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A theory is presented for describing the effect on the transverse NMR relaxation rate of microscopic spatial inhomogeneities in the static magnetic field. The theory applies when the inhomogeneities are weak in magnitude and the nuclear spins diffuse a significant distance in comparison with a length scale characterizing the inhomogeneities. It is shown that the relaxation rate is determined by a temporal correlation function and depends quadratically on the magnitude of the inhomogeneities. For the case of unrestricted diffusion, a simple algebraic approximation for the temporal correlation function is derived. The theory is illustrated by applying it to a model of randomly distributed magnetized spheres. The theory is also used to fit experimental data for the dependence of the relaxation rate on the interecho time for a Carr-Purcell-Meiboom-Gill pulse sequence. Key words: relaxation rate; magnetic inhomogeneities; brain; blood; diffusion Some biological tissues, when placed in a uniform external magnetic field, generate a secondary inhomogeneous field that can significantly increase the transverse NMR relaxation rate (1,2). The inhomogeneous field may be due to intrinsic structures, such as iron-rich cells in the brain (3) and deoxygenated red blood cells (4), or it may be induced by administering a contrast agent (5). A variety of applications of this effect to MR imaging have been studied (1,2,5-9).The purpose of this article is to provide a quantitative theoretical description for the relaxation rate shift caused by static microscopic field inhomogeneities that are weak in magnitude. We assume that the nuclear spins (usually water protons) diffuse with an effective diffusion constant D. Our theory is most useful if the relaxation rate shift is less than D/L 2 , where L is a length scale characterizing the inhomogeneities. Our results are thus complementary to those of static dephasing and weak diffusion approaches (10 -13).As an illustration, the theory is first applied to a system of randomly distributed, uniformly magnetized spheres. We compare our predictions with the results of other theoretical methods, numerical simulations, and experiments. Then, to demonstrate its application to biological systems, we use the theory to analyze experimental measurements made by Ye and Allen (17) for in vitro rat liver. The theory is applied to fit the dependence of the relaxation rate on the interecho time of a Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. We show that the theory gives a better fit than the commonly used Luz-Meiboom chemical exchange formula (18). MODELWe consider a system with a total static magnetic field magnitude at a position r ofwhere B 0 represents the uniform part of the field and B represents the inhomogeneous part. In practice, B is often highly irregular, and hence we formally treat it as a random quantity with an associated probability distribution. Averages over this distribution are indicated with angle brackets ͗. . .͘ fld . Without loss of generality, we may takeLet us make the n...

A quantitative theory is proposed for the nonexponential NMR proton signal decay observed in liver with iron overload or superparamagnetic iron oxide particles. This effect occurs for Carr-Purcell-Meiboom-Gill (CPMG) sequences and is argued to be a direct consequence of the strong magnetic field inhomogeneities generated by the iron, rather than being due to tissue compartments. An approximate mathematical form is given for the signal decay, which is fit to experimental data for samples of rat liver with iron oxide particles, for samples of marmoset liver with hemosiderosis, and for in vivo human liver with hereditary hemochromatosis. The fitting parameters obtained are consistent with the pattern of iron deposition determined from histology. For the case of hereditary hemochromatosis, a good correlation is found between a parameter characterizing the nonexponential decay and the iron concentration. Implications for practical MR quantification of hepatic iron are discussed. Magn

Clinical studies have revealed a strong link between increased burden of cerebral microinfarcts and risk for cognitive impairment. Since the sum of tissue damage incurred by microinfarcts is a miniscule percentage of total brain volume, we hypothesized that microinfarcts disrupt brain function beyond the injury site visible to histological or radiological examination. We tested this idea using a mouse model of microinfarcts, where single penetrating vessels that supply mouse cortex were occluded by targeted photothrombosis. We found that in vivo structural and diffusion MRI reliably reported the acute microinfarct core, based on spatial co-registrations with post-mortem stains of neuronal viability. Consistent with our hypothesis, c-Fos assays for neuronal activity and in vivo imaging of single vessel hemodynamics both reported functional deficits in viable peri-lesional tissues beyond the microinfarct core. We estimated that the volume of tissue with functional deficit in cortex was at least 12-fold greater than the volume of the microinfarct core. Impaired hemodynamic responses in peri-lesional tissues persisted at least 14 days, and were attributed to lasting deficits in neuronal circuitry or neurovascular coupling. These data show how individually miniscule microinfarcts could contribute to broader brain dysfunction during vascular cognitive impairment and dementia.

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