Magnetic susceptibility induced white matter MR signal frequency shifts--experimental comparison between Lorentzian sphere and generalized Lorentzian approaches.

PURPOSE: The nature of the remarkable phase contrast in high-field gradient echo MRI studies of human brain is a subject of intense debates. The generalized Lorentzian approach (He and Yablonskiy, Proc Natl Acad Sci USA 2009;106:13558-13563) provides an explanation for the anisotropy of phase contrast, the near absence of phase contrast between white matter and cerebrospinal fluid, and changes of phase contrast in multiple sclerosis. In this study, we experimentally validate the generalized Lorentzian approach. THEORY AND METHODS: The Generalized Lorentzian Approach suggests that the local contribution to frequency shifts in white matter does not depend on the average tissue magnetic susceptibility (as suggested by Lorentzian sphere approximation), but on the distribution and symmetry of magnetic susceptibility inclusions at the cellular level. We use ex vivo rat optic nerve as a model system of highly organized cellular structure containing longitudinally arranged myelin and neurofilaments. The nerve's cylindrical shape allowed accurate measurement of its magnetic susceptibility and local frequency shifts. RESULTS: We found that the volume magnetic susceptibility difference between nerve and water is -0.116 ppm, and the magnetic susceptibilities of longitudinal components are -0.043 ppm in fresh nerve, and -0.020 ppm in fixed nerve. CONCLUSION: The frequency shift observed in the optic nerve as a representative of white matter is consistent with generalized Lorentzian approach but inconsistent with Lorentzian sphere approximation.

Lung morphometry with hyperpolarized 129Xe: theoretical background.

The (3) He lung morphometry technique, based on MRI measurements of hyperpolarized (3) He gas diffusion in lung airspaces, provides unique information on the lung microstructure at the alveolar level. In vivo 3D tomographic images of standard morphological parameters (airspace chord length, lung parenchyma surface-to-volume ratio, and number of alveoli per unit volume) can be generated from a rather short (several seconds) MRI scan. The technique is based on a theory of gas diffusion in lung acinar airways and experimental measurements of diffusion-attenuated MRI signal. The present work aims at developing the theoretical background of a similar technique based on hyperpolarized (129) Xe gas. As the diffusion coefficient and gyromagnetic ratio of (129) Xe gas are substantially different from those of (3) He gas, the specific details of the theory and experimental measurements with (129) Xe should be amended. We establish phenomenological relationships between acinar airway geometrical parameters and the diffusion-attenuated MR signal for human and small animal lungs, both normal lungs and lungs with mild emphysema. Optimal diffusion times are shown to be about 5 ms for human and 1.3 ms for small animals. The expected uncertainties in measuring main morphometrical parameters of the lungs are estimated in the framework of Bayesian probability theory.

Improved calibration technique for in vivo proton MRS thermometry for brain temperature measurement.

The most common MR-based approach to noninvasively measure brain temperature relies on the linear relationship between the (1)H MR resonance frequency of tissue water and the tissue's temperature. Herein we provide the most accurate in vivo assessment existing thus far of such a relationship. It was derived by acquiring in vivo MR spectra from a rat brain using a high field (11.74 Tesla [T]) MRI scanner and a single-voxel MR spectroscopy technique based on a LASER pulse sequence. Data were analyzed using three different methods to estimate the (1)H resonance frequencies of water and the metabolites NAA, Cho, and Cr, which are used as temperature-independent internal (frequency) references. Standard modeling of frequency-domain data as composed of resonances characterized by Lorentzian line shapes gave the tightest resonance-frequency versus temperature correlation. An analysis of the uncertainty in temperature estimation has shown that the major limiting factor is an error in estimating the metabolite frequency. For example, for a metabolite resonance linewidth of 8 Hz, signal sampling rate of 2 Hz and SNR of 5, an accuracy of approximately 0.5 degrees C can be achieved at a magnetic field of 3T. For comparison, in the current study conducted at 11.74T, the temperature estimation error was approximately 0.1 degrees C.

In vivo lung morphometry with hyperpolarized 3He diffusion MRI: theoretical background.

MRI-based study of (3)He gas diffusion in lungs may provide important information on lung microstructure. Lung acinar airways can be described in terms of cylinders covered with alveolar sleeve [Haefeli-Bleuer, Weibel, Anat. Rec. 220 (1988) 401]. For relatively short diffusion times (on the order of a few ms) this geometry allows description of the (3)He diffusion attenuated MR signal in lungs in terms of two diffusion coefficients-longitudinal (D(L)) and transverse (D(T)) with respect to the individual acinar airway axis [Yablonskiy et al., PNAS 99 (2002) 3111]. In this paper, empirical relationships between D(L) and D(T) and the geometrical parameters of airways and alveoli are found by means of computer Monte Carlo simulations. The effects of non-Gaussian signal behavior (dependence of D(L) and D(T) on b-value) are also taken into account. The results obtained are quantitatively valid in the physiologically important range of airway parameters characteristic of healthy lungs and lungs with mild emphysema. In lungs with advanced emphysema, the results provide only "apparent" characteristics but still could potentially be used to evaluate emphysema progression. This creates a basis for in vivo lung morphometry-evaluation of the geometrical parameters of acinar airways from hyperpolarized (3)He diffusion MRI, despite the airways being too small to be resolved by direct imaging. These results also predict a rather substantial dependence of (3)He ADC on the experimentally-controllable diffusion time, Delta. If Delta is decreased from 3 ms to 1 ms, the ADC in normal human lungs may increase by almost 50%. This effect should be taken into account when comparing experimental data obtained with different pulse sequences.

Theory of FID NMR signal dephasing induced by mesoscopic magnetic field inhomogeneities in biological systems.

A theory of the NMR signal dephasing due to the presence of tissue-specific magnetic field inhomogeneities is developed for a two-compartment model. Randomly distributed magnetized objects of finite size embedded in a given media are modeled by ellipsoids of revolution (prolate and oblate spheroids). The model can be applied for describing blood vessels in a tissue, red blood cells in the blood, marrow within trabecular bones, etc. The time dependence of the dephasing function connected with the spins inside of the objects, s(i), is shown to be expressed by Fresnel functions and creates a powder-type signal in the frequency domain. The short-time regime of the dephasing function for spins outside the objects, s(e), is always characterized by Gaussian time dependence, s(e) approximately exp[-zeta(k)(t/tc)2], with zeta being a volume fraction occupied by the objects, t(c) being a characteristic dephasing time, and the coefficient k depending on the ellipsoid's shape through the aspect ratio of its axes (a/c). The long-time asymptotic behavior of s(e) is always "quasispherical"-linear exponential in time, s(e) approximately exp(-zetaCt/tc), with the same "spherical" decay rate for any ellipsoidal shape. For long prolate spheroids (a/c)<<1, there exists an intermediate characteristic regime with a linear exponential time behavior and an aspect-ratio-dependent decay rate smaller than (zetaC/tc).

Effects of permeable boundaries on the diffusion-attenuated MR signal: insights from a one-dimensional model.

The local magnetization distribution M(x,t) and the net MR signal S arising from a one-dimensional periodic structure with permeable barriers in a Tanner-Stejskal pulsed-field gradient experiment are considered. In the framework of the narrow pulse approximation, the general expressions for M(x,t) and S as functions of diffusion time and the bipolar field gradient strength are obtained and analyzed. In contrast to a system with impermeable boundaries, the signal S as a function of the b-value is modeled well as a bi-exponential decay not only in the short-time regime but also in the long-time regime. At short diffusion times, the local magnetization M(x,t) is strongly spatially inhomogeneous and the two exponential components describing S have a clear physical interpretation as two "population fractions" of the slow- and fast-diffusing quasi-compartments (pools). In the long-diffusion time regime, the two exponential components do not have clear physical meaning but rather serve to approximate a more complex functional signal form. The average diffusion propagator, obtained by means of standard q-space analysis procedures in the long-diffusion time regime is explored; its structure creates the deceiving appearance of a system with multiple compartments of different sizes, while in reality, it reflects the permeable nature of boundaries in a system with multiple compartments all of the same size.

Morphometric changes in the human pulmonary acinus during inflation.

Despite decades of research into the mechanisms of lung inflation and deflation, there is little consensus about whether lung inflation occurs due to the recruitment of new alveoli or by changes in the size and/or shape of alveoli and alveolar ducts. In this study we use in vivo (3)He lung morphometry via MRI to measure the average alveolar depth and alveolar duct radius at three levels of inspiration in five healthy human subjects and calculate the average alveolar volume, surface area, and the total number of alveoli at each level of inflation. Our results indicate that during a 143 ± 18% increase in lung gas volume, the average alveolar depth decreases 21 ±5%, the average alveolar duct radius increases 7 ± 3%, and the total number of alveoli increases by 96 ± 9% (results are means ± SD between subjects; P < 0.001, P < 0.01, and P < 0.00001, respectively, via paired t-tests). Thus our results indicate that in healthy human subjects the lung inflates primarily by alveolar recruitment and, to a lesser extent, by anisotropic expansion of alveolar ducts.

Imaging alveolar-duct geometry during expiration via ³He lung morphometry.

Acinar geometry has been the subject of several morphological and imaging studies in the past; however, surprisingly little is known about how the acinar microstructure changes when the lung inflates or deflates. Lung morphometry with hyperpolarized (3)He diffusion MRI allows non-destructive evaluation of lung microstructure and acinar geometry, which has important applications in understanding basic lung physiology and disease. In this study, we have measured the alveolar and acinar duct sizes at physiologically relevant volumes by (3)He lung morphometry in six normal, excised, and unfixed canine lungs. Our results imply that, during a 37% decrease in lung volume, the acinar duct radius decreases by 19%, whereas the alveolar depth increases by 9% (P < 0.0001 and P < 0.05, respectively via paired t-tests with a Bonferroni correction). A comparison to serial sections under the microscope validates the imaging results and opens the door to in vivo human studies of lung acinar geometry and physiology during respiration using (3)He lung morphometry.

³He lung morphometry technique: accuracy analysis and pulse sequence optimization.

The (3)He lung morphometry technique (Yablonskiy et al., JAP, 2009), based on MRI measurements of hyperpolarized gas diffusion in lung airspaces, provides unique information on the lung microstructure at the alveolar level. 3D tomographic images of standard morphological parameters (mean airspace chord length, lung parenchyma surface-to-volume ratio, and the number of alveoli per unit lung volume) can be created from a rather short (several seconds) MRI scan. These parameters are most commonly used to characterize lung morphometry but were not previously available from in vivo studies. A background of the (3)He lung morphometry technique is based on a previously proposed model of lung acinar airways, treated as cylindrical passages of external radius R covered by alveolar sleeves of depth h, and on a theory of gas diffusion in these airways. The initial works approximated the acinar airways as very long cylinders, all with the same R and h. The present work aims at analyzing effects of realistic acinar airway structures, incorporating airway branching, physiological airway lengths, a physiological ratio of airway ducts and sacs, and distributions of R and h. By means of Monte-Carlo computer simulations, we demonstrate that our technique allows rather accurate measurements of geometrical and morphological parameters of acinar airways. In particular, the accuracy of determining one of the most important physiological parameter of lung parenchyma - surface-to-volume ratio - does not exceed several percent. Second, we analyze the effect of the susceptibility induced inhomogeneous magnetic field on the parameter estimate and demonstrate that this effect is rather negligible at B(0) ≤ 3T and becomes substantial only at higher B(0) Third, we theoretically derive an optimal choice of MR pulse sequence parameters, which should be used to acquire a series of diffusion-attenuated MR signals, allowing a substantial decrease in the acquisition time and improvement in accuracy of the results. It is demonstrated that the optimal choice represents three not equidistant b-values: b(1)=0, b(2)∼2 s/cm(2), b(3)∼8 s/cm(2).

Quantitative assessment of lung microstructure in healthy mice using an MR-based 3He lung morphometry technique.

The recently developed technique of lung morphometry using hyperpolarized (3)He diffusion magnetic resonance (MR) (Yablonskiy DA, Sukstanskii AL, Woods JC, Gierada DS, Quirk JD, Hogg JC, Cooper JD, Conradi MS. J Appl Physiol 107: 1258-1265, 2009) permits in vivo study of lung microstructure at the alveolar level. Originally proposed for human lungs, it also has the potential to study small animals. The technique relies on theoretical developments in the area of gas diffusion in lungs linking the diffusion attenuated MR signal to the lung microstructure. To adapt this technique to small animals, certain modifications in MR protocol and data analysis are required, reflecting the smaller size of mouse alveoli and acinar airways. This is the subject of the present paper. Herein, we established empirical relationships relating diffusion measurements to geometrical parameters of lung acinar airways with dimensions typical for mice and rats by using simulations of diffusion in the airways. We have also adjusted the MR protocol to acquire data with much shorter diffusion times compared with humans to accommodate the substantially smaller acinar airway length. We apply this technique to study mouse lungs ex vivo. Our MR-based measurements yield mean values of lung surface-to-volume ratio of 670 cm(-1), alveolar density of 3,200 per mm(3), alveolar depth of 55 µm, and mean chord length of 62 µm, all consistent with published data obtained histologically in mice by unbiased methods. The proposed technique can be used for in vivo experiments, opening a door for longitudinal studies of lung morphometry in mice and other small animals.

Theoretical limits on brain cooling by external head cooling devices.

Numerous experimental studies have demonstrated that mild hypothermia is a rather promising therapy for acute brain injury in neonates. Because measurement of the resultant cooling of human brain in vivo is beyond current technology, an understanding of physical factors limiting the possible brain cooling would be a substantial achievement. Herein brain cooling by external head cooling devices is studied within the framework of an analytical model of temperature distribution in the brain. Theoretical limits on brain hypothermia induced by such devices are established. Analytical expressions are obtained that allow evaluation of changes in brain temperature under the influence of measurable input parameters. We show that a mild hypothermia can be successfully induced in neonates only if two necessary conditions are fulfilled: sufficiently low cerebral blood flow and sufficiently high value of the heat transfer coefficient describing the heat exchange between the head surface and a cooling device.

Quantitation of intrinsic magnetic susceptibility-related effects in a tissue matrix. Phantom study.

A theoretical background and experimental method that allows a separation of intrinsic, tissue-matrix-specific magnetic-field inhomogeneity effects from both macroscopic (large compared with voxel dimensions) and microscopic (on the order of molecular dimensions) inhomogeneities is proposed. Such separation allows one to take full advantage of these tissue-matrix-specific magnetic field inhomogeneity effects to extract information about tissue structure. A method to measure the volume fraction occupied by the susceptibility-perturbing component in a tissue matrix, the R2' relaxation rate constant, and the susceptibility difference between the bulk component and the susceptibility-perturbing component in a tissue matrix has been developed and tested on phantoms. This method offers the potential to assess a variety of tissue parameters, including cerebral blood volume, blood volume and blood oxygenation-level changes in functional MRI, the structure of trabecular bone, and other physiologically important issues.

An MRI method for measuring T2 in the presence of static and RF magnetic field inhomogeneities.

A magnetic resonance imaging method for measuring the T2 relaxation time constant is proposed. It is based on the assumption that, under very general conditions, the MR signal near a spin echo has a special symmetry arising from the refocusing nature of the 180 degrees RF pulse. A gradient echo sampling of the spin echo (GESSE) sequence is implemented to evaluate T2 by collecting multiple gradient echoes before and after the spin echo. This approach is a modification of the GESFIDE sequence proposed by Ma and Wehrli. However, our approach compares images that are not separated by any RF pulses and, as a result, is insensitive to slice profile imperfections. In addition, the calculated T2 value does not rely on any special assumptions about the MRI signal behavior in the presence of an inhomogeneous static magnetic field and, hence, is insensitive to the presence of static magnetic field inhomogeneities.

Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime.

This paper is devoted to a theory of the NMR signal behavior in biological tissues in the presence of static magnetic field inhomogeneities. We have developed an approach that analytically describes the NMR signal in the static dephasing regime where diffusion phenomena may be ignored. This approach has been applied to evaluate the NMR signal in the presence of a blood vessel network (with an application to functional imaging), bone marrow (for two specific trabecular structures, asymmetrical and columnar) and a ferrite contrast agent. All investigated systems have some common behavior. If the echo time TE is less than a known characteristic time tc for a given system, then the signal decays exponentially with an argument which depends quadratically on TE. This is equivalent to an R2* relaxation rate which is a linear function of TE. In the opposite case, when TE is greater than tc, the NMR signal follows a simple exponential decay and the relaxation rate does not depend on the echo time. For this time interval, R2* is a linear function of a) volume fraction sigma occupied by the field-creating objects, b) magnetic field Bo or just the objects' magnetic moment for ferrite particles, and c) susceptibility difference delta chi between the objects and the medium.

Coupling between changes in human brain temperature and oxidative metabolism during prolonged visual stimulation.

A fundamental discovery of modern human brain imaging with positron-emission tomography that the blood flow to activated regions of the normal human brain increases substantially more than the oxygen consumption has led to a broad discussion in the literature concerning possible mechanisms responsible for this phenomenon. Presently no consensus exists. It is well known that oxygen delivery is not the only function of systemic circulation. Additional roles include delivery of nutrients and other required substances to the tissue, waste removal, and temperature regulation. Among these other functions, the role of regional cerebral blood flow in local brain temperature regulation has received scant attention. Here we present a theoretical analysis supported by empirical data obtained with functional magnetic resonance suggesting that increase in regional cerebral blood flow during functional stimulation can cause local changes in the brain temperature and subsequent local changes in the oxygen metabolism. On average, temperature decreases by 0.2 degrees C, but individual variations up to +/-1 degrees C were also observed. Major factors contributing to temperature regulation during functional stimulation are changes in the oxygen consumption, changes in the temperature of incoming arterial blood, and extensive heat exchange between activated and surrounding brain tissue.

Homonuclear J coupling effects in volume localized NMR spectroscopy: pitfalls and solutions.

It has been observed that the signal amplitude of multiplet resonances such as the 1H doublet resonance of lactate varies with pulse sequence timing when echo-driven volume selective methods such as point resolved spectroscopy are used. Herein a standard vectorial description is presented for the mechanism of this artifact, which results from the chemical shift between homonuclear scalar-coupled (i.e., J coupled) nuclei. The chemical shift causes the extent of a signal phase modulation to vary for different spatial regions of the excited voxel. This variation results in spatial interference effects that can lead to marked loss of signal intensity as well as corruption of the size and shape of the voxel from which signal is obtained. The phenomenon is substantial at an imaging field of 1.5 T and becomes especially pronounced at higher field strengths. Several strategies to avoid the artifact are provided.

Quantitation of T2' anisotropic effects on magnetic resonance bone mineral density measurement.

In this paper, the authors quantitate the anisotropy of susceptibility effects in an uniaxial trabecular bone model and show its relevance to clinical MR bone mineral density measurements. A physical model is described that quantitates the anisotropic MR behavior of uniaxial trabecular bone. To test the model; a phantom of parallel polyethylene filaments was scanned every 15 degrees between 0 degrees and 90 degrees with respect to the system's main magnetic field (B0). The distal radial metaphysis of a healthy female volunteer was scanned in orthogonal projections. The signal from each phantom image and each radial image was separated in a pixel-wise fashion into R2 and R2' maps. As predicted, R2' relaxation showed anisotropic behavior and changed according to sin2 (theta), confirming that columnar structures parallel with B0 will cause no MR susceptibility effects. Scans of the distal radius showed that R2' relaxation was twice as great with the forearm perpendicular to B0 as when it was parallel to it, demonstrating different contributions from struts and columns. For both phantom and radial bone scans, R2 relaxation was isotropic and did not change with object orientation.

Rapid imaging of hyperpolarized gas using EPI.

Rapid repetitive MRI of hyperpolarized (HP) gases using echo-planar imaging (EPI) has been theoretically investigated and experimentally demonstrated for (3)He in human lung. A quantitative treatment of signal attenuation and magnetization consumption for the unique circumstance of a rapidly diffusing nonrenewable magnetization source has been performed. Rapid (compared to the human respiratory cycle) and repetitive imaging of the lung gas space with EPI and a single delivered bolus of HP-(3)He is feasible using low flip angles, provided the voxels are not too small. A coarse-grid (32 x 64) EPI pulse sequence has been developed and implemented to image the lungs of healthy volunteers during rebreathing of a HP-(3)He/N(2) gas mixture. A set of three 10-mm axial slices was imaged every 0.12 sec for the 36 sec duration of rebreathing, yielding a real-time visualization of ventilation. Despite some mild artifacts, the images are of good quality and show changes in gas density related to respiratory physiology. Magn Reson Med 42:507-514, 1999.

Water proton MR properties of human blood at 1.5 Tesla: magnetic susceptibility, T(1), T(2), T*(2), and non-Lorentzian signal behavior.

Accurate knowledge of the magnetic properties of human blood is required for the precise modeling of functional and vascular flow-related MRI. Herein are reported determinations of the relaxation parameters of blood, employing in vitro samples that are well representative of human blood in situ. The envelope of the blood (1)H(2)O free-induction decay signal magnitude during the first 100 msec following a spin echo at time TE is well- described empirically by an expression of the form, S(t) = S(o). exp[-R(*)(2). (t - TE) - AR*. (t - TE)(2)]. The relaxation parameters AR* and R(*)(2) increase as a function of the square of the susceptibility difference between red blood cell and plasma and depend on the spin-echo time. The Gaussian component, AR*, should be recognized in accurate modeling of MRI phenomena that depend upon the magnetic state of blood. The magnetic susceptibility difference between fully deoxygenated and fully oxygenated red blood cells at 37 degrees C is 0.27 ppm, as determined independently by MR and superconducting quantum interference device (SQUID) measurements. This value agrees well with the 1936 report of Pauling and Coryell (Proc Natl Acad Sci USA 1936;22:210-216), but is substantially larger than that frequently used in MRI literature. Magn Reson Med 45:533-542, 2001.

Effects of barrier-induced nuclear spin magnetization inhomogeneities on diffusion-attenuated MR signal.

The spatial distribution of the transverse nuclear spin magnetization, appearing in a single compartment with impermeable boundaries in a Stejskal-Tanner gradient pulse MR experiment, is analyzed in detail. At short diffusion times the presence of diffusion-restrictive barriers (membranes) reduces effective diffusivity near the membranes and leads to an inhomogeneous spin magnetization distribution (the edge-enhancement effect). In this case, the signal reveals a quasi-two-compartment behavior and can be empirically modeled remarkably well by a biexponential function. The current results provide a framework for interpreting experimental MR data on various phenomena, including water diffusion in giant axons, metabolite diffusion in the brain, and hyperpolarized gas diffusion in lung airways.