Monoexponential Model Research Articles

Confidence intervals for the parameters estimated from simulated O2 uptake kinetics: effects of different data treatments

The behaviour of pulmonary O2 uptake following a moderate-intensity step exercise increment is usually described by a first brief increase, followed by a second exponential time course reaching the new steady state (phase II). The parameters describing the phase II kinetics are investigated by applying different data treatments to the acquired O2 uptake data to reduce the effects of their noise before running a non-linear regression procedure. The effects of different data treatments (nothing, resampling at various time intervals or averaging of more repetitions) on the precision and/or accuracy of the kinetics parameters estimated by non-linear regression with a simple mono-exponential model were investigated by artificially generating 10(5) simulated responses with average breath duration of 3.5 s. The simulations showed that, whatever the explored data treatment, the average estimated parameters were close to the theoretical ones. Nevertheless, in all the explored conditions, the non-linear regression provided narrower asymptotic confidence intervals than the real ones. In particular, when the responses were resampled at 1 s time intervals, the width of the asymptotic confidence interval for the time constant was 50% of the real one, even after the averaging of more repetitions. The reasons for this discrepancy were investigated further, allowing us to identify some methods to obtain the correct confidence interval of the O2 uptake kinetics parameters. The simplest method to obtain an asymptotic confidence interval close to the real one is to average more responses resampled to a time interval slightly longer than the average breath duration.

First-day iodine kinetics is useful for individualizing radiation safety precautions for thyroid carcinoma patients

ObjectiveThere is considerable variation in the national regulations of different countries for the release of patients from hospitals after radioiodine therapy. Individual variations make these practices, when based on the worst case scenarios, too restrictive for the majority of patients. However, there are cases in which strict rules are needed to comply with the dose limits to other individuals, especially children. We have developed a method to individualize radiation safety precautions.Materials and methodsTwenty-three patients with differentiated thyroid carcinoma were included in the study. Four weeks after thyroidectomy, 1.1–3.7 GBq of radioiodine was administered and iodine kinetics were followed with external measurements until hospital discharge. The absorbed dose at the wrist holder was measured with thermoluminescence dosimetry (TLD) during hospital stay and after hospital discharge for up to 1 week. The TLD results were compared with the iodine kinetics. The dose to other individuals was estimated with extra TLDs located both on the patient’s bed and given to family members. The kinetics data were fitted in both monoexponential and biexponential models and both for the full measurement period (down to the residual activity level<400 MBq) and for the first 24 h after radioiodine administration.ResultsThe biexponential model was capable of predicting the cumulated dose up to 1 week for both the longer and the shorter measured data set. The occupancy factors both for a person sleeping on the same bed and for a person living in the same apartment with the patient were in agreement with the recommended occupancy factor values of the American Thyroid Association. From these findings it is possible to individualize radiation safety precautions by taking into account the iodine pharmacokinetics and living conditions of a patient.ConclusionBy measuring the activity content within the body for the first 24 h after radioiodine administration it is possible to individualize radiation safety precautions for thyroid carcinoma patients.

A novel semiautomatic parenchyma extraction method for improved MRI R2* relaxometry of iron loaded liver

To propose and evaluate an automatic method of extracting parenchyma from a manually delineated whole liver for the R2* measurement of iron load. In all, 108 transfusion-dependent patients with a wide range of hepatic iron content were scanned with a multiecho gradient-echo sequence. The R2* was measured by fitting the average signal of liver parenchyma, extracted by the proposed semiautomatic parenchyma extraction (SAPE), traditional manually delineated multiple regions-of-interest (mROIs), and T2* thresholding methods to the noise-corrected monoexponential model. The R2* measurement accuracy of the SAPE method was evaluated through simulation; the intra- and interobserver reproducibility of SAPE, mROI, and T2* thresholding were assessed from the in vivo data using coefficient of variation (CoV). In the simulation, the mean absolute percentage error of R2* measurement using SAPE was 0.23% (range 0.01%-1.09%). In vivo study, the CoVs of intra- and interobserver reproducibility were 0.83%, 1.39% for SAPE, 3.63%, 6.28% for mROI, and 1.62%, 2.66% for T2* thresholding, respectively. The SAPE method provides an accurate and reliable approach to assessing the overall hepatic iron content. The improved magnetic resonance imaging (MRI) R2* reproducibility using the SAPE method may lead to more accurate tissue characterization and increased diagnostic confidence.

A reply to the letter to the editor regarding “microstructural changes of the corticospinal tract in idiopathic normal pressure hydrocephalus: a comparison of diffusion tensor and diffusional kurtosis imaging”

Dear Sir, We read with interest the letter concerning our article “Microstructural changes of the corticospinal tract in idiopathic normal pressure hydrocephalus: a comparison of diffusion tensor and diffusional kurtosis imaging.” The correspondents noted that diffusion metrics such as fractional anisotropy (FA) and apparent diffusion coefficient (ADC) depend on the combination of data (i.e., different b values) and theory (Gaussian or non-Gaussian). We quite agree with their opinion that FA of diffusion tensor imaging (DTI) should be calculated from tensor model usually from b = 0 and 1,000. Our description might lead the readers to misunderstanding. We think that our description of the section “Tractography and tract-specific analysis of CST” was unclear because we indeed calculated ADC and FA from a portion of the diffusional kurtosis imaging (DKI) data based on b values of 0 and 1,000 s/mm2 using the conventional model. These calculated values were then used as the estimates for ADC and FA. We also recognize that the conventional DTI metrics for clinical studies should be estimated by using the same b values of 0 and 1,000 s/mm2, as in the many reports in the clinical DTI literatures. In other studies concerning DKI, we explicitly stated that the DTI metrics used for comparison with DKI are calculated using the data obtained from b values of 0 and 1,000 s/mm2 and a mono-exponential fit [1–3]. Moreover, although we did not provide the details in this paper, our software for DTI and DKI calculation (dTV.II.FZRx; Image Computing and Analysis Laboratory, Department of Radiology, The University of Tokyo Hospital, Japan) [4] has the ability to calculate DTI metrics such as FA and ADC on the basis of the mono-exponential model by using user-specified b value data when performing DKI calculations. The letter, which suggests that differences between the diffusion metrics derive from differences in parameters or analysis theories, is still of great value. We agree that in DKI or other diffusion-related studies that employ non-conventional signal-fitting procedures, the authors should clarify the type of method and data used for calculating the diffusion metrics.

An automatic method for myocardial T2* curve fitting in thalassemia patients with severe iron overload

Purpose: Myocardial iron overload assessment by multislice multiecho T2* technique is used in the clinical management of thalassemia major (TM) patients. Signal decay curves are extracted from the 16 left ventricular (LV) segments and the fitting of these curves to a mono-exponential model provides the corresponding T2* values. In patients with severe cardiac iron overload, where signal will decay quickly becoming comparable to image noise, manual truncation of signal decay curves excluding later echo times (TEs) is adopted. In this study an automatic truncation method avoiding the variability associated with the manual selection of the truncation point is introduced and validated. Methods: Twenty patients (13 males, age 33±7 years) enrolled in the MIOT Network and diagnosed for severe iron overload (T2*<10 ms) were considered. Using a previously validated software the segmental T2* values were evaluated by the standard methodology (i.e. manual truncation). Images were independently analysed by the developed automated approach. The percentage fitting error (e) was computed as the root mean square error between the signal decay curve and the mono-exponential model normalized to the mean value of the signal. If e was > 5%, the algorithm cut-off the last TE and performed again the fitting. The procedure was iterated until the error become <5% or the number of TEs become equal to three. To assess the inter-operator variability, the dataset was processed by a second operator. Results: The Coefficient of Variability (CoV) for inter-observer variability was 6.82±4.01%. The CoV between automated and manual analysis was 6.15±3.92%, not significantly different from inter-observer variability (P=0.332). No significant difference was detected between mid-septum and global T2* values evaluated with manual and automated procedure (P=0.26 and P=0.91, respectively). The mean fitting error was not significantly different in manual and automated analysis (4.10±2.11 vs. 4.52±2.12, P=0.53). In segmental analysis, no significant differences were found between manual and automatic procedure (P>0.01 for all segments). Conclusions: Truncation of signal decay curve needed to compensate for low signal in later echoes in patients with severe iron overload can be effectively automatized avoiding operator induced variability.

Toxicokinetics of polybrominated diphenyl ethers across life stages in the northern leopard frog (Lithobates pipiens)

Polybrominated diphenyl ethers (PBDEs), a class of flame retardants, are bioaccumulative toxins that can biomagnify in food webs. However, little is known about the toxicokinetics of total and congener-specific BDEs in lower vertebrates. The authors exposed northern leopard frog (Lithobates (Rana) pipiens) tadpoles to diets containing DE-71 (a pentabromodiphenyl ether mixture (0 ng/g as control, 71.4 ng/g, and 634 DE-71 ng/g wet mass)) for 50 d, followed by a period of depuration during which they were fed only undosed (control) food. After 28 d, tadpoles eliminated over 94% of the ΣPBDEs from their tissues (t½ = 5.9 ± 1.9 d) with no significant differences in elimination rates for the predominant congeners. Elimination of BDE-99 was independent of dose, indicating first-order kinetics. It did not fit a biexponential model significantly better than a monoexponential model, indicating single-compartment elimination. To compare developmental life-stage kinetics following larval exposure, the authors collected individuals at the beginning and end of metamorphosis and at 70 d postmetamorphosis. During metamorphosis, total-body residues per individual did not significantly change, implying little to no elimination. After 70 d, juvenile frogs eliminated 89.7% of the ΣPBDEs from their tissues, and BDE-47 was eliminated at a faster rate (t½ = 17.3 d) than BDE-99 and BDE-100 (t½ = 63.0 d and 69.3 d, respectively). Because the kinetics of PBDEs in L. pipiens differed among life stages, developmental life stage-especially for species that undergo metamorphosis-should be considered when determining the toxicity of persistent organic pollutants.

Quantification of superparamagnetic iron oxide using inversion recovery balanced steady-state free precession

Cellular and molecular MRI trafficking studies using superparamagnetic iron oxide (SPIO) have greatly improved non-invasive investigations of disease progression and drug efficacy, but thus far, these studies have largely been restricted to qualitative assessment of hypo- or hyperintense areas near SPIO. In this work, SPIO quantification using inversion recovery balanced steady-state free precession (IR-bSSFP) was demonstrated at 3T by extracting R2 values from a monoexponential model (P. Schmitt et al., 2004). A low flip angle was shown to reduce the apparent recovery rate of the IR-bSSFP time course, thus extending the dynamic range of quantification. However, low flip angle acquisitions preclude the use of traditional methods for combining RF phase-cycled images to reduce banding artifacts arising from off-resonance due to B0 inhomogeneity. To achieve R2 quantification of SPIO, we present a new algorithm applicable to low flip angle IR-bSSFP acquisitions that is specifically designed to identify on-resonance acquisitions. We demonstrate in this work, using both theoretical and empirical methods, that the smallest estimated R2 from multiple RF phase-cycled acquisitions correspond well to the on-resonance time course. Using this novel minimum R2 algorithm, homogeneous R2 maps and linear R2 calibration curves were created up to 100μg(Fe)/mL with 20° flip angles, despite substantial B0 inhomogeneity. In addition, we have shown this technique to be feasible for pre-clinical research: the minimum R2 algorithm was resistant to off-resonance in a single slice mouse R2 map, whereas maximum intensity projection resulted in banding artifacts and overestimated R2 values. With the application of recent advances in accelerated acquisitions, IR-bSSFP has the potential to quantify SPIO in vivo, thus providing important information for oncology, immunology, and regenerative medicine MRI studies.

The effect of short‐term exercise training and nitric oxide on the adaptation of femoral vascular conductance at the onset of contraction

We tested the hypothesis that short‐term mild‐ (M) and heavy‐intensity (H) exercise training (ET) would speed the adaptation of femoral vascular conductance (FVC) at the onset of contraction by a nitric oxide (NO) dependent mechanism. Sprague‐Dawley rats (n=18) were randomized to sedentary (S), M (20m/min5% grade) or H (40m/min5% grade) ET groups and trained 5d/wkfor 4 wks with equal ET volume. Rats were anesthetised and instrumented for measurement of arterial blood pressure and femoral artery blood flow. FVC was calculated. The triceps surae muscle group was stimulated to contract at 30% and 60% of maximal contractile force (MCF) before and after NO synthase blockade (L‐NAME, 5mg/kg IV). FVC data were fit with a mono‐exponential model. The time constant (τ) for FVC was not different (p&gt;;0.05) between groups at 30% (S = 18 ± 13s; M = 15 ± 5s; H = 13 ± 14s) or 60% MCF (S = 24 ± 17s; M = 16 ± 4s; H = 19 ± 4s). L‐NAME increased (p&lt;0.05) τ in all groups at 30% MCF (S = 25 ± 12s; M = 21 ± 6s; H = 27 ± 13s), but did not alter (p&gt;;0.05) τ at 60% MCF (S = 25 ± 9s; M = 22 ± 9s; H = 20 ± 3s). The primary findings from this study were that: 1) short‐term ET did not alter the adaptation of FVC at the onset of contraction; and 2) regardless of training status, NO contributed to the regulation of FVC kinetics at the onset of moderate‐intensity contraction (30% MCF), whereas NO was not required for vasodilation at the onset of heavy‐intensity contraction (60% MCF). NSERC, Canada.

3:46 PM Abstract No. 105 - Modeling the rate of bilirubin decay after percutaneous drainage prior to chemotherapy

Purpose To evaluate the potential of two models of bilirubin decay to predict response to drainage in patients who underwent biliary drainage to lower serum bilirubin prior to chemotherapy. Materials and Methods IRB-approved retrospective review identified 77 patients with malignant biliary obstruction who underwent a single biliary drainage to decrease bilirubin prior to chemotherapy administration and who had at least four subsequent serum bilirubin determinations (regardless of value) at 7-10 day intervals for the first 4 weeks following the procedure. Data were analyzed in both mono-exponential (ME) (bilirubin level is described in terms of pure exponential decay) and mono-exponential-static (MS) (bilirubin level is described in terms of exponential decay followed by an inflection point where the bilirubin level levels off to a constant value) models. Responders were defined as patients who achieved total serum bilirubin levels Results Across all patients, the MS model had better fit with total serum bilirubin values after drainage than the ME model (R2 0.82 vs 0.62, respectively). When patients were stratified into responders and non-responders, the MS model similarly had better fit to patient data (responders: R2 0.91 v 0.71; non-responders R2 0.66 v 0.45). Parameters extracted from both models (ME and MS) suggest that both estimated pre-drainage bilirubin (10.4 and 10.7 mg/dL, respectively) and the exponential decay rate (0.14 and 0.22 mg/dL/day) of responders was significantly different from the estimated pre-drainage bilirubin (15.0 and 15.1 mg/dL) (P=0.0003 and P Conclusion Models of bilirubin response to percutaneous drainage may be useful to provide early clinical separation of responders from non-responders, prompting additional drainage or internalization of drainage when clinically appropriate.

Sensitivities of statistical distribution model and diffusion kurtosis model in varying microstructural environments: A Monte Carlo study

The aim of this study was to investigate the microstructural sensitivity of the statistical distribution and diffusion kurtosis (DKI) models of non-monoexponential signal attenuation in the brain using diffusion-weighted MRI (DWI). We first developed a simulation of 2-D water diffusion inside simulated tissue consisting of semi-permeable cells and a variable cell size. We simulated a DWI acquisition of the signal in a volume using a pulsed gradient spin echo (PGSE) pulse sequence, and fitted the models to the simulated DWI signals using b-values up to 2500s/mm2. For comparison, we calculated the apparent diffusion coefficient (ADC) of the monoexponential model (b-value=1000s/mm2). In separate experiments, we varied the cell size (5–10–15μm), cell volume fraction (0.50–0.65–0.80), and membrane permeability (0.001–0.01–0.1mm/s) to study how the fitted parameters tracked simulated microstructural changes. The ADC was sensitive to all the simulated microstructural changes except the decrease in membrane permeability. The ADC increased with larger cell size, smaller cell volume fraction, and larger membrane permeability. The σstat of the statistical distribution model increased exclusively with a decrease in cell volume fraction. The Kapp of the DKI model was exclusively increased with decreased cell size and decreased with increasing membrane permeability. These results suggest that the non-monoexponential models of water diffusion have different, specific microstructural sensitivity, and a combination of the models may give insights into the microstructural underpinning of tissue pathology.

Relationship between changes in pulmonary kinetics and autonomic regulation of blood flow

Various regulatory mechanisms of pulmonary oxygen uptake (V̇O2) kinetics have been postulated. The purpose of this study was to investigate the relationship between vagal withdrawal, measured using RMSSDRR, the root mean square of successive differences in cardiac interval (RR) kinetics, a mediator of oxygen delivery, and V̇O2 kinetics. Forty-nine healthy adults (23 ± 3 years; 72 ± 13 kg; 1.80 ± 0.08 m) performed multiple repeat transitions to moderate- and heavy-intensity exercise. Electrocardiography, impedance cardiography, and pulmonary gas exchange parameters were measured throughout; time domain measures of heart rate variability were subsequently derived. The parameters describing the dynamic response of V̇O2, cardiac output (Q) and RMSSDRR were determined using a mono-exponential model. During heavy-intensity exercise, the phase II τ of V̇O2 was significantly correlated with the τ of RR (r = 0.36, P < 0.05), Q (r = 0.67, P < 0.05), and RMSSDRR (r = 0.38, P < 0.05). The τ describing the rise in Q explained 47% of the variation in V̇O2 τ, with 30% of the rate of this rise in Q explained by the τ of RR and RMSSDRR. No relationship was evident between V̇O2 kinetics and those of Q, RR, or RMSSDRR during moderate exercise. Vagal withdrawal kinetics support the concept of a centrally mediated oxygen delivery limitation partly regulating V̇O2 kinetics during heavy-, but not moderate-, intensity exercise.

Model‐based Acceleration of Parameter mapping (MAP) for saturation prepared radially acquired data

A reconstruction technique called Model-based Acceleration of Parameter mapping (MAP) is presented allowing for quantification of longitudinal relaxation time and proton density from radial single-shot measurements after saturation recovery magnetization preparation. Using a mono-exponential model in image space, an iterative fitting algorithm is used to reconstruct one well resolved and consistent image for each of the projections acquired during the saturation recovery relaxation process. The functionality of the algorithm is examined in numerical simulations, phantom experiments, and in-vivo studies. MAP reconstructions of single-shot acquisitions feature the same image quality and resolution as fully sampled reference images in phantom and in-vivo studies. The longitudinal relaxation times obtained from the MAP reconstructions are in very good agreement with the reference values in numerical simulations as well as phantom and in-vivo measurements. Compared to available contrast manipulation techniques, no averaging of projections acquired at different time points of the relaxation process is required in MAP imaging. The proposed technique offers new ways of extracting quantitative information from single-shot measurements acquired after magnetization preparation. The reconstruction simultaneously yields images with high spatiotemporal resolution fully consistent with the acquired data as well as maps of the effective longitudinal relaxation parameter and the relative proton density.

An automatic method for myocardial T2* curve fitting in thalassemia patients with severe iron overload

Background Myocardial iron overload assessment by multislice multiecho T2* technique is used in the clinical management of thalassemia major (TM) patients. Signal decay curves are extracted from the 16 left ventricular (LV) segments and the fitting of these curves to a mono-exponential model provides the corresponding T2* values. In patients with severe cardiac iron overload, where signal will decay quickly becoming comparable to image noise, manual truncation of signal decay curves excluding later echo times (TEs) is adopted. In this study an automatic truncation method avoiding the variability associated with the manual selection of the truncation point is introduced and validated. Methods Twenty patients (13 males, age 33±7 years) enrolled in the MIOT Network and diagnosed for severe iron overload (T2* 5%, the algorithm cut-off the last TE and performed again the fitting. The procedure was iterated until the error become <5% or the number of TEs become equal to three. To

Quantitative analysis of diffusion-weighted magnetic resonance imaging in malignant breast lesions using different b value combinations

ObjectivesTo explore how apparent diffusion coefficients (ADCs) in malignant breast lesions are affected by selection of b values in the monoexponential model and to compare ADCs with diffusion coefficients (Ds) obtained from the biexponential model.MethodsTwenty-four women (mean age 51.3 years) with locally advanced breast cancer were included in this study. Pre-treatment diffusion-weighted magnetic resonance imaging was performed using a 1.5-T system with b values of 0, 50, 100, 250 and 800 s/mm2. Thirteen different b value combinations were used to derive individual monoexponential ADC maps. All b values were used in the biexponential model.ResultsMedian ADC (including all b values) and D were 1.04 × 10-3 mm2/s (range 0.82–1.61 × 10-3 mm2/s) and 0.84 × 10-3 mm2/s (range 0.17–1.56 × 10-3 mm2/s), respectively. There was a strong positive correlation between ADCs and Ds. For clinically relevant b value combinations, maximum deviation between ADCs including and excluding low b values (<100 s/mm2) was 11.8 %.ConclusionSelection of b values strongly affects ADCs of malignant breast lesions. However, by excluding low b values, ADCs approach biexponential Ds, demonstrating that microperfusion influences the diffusion signal. Thus, care should be taken when ADC calculation includes low b values.Key Points• Diffusion-weighted sequences are increasingly used in breast magnetic resonance imaging • Diffusion-weighting (b) values strongly influence apparent diffusion coefficients of malignant lesions • Exclusion of low b values reduces the apparent diffusion coefficient • Flow-insensitive monoexponential apparent diffusion coefficients approach biexponential diffusion coefficients

Mazaheri Y, Vargas HA, Akin O, Goldman DA, Hricak H. Reducing the influence of b‐value selection on diffusion‐weighted imaging of the prostate: evaluation of a revised monoexponential model within a clinical setting. J Magn Reson Imaging 2012;35:660–668

Some of the values reported in the legend of Figure 1 were incorrect as published. The authors regret the error and thank Dr. Daniel G.Q. Chong, PhD, and Dr. Lauren J. Bains, PhD, both from the Department of Diagnostic, Interventional and Pediatric Radiology, Inselspital, Bern Switzerland, for identifying the errors. The legend for Figure 1 appeared as follows: Figure 1. Simulated normalized logarithmic diffusion signal intensity (log(S(b))/S(0)) as a function of b-value based on values reported by Riches et al (13). The estimated values of ADC400 and ADC700 were obtained from the standard monoexponential model and the estimated values of D and f were obtained from the revised monoexponential model. A: For benign PZ, the simulated biexponential signal was generated using the following reported parameters (13): D = 1.45 × 10−3 mm2/s, f = 0.20, and D* = 21.20 × 10−3 mm2/s. Estimated ADC values were: ADC400 = 2.00 × 10−3 mm2/s, ADC700 = 1.80 × 10−3 mm2/s. Estimated values for the revised monoexponential were: D = 1.45 × 10−3 mm2/s, f = 0.20. B: For tumor the simulated biexponential signal was generated using the following reported parameters (13): D = 1.10 × 10−3 mm2/s, f = 0.15, and D* = 25.20 × 10−3 mm2/s. Estimated ADC values were: ADC400 = 1.50 × 10−3 mm2/s, ADC700 = 1.30 × 10−3 mm2/s. Estimated values for the revised monoexponential were: D = 1.10 × 10−3 mm2/s, f = 0.15. It should have appeared as follows: Figure 1. Simulated normalized logarithmic diffusion signal intensity (log(S(b))/S(0)) as a function of b-value based on values reported by Riches et al (13). The estimated values of ADC400 and ADC700 were obtained from the standard monoexponential model and the estimated values of D and f were obtained from the revised monoexponential model. A: For benign PZ, the simulated biexponential signal was generated using the following reported parameters (13): D = 1.45 × 10−3 mm2/s, f = 0.20, and D* = 21.20 × 10−3 mm2/s. Estimated ADC values were: ADC400 = 2.01 × 10−3 mm2/s, ADC700 = 1.77 × 10−3 mm2/s. Estimated values for the revised monoexponential were: D = 1.45 × 10−3 mm2/s, f = 0.22. B: For tumor the simulated biexponential signal was generated using the following reported parameters (13): D = 1.10 × 10−3 mm2/s, f = 0.15, and D* = 25.20 × 10−3 mm2/s. Estimated ADC values were: ADC400 = 1.51 × 10−3 mm2/s, ADC700 = 1.33 × 10−3 mm2/s. Estimated values for the revised monoexponential were: D = 1.10 × 10−3 mm2/s, f = 0.16.

D.O.6 Quantification of inflammation, necrosis or damages by NMR imaging in fatty infiltrated muscles: A practical approach

In NMR imaging of neuromuscular disorders, and particularly in muscle dystrophy, a prolonged T2 of muscle water can be used as a marker of disease activity. However, when fat contributes to the NMR signal, as in non-fat-suppressed images of infiltrated muscles, then the conventional mono-exponential data fit will result in prolonged T2 values that principally reflect the degree of fat infiltration. Fat-suppression schemes at acquisition are an obvious option but fail over large volumes. Here, we propose and validate a solution to measure muscle water T2 on non-fat-suppressed NMR images, based on analysing the multiple echo series by a tri-exponential model. Thigh images of 10 patients with a variety of neuromuscular diseases were retrospectively analyzed. Muscle fatty infiltration was quantified using a 3D 3-point Dixon sequence. For muscle T2 determination, a standard multi-slice multi spin echo (17 echos with TEs ranging from 9.5ms to 161ms) sequence was used, in which muscle signal decay was considered as the combination of two lipid components and one water component. In order to compare the sensitivity to fat infiltration of the mono- and tri- exponential approaches, we determined the T2 values in groups of pixels belonging to the same muscle but with different ranges of fat infiltration, [0–20%] and [20–50%]. The mono-exponential model yielded T2 values that were abnormally high (>70ms) and heavily dependent on the degree of fat infiltration (p<0.0001). In contrast, the estimated T2 was independent of fat fraction when estimated using the tri-exponential model. Whilst the mono-exponential T2 values were highly correlated with the Dixon fat signal fraction (r2=0.87), the T2s obtained with the tri-exponential method were not (r2=0.12). Normal muscle water T2 distribution was narrow: 35±2ms, which permitted detection of T2 alterations of small amplitude, putatively reflecting mild muscle damage, even in heavily fat infiltrated muscles.

Quantifying hepatic fibrosis using a biexponential model of diffusion weighted imaging in ex vivo liver specimens

The purpose of this study was to evaluate the non-Gaussian behavior of diffusion related signal decay of the ex vivo murine liver tissues from a dietary model of hepatic fibrosis. To this end, a biexponential formalism was used to model high b-value diffusion imaging (up to 3500 s/mm2), the findings of which were correlated with liver histopathology and compared to a simple monoexponential model. The presence of a major, fast diffusing component and a minor, slow diffusing component was demonstrated. With increasing hepatic fibrosis, the fractional contribution of the fast diffusing component decreased, as did the diffusion coefficient of the fast diffusing component. Strong correlation between the degrees of liver fibrosis and a two-predictor regression model incorporating parameters of the biexponential model was found. Using Akaike's Information Criterion analyses, the biexponential model resulted in an improved fit of the high b-value diffusion data when compared to the monoexponential model.

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

PurposeTo evaluate which mathematical model (monoexponential, biexponential, statistical, kurtosis) fits best to the diffusion-weighted signal in prostate magnetic resonance imaging (MRI). Materials and Methods24 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. ResultsMonoexponential 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 ADCmono 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. ConclusionAlthough 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

ObjectivesThe 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. MethodsTwelve 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. ResultsThe 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). ConclusionsWe 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.

Quantification of T1ρ relaxation by using rotary echo spin-lock pulses in the presence of B0 inhomogeneity

T1ρ relaxation is traditionally described as a mono-exponential signal decay with spin-lock time. However, T1ρ quantification by fitting to the mono-exponential model can be substantially compromised in the presence of field inhomogeneities, especially for low spin-lock frequencies. The normal approach to address this issue involves the development of dedicated composite spin-lock pulses for artifact reduction while still using the mono-exponential model for T1ρ fitting. In this work, we propose an alternative approach for improved T1ρ quantification with the widely-used rotary echo spin-lock pulses in the presence of B0 inhomogeneities by fitting to a modified theoretical model which is derived to reveal the dependence of T1ρ-prepared magnetization on T1ρ, T2ρ, spin-lock time, spin-lock frequency and off-resonance, without involving complicated spin-lock pulse design. It has potentials for T1ρ quantification improvement at low spin-lock frequencies. Improved T1ρ mapping was demonstrated on phantom and in vivo rat spin-lock imaging at 3 T compared to the mapping using the mono-exponential model.