplitude if short gradient pulses are used. In this study, numerical simulations of such experiments were performed with parameters achievable with whole-body MR systems. It is shown that the theoretical model yields a good approximation of the signal behavior if an additional term describing free diffusion is included. More importantly, it is demonstrated that the shorter gradient pulses sufficient to achieve the desired diffusion weighting for multiple concatenations, increase the signal modulation considerably, e.g. by a factor of about five for five concatenations. Even at identical echo times, achieved by a shortened diffusion time, a moderate number of concatenations significantly improves the signal modulation. Thus, experiments on whole-body MR systems may benefit from multiple concatenations.     

MRI texture analysis on texture test objects, normal brain and intracranial tumors

Texture analysis was performed in three different MRI units on T1 and T2-weighted MR images from 10 healthy volunteers and 63 patients with histologically confirmed intracranial tumors. The goal of this study was a multicenter evaluation of the usefulness of this quantitative approach for the characterization of healthy and pathologic human brain tissues (white matter, gray matter, cerebrospinal fluid, tumors and edema). Each selected brain region of interest was characterized with both its mean gray level values and several texture parameters. Multivariate statistical analyses were then applied in order to discriminate each brain tissue type represented by its own set of texture parameters. Texture analysis was previously performed on test objects to evaluate the method dependence on acquisition parameters and consequently the interest of a multicenter evaluation. Even obtained on different sites with their own acquisition routine protocol, MR brain images contain textural features that can reveal discriminant factors for tissue classification and image segmentation. It can also offer additional information in case of undetermined diagnosis or to develop a more accurate tumor grading.     

Assessment of in vitro vs. in vivo lung structure using hyperpolarized helium-3 diffusion magnetic resonance imaging

The purpose of this study was to assess the properties of a model system for hyperpolarized He-3 (HHe) diffusion MR imaging created from the lungs of New Zealand white rabbits by drying the lungs while inflated at constant pressure. The dried lungs were prepared by sacrificing the animal, harvesting the lungs en bloc and dehydrating the lungs for several days using dry compressed air. In four rabbits, the apparent diffusion coefficient (ADC) of HHe gas was measured in vivo and, within 1 week, in vitro in the dried lungs. To assess long-term repeatability, in vitro ADC values were measured again 3 months later. Dried lungs from four additional rabbits were imaged twice on the same day to assess the short-term repeatability of ADC measurements, and tissue samples from these lungs were then removed for histology. In vivo and in vitro ADC maps showed similar features and similar distributions of ADC values; mean in vivo and in vitro ADC values differed by less than 12%. The in vitro mean ADC values were highly reproducible, with no more than 5% difference between measurements for the short-term repeatability and less than 17% difference between measurements for the long-term repeatability. Histological samples from the dried lungs demonstrated that the lung structure remained intact. These results suggest that the dried lungs are a useful and inexpensive alternative to human or in vivo animal studies for HHe diffusion MR sequence development, testing and optimization.     

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.     

Rates of rotational diffusion and Heisenberg spin exchange as obtained from CW ESR and ESR tomographic experiments on model systems and human skin

The purpose of the present paper is to describe possibilities and limitations for the determination of the rates of rotational diffusion and Heisenberg spin exchange, obtained from continuous-wave electron spin resonance (cw ESR) and ESR tomographic experiments. Model systems including nitroxides as paramagnetic reporter molecules have been examined in order to verify data, which have been obtained from cw ESR and ESR tomography. This has been done with particular emphasis on checking the influence of concentration, temperature, and viscosity on the spectral-spatial properties. These findings have been applied to the evaluation of penetration and permeation studies on human skin. The extracted full spectral information from ESR tomography allows the determination of the above mentioned dynamic parameters for model systems of definite geometry and for samples of human skin. It has been found that the signal-to-noise ratio is critical for all discussed applications.     

Optical anisotropy of a biological tissue under conditions of immersion clearing and without them

The optical anisotropy of a biological tissue is studied under conditions of immersion clearing of the tissue and without them. It is shown that the rate of immersion clearing of a biological tissue depends on its type and is determined by the rate of diffusion of immersion liquids into the sample. The parameters that characterize the rate of diffusion of an immersion liquid into a biological tissue are determined. The types of anisotropy of different samples of biological tissues are found. Based on the Müller matrix formalism, a model for calculating the spectrum of collimated polarized transmission of a biological tissue is constructed. Comparison of calculated and experimental transmission spectra of biological tissues showed their good quantitative coincidence.     

q-Space high b value diffusion MRI of hemi-crush in rat spinal cord: evidence for spontaneous regeneration

The development of the damage following hemi-crush trauma in rat spinal cord was studied ex vivo using high b value (bmax = 1 x 10(7) s cm(-2)) q-space diffusion weighted MRI (DWI) at five days, ten days and six weeks post-trauma. Rat spinal cord trauma, produced by hemi-crush of 15s and 60s duration, was studied. The water signal decay in these diffusion experiments was found to be non mono-exponential and was analyzed using the q-space approach. The q-space MRI parameters were compared with T1 and T2 MR images, behavioral tests and histopathological osmium staining. A very good anatomical correlation was found between the q-space MRI parameters and the osmium staining. Interestingly, we found that in the 15s hemi-crush model significant recovery was observed in both the q-space MR images and the osmium staining six weeks post-trauma. However, in the 60s hemi-crush trauma model very little recovery was observed. These results paralleled those obtained from behavioral tests demonstrating that partial spontaneous recovery seems to occur in the 15s hemi-crush spinal cord model, which should be taken in consideration when using it to evaluate new therapies.     

MR cell size imaging with temporal diffusion spectroscopy

Cytological features such as cell size and intracellular morphology provide fundamental information on cell status and hence may provide specific information on changes that arise within biological tissues. Such information is usually obtained by invasive biopsy in current clinical practice, which suffers several well-known disadvantages. Recently, novel MRI methods such as IMPULSED (imaging microstructural parameters using limited spectrally edited diffusion) have been developed for direct measurements of mean cell size non-invasively. The IMPULSED protocol is based on using temporal diffusion spectroscopy (TDS) to combine measurements of water diffusion over a wide range of diffusion times to probe cellular microstructure over varying length scales. IMPULSED has been shown to provide rapid, robust, and reliable mapping of mean cell size and is suitable for clinical imaging. More recently, cell size distributions have also been derived by appropriate analyses of data acquired with IMPULSED or similar sequences, which thus provides MRI-cytometry. This review summarizes the basic principles, practical implementations, validations, and example applications of MR cell size imaging based on TDS and demonstrates how cytometric information can be used in various applications. In addition, the limitations and potential future directions of MR cytometry are identified including the diagnosis of nonalcoholic steatohepatitis of the liver and the assessment of treatment response of cancers.     

Neural Computation of Wide Aperture Dimension of Optimum Gain Pyramidal Horn

A new method based on the multilayered perceptron neural network architecture for computing the wide aperture dimension of the pyramidal horn is presented. The computed wide aperture dimension is used in successfully designing optimum gain pyramidal horn. The other design parameters of the horn are determined from the simple and explicit analytical formulas. These formulas do not need the application of the iterative methods, and are not restricted to the high gain horn designs. The gain of a designed pyramidal horn is determined with no path length error approximation. Better accuracy with respect to the previous design methods is obtained for various pyramidal horn design examples.     

Reduced field-of-view DTI segmentation of cervical spine tissue

The number of diffusion tensor imaging (DTI) studies regarding the human spine has considerably increased and it is challenging because of the spine’s small size and artifacts associated with the most commonly used clinical imaging method. A novel segmentation method based on the reduced field-of-view (rFOV) DTI dataset is presented in cervical spinal canal cerebrospinal fluid, spinal cord grey matter and white matter classification in both healthy volunteers and patients with neuromyelitis optica (NMO) and multiple sclerosis (MS). Due to each channel based on high resolution rFOV DTI images providing complementary information on spinal tissue segmentation, we want to choose a different contribution map from multiple channel images. Via principal component analysis (PCA) and a hybrid diffusion filter with a continuous switch applied on fourteen channel features, eigen maps can be obtained and used for tissue segmentation based on the Bayesian discrimination method. Relative to segmentation by a pair of expert readers, all of the automated segmentation results in the experiment fall in the good segmentation area and performed well, giving an average segmentation accuracy of about 0.852 for cervical spinal cord grey matter in terms of volume overlap. Furthermore, this has important applications in defining more accurate human spinal cord tissue maps when fusing structural data with diffusion data. rFOV DTI and the proposed automatic segmentation outperform traditional manual segmentation methods in classifying MR cervical spinal images and might be potentially helpful for detecting cervical spine diseases in NMO and MS.     

Application of hierarchical clustering to multi-parametric MR in prostate: Differentiation of tumor and normal tissue with high accuracy

PurposeHierarchical clustering (HC), an unsupervised machine learning (ML) technique, was applied to multi-parametric MR (mp-MR) for prostate cancer (PCa). The aim of this study is to demonstrate HC can diagnose PCa in a straightforward interpretable way, in contrast to deep learning (DL) techniques.MethodsHC was constructed using mp-MR including intravoxel incoherent motion, diffusion kurtosis imaging, and dynamic contrast-enhanced MRI from 40 tumor and normal tissues in peripheral zone (PZ) and 23 tumor and normal tissues in transition zone (TZ). HC model was optimized by assessing the combinations of several dissimilarity and linkage methods. Goodness of HC model was validated by internal methods.ResultsAccuracy for differentiating tumor and normal tissue by optimal HC model was 96.3% in PZ and 97.8% in TZ, comparable to current clinical standards. Relationship between input (DWI and permeability parameters) and output (tumor and normal tissue cluster) was shown by heat maps, consistent with literature.ConclusionHC can accurately differentiate PCa and normal tissue, comparable to state-of-the-art diffusion based parameters. Contrary to DL techniques, HC is an operator-independent ML technique producing results that can be interpreted such that the results can be knowledgeably judged.     

A nonrigid registration algorithm for longitudinal breast MR images and the analysis of breast tumor response

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can estimate parameters relating to blood flow and tissue volume fractions and therefore may be used to characterize the response of breast tumors to treatment. To assess treatment response, values of these DCE-MRI parameters are observed at different time points during the course of treatment. We propose a method whereby DCE-MRI data sets obtained in separate imaging sessions can be co-registered to a common image space, thereby retaining spatial information so that serial DCE-MRI parameter maps can be compared on a voxel-by-voxel basis. In performing inter-session breast registration, one must account for patient repositioning and breast deformation, as well as changes in tumor shape and volume relative to other imaging sessions. One challenge is to optimally register the normal tissues while simultaneously preventing tumor distortion. We accomplish this by extending the adaptive bases algorithm through adding a tumor-volume preserving constraint in the cost function. We also propose a novel method to generate the simulated breast magnetic resonance (MR) images, which can be used to evaluate the proposed registration algorithm quantitatively. The proposed nonrigid registration algorithm is applied to both simulated and real longitudinal 3D high resolution MR images and the obtained transformations are then applied to lower resolution physiological parameter maps obtained via DCE-MRI. The registration results demonstrate the proposed algorithm can successfully register breast MR images acquired at different time points and allow for analysis of the registered parameter maps.