Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

Statistical model for diffusion-weighted imaging (DWI) has been proposed for better tissue characterization by introducing a distribution function for apparent diffusion coefficients (ADC) to account for the restrictions and hindrances to water diffusion in biological tissues. This paper studies the precision and uncertainty in the estimation of parameters for statistical DWI model with Gaussian distribution, i.e. the position of distribution maxima (Dm) and the distribution width (σ), by using non-linear least-square (NLLS) fitting. Numerical simulation shows that precise parameter estimation, particularly for σ, imposes critical requirements on the extremely high signal-to-noise ratio (SNR) of DWI signal when NLLS fitting is used. Unfortunately, such extremely high SNR may be difficult to achieve for the normal setting of clinical DWI scan. For Dm and σ parameter mapping of in vivo human brain, multiple local minima are found and result in large uncertainties in the estimation of distribution width σ. The estimation error by using NLLS fitting originates primarily from the insensitivity of DWI signal intensity to distribution width σ, as given in the function form of the Gaussian-type statistical DWI model.

Age- and gender-related changes in the normal human brain using hybrid diffusion imaging (HYDI)

PurposeTo develop a biomimetic tumor tissue phantom which more closely reflects water diffusion in biological tissue than previously used phantoms, and to evaluate the stability of the phantom and its potential as a tool for validating diffusion‐weighted (DW) MRI measurements.MethodsCoaxial‐electrospraying was used to generate micron‐sized hollow polymer spheres, which mimic cells. The bulk structure was immersed in water, providing a DW‐MRI phantom whose apparent diffusion coefficient (ADC) and microstructural properties were evaluated over a period of 10 months. Independent characterization of the phantom's microstructure was performed using scanning electron microscopy (SEM). The repeatability of the construction process was investigated by generating a second phantom, which underwent high resolution synchrotron‐CT as well as SEM and MR scans.ResultsADC values were stable (coefficients of variation (CoVs) < 5%), and varied with diffusion time, with average values of 1.44 ± 0.03 µm2/ms (Δ = 12 ms) and 1.20 ± 0.05 µm2/ms (Δ = 45 ms). Microstructural parameters showed greater variability (CoVs up to 13%), with evidence of bias in sphere size estimates. Similar trends were observed in the second phantom.ConclusionA novel biomimetic phantom has been developed and shown to be stable over 10 months. It is envisaged that such phantoms will be used for further investigation of microstructural models relevant to characterizing tumor tissue, and may also find application in evaluating acquisition protocols and comparing DW‐MRI‐derived biomarkers obtained from different scanners at different sites. Magn Reson Med 80:147–158, 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 License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch–Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization is done using the explicit Runge–Kutta–Chebyshev method, which is more efficient than the forward Euler time discretization for diffusive-type problems. We use this approach to simulate the diffusion MRI signal from the extra-cylindrical compartment in a tissue model of the brain gray matter consisting of cylindrical and spherical cells and illustrate the effect of cell membrane permeability.

In this chapter, we present methods to analyze three types of diffusion-weighted imaging (DWI), i.e., diffusion tensor imaging (DTI), Q-ball imaging (QBI), and diffusion spectrum imaging (DSI). DWI is one of the methods to measure water diffusion in tissues. It provides unique biologically and clinically relevant information that is not available from other imaging modalities. Because of its noninvasive nature, DWI has been applied widely in many studies, including but not limited to fiber tracts in cerebral cortex. We will begin with the physical background of diffusion MRI (dMRI), and then we will present method to compute the apparent diffusion coefficient (ADC) map and the eigenvalues for DTI study. After that, we introduce the measures for the water diffusion anisotropy and give one example fiber tractography method using DTI.

ObjectiveTo explore the value of quantitative parameters derived from diffusion spectrum imaging (DSI) in preoperatively predicting human epidermal growth factor receptor 2 (HER2) status in patients with breast cancer.MethodsIn this prospective study, 114 and 56 female patients with invasive ductal carcinoma were consecutively included in a derivation cohort and an independent validation cohort, respectively. Each patient was categorized into HER2-positive or HER2-negative groups based on the pathologic result. All patients underwent DSI and conventional MRI including dynamic contrast-enhanced MRI (DCE-MRI) and diffusion-weighted imaging (DWI). The tumor size, type of the time-signal intensity curve (TIC) from DCE-MRI, apparent diffusion coefficient (ADC) from DWI, and quantitative parameters derived from DSI, including diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), mean apparent propagator (MAP), and neurite orientation dispersion and density imaging (NODDI) of primary tumors, were measured and compared between the HER2-positive and HER2-negative groups in the derivation cohort. Univariable and multivariable logistic regression analyses were used to determine the potential independent predictors of HER2 status. The discriminative ability of quantitative parameters was assessed by receiver operating characteristic (ROC) curve analyses and validated in the independent cohort.ResultsIn the derivation cohort, the tumor size, TIC type, and ADC values did not differ between the HER2-positive and HER2-negative groups (p = 0.126–0.961). DSI quantitative parameters including axial kurtosis of DKI (DKI_AK), non-Gaussianity (MAP_NG), axial non-Gaussianity (MAP_NGAx), radial non-Gaussianity (MAP_NGRad), return-to-origin probability (MAP_RTOP), return-to-axis probability of MAP (MAP_RTAP), and intracellular volume fraction of NODDI (NODDI_ICVF) were lower in the HER2-positive group than in the HER2-negative group (p ≤ 0.001–0.035). DSI quantitative parameters including radial diffusivity (DTI_RD), mean diffusivity of DTI (DTI_MD), mean squared diffusion (MAP_MSD), and q-space inverse variance of MAP (MAP_QIV) were higher in the HER2-positive group than in the HER2-negative group (p = 0.016–0.049). The ROC analysis showed that the area under the curve (AUC) of ADC was 0.632 and 0.568, respectively, in the derivation and validation cohorts. The AUC values of DSI quantitative parameters ranged from 0.628 to 0.700 and from 0.673 to 0.721, respectively, in the derivation and validation cohorts. Logistic regression analysis showed that only NODDI_ICVF was an independent predictor of HER2 status (p = 0.001), with an AUC of 0.700 and 0.721, respectively, in the derivation and validation cohorts.ConclusionsDSI could be helpful for preoperative prediction of HER2, but DSI alone may not be sufficient in predicting HER2 status preoperatively in patients with breast cancer.

Based on Brownian motion, diffusion statement of proton hydro inside body is one of the most important variables affected on the diagnosis, treatment planning, and disease response to treatment. There are some different kinds of diffusion-weighted magnetic resonance imaging types such as diffusion-weighted imaging, diffusion tensor imaging, diffusion kurtosis imaging, intravoxel incoherent motion imaging, zoom diffusion imaging, and diffusion spectrum imaging. In this short communication, we aimed to introduce clinical applications of these diffusion-weighted magnetic resonance imaging types.

A diffusion-weighted (DW) template in a standard coordinate system is often necessary for the analysis of white matter (WM) structures using DW images. Although several DW templates have been constructed in the ICBM-152 space, a template for diffusion spectrum imaging (DSI) is still lacking. In this study, we developed a DSI template in the ICBM-152 space from 122 healthy adults. This high quality template, NTU-DSI-122, was built through incorporating the macroscopic anatomical information using high-resolution T1 -weighted images and the microscopic structural information obtained from DSI datasets. Two evaluations were conducted to examine the quality of NTU-DSI-122. The first evaluation examined the anatomical consistency of NTU-DSI-122 in matching to the ICBM-152 coordinate system. The results showed that this template matched to the ICBM-152 templates very well across the whole brain, not only in the deep white matter regions as other DW templates but also in the superficial white matter regions. In the second evaluation, a large number of independent diffusion tensor imaging (DTI) datasets were registered to the DTI template derived from NTU-DSI-122. The examination was performed by quantifying the anatomical consistency among the registered DTI datasets. The results showed that using NTU-DSI-122 as the registration template the registered DTI datasets can achieve high anatomical alignment. Both evaluations demonstrate that NTU-DSI-122 is a useful high quality DW template. Therefore, NTU-DSI-122 can serve as a representative DSI dataset for a healthy adult population, and will be of potential value for brain research and clinical applications. The NTU-DSI-122 template is available at http://www.nitrc.org/projects/ntu-dsi-122/.

Over the last few years, diffusion-weighted imaging (DWI) has become increasingly relevant in the diagnostic assessment of peritoneal carcinomatosis. The aim of this study was to investigate the benefits of high-b DWI (c-DWI) compared to standard DWI in patients with peritoneal carcinomatosis. A cohort of 40 patients with peritoneal carcinomatosis were included in this retrospective study. DWI was performed with b-values of 50, 400, and 800 or 1000 s/mm² on a 1.5-T magnetic resonance imaging (MRI) scanner. C-DWI was calculated using a mono-exponential model with high b-values of 1000, 2000, 3000, 4000, and 5000 s/mm². All c-DWI images with high b-values were compared in terms of volume, detectability of peritoneal lesions, and image quality with the DWI sequence acquired with a b-value of 800 or 1000 s/mm² by two readers. In the group with a b-value of 800 s/mm², there was no statistically significant difference in terms of lesion volume. In the second group with a b-value of 1000 s/mm², peritoneal carcinomatosis lesions were statistically significantly larger than in the c-DWI with a- high b-value of 2000 s/mm² (median 7 cm³, range 1–26 cm³vs. median 6 cm³, range 1–83 cm³, p < 0.05). In both groups, there was a marked decrease in the detectability of peritoneal lesions starting at b = 2000 s/mm². In addition, image quality decreased noticeably from c-DWI at b = 3000 s/mm². In both groups, all images with high b-values at b = 4000 s/mm² and 5000 s/mm² were not diagnostically valuable due to poor image quality. The c-DWI technique offers good diagnostic performance without additional scanning time. High c-DWI b-values up to b = 1000 s/mm² provide comparable detectability of peritoneal carcinomatosis compared to standard DWI. Higher b-values over 1500 s/mm² result in lower image quality, which might lead to misdiagnosis.

The study of complex computational systems is facilitated by network maps, such as circuit diagrams. Such mapping is particularly informative when studying the brain, as the functional role that a brain area fulfills may be largely defined by its connections to other brain areas. In this report, we describe a novel, non-invasive approach for relating brain structure and function using magnetic resonance imaging (MRI). This approach, a combination of structural imaging of long-range fiber connections and functional imaging data, is illustrated in two distinct cognitive domains, visual attention and face perception. Structural imaging is performed with diffusion-weighted imaging (DWI) and fiber tractography, which track the diffusion of water molecules along white-matter fiber tracts in the brain (Figure 1). By visualizing these fiber tracts, we are able to investigate the long-range connective architecture of the brain. The results compare favorably with one of the most widely-used techniques in DWI, diffusion tensor imaging (DTI). DTI is unable to resolve complex configurations of fiber tracts, limiting its utility for constructing detailed, anatomically-informed models of brain function. In contrast, our analyses reproduce known neuroanatomy with precision and accuracy. This advantage is partly due to data acquisition procedures: while many DTI protocols measure diffusion in a small number of directions (e.g., 6 or 12), we employ a diffusion spectrum imaging (DSI)(1, 2) protocol which assesses diffusion in 257 directions and at a range of magnetic gradient strengths. Moreover, DSI data allow us to use more sophisticated methods for reconstructing acquired data. In two experiments (visual attention and face perception), tractography reveals that co-active areas of the human brain are anatomically connected, supporting extant hypotheses that they form functional networks. DWI allows us to create a "circuit diagram" and reproduce it on an individual-subject basis, for the purpose of monitoring task-relevant brain activity in networks of interest.

Diffusion-weighted magnetic resonance imaging is an advanced imaging technique that provides detailed information for clinical diagnosis and treatment monitoring. The purpose of this thesis is to establish fractional dynamic models for better characterising anomalous diffusion in biological tissues of the human brain and explore reliable numerical methods. The introduced generalised fractional operators and variable diffusion coefficients provide more possibilities for capturing structural heterogeneity and diffusion complexities in biological tissues. Robust and efficient numerical methods are developed to solve the proposed fractional systems with lower computational costs.

The purpose of this study was to determine the difference in discrimination between high- and low-grade supratentorial nonenhancing gliomas (HGGs and LGGs, respectively) when using apparent diffusion coefficient (ADC) values with high or standard b-value. Thirty-nine patients underwent conventional magnetic resonance imaging and diffusion-weighted imaging (DWI) with standard and high b-values (b = 1000 and 3000s/mm2, respectively). Minimum, maximum, and mean ADC values (ADCMIN, ADCMAX, and ADCMEAN, respectively) were measured from ADC maps with both b-values. Receiver operating curve analysis was used to determine the cutoff ADC values for distinguishing between nonenhancing HGGs and LGGs. ADCMIN, ADCMAX, and ADCMEAN values for the nonenhancing HGGs were lower than those for LGGs. These differences were much larger when a high b-value was used (all P < 0.0001) than when a standard b-value was used (P = 0.0001, <0.0001, and <0.0001, respectively). Discriminant analysis indicated that the greatest likelihood for discriminating HGGs and LGGs when ADCMEAN was obtained with a high b-value, with cutoff value of 0.814 × 10-3mm2/s. ADC values obtained with a high b-value can be useful for grading and surgical management of nonenhancing HGGs and LGGs. The lowest degree of overlap was obtained when ADCMEAN was determined with a b-value of 3000s/mm2.

Over the past few years, diffusion-weighted imaging (DWI) has become an increasingly important diagnostic tool in the diagnosis of liver lesions. The objective of the present study was to evaluate the diagnostic benefit of high b-value computed diffusion-weighted imaging (c-DWI) compared with standard DWI in patients with hepatocellular carcinoma (HCC) and whether there is an association with microvascular invasion (MVI). In total, 37 patients with histopathologically confirmed HCC were retrospectively ana-lyzed. DWI was acquired with b-values of 50, 400, and 800 or 1000 s/mm² on a 1.5 T magnetic resonance imaging (MRI) scanner. The c-DWI was calculated using a monoexponential model with high b-values of 1000, 2000, 3000, 4000, and 5000 s/mm². All high b-value c-DWI images were compared to the standard DWI in terms of volume, detectability of hepatic lesions, and image quality. Regarding lesion volume and image quality there were no statistically significant differences between standard and c-DWI. HCC lesions measured on DWI images were statistically significantly larger compared to c-DWI images starting from a b value of 2000 s/mm2 (DWI vs. c-DWI b 2000 s/mm2: 2 cm3 [1-12] cm3 vs. 1 cm3 [0-17] cm3, p < 0.05). Moreover, there was deterioration of image quality starting at b = 2000 s/mm2. There were no significant differences in terms of lesion signal intensity in DWI and c-DWI images. There were no differences for the DWI parameters according to MVI status. C-DWI images with high b-values up to b = 1000 s/mm2 demonstrate comparable detectability of HCC compared to standard DWI. The investigated DWI parameters were not associated with MVI status. Further research is needed to evaluate the potential benefit of high b-value c-DWI.

The non-Gaussian noise distribution in magnitude Diffusion-Weighted Images (DWIs) can severely affect the estimation and reconstruction of the true diffusion signal. As a consequence, also the estimated diffusion metrics can be biased. We study the effect of phase correction, a procedure that re-establishes the Gaussianity of the noise distribution in DWIs by taking into account the corresponding phase images. We quantify the debiasing effects of phase correction in terms of diffusion signal estimation and calculated metrics. We perform in silico experiments based on a MGH Human Connectome Project dataset and on a digital phantom, accounting for different acquisition schemes, diffusion-weightings, signal to noise ratios, and for metrics based on Diffusion Tensor Imaging and on Mean Apparent Propagator Magnetic Resonance Imaging, i.e. q-space metrics. We show that phase correction is still a challenge, but also an effective tool to debias the estimation of diffusion signal and metrics from DWIs, especially at high b-values.

Distortion correction of high b-valued and high angular resolution diffusion images using iterative simulated images