Navigator-based motion compensation for liver BOLD measurement with five-echo SAGE EPI and breath-hold task.

PURPOSE: The purpose of this work is to apply multi-echo spin- and gradient-echo (SAGE) echo-planar imaging (EPI) combined with a navigator-based (NAV) prospective motion compensation method for a quantitative liver blood oxygen level dependent (BOLD) measurement with a breath-hold (BH) task. METHODS: A five-echo SAGE sequence was developed to quantitatively measure T2 and T2* to depict function with sufficient signal-to-noise ratio, spatial resolution and sensitivity to BOLD changes induced by the BH task. To account for respiratory motion, a navigator was employed in the form of a single gradient-echo projection readout, located at the diaphragm along the inferior-superior direction. Prior to each transverse imaging slice of the spin-echo EPI-based readouts, navigator acquisition and fat suppression were incorporated. Motion data was obtained from the navigator and transmitted back to the sequence, allowing real-time adjustments to slice positioning. Six healthy volunteers and three patients with liver carcinoma were included in this study. Quantitative T2 and T2* were calculated at each time point of the BH task. Parameters of t value from first-level analysis using a general linear model and hepatovascular reactivity (HVR) of Echo1, T2 and T2* were calculated. RESULTS: The motion caused by respiratory activity was successfully compensated using the navigator signal. The average changes of T2 and T2* during breath-hold were about 1% and 0.7%, respectively. With the help of NAV prospective motion compensation whole liver t values could be obtained without motion artifacts. The quantified liver T2 (34.7 ± 0.7 ms) and T2* (29 ± 1.2 ms) values agreed with values from literature. In healthy volunteers, the distribution of statistical t value and HVR was homogeneous throughout the whole liver. In patients with liver carcinoma, the distribution of t value and HVR was inhomogeneous due to metastases or therapy. CONCLUSIONS: This study demonstrates the feasibility of using a NAV prospective motion compensation technique in conjunction with five-echo SAGE EPI for the quantitative measurement of liver BOLD with a BH task.

Simultaneous T1, T2 and T2⁎ mapping of the liver with multi-shot MI-SAGE.

PURPOSE: To apply multi-shot high-resolution multi inversion spin and gradient echo (MI-SAGE) acquisition for simultaneous liver T1, T2 and T2* mapping. METHODS: Inversion prepared spin- and gradient-echo EPI was developed with ascending slice order across measurements for efficient acquisition with T1, T2, and T2⁎ weighting. Multi-shot EPI was also implemented to minimize distortion and blurring while enabling high in-plane resolution. A dictionary-matching approach was used to fit the images to quantitative parameter maps, which were compared to T1 measured by modified Look-Locker (MOLLI), T1 measured by variable flip angle (VFA), T2 measured by multiple echo time-based Half Fourier Single-shot Turbo spin-Echo (HASTE), T2 measured by radial turbo-spin-echo (rTSE) and T2⁎ measured by multiple gradient echo (MGRE) sequences. RESULTS: The multi-shot variant of the sequence achieved higher in-plane resolution of 1.7 × 1.7 mm2 with good image quality in 28 s. Derived quantitative maps showed comparable values to conventional mapping methods. As measured in phantom and in vivo, MOLLI, MESE and MGRE give closest values to MISAGE. VFA, HASTE and rTSE show obvious overestimation. CONCLUSIONS: The proposed multi-shot inversion prepared spin- and gradient-echo EPI sequence allows for high-resolution quantitative T1, T2 and T2 liver tissue characterization in a single breath-hold scan.

Navigator-based slice tracking for kidney pCASL using spin-echo EPI acquisition.

PURPOSE: To apply a navigator-based slice-tracking method to prospectively compensate respiratory motion for kidney pseudo-continuous arterial spin labeling (pCASL), using spin-echo (SE) EPI acquisition. METHODS: A single gradient-echo slice selection and projection readout at the location of the diaphragm along the inferior-superior direction was applied as a navigator. Navigator acquisition and fat suppression were inserted before each transverse imaging slice of the readouts of a 2D-SE-EPI-based pCASL sequence. Motion information was calculated after exclusion of the signal saturation in the navigator signal caused by EPI excitations. The motion information was then used to directly adjust the slice positioning in real time. RESULTS: The respiratory motion from the navigator signal was calculated, and slice positioning was changed in real time based on the motion information. We could show that motion compensation reduces kidney movement, and that the coefficients of variation across renal perfusion values were significantly reduced when motion correction was applied. The average reduction of coefficients of variation was approximately 20%, resulting in a more accurate and detailed structure of the respective perfusion maps. CONCLUSIONS: This study demonstrates the feasibility of a navigator-based slice-tracking technique in kidney imaging with a SE-EPI readout pCASL sequence to reduce kidney motion.

Influence of heart rate and heart rate variability on the feasibility of ultra-fast, high-pitch coronary photon-counting computed tomography angiography.

Coronary computed tomography angiography has become a mainstay in diagnosing coronary artery disease and is increasingly used in screening symptomatic patients. Recently, photon-counting computed tomography (PCCT) has been introduced into clinical practice, offering higher spatial and temporal resolution. As the applied radiation dose is highly dependent on the choice of scan mode and is lowest using the ultra-fast high-pitch (FLASH) mode, guidelines for their application are needed. From a retrospective study investigating the properties of a novel photon-counting computed tomography, all patients who underwent FLASH-mode PCCT angiography were selected between January and April 2022. This resulted in a study population of 46 men and 27 women. We recorded pre- and intrascan ECG readings and calculated heart rate (maximum heart rate 73 bpm) as well heart rate variability (maximum HRV 37 bpm) as measured by the standard deviation of the heart rate. Diagnostic quality and motion artifacts scores were recorded for each coronary artery segment by consensus between two readers. We found a highly significant association between heart rate variability and image quality (p < 0.001). The heart rate itself was not independently associated with image quality. Both heart rate and heart rate variability were significantly associated with the presence of motion artifacts in a combined model. Scan heart rate variability-but not heart rate itself-is a highly significant predictor of reduced image quality on high-pitch coronary photon-counting computed tomography angiography. This may be due to better scanner architecture and an increased temporal resolution compared to conventional energy-integrating detector computed tomography, which has to be addressed in a comparison study in the future.

Navigator-based slice tracking for prospective motion correction in kidney vessel architecture imaging.

OBJECTIVES: To apply a navigator-based slice tracking method to prospectively compensate the respiratory motion for kidney vessel architecture imaging (VAI). MATERIALS AND METHODS: A dual gradient echo spin echo 2D EPI sequence was developed for kidney VAI. A single gradient-echo slice selection and projection readout at the location of the diaphragm along the inferior-superior direction was applied as a navigator. Navigator acquisition and fat suppression were inserted before each transverse imaging slice. Motion information was calculated after exclusion of the signal saturation in the navigator signal caused by imaging slices. The motion information was then directly sent back to the sequence and slice positioning was adjusted in real-time. The whole sequence was applied during a contrast agent pass-through. RESULTS: VAI parametric maps show the structural heterogeneity of the renal vasculature. The respiratory motion from the navigator signal was precisely calculated and slice positioning was changed in real-time based on the motion information. The vibration amplitude of the signal intensity of the liver tissue at the liver-lung interface in the case of prospective motion correction (PMC) on is about 28% of the PMC off case. Compared to the case of PMC off, the coefficient of variation was reduced 30% of the case of PMC on. CONCLUSIONS: This study demonstrates the feasibility of the motion-compensating technique in kidney VAI. The sequence may improve the evaluation of microvasculature in kidney diseases.

Influence of flow and susceptibility effects on spin dephasing in lung tissue.

PURPOSE: Magnetic resonance imaging (MRI) of the lung can be used for diagnosis and monitoring of interstitial lung disease. Biophysical models of alveolar lung tissue are needed to understand the complex interplay of susceptibility, diffusion, and flow effects, and their influence on magnetic resonance (MR) spin dephasing. METHODS: In this work, we present a method for modeling the signal decay of lung tissue by utilizing a two-compartment model, which considers the different spin dephasing mechanisms in the alveolar vasculature and interstitial tissue. This allows calculating the magnetization dynamics and the MR lineshape, which can be measured noninvasively using clinical MR scanners. RESULTS: The accuracy of the method was evaluated using finite element simulations and the experimentally measured lineshapes of a healthy volunteer. In this comparison, the model performs well, indicating that the relevant spin dephasing mechanisms are correctly taken into account. CONCLUSIONS: The proposed method can be used to estimate the influence of blood flow and alveolar geometry on the MR lineshape of lung tissue.

Brain tumor classification of virtual NMR voxels based on realistic blood vessel-induced spin dephasing using support vector machines.

Remodeling of tissue microvasculature commonly promotes neoplastic growth; however, there is no imaging modality in oncology yet that noninvasively quantifies microvascular changes in clinical routine. Although blood capillaries cannot be resolved in typical magnetic resonance imaging (MRI) measurements, their geometry and distribution influence the integral nuclear magnetic resonance (NMR) signal from each macroscopic MRI voxel. We have numerically simulated the expected transverse relaxation in NMR voxels with different dimensions based on the realistic microvasculature in healthy and tumor-bearing mouse brains (U87 and GL261 glioblastoma). The 3D capillary structure in entire, undissected brains was acquired using light sheet fluorescence microscopy to produce large datasets of the highly resolved cerebrovasculature. Using this data, we trained support vector machines to classify virtual NMR voxels with different dimensions based on the simulated spin dephasing accountable to field inhomogeneities caused by the underlying vasculature. In prediction tests with previously blinded virtual voxels from healthy brain tissue and GL261 tumors, stable classification accuracies above 95% were reached. Our results indicate that high classification accuracies can be stably attained with achievable training set sizes and that larger MRI voxels facilitated increasingly successful classifications, even with small training datasets. We were able to prove that, theoretically, the transverse relaxation process can be harnessed to learn endogenous contrasts for single voxel tissue type classifications on tailored MRI acquisitions. If translatable to experimental MRI, this may augment diagnostic imaging in oncology with automated voxel-by-voxel signal interpretation to detect vascular pathologies.

Dependence of the frequency distribution around a sphere on the voxel orientation.

Microscopically small magnetic field inhomogeneities within an external static magnetic field cause a free induction decay in magnetic resonance imaging that generally exhibits two transverse components that are usually summarized to a complex entity. The Fourier transform of the complex-valued free induction decay is the purely real and positive-valued frequency distribution which allows an easy interpretation of the underlying dephasing mechanism. Typically, the frequency distribution inside a cubic voxel as caused by a spherical magnetic field inhomogeneity is determined by a histogram technique in terms of subdivision of the whole voxel into smaller subvoxels. A faster and more accurate computation is achieved by analytical expressions for the frequency distribution that are derived in this work. In contrast to the usually assumed simplified case of a spherical voxel, we also consider the tilt angles of the cubic voxel to the external magnetic field. The typical asymmetric form of the frequency distribution is reproduced and analyzed for the more realistic case of a cubic voxel. We observe a splitting of frequency distribution peaks for increasing tilt of the cubic voxel against the direction of the external magnetic field in analogy to the case for dephasing around cylindrical, vessel-like objects inside cubic voxels. These results are of value, e.g., for the analysis of susceptibility-weighted images or in quantitative susceptibility imaging since the reconstruction of these images is performed in cubic-shaped voxels.

Potential of contrast agents based on high-Z elements for contrast-enhanced photon-counting computed tomography.

PURPOSE: In clinics, only iodine- and barium-based contrast agents are currently used for contrast-enhanced x-ray computed tomography (CT). Recently, the introduction of new photon-counting (PC) detectors increased the interest in developing new contrast agents based on heavier elements. These elements may provide more contrast and spectral information compared to iodine and barium thanks to their k-edges at higher energies. In this paper, the potential of high-Z elements in contrast-enhanced CT was evaluated for different patient sizes and x-ray spectra using a PC detector. METHODS: An adult liver phantom with five high-Z element solutions (iodine, gadolinium, ytterbium, tungsten, and bismuth) was scanned with a whole-body photon-counting computed tomography (PCCT) prototype. For each element, the contrast-to-noise ratio at unit concentration and at unit dose (CNRCD) was evaluated in low threshold images ( T 0 = 20 keV ) as function of the tube voltage (80, 100, 120, and 140 kV) and in bin images (tube voltage = 120 kV) as function of the higher threshold ( T 0 = 20 keV and T 1 ∈ [ 50 , 90 ] keV ). Simulations were performed for validation with measurements and to investigate more elements (cerium and gold), different patient sizes (infant, adult, and obese), and spectrum filtration (with and without 0.4-mm tin filter). The dose reductions associated with the CNRCD improvements over iodine were quantified as well. RESULTS: CNRCD improvements and dose reductions depend on the investigated scenario. For the infant phantom, dose reductions around 30% were reached using cerium or gadolinium in combination with the tin filter. For the adult and obese phantom, reductions around 50% were provided by gadolinium or ytterbium in combination with the tin filter. Independently of the high-Z element, the CNRCD of two optimally combined bin images was higher than the CNRCD of the low threshold image. Good agreement was found between measurements and simulations. CONCLUSIONS: Between the investigated elements, gadolinium resulted to have the highest potential as novel contrast agent in PCCT, providing significant dose reductions for all patient sizes. Compared to the other elements, the implementation of gadolinium as CT contrast agent may be facilitated since it is already deployed as contrast agents for magnetic resonance imaging.

Gibbs point field model quantifies disorder in microvasculature of U87-glioblastoma.

Microvascular proliferation in glioblastoma multiforme is a biological key mechanism to facilitate tumor growth and infiltration and a main target for treatment interventions. The vascular architecture can be obtained by Single Plane Illumination Microscopy (SPIM) to evaluate vascular heterogeneity in tumorous tissue. We make use of the Gibbs point field model to quantify the order of regularity in capillary distributions found in the U87 glioblastoma model in a murine model and to compare tumorous and healthy brain tissue. A single model parameter Γ was assigned that is linked to tissue-specific vascular topology through Monte-Carlo simulations. Distributions of the model parameter Γ differ significantly between glioblastoma tissue with mean 〈ΓG〉=2.1±0.4, as compared to healthy brain tissue with mean 〈ΓH〉=4.9±0.4, suggesting that the average Γ-value allows for tissue differentiation. These results may be used for diagnostic magnetic resonance imaging, where it has been shown recently that Γ is linked to tissue-inherent relaxation parameters.

Susceptibility based multiparametric quantification of liver disease: Non-invasive evaluation of steatosis and iron overload.

PURPOSE: To evaluate if single-voxel MR spectroscopy (MRS) of iron and fat correlates with biopsy results of hepatic steatosis and iron overload, and to compare MR-measurements with room-temperature susceptometer (RTS), ultrasound, controlled attenuation parameter (CAP) and serum ferritin. MATERIAL AND METHODS: In this prospective study, a set of 42 patients out of 47 screened patients with several chronic liver diseases underwent MRI-examination at 1.5 T including R2-measurements by single-voxel high-speed T2-corrected multiecho spectroscopy, additional liver biopsy, abdominal ultrasound, CAP, and RTS. Routine blood and serum parameters were determined, including ferritin. Atomic absorption spectroscopy (AAS) and histologically confirmed extent of hepatic steatosis from liver biopsy were used as reference standard. For correlation of R2, RTS, CAP, ferritin, and ultrasound with results of AAS and histologically determined fat fraction of liver biopsy specimen, Spearman's and Pearson's correlation as well as receiver operating characteristics curve (ROC) analysis with cut-off values determined by maximizing Youden index was used. RESULTS: MRS iron assessment correlated best with AAS, with a Pearson correlation coefficient of 0.715 (p < 0.001), followed by RTS 0.520 (p < 0.001), and serum ferritin 0.213 (p = 0.088, not significant). MRS fat quantification correlated best with the histological confirmed extent of steatosis hepatis with a Spearman correlation coefficient of 0.836 (p < 0.001), followed by CAP 0.604 (p < 0.001) and sonographically diagnosed steatosis 0.358 (p = 0.013). CONCLUSION: MRS by T2-corrected multiecho single-voxel spectroscopy correlated best with histological results of hepatic fat and iron content compared to RTS, CAP, abdominal ultrasound, and ferritin. Non-invasive methods to assess hepatic fat and iron are of clinical interest for follow-up examinations of patients with chronic liver diseases, where repeated biopsy is not indicated.

Vessel architecture imaging using multiband gradient-echo/spin-echo EPI.

OBJECTIVES: To apply the MB (multiband) excitation and blipped-CAIPI (blipped-controlled aliasing in parallel imaging) techniques in a spin and gradient-echo (SAGE) EPI sequence to improve the slice coverage for vessel architecture imaging (VAI). MATERIALS AND METHODS: Both MB excitation and blipped-CAIPI with in-plane parallel imaging were incorporated into a gradient-echo (GE)/spin-echo (SE) EPI sequence for simultaneous tracking of the dynamic MR signal changes in both GE and SE contrasts after the injection of contrast agent. MB and singleband (SB) excitation were compared using a 20-channel head coil at 3 Tesla, and high-resolution MB VAI could be performed in 32 glioma patients. RESULTS: Whole-brain covered high resolution VAI can be achieved after applying multiband excitation with a factor of 2 and in-plane parallel imaging with a factor of 3. The quality of the images resulting from MB acceleration was comparable to those from the SB method: images were reconstructed without any loss of spatial resolution or severe distortions. In addition, MB and SB signal-to-noise ratios (SNR) were similar. A relative low g-factor induced from the MB acceleration method was achieved after using a blipped-CAIPI technique (1.35 for GE and 1.33 for SE imaging). Performing quantitative VAI, we found that, among all VAI parametric maps, microvessel type indicator (MTI), distance map (I) and vascular-induced bolus peak-time shift (VIPS) were highly correlated. Likewise, VAI parametric maps of slope, slope length and short axis were highly correlated. CONCLUSIONS: Multiband accelerated SAGE successfully doubles the number of readout slices in the same measurement time when compared to conventional readout sequences. The corresponding VAI parametric maps provide insights into the complexity and heterogeneity of vascular changes in glioma.

Improved compressed sensing reconstruction for [Formula: see text]F magnetic resonance imaging.

OBJECTIVE: In magnetic resonance imaging (MRI), compressed sensing (CS) enables the reconstruction of undersampled sparse data sets. Thus, partial acquisition of the underlying k-space data is sufficient, which significantly reduces measurement time. While 19F MRI data sets are spatially sparse, they often suffer from low SNR. This can lead to artifacts in CS reconstructions that reduce the image quality. We present a method to improve the image quality of undersampled, reconstructed CS data sets. MATERIALS AND METHODS: Two resampling strategies in combination with CS reconstructions are presented. Numerical simulations are performed for low-SNR spatially sparse data obtained from 19F chemical-shift imaging measurements. Different parameter settings for undersampling factors and SNR values are tested and the error is quantified in terms of the root-mean-square error. RESULTS: An improvement in overall image quality compared to conventional CS reconstructions was observed for both strategies. Specifically spike artifacts in the background were suppressed, while the changes in signal pixels remained small. DISCUSSION: The proposed methods improve the quality of CS reconstructions. Furthermore, because resampling is applied during post-processing, no additional measurement time is required. This allows easy incorporation into existing protocols and application to already measured data.

Voxel-size dependent quantitative susceptibility mapping of blood vessel networks: A simulation study.

Quantitative susceptibility mapping provides a measure for the local susceptibility within a voxel in magnetic resonance imaging (MRI). So far, theoretical and numerical studies focus on the assumption of a constant susceptibility inside each MR voxel. For blood vessel networks, however, susceptibility differences between blood and surrounding tissue occur on a much smaller length scale than the typical voxel size in routine MRI. In this work, the dependency of the quantitative susceptibility value on vessel size and voxel size is analyzed.

Dual-contrast pCASL using simultaneous gradient-echo/spin-echo multiband EPI.

A 2D gradient-echo EPI is commonly employed for arterial spin labeling (ASL) readout to achieve fast whole brain coverage measurements. However, such a readout suffers from susceptibility artifacts induced by magnetic field inhomogeneities. To reduce these susceptibility effects, single-shot spin-echo EPI was proposed to be used for acquisitions in continuous ASL (CASL). To minimize functional and physiological variations, a gradient-echo (GE)/spin-echo (SE) dual-echo EPI readout of the CASL sequence is needed for a comparison between GE- and SE-based determination of cerebral blood flow (CBF). In this study, we employed a simultaneous GE/SE multiband EPI as the readout of a pseudo-CASL (pCASL) sequence. Motor cortex activations derived from a finger-tapping task and functional networks from resting state fMRI were compared for both GE and SE contrasts. Direct comparison of SE and GE contrasts revealed that GE ASL provides an improved sensitivity of functional activity in finger-tapping and in resting-state imaging. SE ASL, on the other hand, suffered less from susceptibility artifacts induced by magnetic field inhomogeneities and pulsatile flow artifacts.

Vessel radius mapping in an extended model of transverse relaxation.

OBJECTIVES: Spin dephasing of the local magnetization in blood vessel networks can be described in the static dephasing regime (where diffusion effects may be ignored) by the established model of Yablonskiy and Haacke. However, for small capillary radii, diffusion phenomena for spin-bearing particles are not negligible. MATERIAL AND METHODS: In this work, we include diffusion effects for a set of randomly distributed capillaries and provide analytical expressions for the transverse relaxation times T2* and T2 in the strong collision approximation and the Gaussian approximation that relate MR signal properties with microstructural parameters such as the mean local capillary radius. RESULTS: Theoretical results are numerically validated with random walk simulations and are used to calculate capillary radius distribution maps for glioblastoma mouse brains at 9.4 T. For representative tumor regions, the capillary maps reveal a relative increase of mean radius for tumor tissue towards healthy brain tissue of [Formula: see text] (p < 0.001). CONCLUSION: The presented method may be used to quantify angiogenesis or the effects of antiangiogenic therapy in tumors whose growth is associated with significant microvascular changes.

Suitable reference tissues for quantitative susceptibility mapping of the brain.

PURPOSE: Since quantitative susceptibility mapping (QSM) quantifies magnetic susceptibility relative to a reference value, a suitable reference tissue has to be available to compare different subjects and stages of disease. METHODS: To find such a suitable reference tissue for QSM of the brain, melanoma patients with and without brain metastases were measured. Twelve reference regions were chosen and assessed for stability of susceptibility values with respect to multiple intra-individual and inter-individual measurements, age, and stage of disease. RESULTS: Cerebrospinal fluid (CSF), the internal capsule and one region in the splenium of the corpus callosum are the regions with the smallest standard deviations of the mean susceptibility value. The mean susceptibility is 0.010 ± 0.014 ppm for CSF in the atrium of the lateral ventricles (csfpost ), -0.060 ± 0.019 ppm for the posterior limb of the internal capsule (ci2), and -0.008 ± 0.019 ppm for the splenium of the corpus callosum. csfpost and ci2 show nearly no dependence on age or stage of disease, whereas some other regions, e.g., the red nucleus, show moderate dependence on age or disease. CONCLUSION: The internal capsule and CSF appear to be the most suitable reference regions for QSM of the brain in the melanoma patients studied. Both showed virtually no dependence on age or disease and small variations among patients. Magn Reson Med 78:204-214, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Potential of quantitative susceptibility mapping for detection of prostatic calcifications.

PURPOSE: To evaluate whether quantitative susceptibility (QSM) may be used as an alternative to computed tomography (CT) to detect calcification in prostate cancer patients. MATERIALS AND METHODS: Susceptibility map calculation was performed using 3D gradient echo magnetic resonance imaging (MRI) data from 26 patients measured at 3T who previously received a planning CT of the prostate. Phase images were unwrapped using Laplacian-based phase unwrapping, the background field was removed with the V-SHARP method, and susceptibility maps were calculated with the iLSQR method. Two blinded readers were asked to identify peri- and intraprostatic calcifications. RESULTS: Average mean and minimum susceptibility values (referenced to iliopsoas muscle) of calcifications were -0.249 ± 0.179 ppm and -0.551 ± 0.323 ppm, and average mean and maximum intensities in CT images were 319 ± 164 HU and 679 ± 392 HU. Twenty-one and 17 out of 22 prostatic calcifications were identified using susceptibility maps and magnitude images, respectively, as well as more than half of periprostatic phleboliths depicted by CT. Calcifications in the prostate and its periphery were quantitatively differentiable from noncalcified prostate tissue in CT (mean values for calcifications / for noncalcified tissue: 71 to 649 / -1 to 83 HU) and in QSM (mean values for calcifications / for noncalcified tissue: -0.641 to 0.063 / -0.046 to 0.181 ppm). Moreover, there was a significant correlation between susceptibility values and CT image intensities for calcifications (P < 0.004). CONCLUSION: Prostatic calcifications could be well identified with QSM. Susceptibility maps can be easily obtained from clinical prostate MR protocols that include a 3D gradient echo sequence, rendering it a promising technique for detection and quantification of intraprostatic calcifications. LEVEL OF EVIDENCE: 1 J. Magn. Reson. Imaging 2017;45:889-898.

Microstructural Analysis of Peripheral Lung Tissue through CPMG Inter-Echo Time R2 Dispersion.

Since changes in lung microstructure are important indicators for (early stage) lung pathology, there is a need for quantifiable information of diagnostically challenging cases in a clinical setting, e.g. to evaluate early emphysematous changes in peripheral lung tissue. Considering alveoli as spherical air-spaces surrounded by a thin film of lung tissue allows deriving an expression for Carr-Purcell-Meiboom-Gill transverse relaxation rates R2 with a dependence on inter-echo time, local air-tissue volume fraction, diffusion coefficient and alveolar diameter, within a weak field approximation. The model relaxation rate exhibits the same hyperbolic tangent dependency as seen in the Luz-Meiboom model and limiting cases agree with Brooks et al. and Jensen et al. In addition, the model is tested against experimental data for passively deflated rat lungs: the resulting mean alveolar radius of RA = 31.46 ± 13.15 µm is very close to the literature value (∼34 µm). Also, modeled radii obtained from relaxometer measurements of ageing hydrogel foam (that mimics peripheral lung tissue) are in good agreement with those obtained from µCT images of the same foam (mean relative error: 0.06 ± 0.01). The model's ability to determine the alveolar radius and/or air volume fraction will be useful in quantifying peripheral lung microstructure.

Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions.

The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros [Formula: see text] and [Formula: see text] are considered in the complex plane for real as well as complex values of the index [Formula: see text] and approximations for the exceptional zero [Formula: see text] are obtained. A numerical scheme based on the discretization of the two-dimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.