Improved reconstruction of crossing fibers in the mouse optic pathways with orientation distribution function fingerprinting.

PURPOSE: The accuracy of diffusion MRI tractography reconstruction decreases in the white matter regions with crossing fibers. The optic pathways in rodents provide a challenging structure to test new diffusion tractography approaches because of the small crossing volume within the optic chiasm and the unbalanced 9:1 proportion between the contra- and ipsilateral neural projections from the retina to the lateral geniculate nucleus, respectively. METHODS: Common approaches based on Orientation Distribution Function (ODF) peak finding or statistical inference were compared qualitatively and quantitatively to ODF Fingerprinting (ODF-FP) for reconstruction of crossing fibers within the optic chiasm using in vivo diffusion MRI ( n = 18 $$ n=18 $$ healthy C57BL/6 mice). Manganese-Enhanced MRI (MEMRI) was obtained after intravitreal injection of manganese chloride and used as a reference standard for the optic pathway anatomy. RESULTS: ODF-FP outperformed by over 100% all the tested methods in terms of the ratios between the contra- and ipsilateral segments of the reconstructed optic pathways as well as the spatial overlap between tractography and MEMRI. CONCLUSION: In this challenging model system, ODF-Fingerprinting reduced uncertainty of diffusion tractography for complex structural formations of fiber bundles.

Tractography passes the test: Results from the diffusion-simulated connectivity (disco) challenge.

Estimating structural connectivity from diffusion-weighted magnetic resonance imaging is a challenging task, partly due to the presence of false-positive connections and the misestimation of connection weights. Building on previous efforts, the MICCAI-CDMRI Diffusion-Simulated Connectivity (DiSCo) challenge was carried out to evaluate state-of-the-art connectivity methods using novel large-scale numerical phantoms. The diffusion signal for the phantoms was obtained from Monte Carlo simulations. The results of the challenge suggest that methods selected by the 14 teams participating in the challenge can provide high correlations between estimated and ground-truth connectivity weights, in complex numerical environments. Additionally, the methods used by the participating teams were able to accurately identify the binary connectivity of the numerical dataset. However, specific false positive and false negative connections were consistently estimated across all methods. Although the challenge dataset doesn't capture the complexity of a real brain, it provided unique data with known macrostructure and microstructure ground-truth properties to facilitate the development of connectivity estimation methods.

Performance of orientation distribution function-fingerprinting with a biophysical multicompartment diffusion model.

PURPOSE: Orientation Distribution Function (ODF) peak finding methods typically fail to reconstruct fibers crossing at shallow angles below 40°, leading to errors in tractography. ODF-Fingerprinting (ODF-FP) with the biophysical multicompartment diffusion model allows for breaking this barrier. METHODS: A randomized mechanism to generate a multidimensional ODF-dictionary that covers biologically plausible ranges of intra- and extra-axonal diffusivities and fraction volumes is introduced. This enables ODF-FP to address the high variability of brain tissue. The performance of the proposed approach is evaluated on both numerical simulations and a reconstruction of major fascicles from high- and low-resolution in vivo diffusion images. RESULTS: ODF-FP with the suggested modifications correctly identifies fibers crossing at angles as shallow as 10 degrees in the simulated data. In vivo, our approach reaches 56% of true positives in determining fiber directions, resulting in visibly more accurate reconstruction of pyramidal tracts, arcuate fasciculus, and optic radiations than the state-of-the-art techniques. Moreover, the estimated diffusivity values and fraction volumes in corpus callosum conform with the values reported in the literature. CONCLUSION: The modified ODF-FP outperforms commonly used fiber reconstruction methods at shallow angles, which improves deterministic tractography outcomes of major fascicles. In addition, the proposed approach allows for linearization of the microstructure parameters fitting problem.

Free-breathing radial imaging using a pilot-tone radiofrequency transmitter for detection of respiratory motion.

PURPOSE: To describe an approach for detection of respiratory signals using a transmitted radiofrequency (RF) reference signal called Pilot-Tone (PT) and to use the PT signal for creation of motion-resolved images based on 3D stack-of-stars imaging under free-breathing conditions. METHODS: This work explores the use of a reference RF signal generated by a small RF transmitter, placed outside the MR bore. The reference signal is received in parallel to the MR signal during each readout. Because the received PT amplitude is modulated by the subject's breathing pattern, a respiratory signal can be obtained by detecting the strength of the received PT signal over time. The breathing-induced PT signal modulation can then be used for reconstructing motion-resolved images from free-breathing scans. The PT approach was tested in volunteers using a radial stack-of-stars 3D gradient echo (GRE) sequence with golden-angle acquisition. RESULTS: Respiratory signals derived from the proposed PT method were compared to signals from a respiratory cushion sensor and k-space-center-based self-navigation under different breathing conditions. Moreover, the accuracy was assessed using a modified acquisition scheme replacing the golden-angle scheme by a zero-angle acquisition. Incorporating the PT signal into eXtra-Dimensional (XD) motion-resolved reconstruction led to improved image quality and clearer anatomical depiction of the lung and liver compared to k-space-center signal and motion-averaged reconstruction, when binned into 6, 8, and 10 motion states. CONCLUSION: PT is a novel concept for tracking respiratory motion. Its small dimension (8 cm), high sampling rate, and minimal interaction with the imaging scan offers great potential for resolving respiratory motion.

Fingerprinting Orientation Distribution Functions in diffusion MRI detects smaller crossing angles.

Diffusion tractography is routinely used to study white matter architecture and brain connectivity in vivo. A key step for successful tractography of neuronal tracts is the correct identification of tract directions in each voxel. Here we propose a fingerprinting-based methodology to identify these fiber directions in Orientation Distribution Functions, dubbed ODF-Fingerprinting (ODF-FP). In ODF-FP, fiber configurations are selected based on the similarity between measured ODFs and elements in a pre-computed library. In noisy ODFs, the library matching algorithm penalizes the more complex fiber configurations. ODF simulations and analysis of bootstrapped partial and whole-brain in vivo datasets show that the ODF-FP approach improves the detection of fiber pairs with small crossing angles while maintaining fiber direction precision, which leads to better tractography results. Rather than focusing on the ODF maxima, the ODF-FP approach uses the whole ODF shape to infer fiber directions to improve the detection of fiber bundles with small crossing angle. The resulting fiber directions aid tractography algorithms in accurately displaying neuronal tracts and calculating brain connectivity.

Cardiorespiratory motion-tracking via self-refocused rosette navigators.

PURPOSE: To develop a flexible method for tracking respiratory and cardiac motions throughout MR and PET-MR body examinations that requires no additional hardware and minimal sequence modification. METHODS: The incorporation of a contrast-neutral rosette navigator module following the RF excitation allows for robust cardiorespiratory motion tracking with minimal impact on the host sequence. Spatial encoding gradients are applied to the FID signal and the desired motion signals are extracted with a blind source separation technique. This approach is validated with an anthropomorphic, PET-MR-compatible motion phantom as well as in 13 human subjects. RESULTS: Both respiratory and cardiac motions were reliably extracted from the proposed rosette navigator in phantom and patient studies. In the phantom study, the MR-derived motion signals were additionally validated against the ground truth measurement of diaphragm displacement and left ventricle model triggering pulse. CONCLUSION: The proposed method yields accurate respiratory and cardiac motion-state tracking, requiring only a short (1.76 ms) additional navigator module, which is self-refocusing and imposes minimal constraints on sequence design.

Low Rank plus Sparse decomposition of ODFs for improved detection of group-level differences and variable correlations in white matter.

A novel approach is presented for group statistical analysis of diffusion weighted MRI datasets through voxelwise Orientation Distribution Functions (ODF). Recent advances in MRI acquisition make it possible to use high quality diffusion weighted protocols (multi-shell, large number of gradient directions) for routine in vivo study of white matter architecture. The dimensionality of these data sets is however often reduced to simplify statistical analysis. While these approaches may detect large group differences, they do not fully capitalize on all acquired image volumes. Incorporation of all available diffusion information in the analysis however risks biasing the outcome by outliers. Here we propose a statistical analysis method operating on the ODF, either the diffusion ODF or fiber ODF. To avoid outlier bias and reliably detect voxelwise group differences and correlations with demographic or behavioral variables, we apply the Low-Rank plus Sparse (L+S) matrix decomposition on the voxelwise ODFs which separates the sparse individual variability in the sparse matrix S whilst recovering the essential ODF features in the low-rank matrix L. We demonstrate the performance of this ODF L+S approach by replicating the established negative association between global white matter integrity and physical obesity in the Human Connectome dataset. The volume of positive findings p<0.01,227cm3, agrees with and expands on the volume found by TBSS (17 cm3), Connectivity based fixel enhancement (15 cm3) and Connectometry (212 cm3). In the same dataset we further localize the correlations of brain structure with neurocognitive measures such as fluid intelligence and episodic memory. The presented ODF L+S approach will aid in the full utilization of all acquired diffusion weightings leading to the detection of smaller group differences in clinically relevant settings as well as in neuroscience applications.

Accelerated radial diffusion spectrum imaging using a multi-echo stimulated echo diffusion sequence.

PURPOSE: Diffusion spectrum imaging (DSI) provides us non-invasively and robustly with anatomical details of brain microstructure. To achieve sufficient angular resolution, DSI requires a large number of q-space samples, leading to long acquisition times. This need is mitigated here by combining the beneficial properties of Radial q-space sampling for DSI with a Multi-Echo Stimulated Echo Sequence (MESTIM). METHODS: Full 2D k-spaces for each of several q-space samples, along the same radially outward line in q-space, are acquired in one readout train with one spin and three stimulated echoes. RF flip angles are carefully chosen to distribute spin magnetization over the echoes and the DSI reconstruction is adapted to account for differences in diffusion time among echoes. RESULTS: Individual datasets and bootstrapped reproducibility analysis demonstrate image quality and SNR of the more-than-twofold-accelerated RDSI MESTIM sequence. Orientation distribution functions (ODF) and tractography results benefit from the longer diffusion times of the latter echoes in the echo train. CONCLUSION: A MESTIM sequence can be used to shorten RDSI acquisition times significantly without loss of image or ODF quality. Further acceleration is possible by combination with simultaneous multi-slice techniques. Magn Reson Med 79:306-316, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Voxelwise analysis of simultaneously acquired and spatially correlated 18 F-fluorodeoxyglucose (FDG)-PET and intravoxel incoherent motion metrics in breast cancer.

PURPOSE: Diffusion-weighted imaging (DWI) and 18 F-fluorodeoxyglucose-positron emission tomography (18 F-FDG-PET) independently correlate with malignancy in breast cancer, but the relationship between their structural and metabolic metrics is not completely understood. This study spatially correlates diffusion, perfusion, and glucose avidity in breast cancer with simultaneous PET/MR imaging and compares correlations with clinical prognostics. METHODS: In this Health Insurance Portability and Accountability Act-compliant prospective study, with written informed consent and approval of the institutional review board and using simultaneously acquired FDG-PET and DWI, tissue diffusion (Dt ), and perfusion fraction (fp ) from intravoxel incoherent motion (IVIM) analysis were registered to FDG-PET within 14 locally advanced breast cancers. Lesions were analyzed using 2D histograms and correlation coefficients between Dt , fp , and standardized uptake value (SUV). Correlations were compared with prognostics from biopsy, metastatic burden from whole-body PET, and treatment history. RESULTS: SUV||Dt correlation coefficient significantly distinguished treated (0.11 ± 0.24) from nontreated (-0.33 ± 0.26) patients (P = 0.005). SUV||fp correlations were on average negative for the whole cohort (-0.17 ± 0.13). CONCLUSION: Simultaneously acquired and registered FDG-PET/DWI allowed quantifiable descriptions of breast cancer microenvironments that may provide a framework for monitoring and predicting response to treatment. Magn Reson Med 78:1147-1156, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Radial q-space sampling for DSI.

PURPOSE: Diffusion spectrum imaging (DSI) has been shown to be an effective tool for noninvasively depicting the anatomical details of brain microstructure. Existing implementations of DSI sample the diffusion encoding space using a rectangular grid. Here we present a different implementation of DSI whereby a radially symmetric q-space sampling scheme for DSI is used to improve the angular resolution and accuracy of the reconstructed orientation distribution functions. METHODS: Q-space is sampled by acquiring several q-space samples along a number of radial lines. Each of these radial lines in q-space is analytically connected to a value of the orientation distribution functions at the same angular location by the Fourier slice theorem. RESULTS: Computer simulations and in vivo brain results demonstrate that radial diffusion spectrum imaging correctly estimates the orientation distribution functions when moderately high b-values (4000 s/mm2) and number of q-space samples (236) are used. CONCLUSION: The nominal angular resolution of radial diffusion spectrum imaging depends on the number of radial lines used in the sampling scheme, and only weakly on the maximum b-value. In addition, the radial analytical reconstruction reduces truncation artifacts which affect Cartesian reconstructions. Hence, a radial acquisition of q-space can be favorable for DSI. Magn Reson Med 76:769-780, 2016. © 2015 Wiley Periodicals, Inc.

In vivo brain rosette spectroscopic imaging (RSI) with LASER excitation, constant gradient strength readout, and automated LCModel quantification for all voxels.

PURPOSE: To optimize the Rosette trajectories for high-sensitivity in vivo brain spectroscopic imaging and reduced gradient demands. METHODS: Using LASER localization, a rosette based sampling scheme for in vivo brain spectroscopic imaging data on a 3 Tesla (T) system is described. The two-dimensional (2D) and 3D rosette spectroscopic imaging (RSI) data were acquired using 20 × 20 in-plane resolution (8 × 8 mm(2) ), and 1 (2D) -18 mm (1.1 cc) or 12 (3D) -8 mm partitions (0.5 cc voxels). The performance of the RSI acquisition was compared with a conventional spectroscopic imaging (SI) sequence using LASER localization and 2D or 3D elliptical phase encoding (ePE). Quantification of the entire RSI data set was performed using an LCModel based pipeline. RESULTS: The RSI acquisitions took 32 s for the 2D scan, and as short as 5 min for the 3D 20 × 20 × 12 scan, using a maximum gradient strength Gmax=5.8 mT/m and slew-rate Smax=45 mT/m/ms. The Bland-Altman agreement between RSI and ePE CSI, characterized by the 95% confidence interval for their difference (RSI-ePE), is within 13% of the mean (RSI+ePE)/2. Compared with the 3D ePE at the same nominal resolution, the effective RSI voxel size was three times smaller while the measured signal-to-noise ratio sensitivity, after normalization for differences in effective size, was 43% greater. CONCLUSION: 3D LASER-RSI is a fast, high-sensitivity spectroscopic imaging sequence, which can acquire medium-to-high resolution SI data in clinically acceptable scan times (5-10 min), with reduced stress on the gradient system. Magn Reson Med 76:380-390, 2016. © 2015 Wiley Periodicals, Inc.

Short-T2 imaging for quantifying concentration of sodium (23 Na) of bi-exponential T2 relaxation.

PURPOSE: This work intends to demonstrate a new method for quantifying concentration of sodium (23 Na) of bi-exponential T2 relaxation in patients on MRI scanners at 3.0 Tesla. THEORY AND METHODS: Two single-quantum (SQ) sodium images acquired at very-short and short echo times (TE = 0.5 and 5.0 ms) are subtracted to produce an image of the short-T2 component of the bi-exponential (or bound) sodium. An integrated calibration on the SQ and short-T2 images quantifies both total and bound sodium concentrations. Numerical models were used to evaluate signal response of the proposed method to the short-T2 components. MRI scans on agar phantoms and brain tumor patients were performed to assess accuracy and performance of the proposed method, in comparison with a conventional method of triple-quantum filtering. RESULTS: A good linear relation (R2 = 0.98) was attained between the short-T2 image intensity and concentration of bound sodium. A reduced total scan time of 22 min was achieved under the SAR restriction for human studies in quantifying both total and bound sodium concentrations. CONCLUSION: The proposed method is feasible for quantifying bound sodium concentration in routine clinical settings at 3.0 Tesla. Magn Reson Med 74:162-174, 2015. © 2014 Wiley Periodicals, Inc.

Repeatability of ultrashort echo time-based two-component T2* measurements on cartilages in human knee at 3 T.

Repeatability of in vivo measurement of multicomponent T2* relaxation in articular cartialges in human knee is important to clinical use. This study evaluated the repeatability of two-component T2* relaxation on seven healthy human subjects. The left knee was scanned once a day in three consecutive days, on a clinical 3T MRI scanner with eight-channel knee coil and ultrashort echo time pulse sequence at 11 echo times=0.6-40 ms. The intrasubject and intersubject repeatability was evaluated via coefficient of variation (CV=standard deviation/mean) in four typical cartilage regions: patellar, anterior articular, femoral, and tibial regions. It was found that the intrasubject repeatability was good, with CV<10% for the short- and long-T2* relaxation time in the layered regions in the four cartilages (with one exception) and CV<13% for the component intensity fraction (with two exceptions). The intersubject repeatability was also good, with CV∼8% (range 1-15%) for the short- and long-T2* relaxation time and CV∼10% (range 2-20%) for the component intensity fraction. The long-T2* component showed significantly better repeatability (CV∼8%) than the short-T2* component (CV∼12%) (P<0.005). These CV values suggest that in vivo measurement of two-component T2* relaxation in the knee cartilages is repeatable on clinical scanner at 3 T, with a signal-to-noise ratio of 90.

High-resolution sodium imaging of human brain at 7 T.

The feasibility of high-resolution sodium magnetic resonance imaging on human brain at 7 T was demonstrated in this study. A three-dimensional anisotropic resolution data acquisition was used to address the challenge of low signal-to-noise ratio associated with high resolution. Ultrashort echo-time sequence was used for the anisotropic data acquisition. Phantoms and healthy human brains were studied on a whole-body 7-T magnetic resonance imaging scanner. Sodium images were obtained at two high nominal in-plane resolutions (1.72 and 0.86 mm) at a slice thickness of 4 mm. Signal-to-noise ratio in the brain image (cerebrospinal fluid) was measured as 14.4 and 6.8 at the two high resolutions, respectively. The actual in-plane resolution was measured as 2.9 and 1.6 mm, 69-86% larger than their nominal values. The quantification of sodium concentration on the phantom and brain images enabled better accuracy at the high nominal resolutions than at the low nominal resolution of 3.44 mm (measured resolution 5.5 mm) due to the improvement of in-plane resolution.

Suppression of effects of gradient imperfections on imaging with alternate ascending/descending directional navigation.

Alternate ascending/descending directional navigation (ALADDIN) is a new imaging technique that provides interslice perfusion-weighted and magnetization transfer (MT) asymmetry images. In this article, we investigated the effects of gradient imperfections on ALADDIN MT asymmetry (MTA) signals. Subtraction artifacts increasing with readout offsets were detectable in ALADDIN MTA images from an agarose phantom but not from a water phantom. Slice-select offsets had no significant effect on the artifacts in MTA. The artifacts were suppressed by averaging signals over the readout gradient polarities independent of scan parameters. All these results suggested that the subtraction artifacts were induced by readout eddy currents. With suppression of the artifacts, ALADDIN signals in human brain and skeletal muscle varied less with scan conditions. Percent signal changes of MTA in human skeletal muscle (0.51 ± 0.11%, N = 3) were about 30% of those in white matter. The new averaging scheme will allow for more accurate MTA imaging with ALADDIN, especially at off-center positions.

Sodium imaging of human brain at 7 T with 15-channel array coil.

Signal-to-noise ratio (SNR) is a major challenge to sodium magnetic resonance imaging. Phased array coils have been shown significantly improving SNR in proton imaging over volume coils. This study investigates SNR advantage of a 15-channel array head coil (birdcage volume coil for transmit/receive and 15-channel array insert for receive-only) in sodium imaging at 7 T. Phantoms and healthy human brains were scanned on a whole-body 7 T magnetic resonance imaging scanner using a customer-developed pulse sequence with the twisted projection imaging trajectory. Noise-only images were acquired with blanked radiofrequency excitations for noise measurement on a pixel basis. SNR was calculated on the root of sum-of-squares images. When compared with the volume coil, the 15-channel array produced SNR more than doubled at the periphery and slightly increased at the center of the phantoms and human brains. Decorrelation of noise across channels of the array coil extended the SNR-doubled region into deep area of the brain. The spatial modulation of element sensitivities on the sum-of-squares combined image was removed by performing self-calibrated sensitivity encoding parallel image reconstruction and uniform image intensity across entire field of view was attained. The 15-channel array coil is an efficient tool to substantially improve SNR in sodium imaging on human brain.

High-resolution ultrashort echo time (UTE) imaging on human knee with AWSOS sequence at 3.0 T.

PURPOSE: To demonstrate the technical feasibility of high-resolution (0.28-0.14 mm) ultrashort echo time (UTE) imaging on human knee at 3T with the acquisition-weighted stack of spirals (AWSOS) sequence. MATERIALS AND METHODS: Nine human subjects were scanned on a 3T MRI scanner with an 8-channel knee coil using the AWSOS sequence and isocenter positioning plus manual shimming. RESULTS: High-resolution UTE images were obtained on the subject knees at TE = 0.6 msec with total acquisition time of 5.12 minutes for 60 slices at an in-plane resolution of 0.28 mm and 10.24 minutes for 40 slices at an in-plane resolution of 0.14 mm. Isocenter positioning, manual shimming, and the 8-channel array coil helped minimize image distortion and achieve high signal-to-noise ratio (SNR). CONCLUSION: It is technically feasible on a clinical 3T MRI scanner to perform UTE imaging on human knee at very high spatial resolutions (0.28-0.14 mm) within reasonable scan time (5-10 min) using the AWSOS sequence.

Stepwise Stochastic Dictionary Adaptation Improves Microstructure Reconstruction with Orientation Distribution Function Fingerprinting.

Fitting of the multicompartment biophysical model of white matter is an ill-posed optimization problem. One approach to make it computationally tractable is through Orientation Distribution Function (ODF) Fingerprinting. However, the accuracy of this method relies solely on ODF dictionary generation mechanisms which either sample the microstructure parameters on a multidimensional grid or draw them randomly with a uniform distribution. In this paper, we propose a stepwise stochastic adaptation mechanism to generate ODF dictionaries tailored specifically to the diffusion-weighted images in hand. The results we obtained on a diffusion phantom and in vivo human brain images show that our reconstructed diffusivities are less noisy and the separation of a free water fraction is more pronounced than for the prior (uniform) distribution of ODF dictionaries.

Improved large tip angle parallel transmission pulse design through a perturbation analysis of the Bloch equation.

Parallel transmission has emerged as an efficient means for implementing multidimensional spatially selective radiofrequency excitation pulses. To date, most theoretical and experimental work on parallel transmission radiofrequency (RF) pulse design is based on the small-tip-angle approximation to the Bloch equation. The small-tip-angle, while mathematically compact, is not an exact solution and leads to significant errors when large-tip-angle pulses are designed. Methods have been proposed to overcome the limitations of the small-tip-angle using regularized least-square optimization or optimal control algorithms. These methods, however, are based on further approximations to the Bloch equation or require the use of general purpose algorithms that do not capitalize fully on the dynamics of the physical model at hand. In this article, a novel algorithm for large-tip-angle parallel transmission pulse design is proposed. The algorithm relies on a perturbation analysis of the Bloch equation and it depicts the relationship between the excited magnetization, its deviation from the target pattern and the desired pulses. Simulations and experiments are used to validate the proposed method on a 7 T 8-channel transmit array. The results demonstrate that the perturbation analysis algorithm provides a fast and accurate approach for multidimensional large-tip-angle pulse design, especially when large acceleration factors and/or echo-planar trajectories are used.

K⁺ dynamics in ischemic rat brain in vivo by 87Rb MRI at 7 T.

The aims of the present study were as follows: (i) to perform the first (87)Rb MRI in live rats with focal ischemic stroke; and (ii) to test the hypothesis that K(+) egress from the brain in this model is quantifiable in individual animals by high-field (7-T) K/Rb substitution MRI. Rats preloaded with dietary Rb(+) (resulting in Rb/(K + Rb) replacement ratios of 0.1-0.2 in the brain) were subjected to permanent occlusion of the middle cerebral artery, and (87)Rb MRI was implemented with 13-min temporal resolution using a dedicated RF coil and a spiral ultrashort-TE sequence (TR/TE = 3/0.07 ms). The ischemic core was localized by apparent diffusion coefficient mapping, by microtubule-associated protein-2 immunohistochemistry and by changes in surface reflectivity. [K], [Na] and [Rb] were determined independently in the micropunched samples by post-mortem flame photometry. Both techniques were generally in agreement in the nonischemic cortex; however, the MRI-assessed [K(+) + Rb(+)] drop in ischemic brain was less pronounced (average efflux rate of 4.8 ± 0.2 nEq/mm(3) /h versus 10 ± 1 nEq/mm(3)/h by flame photometry; p < 0.0001). The use of higher field gradients for better spatial resolution, and hence more accurate quantification, is suggested.