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.

The study of lung emphysema dates back to the beginning of the 17th century. Nevertheless, a number of important questions remain unanswered because a quantitative localized characterization of emphysema requires knowledge of lung structure at the alveolar level in the intact living lung. This information is not available from traditional imaging modalities and pulmonary function tests. Herein, we report the first in vivo measurements of lung geometrical parameters at the alveolar level obtained with 3 He diffusion MRI in healthy human subjects and patients with severe emphysema. We also provide the first experimental data demonstrating that 3 He gas diffusivity in the acinus of human lung is highly anisotropic. A theory of anisotropic diffusion is presented. Our results clearly demonstrate substantial differences between healthy and emphysematous lung at the acinar level and may provide new insights into emphysema progression. The technique offers promise as a clinical tool for early diagnosis of emphysema.C hronic obstructive pulmonary disease in general and emphysema in particular are leading causes of death in industrialized countries and account for a substantial portion of health care spending (1). Several definitions of emphysema have been formulated by scientific bodies: according to ref. 2, emphysema is ''a condition of the lung characterized by abnormal, permanent enlargement of air spaces distal to the terminal bronchioles, accompanied by destruction of their walls, without fibrosis.'' This definition means that an accurate characterization of emphysema requires diagnostic methods that are noninvasive and sensitive to the regional lung microstructure at the alveolar level in the living lung. Diffusion MRI of 3 He gas, which has become available after recent advances in the physics of optical pumping and semiconductor diode lasers (see, for example, refs. 3-5), can provide this sensitivity. Previously, we and others have suggested (6-10) that measurement of 3 He gas diffusivity in the lung air spaces has potential for identifying changes in lung structure from emphysema at the alveolar level.In any medium, atoms or molecules diffuse; that is, atoms perform a Brownian-motion random walk. In time interval ⌬, in the absence of restricting walls or barriers, molecules will move a rms distance l 0 ϭ (2D 0 ⌬) 1/2 along any axis. The parameter D 0 is termed the free diffusion coefficient, which for 3 He in air at 37°C is D 0 ϭ 0.88 cm 2 ͞sec. Hence 3 He gas atoms can wander distances on the order of 1 mm in times as short as 1 ms. The alveolar walls, as well as the walls of bronchioles, alveolar ducts, sacs, and other branches of the airway tree, serve as obstacles to the path of diffusing 3 He atoms and reduce 3 He displacement. Indeed, the MR-measured average 3 He diffusion coefficient (the so-called apparent diffusion coefficient or ADC) in healthy human lungs is about 0.20 cm 2 ͞sec, more than a factor of four smaller than the free diffusion coefficient of 3 He in air (6, 7). In emphysema, the restriction...

The fundamental discovery by Ogawa and coworkers (1) of blood oxygenation level-dependent (BOLD) contrast in MRI opened up broad opportunities to study the hemodynamic properties of the brain. While the "dynamic" properties of BOLD contrast during functional activation have received much consideration, very little attention has been paid to the nature of BOLD contrast during the resting or baseline state of the brain. Raichle et al. (2) identified the baseline state of the normal human brain in terms of the brain tissue oxygen extraction fraction (OEF). OEF maps in subjects who are resting quietly with their eyes closed define a baseline level of neuronal activity. OEF maps in normal resting humans demonstrate remarkable uniformity despite substantial regional variations in CBF and CMRO 2 (3,4). Understanding brain function in the baseline state is important for understanding normal human performance because it accounts for most of the enormous energy budget of the brain, whereas evoked activity represents very small incremental changes (5). Such an understanding is also crucial for deciphering the consequences of baseline-state impairment by diseases of the brain such as stroke (6) and Alzheimer's disease (7,8). Importantly, the OEF has been shown to be an accurate predictor of subsequent stroke occurrence in patients with cerebrovascular disease (9,10). Previous studies were conducted using PET imaging techniques; however, such studies would be more available for research and clinical applications if they could be performed based on MRI methods. One such MRI approach is discussed in this article.The magnetic field inside practically any system that is put into an MRI scanner is always inhomogeneous. The relative scale of this inhomogeneity compared to an imaging voxel can be roughly divided into three categories: macroscopic, mesoscopic, and microscopic (11). These three types of inhomogeneities all affect MRI signal formation. The macroscopic scale refers to magnetic field changes that occur over distances that are larger than the dimensions of the imaging voxel. Macroscopic field inhomogeneities arise from magnet imperfections, body-air interfaces, large (compared to voxel size) sinuses inside the body, etc. These field inhomogeneities are mostly undesirable in MRI because they generally provide no information of physiologic or anatomic interest. Rather, they lead to effects such as signal loss in gradient-echo (GRE) imaging, and image spatial distortions in both GRE and spin-echo (SE) imaging. The microscopic scale refers to changes in magnetic field over distances that are comparable to atomic and molecular lengths (i.e., over distances that are orders of magnitude smaller than the imaging voxel dimensions). Fluctuating microscopic field inhomogeneities lead to the irreversible signal dephasing characterized by the T 2 relaxation time constant, as well as to the longitudinal magnetization changes characterized by the T 1 relaxation time constant. The mesoscopic scale refers to distances that are smaller th...

Knowledge of the 1 H magnetic properties of blood is important for developing models of the MR signal behavior in, for instance, the BOLD effect (1). Such models of free induction decay (FID) or spin echo (SE) experiments require accurate knowledge of the blood susceptibility and relaxation parameters as a function of blood oxygenation level. The blood signal is especially important in situations where the volume of interest contains large vessels and a major signal component arises directly from the MR behavior of bulk blood.It is widely assumed, and has been used in several modeling reports, that blood relaxation in the FID experiment can be described as pure Lorentzian behavior of the blood signal magnitude: S(t) ϰ exp(-R* 2 ⅐ t). It is shown herein that a substantial oxygenation-level-dependent non-Lorentzian component is an attribute of the bulk blood signal relaxation.As a note on nomenclature, the reader is reminded that exponential signal decay in the time domain (S(t) ϰ exp(-R* 2 ⅐ t)) leads to a Lorentzian lineshape (S() ϰ R* 2 / R* 2 2 ϩ 2 ) in the frequency domain. Herein we use the term "Lorentzian behavior" to describe frequency domain and time domain signal characteristics interchangeably. Likewise, Gaussian signal decay in the time domain (S(t) ϰ exp(-AR* ⅐ t 2 )) leads to a Gaussian lineshape (S() ϰ exp(-2 /4AR*)) in the frequency domain. As will be shown in this work, a Gaussian component arises in empirical modeling of the first 100 msec of the blood time domain signal magnitude. However, this is only a useful approximation. Time domain data demonstrate small (less than 2%) but significant systematic deviations from our empirical model, a simple product of Lorentzian and Gaussian components. To emphasize the fact that our empirical model does not fully account for the blood signal's relaxation characteristics (and that the model is not based on a biophysical model of blood magnetic properties) we use the generic phrase "non-Lorentzian signal behavior" to indicate as yet unexplained deviations from pure exponential/Lorentzian characteristics.Studies of the magnetic properties of human blood have been undertaken previously, and the results were insightful (2-13). However, as BOLD-related functional MRI (fMRI) procedures increase in precision, there is need to ensure the quantitative nature of the blood MR parameters upon which interpretation of experimental results may depend. Previous blood MR literature describes varying degrees of mismatch between the experimental conditions used for in vitro studies and human blood in situ. These differences include temperature (6,13,14), pH (13), and the settling of erythrocytes from plasma in the case of static samples (3,5-7,10 -12,14). Further, the relaxation rate constants in whole blood depend on magnetic field strength (3,6); hence it is important to determine these relaxation parameters at magnetic field strengths typical of human imaging systems.Of the in vitro studies cited herein, only two ensured a continuous mixing of the blood sample in order t...

Recently reported contrast in phase images of human and animal brains obtained with gradient-recalled echo MRI holds great promise for the in vivo study of biological tissue structure with substantially improved resolution. Herein we investigate the origins of this contrast and demonstrate that it depends on the tissue ''magnetic architecture'' at the subcellular and cellular levels. This architecture is mostly determined by the structural arrangements of proteins, lipids, non-heme tissue iron, deoxyhemoglobin, and their magnetic susceptibilities. Such magnetic environment affects/shifts magnetic resonance (MR) frequencies of the water molecules moving/diffusing in the tissue. A theoretical framework allowing quantitative evaluation of the corresponding frequency shifts is developed based on the introduced concept of a generalized Lorentzian approximation. It takes into account both tissue architecture and its orientation with respect to the external magnetic field. Theoretical results quantitatively explain frequency contrast between GM, WM, and CSF previously reported in motor cortex area, including the absence of the contrast between WM and CSF. Comparison of theory and experiment also suggests that in a normal human brain, proteins, lipids, and non-heme iron provide comparable contributions to tissue phase contrast; however, the sign of iron and lipid contributions is opposite to the sign of contribution from proteins. These effects of cellular composition and architecture are important for quantification of tissue microstructure based on MRI phase measurements. Also theory predicts the dependence of the signal phase on the orientation of WM fibers, holding promise as additional information for fiber tracking applications. cellular architecture ͉ contrast mechanisms ͉ grey matter ͉ white matter