Calculating Cross Sections of Composite Interstellar Grains

Interstellar grains may be composite collections of particles of distinct materials, including voids, agglomerated together. We determine the various optical cross sections of such composite grains, given the optical properties of each constituent, using an approximate model of the composite grain. We assume it consists of many concentric spherical layers of the various materials, each with a specified volume fraction. In such a case the usual Mie theory can be generalized and the extinction, scattering, and other cross sections determined exactly. We find that the ordering of the materials in the layering makes some difference to the derived cross sections, but averaging over the various permutations of the order of the materials provides rapid convergence as the number of shells (each of which is filled by all of the materials proportionately to their volume fractions) is increased. Three shells, each with one layer of a particular constituent material, give a very satisfactory estimate of the average cross section produced by larger numbers of shells. We give the formulae for the Rayleigh limit (small size parameter) for multi-layered spheres and use it to propose an ``Effective Medium Theory'' (EMT), in which an average optical constant is taken to represent the ensemble of materials. Multi-layered models are used to compare the accuracies of several EMTs already in the literature.Comment: 29 pages, 6 figures, accepted for publication in the Astrophysical Journal (part 1, scheduled in Vol. 526, #1, Nov. 20

Dynamic susceptibility contrast MRI with localized arterial input functions

Compared to gold-standard measurements of cerebral perfusion with positron emission tomography (PET) using H2[15O] tracers, measurements with dynamic susceptibility contrast (DSC) MR are more accessible, less expensive and less invasive. However, existing methods for analyzing and interpreting data from DSC MR have characteristic disadvantages that include sensitivity to incorrectly modeled delay and dispersion in a single, global arterial input function (AIF). We describe a model of tissue microcirculation derived from tracer kinetics which estimates for each voxel a unique, localized AIF (LAIF). Parameters of the model were estimated using Bayesian probability theory and Markov-chain Monte Carlo, circumventing difficulties arising from numerical deconvolution. Applying the new method to imaging studies from a cohort of fourteen patients with chronic, atherosclerotic, occlusive disease showed strong correlations between perfusion measured by DSC MR with LAIF and perfusion measured by quantitative PET with H2[15O]. Regression to PET measurements enabled conversion of DSC MR to a physiological scale. Regression analysis for LAIF gave estimates of a scaling factor for quantitation which described perfusion accurately in patients with substantial variability in hemodynamic impairment

Human Cerebral Osmolytes during Chronic Hyponatremia A Proton Magnetic Resonance Spectroscopy Study

The pathogenesis of morbidity associated with hyponatremia is postulated to be determined by the state of intracellular cerebral osmolytes. Previously inaccessible, these metabolites can now be quantitated by proton magnetic resonance spectroscopy. An in vivo quantitative assay of osmolytes was performed in 12 chronic hyponatremic patients (mean serum sodium 120 meq/liter) and 10 normal controls. Short echo time proton magnetic resonance spectroscopy of occipital gray and parietal white matter locations revealed dramatic reduction in the concentrations of several metabolites. In gray matter, myo-inositol was most profoundly reduced at 49 % of control value. Choline containing compounds were reduced 36%, creatine/phosphocreatine 19%, and N-acetylaspartate 11 % from controls. Similar changes were found in white matter. Recovery of osmolyte concentrations was demonstrated in four patients studied 8-14 wk later. These results are consistent with a reversible osmolyte reduction under hypoosmolar stress in the intact human brain and offer novel suggestions for treatment and monitoring of this common clinical event. (J. Clin. Invest. 1995.95:788-793.) Key words: hyponatremia * magnetic resonance spectroscopy * osmolytes * myo-inosito