Diffusion Signal Decay Research Articles

High-fidelity intravoxel incoherent motion parameter mapping using locally low-rank and subspace modeling

PurposeIntravoxel incoherent motion (IVIM) is a quantitative magnetic resonance imaging (MRI) method used to quantify perfusion properties of tissue non-invasively without contrast. However, clinical applications are limited by unreliable parameter estimates, particularly for the perfusion fraction (f) and pseudodiffusion coefficient (D*). This study aims to develop a high-fidelity reconstruction for reliable estimation of IVIM parameters. The proposed method is versatile and amenable to various acquisition schemes and fitting methods. MethodsTo address current challenges with IVIM, we adapted several advanced reconstruction techniques. We used a low-rank approximation of IVIM images and temporal subspace modeling to constrain the magnetization dynamics of the bi-exponential diffusion signal decay. In addition, motion-induced phase variations were corrected between diffusion directions and b-values, facilitating the use of high SNR real-valued diffusion data. The proposed method was evaluated in simulations and in vivo brain acquisitions in six healthy subjects and six individuals with a history of SARS-CoV-2 infection and compared with the conventionally reconstructed magnitude data. Following reconstruction, IVIM parameters were estimated voxel-wise. ResultsOur proposed method reduced noise contamination in simulations, resulting in a 60%, 58.9%, and 83.9% reduction in the NRMSE for D, f, and D*, respectively, compared to the conventional reconstruction. In vivo, anisotropic properties of D, f, and D* were preserved with the proposed method, highlighting microvascular differences in gray matter between individuals with a history of COVID-19 and those without (p = 0.0210), which wasn't observed with the conventional reconstruction. ConclusionThe proposed method yielded a more reliable estimation of IVIM parameters with less noise than the conventional reconstruction. Further, the proposed method preserved anisotropic properties of IVIM parameter estimates and demonstrated differences in microvascular perfusion in COVID-affected subjects, which weren't observed with conventional reconstruction methods.

Diffusion kurtosis imaging as a biomarker of breast cancer.

DKI, which increases the sensitivity to complex tissue microstructure compared to standard DWI, has been applied in the breast, allowing to increase clinical performance in distinguishing malignant from benign lesions and in predicting prognosis or treatment response in breast cancer.

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

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, in mm2 s-1 and a fractional exponent, , 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. 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 and 5000 smm-2 . The effects of varying maximum b-value ( ), number of b-value shells, and the effects of Rician noise were investigated. QDTI measures showed dependence, most significantly for in white matter, which monotonically decreased with higher 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 and underestimation of in white matter, and overestimation of and anisotropies in gray and white matter. Additional shells improved the accuracy, precision, and reliability of QDTI estimates with 3 and 4 shells at s mm-2 , and 4 b-value shells at s mm-2 , providing minimal bias in and compared to the MbR. 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.

Optimized bias and signal inference in diffusion-weighted image analysis (OBSIDIAN).

Correction of Rician signal bias in magnitude MR images. A model-based, iterative fitting procedure is used to simultaneously estimate true signal and underlying Gaussian noise with standard deviation on a pixel-by-pixel basis in magnitude MR images. A precomputed function that relates absolute residuals between measured signals and model fit to is used to iteratively estimate . The feasibility of the method is evaluated and compared to maximum likelihood estimation (MLE) for diffusion signal decay simulations and diffusion-weighted images of the prostate considering 21 linearly spaced b-values from 0 to 3000s/mm2 . A multidirectional analysis was performed with publically available brain data. Model simulations show that the Rician bias correction algorithm is fast, with an accuracy and precision that is on par to model-based MLE and direct fitting in the case of pure Gaussian noise. Increased accuracy in parameter prediction in a low signal-to-noise ratio (SNR) scenario is ideally achieved by using a composite of multiple signal decays from neighboring voxels as input for the algorithm. For patient data, good agreement with high SNR reference data of diffusion in prostate is achieved. OBSIDIAN is a novel, alternative, simple to implement approach for rapid Rician bias correction applicable in any case where differences between true signal decay and underlying model function can be considered negligible in comparison to noise. The proposed composite fitting approach permits accurate parameter estimation even in typical clinical scenarios with low SNR, which significantly simplifies comparison of complex diffusion parameters among studies.

In Depth Analysis of Stretch Function Resulting from Solving the Generalize Fractional-Order Bloch Equations Using Fractional Calculus

In this paper the stretch function resulting from solving the fractional-order Bloch equations using fractional calculus was discussed. This function has promising results to represent diffusion signal decay from MRI images. Conventional analyses of (DWI) measurements resolve the normalized magnetization decay profiles in terms of discrete and mono-exponential components with distinct lifetimes. In complex, heterogeneous biological and biophysical samples such as tissue, multi-exponential decay functions can appear to provide truer representation to normalized magnetization decay profile than the assumption of a mono-exponential decay, but the assumption of multiple discrete components is arbitrary and is often erroneous. Moreover, interactions, between both normalized magnetization and with their environment, can result in complex normalized magnetization decay profiles that represent a continuous distribution of lifetimes. The purpose in this paper is to study different factors that influence the stretch function strength, clarity, and contrast of MRI magnetization signal relaxation by manipulating the anomalous diffusion parameters Δ,δ,Gz,β and μ. of Bloch equations. Through this study, it was found that complex normalized magnetization decay profiles behave like stretch exponential function inside power law. Further developments of this study may be useful in optimizing anomalous diffusion in tissues with neurodegenerative, and ischemic diseases.

Development of a Radial Basis Function Neural Network Model to Predict High b-value Diffusion MR Signals of the Prostate

This study aims development of a neural network model to predict the signal amplitudes of diffusion MR signals of prostate tissues at high b-values from the amplitudes of low b-values obtained by using diffusion weighted imaging. Synthetic diffusion MR signals are generated using a kurtosis model for noise-free and noisy conditions considering nine b-values: the low b-values are 0, 50, 250, 500, 750s/mm2 and the high b-values are 1000, 1250, 1500, 2000s/mm2. Four radial basis functions neural networks (RBF-NN) connected in parallel are designed to accept the signal amplitudes at low b-values and to provide signal amplitudes at the high b-values. RBF-NNs housing altered number of neurons with radial basis functions attributing different widths in the hidden layers of the networks are analyzed. Learning and prediction performances of the NNs are assessed from training and testing datasets. For the noise-free condition, RBF-NNs reveal perfect predictions (r= 1.000) with very good learnings (MSE= 0.76-0.02×10-6). For the noisy conditions, the RBF-NNs achieve moderate to strong predictions (r= 0.981-0.463) with good learnings (MSE= 0.32-10.33×10-3). Prediction performance reduces as the level of noise and/or targeted high b-value increases. RBF-NNs facilitate prediction of high b-value diffusion MR signals of the prostate by requiring no diffusion signal decay function, optimization algorithm or initial/boundary values for the optimization algorithm. They may be quite functional in accurate voxel-wise generation of high b-value MR images for early detection and diagnosis of prostate cancer. Further prospective studies are needed to justify the potential benefits in clinical practice.

Quasi-diffusion magnetic resonance imaging (QDI): A fast, high b-value diffusion imaging technique

To enable application of non-Gaussian diffusion magnetic resonance imaging (dMRI) techniques in large-scale clinical trials and facilitate translation to clinical practice there is a requirement for fast, high contrast, techniques that are sensitive to changes in tissue structure which provide diagnostic signatures at the early stages of disease. Here we describe a new way to compress the acquisition of multi-shell b-value diffusion data, Quasi-Diffusion MRI (QDI), which provides a probe of subvoxel tissue complexity using short acquisition times (1–4 ​min). We also describe a coherent framework for multi-directional diffusion gradient acquisition and data processing that allows computation of rotationally invariant quasi-diffusion tensor imaging (QDTI) maps.QDI is a quantitative technique that is based on a special case of the Continuous Time Random Walk model of diffusion dynamics and assumes the presence of non-Gaussian diffusion properties within tissue microstructure. QDI parameterises the diffusion signal attenuation according to the rate of decay (i.e. diffusion coefficient, D in mm2 s−1) and the shape of the power law tail (i.e. the fractional exponent, α). QDI provides analogous tissue contrast to Diffusional Kurtosis Imaging (DKI) by calculation of normalised entropy of the parameterised diffusion signal decay curve, Hn, but does so without the limitations of a maximum b-value.We show that QDI generates images with superior tissue contrast to conventional diffusion imaging within clinically acceptable acquisition times of between 84 and 228 ​s. We show that QDI provides clinically meaningful images in cerebral small vessel disease and brain tumour case studies. Our initial findings suggest that QDI may be added to routine conventional dMRI acquisitions allowing simple application in clinical trials and translation to the clinical arena.

Fractional Order Complexity Model of the Diffusion Signal Decay in MRI

Fractional calculus models are steadily being incorporated into descriptions of diffusion in complex, heterogeneous materials. Biological tissues, when viewed using diffusion-weighted, magnetic resonance imaging (MRI), hinder and restrict the diffusion of water at the molecular, sub-cellular, and cellular scales. Thus, tissue features can be encoded in the attenuation of the observed MRI signal through the fractional order of the time- and space-derivatives. Specifically, in solving the Bloch-Torrey equation, fractional order imaging biomarkers are identified that connect the continuous time random walk model of Brownian motion to the structure and composition of cells, cell membranes, proteins, and lipids. In this way, the decay of the induced magnetization is influenced by the micro- and meso-structure of tissues, such as the white and gray matter of the brain or the cortex and medulla of the kidney. Fractional calculus provides new functions (Mittag-Leffler and Kilbas-Saigo) that characterize tissue in a concise way. In this paper, we describe the exponential, stretched exponential, and fractional order models that have been proposed and applied in MRI, examine the connection between the model parameters and the underlying tissue structure, and explore the potential for using diffusion-weighted MRI to extract biomarkers associated with normal growth, aging, and the onset of disease.

Analysis of Diffusion-weighted MR Images Based on a Gamma Distribution Model to Differentiate Prostate Cancers with Different Gleason Score.

Purpose:Prostate cancer management includes identification of clinically significant cancers that may require curative treatment. Statistical models based on gamma distribution can describe diffusion signal decay curves of prostate cancer. The purpose of this study was to evaluate the ability of parameters obtained with the gamma model in differentiating prostate cancers with different Gleason score values.Methods:This study included 155 patients with prostate cancer who underwent multiparametric magnetic resonance imaging prior to prostate biopsy (127 patients) or radical prostatectomy (28 patients) between January 2015 and June 2017; 159 foci of prostate cancer were included in our study. We compared cases scored as Gleason score (GS) 3 + 3 and GS ≥ 3 + 4, and analyzed cases scored as GS ≤ 3+ 4 and GS ≥ 4 + 3 based on the gamma model (Frac < 1.0, Frac < 0.8, Frac < 0.5, Frac < 0.3, and Frac > 3.0), and apparent diffusion coefficient (ADC).Results:Among 159 cancerous lesions in 155 patients, 13 (8.2%) were GS 3 + 3 prostate cancers, 51 (32.0%) were GS 3 + 4 prostate cancers, 30 (18.2%) were GS 4 + 3 cancers, and 65 (40.9%) were GS ≥ 4 + 4 cancers. Frac < 0.3, Frac < 0.5, Frac < 0.8, and Frac < 1.0 were significantly higher and ADC values were significantly lower in GS ≥ 4 + 3 cancers than in GS ≤ 3 + 4 cancers (P < 0.01, P < 0.01, P < 0.01, P = 0.01, and P < 0.01, respectively). With receiver operating characteristic (ROC) analysis, Frac < 0.3 and Frac < 0.5 had significantly greater area under the ROC curve for discriminating GS ≥ 4 + 3 cancers from GS ≤ 3 + 4 cancers than ADC (P = 0.03, P < 0.01, respectively).Conclusion:Frac < 0.3 and Frac < 0.5 showed higher diagnostic performance than ADC for differentiating GS ≥ 4 + 3 from GS ≤ 3 + 4 cancers. The gamma model may add additional value in discrimination of tumor grades.

Multi-component diffusion characterization of radiation-induced white matter damage.

We used multi-b-value diffusion models to characterize microstructural white matter changes after brain radiation into fast and slow components, in order to better understand the pathophysiology of radiation-induced tissue damage. Fourteen patients were included in this retrospective analysis with imaging prior to, and at 1, 4-5, and 9-10 months after radiotherapy (RT). Diffusion signal decay within brain white matter was fit to a biexponential model to separate changes within the slow and fast components. Linear mixed-effects models were used to obtain estimates of the effect of radiation dose and time on the model parameters. We found an increase of 0.11 × 10-4 and 0.14 × 10-4 mm2 /s in the fast diffusion coefficient per unit dose-time (Gy-month) in the longitudinal and transverse directions, respectively. By contrast, the longitudinal slow diffusion coefficient decreased independently of dose, by 0.18 × 10-4 , 0.16 × 10-4 , and 0.098 × 10-4 mm2 /s at 1, 4, and 9 months post-RT, respectively. Radiation-induced white matter changes in the first year following RT are driven by dose-dependent increases in the fast component and dose-independent decreases in the slow component.

Using spectral and cumulative spectral entropy to classify anomalous diffusion in Sephadex™ gels

Sephadex™ gel beads are commonly used to separate mixtures of similar molecules based on trapping and size exclusion from internal submicron diameter cavities. Water, as it freely moves through the porous gel and enclosed chambers of Sephadex™ beads, exhibits both normal (Gaussian) and anomalous (non-Gaussian) water diffusion. The apparent diffusion coefficient (ADC) of water in Sephadex™ gels can be measured using magnetic resonance imaging (MRI) by applying diffusion-weighted pulse sequences. This study investigates the relationship between the ADC of water and the complexity (i.e., size and number of cavities) of a series of Sephadex™ beads. We first classified the stochastic movement of water by using the solution to the space and time fractional diffusion equation to extract the ADC and the fractional time and space parameters (α, β), which are essentially the order of the respective fractional derivatives in Fick’s second law. From the perspective of the continuous time random walk (CTRW) model of anomalous diffusion, these parameters reflect waiting times (trapping) and jump increments (nano-flow) of the water in the gels. The observed MRI diffusion signal decay represents the Fourier transform of the diffusion propagator (i.e., the characteristic function of the stochastic process). In two series of Sephadex™ gel beads, we observed a strong inverse correlation between bead porosity (which is also responsible for molecular size exclusion) and the fractional order parameters; as the gels become more heterogeneous, the ADC decreases, both α and β are reduced and the diffusion exhibits anomalous (sub-diffusion) behavior. In addition, as a new measure for the structural complexity in Sephadex™ gel beads, we propose using the spectral and the cumulative spectral entropy that are derived from the observed characteristic function. We find that both measures of entropy increase with the porosity and tortuosity of the gel in a manner consistent with fractional order diffusional dynamics.

Models of diffusion signal decay in magnetic resonance imaging: Capturing complexity

AbstractDiffusion‐weighted MRI is a key diagnostic component of clinical medicine. Radiologists use models of the effects of diffusion weighting to connect the decay of the signal intensity in tissues with macroscopic (diffusion tensor imaging) and microscopic (q‐space imaging) structures. This multi‐scale problem has stimulated the creation of many diffusion models spanning phenomenon in cells, in tissues, and in organs. Such models can be heuristic or based on simulations, stochastic processes, histological structure or physical and physiological constraints. The goal of this paper is to provide an overview of these approaches by considering several different classes of mathematical models (linear, nonlinear, integer, and fractional orders) that can, and have in some cases, been used to fit diffusion attenuation in complex biological tissues, such as brain white and gray matter. The focus here is not on solving the Bloch‐Torrey equation or on fitting curves to data, but on the choices (Gaussian, anomalous, isotropic, anisotropic) one often has to make when beginning the analysis of diffusion data. It is hoped that this presentation, while oversimplified, will be of use to students and to new investigators who seek an introduction to diffusion attenuation model selection and characterization. Examples are given that illustrate the relationship between the functional form of the diffusion decay rate and, in the case of a Stejskal‐Tanner gradient pulse sequence, the expected signal decay. Model limitations are noted and connections to more advanced treatments of diffusion modeling methods are provided.

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or ‘long tail’ behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the perspective of computational accuracy and efficiency.

Spatially-constrained probability distribution model of incoherent motion (SPIM) for abdominal diffusion-weighted MRI.

Quantitative diffusion-weighted MR imaging (DW-MRI) of the body enables characterization of the tissue microenvironment by measuring variations in the mobility of water molecules. The diffusion signal decay model parameters are increasingly used to evaluate various diseases of abdominal organs such as the liver and spleen. However, previous signal decay models (i.e., mono-exponential, bi-exponential intra-voxel incoherent motion (IVIM) and stretched exponential models) only provide insight into the average of the distribution of the signal decay rather than explicitly describe the entire range of diffusion scales. In this work, we propose a probability distribution model of incoherent motion that uses a mixture of Gamma distributions to fully characterize the multi-scale nature of diffusion within a voxel. Further, we improve the robustness of the distribution parameter estimates by integrating spatial homogeneity prior into the probability distribution model of incoherent motion (SPIM) and by using the fusion bootstrap solver (FBM) to estimate the model parameters. We evaluated the improvement in quantitative DW-MRI analysis achieved with the SPIM model in terms of accuracy, precision and reproducibility of parameter estimation in both simulated data and in 68 abdominal in-vivo DW-MRIs. Our results show that the SPIM model not only substantially reduced parameter estimation errors by up to 26%; it also significantly improved the robustness of the parameter estimates (paired Student's t-test, p < 0.0001) by reducing the coefficient of variation (CV) of estimated parameters compared to those produced by previous models. In addition, the SPIM model improves the parameter estimates reproducibility for both intra- (up to 47%) and inter-session (up to 30%) estimates compared to those generated by previous models. Thus, the SPIM model has the potential to improve accuracy, precision and robustness of quantitative abdominal DW-MRI analysis for clinical applications.

Diffusion-weighted MR Imaging for the Assessment of Renal Function: Analysis Using Statistical Models Based on Truncated Gaussian and Gamma Distributions.

Purpose:To determine the appropriateness of statistical models using the truncated Gaussian distribution and gamma distribution for diffusion signal decay, and to assess the correlation between the parameters obtained from the statistical models and estimated glomerular filtration rate (eGFR).Methods:Twenty-nine patients with chronic kidney disease and 21 healthy volunteers were included and classified in four groups according to eGFR (ml/min/1.73 m2): group 1 (90 ≤ eGFR, n = 10), group 2 (eGFR 60–90, n = 15), group 3 (eGFR 30–60, n = 17), and group 4 (eGFR < 30, n = 8). Diffusion-weighted imaging using five b-values (0, 500, 1000, 1500, and 2000 s/mm2) was performed. Truncated Gaussian and gamma models were compared for goodness of fit. Area fractions for the diffusion coefficient D < 1.0 × 10−3 mm2/s (Frac < 1.0) and D > 3.0 × 10−3 mm2/s (Frac > 3.0) obtained from the statistical model were compared among four groups. Correlation between proposed parameters and conventional apparent diffusion coefficient (ADC) with eGFR was calculated.Results:There was no significant difference in goodness of fit between the truncated Gaussian and gamma models. Frac < 1.0 and Frac > 3.0 showed good correlation with eGFR, as did ADC. Comparison between groups 1 and 2 showed that only Frac < 1.0 in both distribution models had significant differences.Conclusion:Statistical models yield robust interpretation of diffusion magnetic resonance (MR) signals with relevance to histological changes in the kidney. The parameters of the statistical models, particularly Frac < 1.0, strongly correlated with eGFR.

Diffusion-weighted imaging of prostate cancer using a statistical model based on the gamma distribution.

To assess the adequacy of a statistical model based on the gamma distribution for diffusion signal decays of prostate cancer (PCa) using b-values ranging up to 2000 sec/mm(2) , and to evaluate the differences in gamma model parameters for PCa, benign prostatic hyperplasia (BPH), and peripheral zone (PZ). Twenty-six patients with histologically proven PCa underwent diffusion-weighted magnetic resonance imaging using five b-values (0, 500, 1000, 1500, 2000 sec/mm(2) ). The acquired signal decay curves were fit with both gamma and truncated Gaussian models and a statistical comparison between the two fits was performed. The acquired parameters using the gamma model (mean, standard deviation, the area fraction for D < 1.0 mm(2) /s [Frac<1.0], the area fraction of D > 3.0 mm(2) /s [Frac>3.0]) were compared between PCa, BPH, and PZ. The gamma model provided a statistically improved fit over the truncated Gaussian model in PCa. The mean and the standard deviation were significantly lower in PCa than in BPH and PZ (P < 0.01). Frac<1.0 was significantly higher in PCa than in BPH and PZ, and Frac>3.0 was significantly lower in PCa than in BPH and PZ (P < 0.01). A statistical model based on the gamma distribution proved suitable for describing diffusion signal decay curves of PCa. This approach may provide better correlation between diffusion signal decay and histological information in the prostate gland.

Avian egg latebra as brain tissue water diffusion model

Simplified models of non-monoexponential diffusion signal decay are of great interest to study the basic constituents of complex diffusion behavior in tissues. The latebra, a unique structure uniformly present in the yolk of avian eggs, exhibits a non-monoexponential diffusion signal decay. This model is more complex than simple phantoms based on differences between water and lipid diffusion, but is also devoid of microscopic structures with preferential orientation or perfusion effects. Diffusion scans with multiple b-values were performed on a clinical 3 Tesla system in raw and boiled chicken eggs equilibrated to room temperature. Diffusion encoding was applied over the ranges 5-5,000 and 5-50,000 s/mm(2). A low read-out bandwidth and chemical shift was used for reliable lipid/water separation. Signal decays were fitted with exponential functions. The latebra, when measured over the 5-5,000 s/mm(2) range, exhibited independent of preparation clearly biexponential diffusion, with diffusion parameters similar to those typically observed in in vivo human brain. For the range 5-50,000 s/mm(2), there was evidence of a small third, very slow diffusing water component. The latebra of the avian egg contains membrane structures, which may explain a deviation from a simple monoexponential diffusion signal decay, which is remarkably similar to the deviation observed in brain tissue.

Permeability–diffusivity modeling vs. fractional anisotropy on white matter integrity assessment and application in schizophrenia

IntroductionDiffusion tensor imaging (DTI) assumes a single pool of anisotropically diffusing water to calculate fractional anisotropy (FA) and is commonly used to ascertain white matter (WM) deficits in schizophrenia. At higher b-values, diffusion-signal decay becomes bi-exponential, suggesting the presence of two, unrestricted and restricted, water pools. Theoretical work suggests that semi-permeable cellular membrane rather than the presence of two physical compartments is the cause. The permeability–diffusivity (PD) parameters measured from bi-exponential modeling may offer advantages, over traditional DTI-FA, in identifying WM deficits in schizophrenia.MethodsImaging was performed in N = 26/26 patients/controls (age = 20–61 years, average age = 40.5 ± 12.6). Imaging consisted of fifteen b-shells: b = 250–3800 s/mm2 with 30 directions/shell, covering seven slices of mid-sagittal corpus callosum (CC) at 1.7 × 1.7 × 4.6 mm. 64-direction DTI was also collected. Permeability–diffusivity-index (PDI), the ratio of restricted to unrestricted apparent diffusion coefficients, and the fraction of unrestricted compartment (Mu) were calculated for CC and cingulate gray matter (GM). FA values for CC were calculated using tract-based-spatial-statistics.ResultsPatients had significantly reduced PDI in CC (p ≅ 10− 4) and cingulate GM (p = 0.002), while differences in CC FA were modest (p ≅ .03). There was no group-related difference in Mu. Additional theoretical-modeling analysis suggested that reduced PDI in patients may be caused by reduced cross-membrane water molecule exchanges.ConclusionPDI measurements for cerebral WM and GM yielded more robust patient–control differences than DTI-FA. Theoretical work offers an explanation that patient–control PDI differences should implicate abnormal active membrane permeability. This would implicate abnormal activities in ion-channels that use water as substrate for ion exchange, in cerebral tissues of schizophrenia patients.

Bi-exponential diffusion signal decay in normal appearing white matter of multiple sclerosis

PurposeOur aim was to characterize bi-exponential diffusion signal changes in normal appearing white matter of multiple sclerosis (MS) patients. MethodsDiffusion parameters were measured using mono-exponential (0–1000 s/mm2) and bi-exponential (0–5000 s/mm2) approaches from 14 relapsing-remitting subtype of MS patients and 14 age- and sex-matched controls after acquiring diffusion-weighted images on a 3T MRI system. The results were analyzed using parametric or nonparametric tests and multiple linear regression models. ResultsMono-exponential apparent diffusion coefficient (ADC) slightly increased in controls (P=.09), but decreased significantly in MS as a function of age, nonetheless an elevated ADC was observed with increasing lesion number in patients. Bi-exponential analyses showed that the increased ADC is the result of decreased relative volume fraction of slow diffusing component (fs). However, the fast and slow diffusion components (ADCf, ADCs) did not change as a function of either age in controls or lesion number and age in MS patients. ConclusionsThese data demonstrated that the myelin content of the white matter affects diffusion in relapsing-remitting subtype of multiple sclerosis that is possibly a consequence of the shift between different water fractions.

Diffusion imaging of brain tumors

MRI offers a tremendous armamentarium of different methods that can be employed in brain tumor characterization. MR diffusion imaging has become a widely accepted method to probe for the presence of fluid pools and molecular tissue water mobility. For most clinical applications of diffusion imaging, it is assumed that the diffusion signal vs diffusion weighting factor b decays monoexponentially. Within this framework, the measurement of a single diffusion coefficient in brain tumors permits an approximate categorization of tumor type and, for some tumors, definitive diagnosis. In most brain tumors, when compared with normal brain tissue, the diffusion coefficient is elevated. The presence of peritumoral edema, which also exhibits an elevated diffusion coefficient, often precludes the delineation of the tumor on the basis of diffusion information alone. Serially obtained diffusion data are useful to document and even predict the cellular response to drug or radiation therapy. Diffusion measurements in tissues over an extended range of b factors have clearly shown that the monoparametric description of the MR diffusion signal decay is incomplete. Very high diffusion weighting on clinical systems requires substantial compromise in spatial resolution. However, after suitable analysis, superior separation of malignant brain tumors, peritumoral edema and normal brain tissue can be achieved. These findings are also discussed in the light of tissue-specific differences in membrane structure and the restrictions exerted by membranes on diffusion. Finally, measurement of the directional dependence of diffusion permits the assessment of white matter integrity and dislocation. Such information, particularly in conjunction with advanced post-processing, is considered to be immensely useful for therapy planning. Diffusion imaging, which permits monoexponential analysis and provides directional diffusion information, is performed routinely in brain tumor patients. More advanced methods require improvement in acquisition speed and spatial resolution to gain clinical acceptance.