Biexponential apparent diffusion coefficients in prostate cancer

Purpose

The purpose of this study was to investigate the need for biexponential signal decay modeling for prostate cancer diffusion signal decays with b-factor over an extended b-factor range.

Materials and Methods

Ten healthy volunteers and 12 patients with a bulky prostate cancer underwent line scan diffusion-weighted MR imaging in which b-factors from 0 to 3000 s/mm² in 16 steps were sampled. The acquired signal decay curves were fit with both monoexponential and biexponential signal decay functions and a statistical comparison between the two fits was performed.

Results

The biexponential model provided a statistically better fit over the monoexponential model on the peripheral zone (PZ), transitional zone (TZ) and prostate cancer. The fast and slow apparent diffusion coefficients (ADCs) in the PZ, TZ and cancer were 2.9±0.2, 0.7±0.2×10⁻³ mm²/ms (PZ); 2.9±0.4, 0.7±0.2×10⁻³ mm²/ms (TZ); and 1.7±0.4, 0.3±0.1×10⁻³ mm²/ms (cancer), respectively. The apparent fractions of the fast diffusion component in the PZ, TZ and cancer were 70±10%, 60±10% and 50±10%, respectively. The fast and slow ADCs of cancer were significantly lower than those of TZ and PZ, and the apparent fraction of the fast diffusion component was significantly smaller in cancer than in PZ.

Conclusions

Biexponential diffusion decay functions are required for prostate cancer diffusion signal decay curves when sampled over an extended b-factor range, providing additional, unique tissue characterization parameters for prostate cancer.     

Comparison of different mathematical models of diffusion-weighted prostate MR imaging

Purpose

To evaluate which mathematical model (monoexponential, biexponential, statistical, kurtosis) fits best to the diffusion-weighted signal in prostate magnetic resonance imaging (MRI).

Materials and Methods

24 prostate 3-T MRI examinations of young volunteers (YV, n= 8), patients with biopsy proven prostate cancer (PC, n= 8) and an aged matched control group (AC, n= 8) were included. Diffusion-weighted imaging was performed using 11 b-values ranging from 0 to 800 s/mm².

Results

Monoexponential apparent diffusion coefficient (ADC) values were significantly (P<.001) lower in the peripheral (PZ) zone (1.18±0.16 mm²/s) and the central (CZ) zone (0.73±0.13 mm²/s) of YV compared to AC (PZ 1.92±0.17 mm²/s; CZ 1.35±0.21 mm²/s). In PC ADC_mono values (0.61±0.06 mm²/s) were significantly (P<.001) lower than in the peripheral of central zone of AC. Using the statistical analysis (Akaike information criteria) in YV most pixels were best described by the biexponential model (82%), the statistical model, respectively kurtosis (93%) each compared to the monoexponential model. In PC the majority of pixels was best described by the monoexponential model (57%) compared to the biexponential model.

Conclusion

Although a more complex model might provide a better fitting when multiple b-values are used, the monoexponential analyses for ADC calculation in prostate MRI is sufficient to discriminate prostate cancer from normal tissue using b-values ranging from 0 to 800 s/mm².     

Assessment of hepatocellular carcinoma using apparent diffusion coefficient and diffusion kurtosis indices: preliminary experience in fresh liver explants

Objectives

The objective was to perform ex vivo evaluation of non-Gaussian diffusion kurtosis imaging (DKI) for assessment of hepatocellular carcinoma (HCC), including presence of treatment-related necrosis, using fresh liver explants.

Methods

Twelve liver explants underwent 1.5-T magnetic resonance imaging using a DKI sequence with maximal b-value of 2000 s/mm². A standard monoexponential fit was used to calculate apparent diffusion coefficient (ADC), and a non-Gaussian kurtosis fit was used to calculate K, a measure of excess kurtosis of diffusion, and D, a corrected diffusion coefficient accounting for this non-Gaussian behavior. The mean value of these parameters was measured for 16 HCCs based upon histologic findings. For each metric, HCC-to-liver contrast was calculated, and coefficient of variation (CV) was computed for voxels within the lesion as an indicator of heterogeneity. A single hepatopathologist determined HCC necrosis and cellularity.

Results

The 16 HCCs demonstrated intermediate-to-substantial excess diffusional kurtosis, and mean corrected diffusion coefficient D was 23% greater than mean ADC (P=.002). HCC-to-liver contrast and CV of HCC were greater for K than ADC or D, although these differences were significant only for CV of HCCs (P≤.046). ADC, D and K all showed significant differences between non-, partially and completely necrotic HCCs (P≤.004). Among seven nonnecrotic HCCs, cellularity showed a strong inverse correlation with ADC (r=−0.80), a weaker inverse correlation with D (− 0.24) and a direct correlation with K (r= 0.48).

Conclusions

We observed non-Gaussian diffusion behavior for HCCs ex vivo; this DKI model may have added value in HCC characterization in comparison with a standard monoexponential model of diffusion-weighted imaging.     

Diffusion tensor parameters and principal eigenvector coherence: Relation to b-value intervals and field strength

Diffusion-weighted MRI images acquired at b-value greater than 1000 s mm^− 2 measure the diffusion of a restricted pool of water molecules. High b-value images are accompanied by a reduction in signal-to-noise ratio (SNR) due to the application of large diffusion gradients. By fitting the diffusion tensor model to data acquired at incremental b-value intervals, we determined the effect of SNR on tensor parameters in normal human brains, in vivo. In addition, we also investigated the impact of field strength on the diffusion tensor model. Data were acquired at 1.5 and 3 T, at b-values 0, 1000, 2000 and 3000 s mm^− 2 in twenty diffusion-sensitised directions. Fractional anisotropy (FA), mean diffusivity (MD) and principal eigenvector coherence (κ) were calculated from diffusion tensors fitted between datasets with b-values 0–1000, 0–2000, 0–3000, 1000–2000 and 2000–3000 s mm^− 2. Field strength and b-value effects on diffusion parameters were analysed in white and grey matter regions of interest. Decreases in FA, κ and MD were found with increasing b-value in white matter. Univariate analysis showed a significant increase in FA with increasing field strength in highly organised white matter. These results suggest there are significant differences in diffusion parameters at 1.5 and 3 T and that the optimal results, in terms of the highest values of FA in white matter, are obtained at 3 T with a maximum b = 1000 s mm^− 2.     

Assessment of liver fat quantification in the presence of iron

This study assesses the stability of magnetic resonance liver fat measurements against changes in T2* due to the presence of iron, which is a confound for accurate quantification. The liver T2* was experimentally shortened by intravenous infusion of a super paramagnetic iron oxide contrast agent. Low flip angle multiecho gradient echo sequences were performed before, during and after infusion. The liver fat fraction (FF) was calculated in co-localized regions-of-interest using T2* models that assumed no decay, monoexponential decay and biexponential decay. Results show that, when T2* was neglected, there was a strong underestimation of FF and with monoexponential decay there was a weak overestimation of FF. Curve-fitting using the biexponential decay was found to be problematic. The overestimation of FF may be due to remaining deficiencies in the model, although is unlikely to be important for clinical diagnosis of steatosis.     

Can preoperative diffusion-weighted MRI predict postoperative hepatic insufficiency after curative resection of HBV-related hepatocellular carcinoma? A pilot study

Liver fibrosis determines the functional liver reserve. Several studies have reported that the apparent diffusion coefficient (ADC) values of diffusion-weighted magnetic resonance imaging (DW-MRI) can assess liver fibrosis. We investigated whether DW-MRI predicts postoperative hepatic insufficiency and liver fibrosis in patients with hepatitis B virus (HBV)-related hepatocellular carcinoma (HCC). Twenty-six patients with HBV-related HCC who received preoperative DW-MRI on a 3-T MRI system were enrolled between July and December 2008. ADC values were measured twice by two observers. Three “b values” were used: 50, 400 and 800 s/mm². Postoperative hepatic insufficiency was defined as persistent hyperbilirubinemia (total bilirubin level >5 mg/dl for more than 5 days after surgery) or postoperative death without other causes. The mean age (21 men and 5 women) was 51.4 years. Three patients experienced postoperative hepatic insufficiency. liver stiffness measurement predicted postoperative hepatic insufficiency, advanced fibrosis (F3–4), and cirrhosis significantly [area under the receiving operator characteristic curve (AUROC)=0.942, 0.771 and 0.818, respectively, with P=.047, 0.048 and 0.006, respectively]; ADC values of DW-MRI, however, did not (AUROC=0.797, 0.648 and 0.491, respectively, with P=.100, 0.313 and 0.938, respectively). Reliability of ADC values between right and left hepatic lobes (ρ=0.868 and ρ=0.910 in the first and second measures of Observer A; ρ=0.865 and ρ=0.831 in the first and second measures of Observer B) was high and the intra- and interobserver reliability (ρ=0.958 in observer A and ρ=0.977 in observer B; ρ=0.929 in the first measure and ρ=0.978 in the second measure between the two observers) were high. All reliability was significant (P<.001). Our results suggest that DW-MRI on a 3-T MRI system is not suitable for predicting postoperative hepatic insufficiency, advanced liver fibrosis, and cirrhosis in patients with HBV-related HCC, despite significantly high reliability.     

On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted?

The aim of this work was to study the diffusion-related signal attenuation curves (signal-vs.-b curves) measured perpendicular and parallel to the neuronal fibers of the corticospinal tract in vivo and to determine whether effects of restricted diffusion could be observed when varying the diffusion time (T_D). A biexponential model and a two-compartment model including exchange according to the Kärger formalism were employed to analyze the signal-vs.-b curves. To validate the two-compartment model, restricted diffusion with exchange was simulated for uniformly sized cylinders, using different diameters and exchange times. The model was shown to retrieve the simulated parameters well, also when the short gradient pulse approximation was not met. The in vivo measurements performed perpendicular to the tracts, using b values up to 28000 s/mm² and T_D values between 64 and 256 ms, did not show the effects of restricted diffusion as expected from previous ex vivo studies. The applied two-compartment model yielded an average axonal diameter of about 4 μm and an intracellular exchange time of about 300 ms, but did not fit statistically well to the data. In conclusion, this study indicates that if the diffusion is modeled as two compartments, of which one is restricted, exchange must be included in the model.     

Bayesian Modeling of NMR Data: Quantifying Longitudinal Relaxation in Vivo,and in Vitro with a Tissue-Water-Relaxation Mimic (Crosslinked Bovine Serum Albumin)

Recently, a number of magnetic resonance imaging protocols have been reported that seek to exploit the effect of dissolved oxygen (O₂, paramagnetic) on the longitudinal ¹H relaxation of tissue water, thus providing image contrast related to tissue oxygen content. However, tissue water relaxation is dependent on a number of mechanisms and this raises the issue of how best to model the relaxation data. This problem, the model selection problem, occurs in many branches of science and is optimally addressed by Bayesian probability theory. High signal-to-noise, densely sampled, longitudinal ¹H relaxation data were acquired from rat brain in vivo and from a cross-linked bovine serum albumin (xBSA) phantom, a sample that recapitulates the relaxation characteristics of tissue water in vivo. Bayesian-based model selection was applied to a cohort of five competing relaxation models: (1) monoexponential, (2) stretched-exponential, (3) biexponential, (4) Gaussian (normal) R ₁-distribution, and (5) gamma R ₁-distribution. Bayesian joint analysis of multiple replicate datasets revealed that water relaxation of both the xBSA phantom and in vivo rat brain was best described by a biexponential model, while xBSA relaxation datasets truncated to remove evidence of the fast relaxation component were best modeled as a stretched exponential. In all cases, estimated model parameters were compared to the commonly used monoexponential model. Reducing the sampling density of the relaxation data and adding Gaussian-distributed noise served to simulate cases in which the data are acquisition-time or signal-to-noise restricted, respectively. As expected, reducing either the number of data points or the signal-to-noise increases the uncertainty in estimated parameters and, ultimately, reduces support for more complex relaxation models.     

Diffusion-weighted magnetic resonance imaging of human skeletal muscles: gender-, age- and muscle-related differences in apparent diffusion coefficient

Purpose

To evaluate the apparent diffusion coefficient (ADC) of skeletal muscle based on signal intensity (SI) attenuation vs. increasing b values and to determine ADC differences in skeletal muscles between genders, age groups and muscles.

Materials and Methods

Diffusion-weighted images (b values in the range of 0–750 s/mm² at increments of 50 s/mm²) of the ankle dorsiflexors (116 subjects) and the erector spinae muscles (86 subjects) were acquired with a 1.5-T MR device. From the two different slopes obtained in SI vs. b-value logarithmic plots, ADC^b0–50 (b values=0 and 50 s/mm²) reflected diffusion and perfusion, while ADC^b50–750 (b values in the range of 50–750 s/mm² at increments of 50 s/mm²) approximated the true diffusion coefficient. Moreover, to evaluate whether this b-value combination is appropriate for assessing the flow component within muscles, diffusion-weighted images of the ankle dorsiflexors (10 subjects) were obtained before and during temporal arterial occlusion.

Results

ADC^b0–50 and ADC^b50–750 were found to be 2.64×10^–3 and 1.44×10^–3 mm²/s in the ankle dorsiflexors, and 3.02×10^–3 and 1.49×10^–3 mm²/s in the erector spinae muscles, respectively. ADC^b0–50 was significantly higher than ADC^b50–750 in each muscle (P<.01). The erector spinae muscles showed significantly higher ADC values than the ankle dorsiflexors (P<.01). However, for each muscle, there were few significant gender- and age-related ADC differences. Following temporal occlusion, ADC^b0–50 of the ankle dorsiflexors decreased significantly from 2.49 to 1.6×10^–3 mm²/s (P<.01); however, ADC^b50–750 showed no significant change.

Conclusion

Based on the SI attenuation pattern, muscle ADC could be divided into ADC that reflects both diffusion and perfusion, and ADC that approximates a true diffusion coefficient. There were significant differences in ADC of functionally distinct muscles. However, we barely found any gender- or age-related ADC differences for each muscle.     

Evaluation of noncirrhotic hepatic parenchyma with and without significant portal vein stenosis using diffusion-weighted echo-planar MR on the basis of multiple-perfusion-components theory

To determine whether diffusion-weighted echo-planar MR images are sensitive to liver perfusion difference.Noncirrhotic livers of 71 patients (43 males, 28 females; age range, 22-87 years; mean, 61 years) without (n=51) and with (n=20) significant (>70%) portal vein stenosis (accompanying proximal hepatic arterial stenosis and/or biliary tract obstruction in 10) by tumors were examined with diffusion-weighted echo-planar sequences (modified for b factors of 1, 28, 66, 288 and 600 s/mm²). On the basis of multiple-perfusion-components theory, i.e., assuming logarithm of signal intensity for liver perfusion is linearly attenuated versus logarithm of a smaller b factor, we defined the slope of the line as the perfusion-related D′ value. The D′ values of these livers were calculated from images with b factors of 1, 28, and 66 s/mm². The livers' apparent diffusion coefficient values for diffusion (ADC_d values) were calculated from images with b factors of 288 and 600 s/mm².The livers with significant portal vein stenosis had statistically lower mean D′ values than the livers without portal vein stenosis (P<.001 on the Mann-Whitney U test). However, there was no significant difference in ADC_d values between these liver types (P>.05).The D′ value calculated from diffusion-weighted echo-planar sequences with plural smaller b factors may be sensitive to liver perfusion difference.     

Usefulness of diffusion derived vessel density computed from a simplified IVIM imaging protocol: An experimental study with rat biliary duct blockage induced liver fibrosis

ObjectivesLiver vessel density can be evaluated by DDVD (diffusion derived vessel density): DDVD_(b0b1) = Sb0/ROIarea0 – Sb1/ROIarea1, where Sb0 and Sb1 refer to the liver signal when b is 0 or 1 s/mm². Sb1 and ROIarea1 may be replaced by other b-values. With a rat biliary duct ligation (BDL) model, this study assesses the usefulness of liver DDVD computed from a simplified IVIM imaging protocol using b = 25 and b = 50 to replace b = 1 s/mm², alone and in combination with other IVIM parameters.MethodsMale Sprague-Dawley rats were used. The rat number was 5, 5, 5, and 3 respectively, for the timepoints of 7, 14, 21, 28 days post-BDL surgery. 12 rats had partial biliary duct recanalization performed after the rats had BDL for 7 days and then again followed-up for a mean of 14 days. Liver diffusion MRIs were acquired at 3.0 T with a b-value distribution of 0, 25, 50, 75, 100, 150, 300, 700, 1000 s/mm². DDVD_mean (control rats n = 6) was the mean of DDVD_(b0b25) and DDVD_(b0b50). IVIM fitting started from b = 0 s/mm² with segmented fitting and a threshold b of 50 s/mm² (n = 5 for control rats). Three 3-D spaces were constructed using a combination of the four diffusion parameters.ResultsThe control rats and BDL rats (n = 18) had a liver DDVD_mean of 84.0 ± 26.2 and 44.7 ± 14.4 au/pixel (p < 0.001). All 3-D spaces totally separated healthy livers and all fibrotic livers (n = 30, BDL rats and recanalization rats). The mean relative distance between healthy liver cluster and fibrotic liver cluster was 0.331 for PF, D_slow, and D_fast; 0.381 for PF, D_fast, and DDVD_mean; and 0.384 for PF, D_slow, and DDVD_mean.ConclusionA combination of PF, D_slow, and D_fast allows total separation of healthy livers and fibrotic livers and the integration of DDVD improved the separation.     

Intra-voxel incoherent motion MRI in rodent model of diethylnitrosamine-induced liver fibrosis

Rationale and Objectives

To compare the apparent diffusion coefficient (ADC) and the perfusion fraction measured by intra-voxel incoherent motion (IVIM) Magnetic Resonance Imaging (MRI) with liver fibrosis degrees in a rodent model.

Materials and Methods

All experiments received approval from our institutional animal care and use committee. Liver fibrosis was induced in 13 rats by oral gavage with diethylnitrosamine; 4 untreated rats with normal livers were used as controls. Diffusion Weighted MRI was performed and 8 gradient factors (0, 50, 100, 150, 200, 300, 400 and 500 s/mm²) were acquired. The values of ADC, true diffusion coefficient D and perfusion fraction f were measured based on Li Bihan’s method. The percentage of liver fibrosis was assessed via quantitative analysis of Masson trichrome staining using an average of 30 fields per section. The MRI measurements were compared to the histological fibrotic grade to evaluate the correlation between them.

Results

ADC contained the contribution of diffusion and perfusion. The ADC and f values decreased significantly with the increasing fibrosis level (correlation coefficient: ADC: ρ = − 0.781, p < 0.001; f: ρ = − 0.720, p = 0.001); but D was poorly correlated with fibrosis level (ρ = − 0.502, p = 0.040).

Conclusion

The hepatic ADC and the perfusion fraction f were significantly correlated with the liver fibrosis level; however, D was not. This might suggest that hepatic perfusion is altered during the progression of hepatic fibrosis.     

Correction for fast pseudo-diffusive fluid motion contaminations in diffusion tensor imaging

In this prospective study, we quantified the fast pseudo-diffusion contamination by blood perfusion or cerebrospinal fluid (CSF) intravoxel incoherent movements on the measurement of the diffusion tensor metrics in healthy brain tissue.Diffusion-weighted imaging (TR/TE = 4100 ms/90 ms; b-values: 0, 5, 10, 20, 35, 55, 80, 110, 150, 200, 300, 500, 750, 1000, 1300 s/mm², 20 diffusion-encoding directions) was performed on a cohort of five healthy volunteers at 3 Tesla. The projections of the diffusion tensor along each diffusion-encoding direction were computed using a two b-value approach (2b), by fitting the signal to a monoexponential curve (mono), and by correcting for fast pseudo-diffusion compartments using the biexponential intravoxel incoherent motion model (IVIM) (bi). Fractional anisotropy (FA) and mean diffusivity (MD) of the diffusion tensor were quantified in regions of interest drawn over white matter areas, gray matter areas, and the ventricles.A significant dependence of the MD from the evaluation method was found in all selected regions. A lower MD was computed when accounting for the fast-diffusion compartments. A larger dependence was found in the nucleus caudatus (bi: median 0.86 10⁻³ mm²/s, Δ2b: −11.2%, Δmono: −14.4%; p = 0.007), in the anterior horn (bi: median 2.04 10⁻³ mm²/s, Δ2b: −9.4%, Δmono: −11.5%, p = 0.007) and in the posterior horn of the lateral ventricles (bi: median 2.47 10⁻³ mm²/s, Δ2b: −5.5%, Δmono: −11.7%; p = 0.007). Also for the FA, the signal modeling affected the computation of the anisotropy metrics. The deviation depended on the evaluated region with significant differences mainly in the nucleus caudatus (bi: median 0.15, Δ2b: +39.3%, Δmono: +14.7%; p = 0.022) and putamen (bi: median 0.19, Δ2b: +3.1%, Δmono: +17.3%; p = 0.015).Fast pseudo-diffusive regimes locally affect diffusion tensor imaging (DTI) metrics in the brain. Here, we propose the use of an IVIM-based method for correction of signal contaminations through CSF or perfusion.     

Biexponential characterization of prostate tissue water diffusion decay curves over an extended b-factor range

Detailed measurements of water diffusion within the prostate over an extended b-factor range were performed to assess whether the standard assumption of monoexponential signal decay is appropriate in this organ. From nine men undergoing prostate MR staging examinations at 1.5 T, a single 10-mm-thick axial slice was scanned with a line scan diffusion imaging sequence in which 14 equally spaced b factors from 5 to 3,500 s/mm(2) were sampled along three orthogonal diffusion sensitization directions in 6 min. Due to the combination of long scan time and limited volume coverage associated with the multi-b-factor, multidirectional sampling, the slice was chosen online from the available T2-weighted axial images with the specific goal of enabling the sampling of presumed noncancerous regions of interest (ROIs) within the central gland (CG) and peripheral zone (PZ). Histology from prescan biopsy (n=9) and postsurgical resection (n=4) was subsequently employed to help confirm that the ROIs sampled were noncancerous. The CG ROIs were characterized from the T2-weighted images as primarily mixtures of glandular and stromal benign prostatic hyperplasia, which is prevalent in this population. The water signal decays with b factor from all ROIs were clearly non-monoexponential and better served with bi- vs. monoexponential fits, as tested using chi(2)-based F test analyses. Fits to biexponential decay functions yielded intersubject fast diffusion component fractions in the order of 0.73+/-0.08 for both CG and PZ ROIs, fast diffusion coefficients of 2.68+/-0.39 and 2.52+/-0.38 microm(2)/ms and slow diffusion coefficients of 0.44+/-0.16 and 0.23+/-0.16 um(2)/ms for CG and PZ ROIs, respectively. The difference between the slow diffusion coefficients within CG and PZ was statistically significant as assessed with a Mann-Whitney nonparametric test (P<.05). We conclude that a monoexponential model for water diffusion decay in prostate tissue is inadequate when a large range of b factors is sampled and that biexponential analyses are better suited for characterizing prostate diffusion decay curves.     

Magnetic resonance diffusion-weighted imaging: quantitative evaluation of age-related changes in healthy liver parenchyma

The purpose of this study was to verify in healthy liver parenchyma the possible influence of age on DwI-related parameters: apparent diffusion coefficient (ADC), perfusion fraction (PF), diffusion and pseudodiffusion coefficient (D and D^?). Forty healthy adult volunteers (age range 26-86 years), divided into four age groups, were prospectively submitted to a breath-hold magnetic resonance diffusion imaging (MR-DwI) (two b values, 0-300 and 0-1000 s/mm²). A smaller cohort of 16 subjects underwent a free-breath multi-b acquisition (16 b values, 0-750 s/mm²). Quantitative analysis was performed by two observers with manually defined regions of interest, on the most homogeneous portion of the right liver lobe. Individual and group statistical analysis of data was performed: ANOVA to establish differences between groups and Pearson correlation coefficient to investigate the association between DwI parameters and age. The mean, S.D. and 95% limits of agreement of ADC values for each age-defined group are reported. ANOVA showed no significant differences between group means (P always >.05). No significant correlation between subjects' age and DwI parameters was established, both in breath-hold and free-breath acquisitions, on the whole range of adopted b values. Our study conducted on healthy liver parenchyma shows that there are no significant differences in ADC, PF, D and D^? of younger or older subjects.     

Observation of restricted diffusion in the presence of a free diffusion compartment: Single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion–diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.     

Focal nodular hyperplasia of the liver: diffusion and perfusion MRI characteristics

Purpose

To present diffusion and perfusion magnetic resonance imaging (MRI) characteristics of focal nodular hyperplasia (FNH) of the liver.

Materials and Methods

Thirty-five patients with 52 FNHs (21 were pathologically-confirmed) underwent MRI at 1.5-T device. MR diffusion [diffusion-weighted imaging (DWI)] was performed using a free-breathing single-shot, spin-echo, echo-planar sequence with b gradient factor value of 500 s/mm². MR perfusion [perfusion-weighted imaging (PWI)] consisted of a 3D free-breathing LAVA sequence repeated up to 5 minutes after injection of 7 mL Gd-BOPTA (MultiHance, Bracco, Italy) and 20 mL saline flush at a flow rate of 4 mL/s. Apparent diffusion coefficient (ADC) and time-signal intensity curve (TSIC) were obtained for both normal liver and each FNH by two reviewers in conference; maximum enhancement (ME) percentage, time to peak enhancement (TTP), and maximal slope (MS) were also calculated.

Results

On DWI mean ADC value was 1.624×10^− 3 mm²/s for normal liver and 1.629×10^− 3 mm²/s for FNH. ADC value for each FNH and the normal liver was not statistically different (P= .936). On PWI, TSIC-Type 1 (quick and marked enhancement and quick decay followed by slowly decaying) was observed in all 52 FNHs, and TSIC-Type 2 (fast enhancement followed by slowly decaying plateau) in all normal livers. The mean ME, TTP and MS values were significantly different for FNH and normal liver (P= .005).

Conclusion

FNHs of the liver showed typical diffusion and perfusion MRI characteristics in all cases. On the ADC map, we could get similar value between the FNHs and the background parenchyma. On the perfusion imaging, FNHs showed a different pattern distinguished from the background liver.     

In vivo lipid diffusion coefficient measurements in rat bone marrow

The diffusion coefficient of lipids, D_l, within bone marrow, fat deposits and metabolically active intracellular lipids in vivo will depend on several factors including the precise chemical composition of the lipid distribution (chain lengths, degree of unsaturation, etc.) as well as the temperature. As such, D_l may ultimately prove of value in assessing abnormal fatty acid distributions linked to diseases such as cystic fibrosis, diabetes and coronary heart disease. A sensitive temperature dependence of D_l may also prove of value for MR-guided thermal therapies for bone tumors or disease within other fatty tissues like the breast. Measuring diffusion coefficients of high molecular weight lipids in vivo is, however, technically difficult for a number of reasons. For instance, due to the much lower diffusion coefficients compared to water, much higher b factors than those used for central nervous system applications are needed. In addition, the pulse sequence design must incorporate, as much as possible, immunity to motion, susceptibility and chemical shift effects present whenever body imaging is performed. In this work, high b-factor line scan diffusion imaging sequences were designed, implemented and tested for D_l measurement using a 4.7-T horizontal bore animal scanner. The gradient set available allowed for b factors as high as 0.03 μs/nm² (30,000 s/mm²) at echo times as short as 42 ms. The methods were used to measure lipid diffusion coefficients within the marrow of rat paws in vivo, yielding lipid diffusion coefficients approximately two orders of magnitude smaller than typical tissue water diffusion coefficients. Phantom experiments that demonstrate the sensitivity of lipid diffusion coefficients to chain length and temperature were also performed.     

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

Purpose

Our aim was to characterize bi-exponential diffusion signal changes in normal appearing white matter of multiple sclerosis (MS) patients.

Methods

Diffusion 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.

Results

Mono-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 (f_s). However, the fast and slow diffusion components (ADC_f, ADC_s) did not change as a function of either age in controls or lesion number and age in MS patients.

Conclusions

These 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.     

Europium diffusion in SmS

Europium diffusion in samarium sulfide was studied in the temperature range from 780 to 1100°C. Data on the diffusion coefficient and activation energies for the diffusion of europium in single-crystal and polycrystalline SmS samples were obtained. In single-crystal samarium sulfide, europium was shown to migrate predominantly over lattice sites (D ? 10^?12?10^?9 cm²/s). In SmS polycrystals, diffusion was found to exhibit a complex pattern and have both a slow (D ? 10^?10?10^?9 cm²/s) and a fast (D ? 10^?8?10^?7 cm²/s) component. Europium diffusion in a polycrystal is primarily due to europium migration over the boundaries of single-crystal grains in the polycrystal, whose characteristic size is assumed to be that of x-ray coherent-scattering regions.