David C. Ailion

A mathematical model of diamagnetic line broadening in lung tissue and similar heterogeneous systems: Calculations and measurements

Abstract In order to explain recently observed internal inhomogeneous broadening in lung tissue, we constructed and calculated diamagnetic field shifts for models consisting of a spherical shell of water and a hexagonally packed array of spherical air bubbles in water. For the spherical-shell model, the field equations were solved exactly for an arbitrary number of concentric shells. In contrast, in the hexagonal model, a Monte Carlo algorithm was used to pick points within the specimen at which the field was calculated to first order by adding together contributions from all the spheres. The linewidth calculated for the spherical-shell model agrees well with the results of our experimental measurements. Furthermore, the hexagonal model accurately predicts the observed linewidth in rat lung. These models can be used in correlating the NMR linewidth with the state of inflation or injury of the lung. They also may have application in a broad class of heterogeneous systems (e.g., slurries, bone).

Calculation and interpretation of inhomogeneous line broadening in models of lungs and other heterogeneous structures

Abstract To extend previous calculations of internal inhomogeneous line broadening in models of lung, we derived a surface integral expression for the magnetic field shift produced when a structure composed of magnetic material with a magnetic susceptibility of a few parts per million is placed in an otherwise uniform magnetic field. The expression is integrated exactly for rectangular surfaces. NMR lineshapes for simple structures such as spheres, spherical shells, cubes, cubical shells, and rectangular parallelepipeds are calculated and presented. A physical interpretation of the results is given in terms of “thick” and “thin” magnetic material. Application of the results to inhomogeneous line broadening in models of the lung and correlation of NMR lineshapes with lung properties are discussed.

Determination of lung water content and distribution by nuclear magnetic resonance.

The present study was designed to determine the value of nuclear magnetic resonance (NMR) imaging as a technique for quantifying lung water distribution and to estimate the degree of spatial resolution achieved by this technique. The spatial distribution of water was determined in six small (0.76 ml) rat lung tissue specimens by an NMR line-scan technique. After NMR imaging, each lung specimen was frozen and subdivided into slices; the gravimetric lung water content for each lung slice was compared with the integrated NMR water content over the volume corresponding to the same lung slice. In each tissue specimen, NMR and gravimetric lung water values were significantly correlated; the correlation coefficient for the pooled data for all six lung specimens was 0.91 (P less than 0.01). In two lung specimens, NMR values tended to be slightly higher than the gravimetric values. The magnitude of the difference between NMR and gravimetric values was generally less than 20% and only occasionally exceeded 25%. Our results suggest that the NMR-imaging method provides satisfactory estimates of lung water content and its distribution; the resolving power of the technique is excellent, as shown by its ability to detect water content differences between lung tissue slices of volume as small as 0.076 ml.

NMR relaxation study of molecular motions between unequal potential wells in solid trans,trans‐muconodinitrile

We report observations of extremely unusual proton NMR relaxation rates in solid trans,trans‐muconodinitrile (TMD, N≡C–CH=CH–CH=CH–C≡N). In particular we measured, over the temperature range 77–423 °K, proton dipolar relaxation times T1D and spin lattice relaxation times T1 (at 24 and 58 MHz). The relaxation pattern is characterized by the following features: (a) very long motional T1 and T1D even at their respective minima, (b) no detectable motional narrowing of the line even at the T1D minimum, (c) unequal slopes at temperatures below and above the minimum of T1 (and T1D) vs 1/T, and (d) significant deviations from the usual linear dependence on resonance frequency of the values of the relaxation times at their respective minima. We extended an earlier NMR theory to the case of spin lattice relaxation due to molecular reorientations between the extremely unequal potential energy wells of TMD. We were able to explain all features of the above data in terms of this theory. By comparing our data to the re...

NMR observations of molecular motions and Zeeman–quadrupole cross relaxation in 1,2‐difluorotetrachloroethanea)

We report measurements of 19F NMR relaxation times T1, T1ρ, T1D, and T2 in the plastic crystal CFCL2–CFCL2. From the data near the melting point, we obtain the jump time for translational self‐diffusion. At lower temperatures, we observe on the cold side of the T1 and T1ρ minima an unusual field dependence which is substantially less than the normal field‐squared dependence. We also observe a reduction in T1 near 40 MHz due to cross relaxation between the Zeeman levels of the 19F spins and quadrupole levels of the 35Cl and 37Cl spins. We measured the cross relaxation times τIS as a function of field and found good agreement with our theoretical calculation of τIS.

Experimental verification of inhomogeneous line-broadening calculations in lung models and other inhomogeneous structures

Abstract Experimental measurements of nuclear magnetic resonance lineshapes in physical models (slabs, cubes, and cubical shells) of water in hollow plastic containers were performed to validate theoretical methods for calculating lineshapes in models of the lung. Measured values are in excellent agreement with previously reported calculated values. This work demonstrates that the diamagnetic properties of water in a particular geometry can cause the lineshape to have a rich structure characterized by several peaks. The prominent characteristics of the lineshapes are explained in terms of perturbation of the magnetic flux density by interfaces between materials of different magnetic susceptibilities.

Zeeman–quadrupole cross relaxation between two nuclear spin species

We derive an expression for the rate τ−1IS of the cross relaxation between the Zeeman splitting of one nuclear spin species (I spins, I=1/2) and the quadrupole splitting of another spin species (S spins, S≳1/2) via the I–S dipolar interaction. We calculate τIS for the case of CFCL2–CFCL2 (I spins are 19F, and S spins are 35Cl and 37Cl) and compare the results with experimental data.

Characterization of bleomycin lung injury by nuclear magnetic resonance: Correlation between NMR relaxation times and lung water and collagen content

The response of the NMR relaxation times (T1, CPMG T2, and Hahn T2) to bleomycin‐induced lung injury was studied in excised, unperfused rat lungs. NMR, histologic, and biochemical (collagen content measurement) analyses were performed 1, 2, 4, and 8 weeks after intratracheal instillation of saline (control lungs) or 10 U/kg bleomycin sulfate. The control lungs showed no important NMR, water content, histologic, or collagen content changes. The spin‐spin relaxation times for the fast and intermediate components of the CPMG decay (T2f and T2i, respectively) increased 1 week after bleomycin injury (acute inflammatory stage) and then progressively decreased during the following 2–8 weeks (i.e., with the development of the chronic, fibrotic stage of the injury). The slow component (T2s) showed no significant changes. The response of T1 and the slow component of the Hahn T2 was, on the whole, similar to that of CPMG T2f and T2i. T1 changes were very small. Lung water content increased 1 week after injury. Histologic and biochemical assessment of collagen showed that collagen content was close to control at 1 week, but markedly increased at 2, 4, and 8 weeks. T1 and T2 data were directly correlated with lung water content and inversely correlated with collagen content. Our results indicate that NMR relaxation time measurements (particularly T2) reflect the structural changes associated with bleomycin injury. The prolonged T2 relaxation times observed in the acute stage are related to the presence of edema, whereas the subsequent decrease in these values marks the stage of the collagen deposition (fibrotic stage). CPMG‐T2 and Hahn‐T2 measurements can be valuable as a potentially noninvasive method for characterizing bleomycin‐induced lung injury and pathologically related lung disorders. Magn Reson Med 47:246–256, 2002.

Quantitative assessment of pulmonary edema by nuclear magnetic resonance methods.

Considerable progress has been made in the application of nuclear magnetic resonance (NMR) imaging and nonimaging techniques to the quantitative assessment of pulmonary edema. NMR measurements offer the advantages of being noninvasive, relatively rapid, and easily repeatable. In addition, NMR imaging is suitable for the determination of lung water distribution. Studies of various animal models have shown that NMR techniques can adequately detect and quantify relative changes in lung water content and distribution in various types of experimental lung injury. Preliminary observations in humans suggest that NMR measurement of relative lung water changes in clinical pulmonary edema should be feasible. Although the application of NMR to the assessment of pulmonary edema appears to be very promising, it also poses significant problems that must be solved before it can be established as a standard experimental and clinical method.

Determination of lung water content and distribution by nuclear magnetic resonance imaging.

NMR imaging techniques are applicable to the assessment of lung water content and distribution because the NMR signal is, under certain conditions, proportional to tissue proton density. NMR imaging is noninvasive, easily repeatable, free from ionizing radiation, and particularly suitable for the assessment of spatial lung water distribution. Lung water content and distribution have been estimated in excised animal lungs and in intact dead or living animals, under normal conditions and in various types of experimental pulmonary edema. Excised human lungs and human subjects have also been studied. Published data indicate that measurements of lung water content by NMR imaging techniques are feasible. These techniques estimate lung water spatial distribution with satisfactory accuracy and excellent resolving power. The application of NMR imaging techniques poses several problems and limitations, but available data suggest that most of the problems can be solved. NMR imaging has the potential to become a powerful tool for lung water research. Prospects of clinical application are also encouraging; numerous applications can be foreseen, although lack of mobility of NMR imaging systems may be a significant limitation in critical care medicine.