On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.     

Globally optimized fiber tracking and hierarchical clustering -- a unified framework

Structural connectivity between cortical regions of the human brain can be characterized noninvasively with diffusion tensor imaging (DTI)-based fiber tractography. In this paper, a novel fiber tractography technique, globally optimized fiber tracking and hierarchical fiber clustering, is presented. The proposed technique uses k-means clustering in conjunction with modified Hubert statistic to partition fiber pathways, which are evaluated with simultaneous consideration of consistency with underlying DTI data and smoothness of fiber courses in the sense of global optimality, into individual anatomically coherent fiber bundles. In each resulting bundle, fibers are sampled, perturbed and clustered iteratively to approach the optimal solution. The global optimality allows the proposed technique to resist local image artifacts and to possess inherent capabilities of handling complex fiber structures and tracking fibers between gray matter regions. The embedded hierarchical clustering allows multiple fiber bundles between a pair of seed regions to be naturally reconstructed and partitioned. The integration of globally optimized tracking and hierarchical clustering greatly benefits applications of DTI-based fiber tractography to clinical studies, particularly to studies of structure-function relations of the complex neural network of the human. Experiments with synthetic and in vivo human DTI data have demonstrated the effectiveness of the proposed technique in tracking complex fiber structures, thus proving its significant advantages over traditionally used streamline fiber tractography.     

Novel multisection design of anisotropic diffusion phantoms

Diffusion-weighted magnetic resonance imaging provides access to fiber pathways and structural integrity in fibrous tissues such as white matter in the brain. In order to enable better access to the sensitivity of the diffusion indices to the underlying microstructure, it is important to develop artificial model systems that exhibit a well-known structure, on the one hand, but benefit from a reduced complexity on the other hand. In this work, we developed a novel multisection diffusion phantom made of polyethylene fibers tightly wound on an acrylic support. The phantom exhibits three regions with different geometrical configuration of fibers: a region with fibers crossing at right angles, a region with parallel fibers and homogeneous density, and, finally, a region with parallel fibers but with a gradient of fiber density along the axis of symmetry. This gives rise to a gradual change of the degree of anisotropy within the same phantom. In this way, the need to construct several phantoms with different fiber densities is avoided, and one can access different fractional anisotropies in the same experiment under the same physical conditions. The properties of the developed phantom are demonstrated by means of diffusion tensor imaging and diffusion kurtosis imaging. The measurements were performed using a diffusion-weighted spin-echo and a diffusion-weighted stimulated-echo pulse sequence programmed in-house. The influence of the fiber density packing on the diffusion parameters was analyzed. We also demonstrate how the novel phantom can be used for the validation of high angular resolution diffusion imaging data analysis.     

Simulation and experimental verification of the diffusion in an anisotropic fiber phantom

Diffusion weighted magnetic resonance imaging enables the visualization of fibrous tissues such as brain white matter. The validation of this non-invasive technique requires phantoms with a well-known structure and diffusion behavior. This paper presents anisotropic diffusion phantoms consisting of parallel fibers. The diffusion properties of the fiber phantoms are measured using diffusion weighted magnetic resonance imaging and bulk NMR measurements. To enable quantitative evaluation of the measurements, the diffusion in the interstitial space between fibers is modeled using Monte Carlo simulations of random walkers. The time-dependent apparent diffusion coefficient and kurtosis, quantifying the deviation from a Gaussian diffusion profile, are simulated in 3D geometries of parallel fibers with varying packing geometries and packing densities. The simulated diffusion coefficients are compared to the theory of diffusion in porous media, showing a good agreement. Based on the correspondence between simulations and experimental measurements, the fiber phantoms are shown to be useful for the quantitative validation of diffusion imaging on clinical MRI-scanners.     

Diffusion tensor imaging fiber tracking with local tissue property sensitivity: phantom and in vivo validation

Diffusion tensor imaging (DTI) provides directional information that can be used to delineate brain white matter connections noninvasively via fiber tracking. The most commonly used methods for tractography are based on the streamline tracking algorithm for track propagation and a set of empirically and globally defined criteria for track termination. In this study, we propose a streamline tracking algorithm with high-order propagation accuracy and a single termination criterion based on tissue property to minimize user intervention and biases introduced during tracking process. These advantages and the agreement with histological reports are demonstrated in our tracking results in phantoms and in humans.     

Diffusion tensor encoding schemes optimized for white matter fibers with selected orientations

A method to produce gradient encoding schemes that minimize the noise of diffusion tensor imaging (DTI) indices for selected fiber orientations has been developed. The accuracy of DTI measurements depends on the gradient encoding scheme used. Most current acquisition schemes contain diffusion directions uniformly distributed in 3D space in order to provide equal noise levels for fibers in any orientation. However, when considering specific fiber bundles such as the corticospinal tract (CST) or parts of fiber bundles, the range of fiber orientations of interest may be limited. We hypothesized that, when studying fiber tracts with a limited range of orientations, measuring diffusion in directions that are uniformly distributed in 3D space may be suboptimal for the noise levels of various DTI indices. Therefore, we first used simulations to determine six diffusion directions that minimize the noise of DTI measurements for selected fiber orientations. The resulting optimized set of directions was then tested on the right CST of a healthy human subject, and its performance was compared with that of conventional acquisition strategies. Both the simulations and the experiments on the human subject demonstrated that the new scheme significantly reduced the standard deviation of DTI indices for tensors with primary eigenvectors within a selected range of orientations.     

Use of capillaries in the construction of an MRI phantom for the assessment of diffusion tensor imaging: demonstration of performance

Although diffusion tensor imaging (DTI) shows great potential for the diagnosis of a variety of pathologies, no consensus for an appropriate assessment standard of DTI exists. This study examined the feasibility of using water-filled arrays of glass capillaries to construct a DTI phantom suitable for making repeated and reproducible measurements required in a quality assessment program. Three phantoms were constructed using arrays of capillaries with three inner diameters (23, 48, and 82 μm). Data were acquired using DTI protocols; the fractional anisotropy (FA), mean apparent diffusion coefficient (ADC) and principal eigenvectors of the diffusion tensors were calculated. This study demonstrated four results: (1) echo-planar images show that susceptibility within the capillary arrays does not lead to substantial differences in precessional frequency in regions containing the arrays and neither do the regions show noticeable image distortion; (2) principal eigenvectors of the diffusion tensors agree to within <10.3° of the array orientations; (3) mean FA values (0.18–0.50) and ADC values (1.40–1.93×10−³ mm²/s) within specified regions of interest are in general agreement with simulations after a simple noise correction; and (4) these array performance characteristics are observable using a typical clinical DTI protocol.     

Lensless high-resolution photoacoustic imaging scanner for in vivo skin imaging

We previously launched a high-resolution photoacoustic (PA) imaging scanner based on a unique lensless design for in vivo skin imaging. The design, imaging algorithm and characteristics of the system are described in this paper. Neither an optical lens nor an acoustic lens is used in the system. In the imaging head, four sensor elements are arranged quadrilaterally, and by checking the phase differences for PA waves detected with these four sensors, a set of PA signals only originating from a chromophore located on the sensor center axis is extracted for constructing an image. A phantom study using a carbon fiber showed a depth-independent horizontal resolution of 84.0 ± 3.5 µm, and the scan direction-dependent variation of PA signals was about ± 20%. We then performed imaging of vasculature phantoms: patterns of red ink lines with widths of 100 or 200 μm formed in an acrylic block co-polymer. The patterns were visualized with high contrast, showing the capability for imaging arterioles and venues in the skin. Vasculatures in rat burn models and healthy human skin were also clearly visualized in vivo.     

纺织纤维及其制品非破坏性快速鉴别的研究

纺织纤维的快速鉴别对我国纺织品生产过程质量控制、贸易和市场监督具有重要实际意义。文章收集了的12种纺织纤维共214个样品,研究了各种形态样品的近红外光谱测量方法。采用多元光散射校正方法消除噪声和基线漂移对光谱的影响。对样品总集光谱进行系统树分析,发现组成接近的纤维样本能均够聚类在一起,有些不同种类纤维之间有交叠。结合近红外光谱和簇类的独立软模式方法(SIMCA),可以实现化学组成非常接近的不同纤维种类的区分。该研究结果表明,采用近红外分析技术,实现非破坏性地快速鉴别纺织纤维是可行的。     

A Monte Carlo simulation of image misalignment effects in diffusion tensor imaging

Diffusion tensor imaging (DTI) and tractography are noninvasive MRI methods, providing an insight on microscopic structural information of anisotropic tissues in vivo. The success of this technique stems on a watchful choice of imaging parameters and post-acquisition reconstruction. In the present work, we have focused on the problem of residual linear image misalignment in the DTI data and its effects on the parameters of the diffusion tensor and fiber tracking in human brain. We demonstrate substantial sensitivity of the reconstructed diffusion tensor and fiber tractography on increasing amplitude of artificially induced random image misalignment in the DTI. We show that already a submillimeter image misalignment in the DTI is an important source of error, which may potentially mask pathological presentations of the diseases and may partially explain variations in the results obtained from the DTI. Finally, we evaluated four implementations of image registrations and demonstrate their variable performance. This further supports the fact that a robust image registration must be performed to ensure reliable and reproducible diffusion tensor mapping and reconstruction of white matter (WM) fibers.     

低场MRI系统中线扫描扩散张量成像方法的研究

磁共振扩散张量成像(DTI)是在扩散加权成像(DWI)基础上发展起来的一种新型技术,可以无创伤显示脑白质纤维,诊断脑白质病变. 但是由于各种原因,DTI一般只在超导高场磁共振成像(MRI)仪器上进行,这就限制了这一重要诊断手段临床应用的广泛性. 本文在低场磁共振成像系统上应用线扫描实现了扩散张量成像,并测量了健康志愿者大脑内主要解剖结构的表观扩散系数(ADC)和各项异性分数(FA),得到的数据与高场仪器上的相关数据比较是吻合的. 因此临床上使用在低场强上得到的DTI图像评价脑白质是可行的,而且通常在临床上这也是足够的.     

In-vivo diffusion MRI protocol optimization for the chimpanzee brain and examination of aging effects on the primate optic nerve at 3T

BackgroundDiffusion MRI (dMRI) data acquisition protocols are well-established on modern high-field clinical scanners for human studies. However, these protocols are not suitable for the chimpanzee (or other large-brained mammals) because of its substantial difference in head geometry and brain volume compared with humans. Therefore, an optimal dMRI data acquisition protocol dedicated to chimpanzee neuroimaging is needed.MethodsA multi-shot (4 segments) double spin-echo echo-planar imaging (MS-EPI) sequence and a single-shot double spin-echo EPI (SS-EPI) sequence were optimized separately for in vivo dMRI data acquisition of chimpanzees using a clinical 3T scanner. Correction for severe susceptibility-induced image distortion and signal drop-off of the chimpanzee brain was performed and evaluated using FSL software. DTI indices in different brain regions and probabilistic tractography were compared. A separate DTI data set from n=34 chimpanzees (13 to 56 years old) was collected using the optimal protocol. Age-related changes in diffusivity indices of optic nerve fibers were evaluated.ResultsThe SS-EPI sequence acquired dMRI data of the chimpanzee brain with approximately doubled the SNR as the MS-EPI sequence given the same scan time. The quality of white matter fiber tracking from the SS-EPI data was much higher than that from MS-EPI data. However, quantitative analysis of DTI indices showed no difference in most ROIs between the SS-EPI and MS-EPI sequences. The progressive evolution of diffusivity indices of optic nerves indicated mild changes in fiber bundles of chimpanzees aged 40 years and above.ConclusionThe single-shot EPI-based acquisition protocol provided better image quality of dMRI for chimpanzee brains and is recommended for in vivo dMRI study or clinical diagnosis of chimpanzees (or other large animals) using a clinical scanner. Also, the tendency of FA decrease or diffusivity increase in the optic nerve of aged chimpanzees was seen but did not show significant age-related changes, suggesting aging may have less impact on optic nerve fiber integrity of chimpanzees, in contrast to previous results for both macaque monkeys and humans.     

How does distortion correction correlate with anisotropic indices? A diffusion tensor imaging study

PURPOSE: The purpose of this study was to determine a suitable registration algorithm for diffusion tensor imaging (DTI) using conventional preprocessing tools [statistical parametric mapping (SPM) and automated image registration (AIR)] and to investigate how anisotropic indices for clinical assessments are affected by these distortion corrections. MATERIALS AND METHODS: Brain DTI data from 15 normal healthy volunteers were used to evaluate four spatial registration schemes within subjects to correct image distortions: noncorrection, SPM-based affine registration, AIR-based affine registration and AIR-based nonlinear polynomial warping. The performance of each distortion correction was assessed using: (a) quantitative parameters: tensor-fitting error (Ef), mean dispersion index (MDI), mean fractional anisotropy (MFA) and mean variance (MV) within 11 regions of interest (ROI) defined from homogeneous fiber bundles; and (b) fiber tractography through the uncinate fasciculus and the corpus callosum. Fractional anisotropy (FA) and mean diffusivity (MD) were calculated to demonstrate the effects of distortion correction. Repeated-measures analysis of variance was used to investigate differences among the four registration paradigms. RESULTS: AIR-based nonlinear registration showed the best performance for reducing image distortions with respect to smaller Ef (P<.02), MDI (P<.01) and MV (P<.01) with larger MFA (P<.01). FA was decreased to correct distortions (P<.0001) whether the applied registration was linear or nonlinear and was lowest after nonlinear correction (P<.001). No significant differences were found in MD. CONCLUSION: In conventional DTI processing, anisotropic indices of FA can be misestimated by noncorrection or inappropriate distortion correction, which leads to an erroneous increase in FA. AIR-based nonlinear distortion correction would be required for a more accurate measurement of this diffusion parameter.     

Study of myocardial fiber pathway using magnetic resonance diffusion tensor imaging

The purpose of this study was to investigate myocardial fiber pathway distribution in order to provide supplemental information on myocardial fiber architecture and cardiac mechanics. Diffusion tensor imaging (DTI) with medium diffusion resolution (15 directions) was performed on normal canine heart samples (N=6) fixed in formalin. With the use of diffusion tensor fiber tracking, left ventricle (LV) myocardial fiber pathways and helix angles were computed pixel by pixel at short-axis slices from base to apex. Distribution of DTI-tracked fiber pathway length and number was analyzed quantitatively as a function of fiber helix angle in step of 9 degrees . The long fiber pathways were found to have small helix angles. They are mostly distributed in the middle myocardium and run circumferentially. Fiber pathways tracked at the middle and upper LV are generally longer than those near the apex. Majority of fiber pathways have small helix angles between -20 degrees and 20 degrees , dominating the fiber architecture in myocardium. Likely, such myocardial fiber pathway measurement by DTI may reflect the spatial connectiveness or connectivity of elastic myofiber bundles along their preferential pathway of electromechanical activation. The dominance of the long and circumferentially running fiber pathways found in the study may explain the circumferential predominance in left ventricular contraction.     

Diffusion tensor imaging of oral carcinoma: Clinical evaluation and comparison with histopathological findings

PurposeThis study aims to assess the usefulness of diffusion tensor imaging (DTI) as a noninvasive method for the evaluation of histological grade and lymph node metastasis in patients with oral carcinoma (OC).Materials and methodsThirty-six consecutive patients with histologically confirmed OC underwent examination by 3-T MRI. DTI was performed using a single-shot echo-planar imaging sequence with b values of 0 and 1000 s/mm² and motion-probing gradients in 12 noncollinear directions. Fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) maps were compared with histopathological findings. The DTI parameters were correlated with the histological grade of the OCs based on the World Health Organization grading criteria and the presence or absence of lymph node metastasis.ResultsThe FA values (0.275 ± 0.058) of OC were significantly lower than those of normal tongue, muscle, and parotid glands (P < 0.001 for all), and the MD, AD, and RD values (1.220 ± 0.149, 1.434 ± 0.172, and 1.019 ± 0.165 × 10⁻³ mm²/s, respectively) were significantly higher than their respective normal values (P < 0.001 for all). Significant inverse correlations with histological grades were shown for FA, MD, AD, and RD values in OC patients (r = −0.862, r = −0.797, r = −0.747, and r = −0.844, respectively; P < 0.001 for all). In addition, there was a significant difference in the FA values of metastatic and nonmetastatic lymph nodes (0.186 vs. 0.276), MD (0.923 vs. 1.242 × 10⁻³ mm²/s), AD (1.246 vs. 1.621 × 10⁻³ mm²/s), and RD (0.792 vs. 1.100 × 10⁻³ mm²/s; P < 0.001 for all).ConclusionsDTI may be clinically useful for the noninvasive evaluation of histological grade and lymph node metastasis in OC patients.     

Exploratory voxel-based analysis of diffusion indices and hemispheric asymmetry in normal aging

Age-related microstructural changes in brain white matter can be studied by utilizing indices derived from diffusion tensor imaging (DTI): apparent diffusion coefficient (ADC) and fractional anisotropy (FA). The objective of this study is to examine alterations in FA and ADC by employing exploratory voxel-based analysis (VBA) and region(s) of interest (ROI)-based analysis. A highly nonlinear registration algorithm was used to align the ADC and FA image volumes of different subjects to perform accurate voxel-level statistics for two age groups, as well as for hemispheric asymmetry for both age groups. VBA shows significant age-related decline in FA with frontal predominance (frontal white matter, and genu and anterior body of the corpus callosum), superior portions of a splenium and highly oriented fibers of the posterior limb of the internal capsule and the anterior and posterior limbs of the external capsule. Hemispheric asymmetry of FA, as assessed by VBA, showed that for the young-age group, significant right-greater-than-left asymmetry exists in the genu, splenium and body of the corpus callosum and that left-greater-than-right asymmetry exists in the anterior limb of the external capsule and in the posterior limb of the internal capsule, thalamus, cerebral peduncle and temporal-parietal regions. VBA of the hemispheric asymmetry of the middle-age group revealed much less asymmetry. Regions showing age-related changes and hemispheric asymmetry from VBA were, for a majority of the findings, in conformance with ROI analysis and with the known pattern of development and age-related degradation of fiber tracks. The study shows the feasibility of the VBA of DTI indices for exploratory investigations of subtle differences in population cohorts, especially when findings are not localized and/or known a priori.     

An image-processing toolset for diffusion tensor tractography

Diffusion tensor imaging (DTI)-based fiber tractography holds great promise in delineating neuronal fiber tracts and, hence, providing connectivity maps of the neural networks in the human brain. An array of image-processing techniques has to be developed to turn DTI tractography into a practically useful tool. To this end, we have developed a suite of image-processing tools for fiber tractography with improved reliability. This article summarizes the main technical developments we have made to date, which include anisotropic smoothing, anisotropic interpolation, Bayesian fiber tracking and automatic fiber bundling. A primary focus of these techniques is the robustness to noise and partial volume averaging, the two major hurdles to reliable fiber tractography. Performance of these techniques has been comprehensively examined with simulated and in vivo DTI data, demonstrating improvements in the robustness and reliability of DTI tractography.     

Diffusion Tensor Magnetic Resonance Imaging in Ring-Enhancing Cerebral Lesions

The objective of this study is to determine differential diagnostic value of diffusion tensor imaging (DTI) in high-grade brain astrocytomas, brain solitary metastases and brain abscesses. 53 patients with cerebral solitary lesions which showed ring enhancement on contrast-enhanced T ₁-weighted images were enrolled in this study. Brain tissues were examined pathologically from 49 patients to confirm the cerebral occupational diseases. Four patients have been diagnosed with primary cancer plus brain solitary metastasis. DTI measurements were obtained from regions of interest placed on central cavity, white matter of the immediate peritumoral region (IPR) and cerebral white matter of the normal side. The cavity of high-grade astrocytoma and brain metastases displayed hypointense signals; most of the brain abscess cavities displayed high signal intensity except for one case with uneven signal intensity. Mean diffusivity (MD) and fractional anisotropy (FA) values could be used for differentiation between tumor and abscess in brain. The brain abscess cavities showed restricted diffusion and anisotropy [MD = (0.604 ± 0.13) × 10⁻³ mm²/s, FA = 0.185 ± 0.03], whereas the central portion of high-grade astrocytoma [MD = (2.76 ± 0.26) × 10⁻³ mm²/s, FA = 0.069 ± 0.02] and solitary brain metastases [MD = (2.82 ± 0.29) × 10⁻³ mm²/s, FA = 0.064 ± 0.02] showed unrestricted diffusion and isotropy. Brain abscess could be differentiated by MD and FA values in their cavities from brain tumors (P < 0.01). The IPRs were all depicted as hyperintense or isointense signals on diffusion-weighted imaging. The difference between FA values in the IPR of high-grade brain astrocytomas and other groups was statistically significant (P < 0.01). In conclusion, our results suggested the potential role of the cavity MD and FA values in the differential diagnoses of brain tumors and brain abscesses; meanwhile, high-grade astrocytomas could be distinguished from solitary metastases and abscesses by evaluating their corresponding FA values in the IPR on brain magnetic resonance imaging (MRI). Combined with conventional MRI, DTI may help radiologists to facilitate the differential diagnosis of ring-enhancing cerebral lesions in clinical practice.     

Importance of exactb-tensor calculation for quantitative diffusion tensor imaging and tracking of neuronal fiber bundles

Quantitative diffusion tensor imaging (DTI) is a novel method of magnetic resonance (MR) imaging providing information on the brain’s microstructure in vivo. DTI can be effectively measured with modern clinical MR scanners. However, imaging sequence details required for accurateb matrix calculation and for following DTI quantification are normally unknown to the user. In this work, we investigated the accuracy ofb value approximation if theb matrix is calculated without taking into account the effect of imaging gradients. It was found that an error of more than 4% in DTI estimation arises for a quite typical brain imaging protocol. The errors in mean diffusivity and fractional anisotropy index depend on diffusion tensor shape and eigenvectors orientation and exceed noise level in DTI quantification. These errors however have a strong impact on fiber tracking — up to 30% difference was found between the fiber tracks corresponding to exact and approximate calculated DTI data. Since these errors are dependent on imaging parameters and sequence implementation, accurateb matrix calculations are important for adequate comparison between data acquired on different MR scanners and also for data measured with the different imaging protocols.     

A miniature X‐ray tube approach to measuring lead in bone using L‐XRF

Using a miniature X‐ray tube and silicon PiN diode detector, an approach to measuring lead (Pb) in bone phantoms was tested. The X‐ray tube was used to excite L‐line X‐ray fluorescence (L‐XRF) of lead in bone phantoms. The bone phantoms were made from plaster of Paris and dosed with varying quantities of lead. Phantoms were made in two sets with different shapes to model different bone surfaces. One set of bone phantoms was circular in cross‐section (2.5‐cm diameter), the other square in cross‐section (2.2 cm × 2.2 cm). Using an irradiation time of 180 s (real time), five trials were run for each bone phantom. Analysis was performed for both Lα and Lβ lead X‐rays. Based on these calibration trials, (3σ₀/slope) minimum detection limits of 7.4 ± 0.3 µg Pb g^?1 (circular cross‐section) and 8.6 ± 0.6 µg Pb g^?1 (square cross‐section) were determined for the bare bone phantoms. To simulate a more realistic in vivo scenario with soft tissue overlying bone, further trials were performed with a resin material placed between the experimental system and the bone phantom. For the square cross‐section bone phantoms, a layer of resin with a thickness of 1.2 mm was used, and a minimum detection limit of 17 ± 3 µg Pb g^?1 determined. For the circular cross‐section phantoms, a layer of resin with an average thickness of 2.7 mm was used. From these, a more realistic minimum detection limit for in vivo applications (43 ± 7 µg Pb g^?1) was determined. Copyright © 2011 John Wiley & Sons, Ltd.