A simple noise correction scheme for diffusional kurtosis imaging

Diffusion kurtosis imaging and standard diffusion imaging in the magnetic resonance imaging assessment of prostate cancer

Background and Objective

In recent years, magnetic resonance imaging (MRI) has shown excellent results in the study of the prostate gland. MRI has indeed shown to be advantageous in the prostate cancer (PCa) detection, as in guiding targeting biopsy, improving its diagnostic yield. Although current acquisition protocols provide for multiparametric acquisition, recent evidence has shown that biparametric protocols can be non-inferior in PCa detection. Diffusion-weighted imaging (DWI) sequence, in particular, plays a key role, particularly in the peripheral zone which accounts for the larger part of the prostate. High b-values are generally recommended, although with the possibility of obtaining non-Gaussian diffusion effects, which requires a more sophisticated model for the analysis, namely through the diffusion kurtosis imaging (DKI). Purpose of this narrative review was to analyze the current applications and clinical evidence regarding the use of DKI with a main focus on PCa detection, also in comparison with DWI.

Methods

This narrative review synthesized the findings of literature retrieved from main researches, narrative and systematic reviews, and meta-analyses obtained from PubMed.

Key Content and Findings

DKI analyses the non-Gaussian water diffusivity and describe the effect of signal intensity decay related to high b-value through two main metrics (Dapp and Kapp). Differently from DWI-apparent diffusion coefficient (DWI-ADC) which reflects only water restriction outside of cells, DKI metrics are supposed to represent also the direct interaction of water molecules with cell membranes and intracellular compounds. This review describes current evidence on ADC and DKI metrics in clinical imaging, and finally collect the results derived from the main articles focused on DWI and DKI models in detecting PCa.

Conclusions

DKI advantages, compared to conventional ADC analysis, still remain controversial. Wider application and greater technical knowledge of DKI, however, may help in proving its intrinsic validity in the field of oncology and therefore in the study of clinically significant PCa. Finally, a deep understanding of DKI is important for radiologists to better understand what Kapp and Dapp mean in the context of different cancer and how these metrics may vary specifically in PCa imaging.

Influence of adaptive denoising on Diffusion Kurtosis Imaging at 3T and 7T

BACKGROUND AND OBJECTIVE

Choosing the most appropriate denoising method to improve the quality of diagnostic images maximally is key in pre-processing of diffusion MRI images. Recent advancements in acquisition and reconstruction techniques have questioned traditional noise estimation methods favoring adaptive denoising frameworks, circumventing the need to know a priori information that is hardly available in a clinical setting. In this observational study, we compared two innovative adaptive techniques sharing some features, Patch2Self and Nlsam, through application on reference adult data at 3T and 7T. The primary aim was identifying the most effective method in case of Diffusion Kurtosis Imaging (DKI) data - particularly susceptible to noise and signal fluctuations - at 3T and 7T fields. A side goal consisted of investigating the dependence of kurtosis metrics' variability with respect to the magnetic field on the adopted denoising methodology.

METHODS

For comparison purposes, we focused on qualitative and quantitative analysis of DKI data and related microstructural maps before and after applying the two denoising approaches. Specifically, we assessed computational efficiency, preservation of anatomical details via perceptual metrics, consistency of microstructure model fitting, alleviation of degeneracies in model estimation, and joint variability with varying field strength and denoising method.

RESULTS

Accounting for all these factors, Patch2Self framework has turned out to be specifically suitable for DKI data, with improving performance at 7T. Nlsam method is more robust in alleviating degenerate black voxels while introducing some blurring, which in turn is reflected in an overall loss of image sharpness. Regarding the impact of denoising on field-dependent variability, both methods have been shown to make variations from standard to Ultra-High Field more concordant with theoretical evidence, claiming that kurtosis metrics are sensitive to susceptibility-induced background gradients, directly proportional to the magnetic field strength and sensitive to the microscopic distribution of iron and myelin.

CONCLUSIONS

This study serves as a proof-of-concept stressing the need for an accurate choice of a denoising methodology, specifically tailored for the data under analysis and allowing higher spatial resolution acquisition within clinically compatible timings, with all the potential benefits that improving suboptimal quality of diagnostic images entails.

Axisymmetric diffusion kurtosis imaging with Rician bias correction: A simulation study

PURPOSE

To compare the estimation accuracy of axisymmetric diffusion kurtosis imaging (DKI) and standard DKI in combination with Rician bias correction (RBC).

METHODS

Axisymmetric DKI is more robust against noise-induced variation in the measured signal than standard DKI because of its reduced parameter space. However, its susceptibility to Rician noise bias at low signal-to-noise ratios (SNR) is unknown. Here, we investigate two main questions: first, does RBC improve estimation accuracy of axisymmetric DKI?; second, is estimation accuracy of axisymmetric DKI increased compared to standard DKI? Estimation accuracy was investigated on the five axisymmetric DKI tensor metrics (AxTM): the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor, using a noise simulation study based on synthetic data of tissues with varying fiber alignment and in-vivo data focusing on white matter.

RESULTS

RBC mainly increased accuracy for the parallel AxTM in tissues with highly to moderately aligned fibers. For the perpendicular AxTM, axisymmetric DKI without RBC performed slightly better than with RBC. However, the combination of axisymmetric DKI with RBC was the overall best performing algorithm across all five AxTM in white matter and axisymmetric DKI itself substantially improved accuracy in axisymmetric tissues with low fiber alignment.

CONCLUSION

Combining axisymmetric DKI with RBC facilitates accurate DKI parameter estimation at unprecedented low SNRs ( ≈ 15 $$ \approx 15 $$ ) in white matter, possibly making it a valuable tool for neuroscience and clinical research studies where scan time is a limited resource. The tools used here are available in the open-source ACID toolbox for SPM.

Optimization of quasi-diffusion magnetic resonance imaging for quantitative accuracy and time-efficient acquisition

PURPOSE

Quasi-diffusion MRI (QDI) is a novel quantitative technique based on the continuous time random walk model of diffusion dynamics. QDI provides estimates of the diffusion coefficient, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mspace/> <mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> in mm²  s^-1 and a fractional exponent, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> , defining the non-Gaussianity of the diffusion signal decay. Here, the b-value selection for rapid clinical acquisition of QDI tensor imaging (QDTI) data is optimized.

METHODS

Clinically appropriate QDTI acquisitions were optimized in healthy volunteers with respect to a multi-b-value reference (MbR) dataset comprising 29 diffusion-sensitized images arrayed between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn></mml:mrow> <mml:annotation>$$ b=0 $$</mml:annotation></mml:semantics> </mml:math> and 5000 s mm^-2 . The effects of varying maximum b-value ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> ), number of b-value shells, and the effects of Rician noise were investigated.

RESULTS

QDTI measures showed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> dependence, most significantly for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> in white matter, which monotonically decreased with higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}} $$</mml:annotation></mml:semantics> </mml:math> leading to improved tissue contrast. Optimized 2 b-value shell acquisitions showed small systematic differences in QDTI measures relative to MbR values, with overestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mspace/> <mml:mspace/> <mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ \kern0.50em {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and underestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> in white matter, and overestimation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> anisotropies in gray and white matter. Additional shells improved the accuracy, precision, and reliability of QDTI estimates with 3 and 4 shells at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:mn>5000</mml:mn></mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}}=5000 $$</mml:annotation></mml:semantics> </mml:math>  s mm^-2 , and 4 b-value shells at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>b</mml:mi> <mml:mi>max</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:mn>3960</mml:mn></mml:mrow> <mml:annotation>$$ {b}_{\mathrm{max}}=3960 $$</mml:annotation></mml:semantics> </mml:math>  s mm^-2 , providing minimal bias in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>D</mml:mi> <mml:mrow><mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {D}_{1,2} $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow> <mml:annotation>$$ \upalpha $$</mml:annotation></mml:semantics> </mml:math> compared to the MbR.

CONCLUSION

A highly detailed optimization of non-Gaussian dMRI for in vivo brain imaging was performed. QDI provided robust parameterization of non-Gaussian diffusion signal decay in clinically feasible imaging times with high reliability, accuracy, and precision of QDTI measures.

In vivo Correlation Tensor MRI reveals microscopic kurtosis in the human brain on a clinical 3T scanner

Diffusion MRI (dMRI) has become one of the most important imaging modalities for noninvasively probing tissue microstructure. Diffusional Kurtosis MRI (DKI) quantifies the degree of non-gaussian diffusion, which in turn has been shown to increase sensitivity towards, e.g., disease and orientation mapping in neural tissue. However, the specificity of DKI is limited as different sources can contribute to the total intravoxel diffusional kurtosis, including: variance in diffusion tensor magnitudes (K_iso), variance due to diffusion anisotropy (K_aniso), and microscopic kurtosis (μK) related to restricted diffusion, microstructural disorder, and/or exchange. Interestingly, μK is typically ignored in diffusion MRI signal modeling as it is assumed to be negligible in neural tissues. However, recently, Correlation Tensor MRI (CTI) based on Double-Diffusion-Encoding (DDE) was introduced for kurtosis source separation, revealing non negligible μK in preclinical imaging. Here, we implemented CTI for the first time on a clinical 3T scanner and investigated the sources of total kurtosis in healthy subjects. A robust framework for kurtosis source separation in humans is introduced, followed by estimation of μK (and the other kurtosis sources) in the healthy brain. Using this clinical CTI approach, we find that μK significantly contributes to total diffusional kurtosis both in gray and white matter tissue but, as expected, not in the ventricles. The first μK maps of the human brain are presented, revealing that the spatial distribution of μK provides a unique source of contrast, appearing different from isotropic and anisotropic kurtosis counterparts. Moreover, group average templates of these kurtosis sources have been generated for the first time, which corroborated our findings at the underlying individual-level maps. We further show that the common practice of ignoring μK and assuming the multiple gaussian component approximation for kurtosis source estimation introduces significant bias in the estimation of other kurtosis sources and, perhaps even worse, compromises their interpretation. Finally, a twofold acceleration of CTI is discussed in the context of potential future clinical applications. We conclude that CTI has much potential for future in vivo microstructural characterizations in healthy and pathological tissue.

A Joint Framework for Denoising and Estimating Diffusion Kurtosis Tensors Using Multiple Prior Information

Diffusion kurtosis imaging (DKI) has been shown to be valuable in a wide range of neuroscientific and clinical applications. However, reliable estimation of DKI tensors is often compromised by noise, especially for the kurtosis tensor (KT). Here, we propose a joint denoising and estimating framework that integrates multiple sources of prior information, including nonlocal structural self-similarity (NSS), local spatial smoothness (LSS), physical relevance (PR) of the DKI model, and noise characteristics of magnitude diffusion MRI (dMRI) images for improved estimation of DKI tensors. The local and nonlocal spatial smoothing constraints are complementary to each other, making the proposed framework highly effective in reducing the noise fluctuations on DKI tensors, especially KT. As an additional refinement, we propose to impose a physically relevant constraint within our joint denoising and estimation framework. We further adopt the first-moment noise-corrected fitting model (M¹NCM) to remove the noncentral χ -distribution noise bias. The effectiveness of integrating multiple sources of priors into the joint framework is verified by comparing the proposed M¹NCM-NSS-LSS-PR method with various versions of M¹NCM-based estimators and two state-of-the-art methods. Results show that the proposed method outperformed the compared methods in simulations and in-vivo dMRI datasets of both spatially stationary and nonstationary noise distributions. The in-vivo experiments also show that the proposed M¹NCM-NSS-LSS-PR method was robust to the number of diffusion directions.

Diagnostic Performance of Diffusion MRI for differentiating Benign and Malignant Nonfatty Musculoskeletal Soft Tissue Tumors: A Systematic Review and Meta-analysis

Objective: To evaluate the diagnostic performance of standard diffusion-weighted imaging (DWI), intravoxel incoherent motion (IVIM), and diffusion kurtosis imaging (DKI), for differentiating benign and malignant soft tissue tumors (STTs).

Materials and methods: A thorough search was carried out to identify suitable studies published up to September 2020. The quality of the studies involved was evaluated using Quality Assessment of Diagnostic Accuracy Studies-2 (QUADAS-2). The pooled sensitivity (SEN), specificity (SPE), and summary receiver operating characteristic (SROC) curve were calculated using bivariate mixed effects models. A subgroup analysis was also performed to explore the heterogeneity.

Results: Eighteen studies investigating 1319 patients with musculoskeletal STTs (malignant, n=623; benign, n=696) were enrolled. Thirteen standard DWI studies using the apparent diffusion coefficient (ADC) showed that the pooled SEN and SPE of ADC were 0.80 (95% CI: 0.77-0.82) and 0.63 (95% CI: 0.60-0.67), respectively. The area under the curve (AUC) calculated from the SROC curve was 0.806. The subgroup analysis indicated that the percentage of myxoid malignant tumors, magnet strength, study design, and ROI placement were significant factors affecting heterogeneity. Four IVIM studies showed that the AUCs calculated from the SROC curves of the parameters ADC and D were 0.859 and 0.874, respectively. The AUCs for the IVIM parameters pseudo diffusion coefficient (D*) and perfusion fraction (f) calculated from the SROC curve were 0.736 and 0.573, respectively. Two DKI studies showed that the AUCs of the DKI parameter mean kurtosis (MK) were 0.97 and 0.89, respectively.

Conclusion: The DWI-derived ADC value and the IVIM DWI-derived D value might be accurate tools for discriminating musculoskeletal STTs, especially for non-myxoid SSTs, using more than two b values, with maximal b value ranging from 600 to 800 s/mm², additionally, a high-field strength (3.0 T) optimizes the diagnostic performance.

Evaluation of peripheral nerve acute crush injury in rabbits: comparison among diffusion kurtosis imaging, diffusion tensor imaging and electromyography

OBJECTIVE

Diffusion kurtosis imaging (DKI) has been proven to provide additional value for assessing many central nervous system diseases compared with conventional diffusion tensor imaging (DTI); however, whether it has the same value in peripheral nerve injury is unclear. This study aimed to investigate the performance of DKI, DTI, and electromyography (EMG) in evaluating peripheral nerve crush injury (PNCI) in rabbits.

MATERIALS AND METHODS

A total of 27 New Zealand white rabbits were selected to establish a PNCI model. Longitudinal DTI, DKI, and EMG were evaluated before surgery and 1 day, 3 days, 1 week, 2 weeks, 4 weeks, 6 weeks, and 8 weeks after surgery. At each time point, two rabbits were randomly selected for pathological examination.

RESULTS

The results showed that fractional anisotropy (FA) derived from both DKI and DTI demonstrated a significant difference between injured and control nerves at all time points (all P < 0.005) mean kurtosis of the injured nerve was lower than that on the control side after 2-8 weeks (all P < 0.05). No statistically significant difference was found in radial kurtosis, axial kurtosis, and apparent diffusion coefficient at almost every time point. The difference in compound muscle action potential (CMAP) of the bilateral gastrocnemius at each time point was statistically significant (all P < 0.001).

CONCLUSIONS

CMAP was a sensitive and reliable method to assess acute PNCI without being affected by perineural edema. DKI may not be superior to DTI in evaluating peripheral nerves, DTI with a shorter scanning time was preferred as an effective choice for evaluating acute peripheral nerve traumatic injury.

Scan Time Reduction in Intravoxel Incoherent Motion Diffusion-Weighted Imaging and Diffusion Kurtosis Imaging of the Abdominal Organs: Using a Simultaneous Multislice Technique With Different Acceleration Factors

OBJECTIVE

To investigate the feasibility of quantitative intravoxel incoherent motion (IVIM) and diffusion kurtosis imaging (DKI) analyses in the upper abdominal organs by simultaneous multislice diffusion-weighted imaging (SMS-DWI).

SUBJECTS AND METHODS

In this prospective study, a total of 32 participants underwent conventional DWI (C-DWI) and SMS-DWI sequences with acceleration factors of 2 and 3 (SMS2-DWI and SMS3-DWI, respectively) in the upper abdomen with multiple b-values (0, 10, 20, 50, 80, 100, 150, 200, 500, 800, 1000, 1500, and 2000 seconds/mm2) on a 3 T system (MAGNETOM Prisma; Siemens Healthcare, Erlangen, Germany). Image quality and quantitatively measurements of apparent diffusion coefficient (ADC), true diffusion coefficient (D), pseudodiffusion coefficient (D*), perfusion fraction (f), mean kurtosis (MK), and mean apparent diffusivity (MD) for the liver, pancreas, kidney cortex and medulla, spleen, and erector spine muscle were compared between the 3 sequences.

RESULTS

The acquisition times for C-DWI, SMS2-DWI, and SMS3-DWI were 10 minutes 57 seconds, 5 minutes 9 seconds, and 3 minutes 54 seconds. For image quality parameters, C-DWI and SMS2-DWI yielded better results than SMS3-DWI (P < 0.05). SMS2-DWI had equivalent IVIM and DKI parameters compared with that of C-DWI (P > 0.05). No statistically significant differences in the ADC, D, f, and MD values between the 3 sequences (P > 0.05) were observed. The D* and MK values of the liver (P = 0.005 and P = 0.012) and pancreas (P = 0.019) between SMS3-DWI and C-DWI were significantly different.

CONCLUSIONS

SMS2-DWI can substantially reduce the scan time while maintaining equivalent IVIM and DKI parameters in the abdominal organs compared with C-DWI.

Artificial intelligence and imaging biomarkers for prostate radiation therapy during and after treatment

Magnetic resonance imaging (MRI) is increasingly used in the management of prostate cancer (PCa). Quantitative MRI (qMRI) parameters, derived from multi-parametric MRI, provide indirect measures of tumour characteristics such as cellularity, angiogenesis and hypoxia. Using Artificial Intelligence (AI), relevant information and patterns can be efficiently identified in these complex data to develop quantitative imaging biomarkers (QIBs) of tumour function and biology. Such QIBs have already demonstrated potential in the diagnosis and staging of PCa. In this review, we explore the role of these QIBs in monitoring treatment response during and after PCa radiotherapy (RT). Recurrence of PCa after RT is not uncommon, and early detection prior to development of metastases provides an opportunity for salvage treatments with curative intent. However, the current method of monitoring treatment response using prostate-specific antigen levels lacks specificity. QIBs, derived from qMRI and developed using AI techniques, can be used to monitor biological changes post-RT providing the potential for accurate and early diagnosis of recurrent disease.

Diffusion kurtosis imaging: correlation analysis of quantitative model parameters with molecular features in advanced lung adenocarcinoma

Background:

Due to development of magnetic resonance-based functional imaging, it is easier to detect micro-structural alterations of tumor tissues. The aim of this study was to conduct a preliminary evaluation of the correlation of non-Gaussian diffusion kurtosis imaging (DKI) parameters with expression of molecular markers (epidermal growth factor receptor [EGFR]; anaplastic lymphoma kinase [ALK]; Ki-67 protein) in patients with advanced lung adenocarcinoma, using routine diffusion-weighted imaging as the reference standard.

Methods:

Data from patients with primary lung adenocarcinoma diagnosed at Cancer Hospital, Chinese Academy of Medical Sciences (CHCAMS) from 2016 to 2019 were collected for retrospective analysis. The pathologic and magnetic resonance imaging data of 96 patients who met the inclusion criteria were included in this study. Specifically, the K_app and D_app parameters measured from the DKI model; apparent diffusion coefficient (ADC) value from the diffusion-weighted imaging model; and the EGFR, ALK, and Ki-67 biomarkers detected by immunohistochemistry and/or molecular biology techniques after biopsy or surgery were evaluated. The relations between quantitative parameters (ADC, K_app, D_app) and pathologic outcomes (EGFR, ALK, and Ki-67 expression) were analyzed by Spearman correlation test.

Results:

Of the 96 lung adenocarcinoma lesions (from 96 patients), the number of EGFR- and ALK-positive and high Ki-67 expressing lesions were 53, 12, and 83, respectively. The K_app values were significantly higher among patients with EGFR-positive mutations (0.81 ± 0.12 vs. 0.66 ± 0.10, t = 6.41, P < 0.001), ALK rearrangement-negative (0.76 ± 0.12 vs. 0.60 ± 0.15, t = 4.09, P < 0.001), and high Ki-67 proliferative index (PI) (0.76 ± 0.12 vs. 0.58 ± 0.13, t = 4.88, P < 0.001). The D_app values were significantly lower among patients with high Ki-67 PI (3.19 ± 0.69 μm²/ms vs. 4.20 ± 0.83 μm²/ms, t = 4.80, P < 0.001) and EGFR-positive mutations (3.11 ± 0.73 μm²/ms vs. 3.59 ± 0.77 μm²/ms, t = 3.12, P = 0.002). The differences in mean D_app (3.73 ± 1.26 μm²/ms vs. 3.26 ± 0.68 μm²/ms, t = 1.96, P = 0.053) or ADC values ([1.34 ± 0.81] × 10⁻³ mm²/s vs. [1.33 ± 0.41] × 10⁻³ mm²/s, t = 0.07, P = 0.941) between the groups with or without ALK rearrangements were not statistically significant. The ADC values were significantly lower among patients with EGFR-positive mutation ([1.19 ± 0.37] × 10⁻³ mm²/s vs. [1.50 ± 0.53] × 10⁻³ mm²/s, t = 3.38, P = 0.001) and high Ki-67 PI ([1.28 ± 0.39] × 10⁻³ mm²/s vs. [1.67 ± 0.77] × 10⁻³ mm²/s, t = 2.88, P = 0.005). K_app was strongly positively correlated with EGFR mutations (r = 0.844, P = 0.008), strongly positively correlated with Ki-67 PI (r = 0.882, P = 0.001), and strongly negatively correlated with ALK rearrangements (r = −0.772, P = 0.001). D_app was moderately correlated with EGFR mutations (r = −0.650, P = 0.024) or Ki-67 PI (r = −0.734, P = 0.012). ADC was moderately correlated with Ki-67 PI (r = −0.679, P = 0.033).

Conclusions:

The K_app value of DKI parameters was strongly correlated with different expression of EGFR, ALK, and Ki-67 in advanced lung adenocarcinoma. The results potentially indicate a surrogate measure of the status of different molecular markers assessed by non-invasive imaging tools.

Non-local means based Rician noise filtering for diffusion tensor and kurtosis imaging in human brain and spinal cord

BACKGROUND

To investigate the effect of using a Rician nonlocal means (NLM) filter on quantification of diffusion tensor (DT)- and diffusion kurtosis (DK)-derived metrics in various anatomical regions of the human brain and the spinal cord, when combined with a constrained linear least squares (CLLS) approach.

METHODS

Prospective brain data from 9 healthy subjects and retrospective spinal cord data from 5 healthy subjects from a 3 T MRI scanner were included in the study. Prior to tensor estimation, registered diffusion weighted images were denoised by an optimized blockwise NLM filter with CLLS. Mean kurtosis (MK), radial kurtosis (RK), axial kurtosis (AK), mean diffusivity (MD), radial diffusivity (RD), axial diffusivity (AD) and fractional anisotropy (FA), were determined in anatomical structures of the brain and the spinal cord. DTI and DKI metrics, signal-to-noise ratio (SNR) and Chi-square values were quantified in distinct anatomical regions for all subjects, with and without Rician denoising.

RESULTS

The averaged SNR significantly increased with Rician denoising by a factor of 2 while the averaged Chi-square values significantly decreased up to 61% in the brain and up to 43% in the spinal cord after Rician NLM filtering. In the brain, the mean MK varied from 0.70 (putamen) to 1.27 (internal capsule) while AK and RK varied from 0.58 (corpus callosum) to 0.92 (cingulum) and from 0.70 (putamen) to 1.98 (corpus callosum), respectively. In the spinal cord, FA varied from 0.78 in lateral column to 0.81 in dorsal column while MD varied from 0.91 × 10^-3 mm²/s (lateral) to 0.93 × 10^-3 mm²/s (dorsal). RD varied from 0.34 × 10^-3 mm²/s (dorsal) to 0.38 × 10^-3 mm²/s (lateral) and AD varied from 1.96 × 10^-3 mm²/s (lateral) to 2.11 × 10^-3 mm²/s (dorsal).

CONCLUSIONS

Our results show a Rician denoising NLM filter incorporated with CLLS significantly increases SNR and reduces estimation errors of DT- and KT-derived metrics, providing the reliable metrics estimation with adequate SNR levels.

Influence of residual fat signal on diffusion kurtosis MRI of suspicious mammography findings

Recent studies showed the potential of diffusion kurtosis imaging (DKI) as a tool for improved classification of suspicious breast lesions. However, in diffusion-weighted imaging of the female breast, sufficient fat suppression is one of the main factors determining the success. In this study, the data of 198 patients examined in two study centres was analysed using standard diffusion and kurtosis evaluation methods and three DKI fitting approaches accounting phenomenologically for fat-related signal contamination of the lesions. Receiver operating characteristic curve analysis showed the highest area under the curve (AUC) for the method including fat correction terms (AUC = 0.85, p < 0.015) in comparison to the values obtained with the standard diffusion (AUC = 0.77) and kurtosis approach (AUC = 0.79). Comparing the two study centres, the AUC value improved from 0.77 to 0.86 (p = 0.036) using a fat correction term for the first centre, while no significant difference with no adverse effects was observed for the second centre (AUC 0.89 vs. 0.90, p = 0.95). Contamination of the signal in breast lesions with unsuppressed fat causing a reduction of diagnostic performance of diffusion kurtosis imaging may potentially be counteracted by proposed adapted evaluation methods.

Removing rician bias in diffusional kurtosis of the prostate using real-data reconstruction

PURPOSE

To compare prostate diffusional kurtosis imaging (DKI) metrics generated using phase-corrected real data with those generated using magnitude data with and without noise compensation (NC).

METHODS

Diffusion-weighted images were acquired at 3T in 16 prostate cancer patients, measuring 6 b-values (0-1500 s/mm2 ), each acquired with 6 signal averages along 3 diffusion directions, with noise-only images acquired to allow NC. In addition to conventional magnitude averaging, phase-corrected real data were averaged in an attempt to reduce rician noise-bias, with a range of phase-correction low-pass filter (LPF) sizes (8-128 pixels) tested. Each method was also tested using simulations. Pixelwise maps of apparent diffusion (D) and apparent kurtosis (K) were calculated for magnitude data with and without NC and phase-corrected real data. Average values were compared in tumor, normal transition zone (NTZ), and normal peripheral zone (NPZ).

RESULTS

Simulations indicated LPF size can strongly affect K metrics, where 64-pixel LPFs produced accurate metrics. Relative to metrics estimated from magnitude data without NC, median NC K were lower (P < 0.0001) by 6/11/8% in tumor/NPZ/NTZ, 64-LPF real-data K were lower (P < 0.0001) by 4/10/7%, respectively.

CONCLUSION

Compared with magnitude data with NC, phase-corrected real data can produce similar K, although the choice of phase-correction LPF should be chosen carefully.

Analysis of errors in diffusion kurtosis imaging caused by slice crosstalk in simultaneous multi-slice imaging

Simultaneous multi-slice (SMS) imaging techniques accelerate diffusion MRI data acquisition. However, slice separation is imperfect and results in residual signal leakage between the simultaneously excited slices. The resulting consistent bias may adversely affect diffusion model parameter estimation. Although this bias is usually small and might not affect the simplified diffusion tensor model significantly, higher order diffusion models such as kurtosis are likely to be more susceptible to such effects. In this work, two SMS reconstruction techniques and an alternative acquisition approach were tested to quantify the effects of slice crosstalk on diffusion kurtosis parameters. In reconstruction, two popular slice separation algorithms, slice GRAPPA and split-slice GRAPPA, are evaluated to determine the effect of slice leakage on diffusion kurtosis metrics. For the alternative acquisition, the slice pairings were varied across diffusion weighted images such that the signal leakage does not come from the same overlapped slice for all diffusion encodings. Simulation results demonstrated the potential benefits of randomizing the slice pairings. However, various experimental factors confounded the advantages of slice pair randomization. In volunteer experiments, region-of-interest analyses found high metric errors with each of the SMS acquisitions and reconstructions in the brain white matter.

Differentiation between malignant and benign musculoskeletal tumors using diffusion kurtosis imaging

OBJECTIVE

The purpose of this study was to evaluate differences in parameters of diffusion kurtosis imaging (DKI) and minimum apparent diffusion coefficient (ADC_min) between benign and malignant musculoskeletal tumors.

MATERIALS AND METHODS

In this prospective study, 43 patients were scanned using a DKI protocol on a 3-T MR scanner. Eligibility criteria were: non-fatty, non-cystic soft tissue or osteolytic tumors; > 2 cm; location in the retroperitoneum, pelvis, leg, or neck; and no prior treatment. They were clinically or histologically diagnosed as benign (n = 27) or malignant (n = 16). In the DKI protocol, diffusion-weighted imaging was performed using four b values (0-2000 s/mm²) and 21 diffusion directions. Mean kurtosis (MK) values were calculated on the MR console. A recently developed software application enabling reliable calculation was used for DKI analysis.

RESULTS

MK showed a strong correction with ADC_min (Spearman's rs = 0.95). Both MK and ADC_min values differed between benign and malignant tumors (p < 0.01). For benign and malignant tumors, the mean MK values (± SD) were 0.49 ± 0.17 and 1.14 ± 0.30, respectively, and ADC_min values were 1.54 ± 0.47 and 0.49 ± 0.17 × 10^-3 mm²/s, respectively. At cutoffs of MK = 0.81 and ADC_min = 0.77 × 10^-3 mm²/s, the specificity and sensitivity for diagnosis of malignant tumors were 96.3 and 93.8% for MK and 96.3 and 93.8% for ADC_min, respectively. The areas under the curve were 0.97 and 0.99 for MK and ADC_min, respectively (p = 0.31).

CONCLUSIONS

MK and ADC_min showed high diagnostic accuracy and strong correlation, reflecting the accuracy of MK. However, no clear added value of DKI could be demonstrated in differentiating musculoskeletal tumors.

Staging liver fibrosis with DWI: is there an added value for diffusion kurtosis imaging?

OBJECTIVES

To assess liver fibrosis in patients with chronic liver disease using diffusion kurtosis imaging (DKI) in comparison with conventional diffusion-weighted imaging, with histology as reference standard.

METHODS

This prospective study included 81 patients and DKI with b-values of 0, 200, 500, 1,000, 1,500, 2,000 s/mm² were performed. Mean diffusivity (MD), mean kurtosis (MK) and apparent diffusion coefficient (ADC) maps were calculated. The diagnostic efficacy of MD, MK and ADC for predicting stage 2 fibrosis or greater, and stage 3 fibrosis or greater were compared.

RESULTS

The MD (rho=-0.491, p<0.001), MK (rho=0.537, p<0.001) and ADC (rho=-0.496, p<0.001) correlated significantly with fibrosis stages, and ADC exhibited a strong negative correlation with MK (rho=-0.968; p<0.001) and a moderate association with MD (rho=0.601, p<0.001). Areas under the curves (AUCs) for predicting stage 2 fibrosis or greater were not significantly different (p>0.05) between MK (0.809) and ADC (0.797) as well as between MD (0.715) and ADC. AUCs were also similar for MD (0.710), MK (0.768) and ADC (0.747) for predicting stage 3 fibrosis or greater.

CONCLUSION

Although DKI is feasible for predicting liver fibrosis in patients with chronic liver disease, MD and MK offer similar diagnostic performance to ADC values.

KEY POINTS

• Diffusion kurtosis imaging is feasible for staging liver fibrosis. • Diffusion kurtosis and monoexponential model are highly correlated. • The kurtosis model offers no added value to the conventional, monoexponential model.

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.

Diffusion kurtosis imaging of the liver at 3 Tesla: in vivo comparison to standard diffusion-weighted imaging

Background Functional techniques like diffusion-weighted imaging (DWI) are gaining more and more importance in liver magnetic resonance imaging (MRI). Diffusion kurtosis imaging (DKI) is an advanced technique that might help to overcome current limitations of DWI. Purpose To evaluate DKI for the differentiation of hepatic lesions in comparison to conventional DWI at 3 Tesla. Material and Methods Fifty-six consecutive patients were examined using a routine abdominal MR protocol at 3 Tesla which included DWI with b-values of 50, 400, 800, and 1000 s/mm². Apparent diffusion coefficient maps were calculated applying a standard mono-exponential fit, while a non-Gaussian kurtosis fit was used to obtain DKI maps. ADC as well as Kurtosis-corrected diffusion ( D) values were quantified by region of interest analysis and compared between lesions. Results Sixty-eight hepatic lesions (hepatocellular carcinoma [HCC] [n = 25]; hepatic adenoma [n = 4], cysts [n = 18]; hepatic hemangioma [HH] [n = 18]; and focal nodular hyperplasia [n = 3]) were identified. Differentiation of malignant and benign lesions was possible based on both DWI ADC as well as DKI D-values ( P values were in the range of 0.04 to < 0.0001). Conclusion In vivo abdominal DKI calculated using standard b-values is feasible and enables quantitative differentiation between malignant and benign liver lesions. Assessment of conventional ADC values leads to similar results when using b-values below 1000 s/mm² for DKI calculation.

Non-Stationary Rician Noise Estimation in Parallel MRI Using a Single Image: A Variance-Stabilizing Approach

Parallel magnetic resonance imaging (pMRI) techniques have gained a great importance both in research and clinical communities recently since they considerably accelerate the image acquisition process. However, the image reconstruction algorithms needed to correct the subsampling artifacts affect the nature of noise, i.e., it becomes non-stationary. Some methods have been proposed in the literature dealing with the non-stationary noise in pMRI. However, their performance depends on information not usually available such as multiple acquisitions, receiver noise matrices, sensitivity coil profiles, reconstruction coefficients, or even biophysical models of the data. Besides, some methods show an undesirable granular pattern on the estimates as a side effect of local estimation. Finally, some methods make strong assumptions that just hold in the case of high signal-to-noise ratio (SNR), which limits their usability in real scenarios. We propose a new automatic noise estimation technique for non-stationary Rician noise that overcomes the aforementioned drawbacks. Its effectiveness is due to the derivation of a variance-stabilizing transformation designed to deal with any SNR. The method was compared to the main state-of-the-art methods in synthetic and real scenarios. Numerical results confirm the robustness of the method and its better performance for the whole range of SNRs.

Assessment of Microvascular Invasion of Hepatocellular Carcinoma with Diffusion Kurtosis Imaging

Purpose To evaluate the potential role of diffusion kurtosis imaging and conventional magnetic resonance (MR) imaging findings including standard monoexponential model of diffusion-weighted imaging and morphologic features for preoperative prediction of microvascular invasion (MVI) of hepatocellular carcinoma (HCC). Materials and Methods Institutional review board approval and written informed consent were obtained. Between September 2015 and November 2016, 84 patients (median age, 54 years; range, 29-79 years) with 92 histopathologically confirmed HCCs (40 MVI-positive lesions and 52 MVI-negative lesions) were analyzed. Preoperative MR imaging examinations including diffusion kurtosis imaging (b values: 0, 200, 500, 1000, 1500, and 2000 sec/mm²) were performed and kurtosis, diffusivity, and apparent diffusion coefficient maps were calculated. Morphologic features of conventional MR images were also evaluated. Univariate and multivariate logistic regression analyses were used to evaluate the relative value of these parameters as potential predictors of MVI. Results Features significantly related to MVI of HCC at univariate analysis were increased mean kurtosis value (P < .001), decreased mean diffusivity value (P = .033) and apparent diffusion coefficient value (P = .011), and presence of infiltrative border with irregular shape (P = .005) and irregular circumferential enhancement (P = .026). At multivariate analysis, mean kurtosis value (odds ratio, 6.25; P = .001), as well as irregular circumferential enhancement (odds ratio, 6.92; P = .046), were independent risk factors for MVI of HCC. The mean kurtosis value for MVI of HCC showed an area under the receiver operating characteristic curve of 0.784 (optimal cutoff value was 0.917). Conclusion Higher mean kurtosis values in combination with irregular circumferential enhancement are potential predictive biomarkers for MVI of HCC. ^© RSNA, 2017.

Analysis of the effects of noise, DWI sampling, and value of assumed parameters in diffusion MRI models

Purpose

This study was a systematic evaluation across different and prominent diffusion MRI models to better understand the ways in which scalar metrics are influenced by experimental factors, including experimental design (diffusion‐weighted imaging [DWI] sampling) and noise.

Methods

Four diffusion MRI models—diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), mean apparent propagator MRI (MAP‐MRI), and neurite orientation dispersion and density imaging (NODDI)—were evaluated by comparing maps and histogram values of the scalar metrics generated using DWI datasets obtained in fixed mouse brain with different noise levels and DWI sampling complexity. Additionally, models were fit with different input parameters or constraints to examine the consequences of model fitting procedures.

Results

Experimental factors affected all models and metrics to varying degrees. Model complexity influenced sensitivity to DWI sampling and noise, especially for metrics reporting non‐Gaussian information. DKI metrics were highly susceptible to noise and experimental design. The influence of fixed parameter selection for the NODDI model was found to be considerable, as was the impact of initial tensor fitting in the MAP‐MRI model.

Conclusion

Across DTI, DKI, MAP‐MRI, and NODDI, a wide range of dependence on experimental factors was observed that elucidate principles and practical implications for advanced diffusion MRI. Magn Reson Med 78:1767–1780, 2017. © 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.

Comparison of Diffusion Metrics Obtained at 1.5T and 3T in Human Brain With Diffusional Kurtosis Imaging

PURPOSE

To quantitatively compare diffusion metrics for human brain estimated with diffusional kurtosis imaging (DKI) at applied field strengths of 1.5 and 3T.

MATERIALS AND METHODS

DKI data for brain were acquired at both 1.5 and 3T from each of six healthy volunteers using a twice-refocused diffusion-weighted imaging sequence. From these data, parametric maps of mean diffusivity (MD), axial diffusivity (D_‖ ), radial diffusivity (D_⊥ ), fractional anisotropy (FA), mean diffusional kurtosis (MK), axial kurtosis (K_‖ ), radial kurtosis (K_⊥ ), and kurtosis fractional anisotropy (KFA) were estimated. Comparisons of the results from the two field strengths were made for each metric using both Bland-Altman plots and linear regression to calculate coefficients of determination (R² ) and best fit lines.

RESULTS

Diffusion metrics measured at 1.5 and 3T were observed to be similar. Linear regression of the full datasets had coefficients of determination varying from a low of R² = 0.86 for KFA to a high of R² = 0.97 for FA. The slopes of the 3T vs. 1.5T best linear fits varied from 0.881 ± 0.009 for KFA to 1.038 ± 0.010 for D_‖ . From a Bland-Altman analysis of selected regions of interest, the mean differences of the metrics for the two field strengths were all found to be less than 6%, except for KFA, which showed the largest relative discrepancy of 10%.

CONCLUSION

Diffusion metrics measured with DKI at 1.5 and 3T are strongly correlated and typically differ by only a few percent. The somewhat higher discrepancy for the KFA is argued to mainly reflect the effects of signal noise. This supports the robustness DKI results with respect to field strength.

LEVEL OF EVIDENCE

3 J. Magn. Reson. Imaging 2017;45:673-680.

Mapping the Orientation of White Matter Fiber Bundles: A Comparative Study of Diffusion Tensor Imaging, Diffusional Kurtosis Imaging, and Diffusion Spectrum Imaging

BACKGROUND AND PURPOSE

White matter fiber tractography relies on fiber bundle orientation estimates from diffusion MR imaging. However, clinically feasible techniques such as DTI and diffusional kurtosis imaging use assumptions, which may introduce error into in vivo orientation estimates. In this study, fiber bundle orientations from DTI and diffusional kurtosis imaging are compared with diffusion spectrum imaging as a criterion standard to assess the performance of each technique.

MATERIALS AND METHODS

For each subject, full DTI, diffusional kurtosis imaging, and diffusion spectrum imaging datasets were acquired during 2 independent sessions, and fiber bundle orientations were estimated by using the specific theoretic assumptions of each technique. Angular variability and angular error measures were assessed by comparing the orientation estimates. Tractography generated with each of the 3 reconstructions was also examined and contrasted.

RESULTS

Orientation estimates from all 3 techniques had comparable angular reproducibility, but diffusional kurtosis imaging decreased angular error throughout the white matter compared with DTI. Diffusion spectrum imaging and diffusional kurtosis imaging enabled the detection of crossing-fiber bundles, which had pronounced effects on tractography relative to DTI. Diffusion spectrum imaging had the highest sensitivity for detecting crossing fibers; however, the diffusion spectrum imaging and diffusional kurtosis imaging tracts were qualitatively similar.

CONCLUSIONS

Fiber bundle orientation estimates from diffusional kurtosis imaging have less systematic error than those from DTI, which can noticeably affect tractography. Moreover, tractography obtained with diffusional kurtosis imaging is qualitatively comparable with that of diffusion spectrum imaging. Because diffusional kurtosis imaging has a shorter typical scan time than diffusion spectrum imaging, diffusional kurtosis imaging is potentially more suitable for a variety of clinical and research applications.

Diffusion MRI noise mapping using random matrix theory

PURPOSE

To estimate the spatially varying noise map using a redundant series of magnitude MR images.

METHODS

We exploit redundancy in non-Gaussian distributed multidirectional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of principal component analysis eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions.

RESULTS

We present a model-independent local noise mapping method capable of estimating the noise level down to about 1% error. In contrast to current state-of-the-art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal.

CONCLUSIONS

Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the principal component analysis eigenspectrum in terms of the Marchenko-Pastur distribution. Magn Reson Med 76:1582-1593, 2016. © 2015 International Society for Magnetic Resonance in Medicine.

Body diffusion kurtosis imaging: Basic principles, applications, and considerations for clinical practice

Technologic advances enable performance of diffusion-weighted imaging (DWI) at ultrahigh b-values, where standard monoexponential model analysis may not apply. Rather, non-Gaussian water diffusion properties emerge, which in cellular tissues are, in part, influenced by the intracellular environment that is not well evaluated by conventional DWI. The novel technique, diffusion kurtosis imaging (DKI), enables characterization of non-Gaussian water diffusion behavior. More advanced mathematical curve fitting of the signal intensity decay curve using the DKI model provides an additional parameter Kapp that presumably reflects heterogeneity and irregularity of cellular microstructure, as well as the amount of interfaces within cellular tissues. Although largely applied for neural applications over the past decade, a small number of studies have recently explored DKI outside the brain. The most investigated organ is the prostate, with preliminary studies suggesting improved tumor detection and grading using DKI. Although still largely in the research phase, DKI is being explored in wider clinical settings. When assessing extracranial applications of DKI, careful attention to details with which body radiologists may currently be unfamiliar is important to ensure reliable results. Accordingly, a robust understanding of DKI is necessary for radiologists to better understand the meaning of DKI-derived metrics in the context of different tumors and how these metrics vary between tumor types and in response to treatment. In this review, we outline DKI principles, propose biostructural basis for observations, provide a comparison with standard monoexponential fitting and the apparent diffusion coefficient, report on extracranial clinical investigations to date, and recommend technical considerations for implementation in body imaging.

Fiber ball imaging

By modeling axons as thin cylinders, it is shown that the inverse Funk transform of the diffusion MRI (dMRI) signal intensity obtained on a spherical shell in q-space gives an estimate for a fiber orientation density function (fODF), where the accuracy improves with increasing b-value provided the signal-to-noise ratio is sufficient. The method is similar to q-ball imaging, except that the Funk transform of q-ball imaging is replaced by its inverse. We call this new approach fiber ball imaging. The fiber ball method is demonstrated for healthy human brain, and fODF estimates are compared to diffusion orientation distribution function (dODF) approximations obtained with q-ball imaging. The fODFs are seen to have sharper features than the dODFs, reflecting an enhancement of the higher degree angular frequencies. The inverse Funk transform of the dMRI signal intensity data provides a simple and direct method of estimating a fODF. In addition, fiber ball imaging leads to an estimate for the ratio of the fraction of MRI visible water confined to the intra-axonal space divided by the square root of the intra-axonal diffusivity. This technique may be useful for white matter fiber tractography, as well as other types of microstructural modeling of brain tissue.

Gibbs ringing in diffusion MRI

PURPOSE

To study and reduce the effect of Gibbs ringing artifact on computed diffusion parameters.

METHODS

We reduce the ringing by extrapolating the k-space of each diffusion weighted image beyond the measured part by selecting an adequate regularization term. We evaluate several regularization terms and tune the regularization parameter to find the best compromise between anatomical accuracy of the reconstructed image and suppression of the Gibbs artifact.

RESULTS

We demonstrate empirically and analytically that the Gibbs artifact, which is typically observed near sharp edges in magnetic resonance images, has a significant impact on the quantification of diffusion model parameters, even for infinitesimal diffusion weighting. We find the second order total generalized variation to be a good choice for the penalty term to regularize the extrapolation of the k-space, as it provides a parsimonious representation of images, a practically full suppression of Gibbs ringing, and the absence of staircasing artifacts typical for total variation methods.

CONCLUSIONS

Regularized extrapolation of the k-space data significantly reduces truncation artifacts without compromising spatial resolution in comparison to the default option of window filtering. In particular, accuracy of estimating diffusion tensor imaging and diffusion kurtosis imaging parameters improves so much that unconstrained fits become possible. Magn Reson Med 76:301-314, 2016. © 2015 Wiley Periodicals, Inc.

Quantitative assessment of diffusional kurtosis anisotropy

Diffusional kurtosis imaging (DKI) measures the diffusion and kurtosis tensors to quantify restricted, non-Gaussian diffusion that occurs in biological tissue. By estimating the kurtosis tensor, DKI accounts for higher order diffusion dynamics, when compared with diffusion tensor imaging (DTI), and consequently can describe more complex diffusion profiles. Here, we compare several measures of diffusional anisotropy which incorporate information from the kurtosis tensor, including kurtosis fractional anisotropy (KFA) and generalized fractional anisotropy (GFA), with the diffusion tensor-derived fractional anisotropy (FA). KFA and GFA demonstrate a net enhancement relative to FA when multiple white matter fiber bundle orientations are present in both simulated and human data. In addition, KFA shows net enhancement in deep brain structures, such as the thalamus and the lenticular nucleus, where FA indicates low anisotropy. Thus, KFA and GFA provide additional information relative to FA with regard to diffusional anisotropy, and may be particularly advantageous for the assessment of diffusion in complex tissue environments.

Kurtosis analysis of neural diffusion organization

A computational framework is presented for relating the kurtosis tensor for water diffusion in brain to tissue models of brain microstructure. The tissue models are assumed to be comprised of non-exchanging compartments that may be associated with various microstructural spaces separated by cell membranes. Within each compartment the water diffusion is regarded as Gaussian, although the diffusion for the full system would typically be non-Gaussian. The model parameters are determined so as to minimize the Frobenius norm of the difference between the measured kurtosis tensor and the model kurtosis tensor. This framework, referred to as kurtosis analysis of neural diffusion organization (KANDO), may be used to help provide a biophysical interpretation to the information provided by the kurtosis tensor. In addition, KANDO combined with diffusional kurtosis imaging can furnish a practical approach for developing candidate biomarkers for neuropathologies that involve alterations in tissue microstructure. KANDO is illustrated for simple tissue models of white and gray matter using data obtained from healthy human subjects.