Yoram Cohen

The affinities of ferrocene (2) and the cobaltocenium cation (3⁺+), which have roughly the same size and differ in their charge, towards the inner cavity of the dimeric capsule formed by tetraurea calix[4]arene (1) were studied in C₂D₄Cl₂ solutions. While 3⁺+, which occupies more than 75% of the internal volume of the dimer, is readily encapsulated this is not the case for 2. This is probably due to cation–π interactions, which operate only between 3⁺+ and the aromatic rings of the calix[4]arene dimer. We found that the affinity of the cobaltocenium cation is higher than that of the tropylium cation (4⁺) and is only 2–3 times less than that of the tetraethylammoniun cation (5⁺). From the variable temperature ¹H NMR spectra of this capsule, the free energy of activation at 298 K (ΔG^‡ _298K) for the reorientation of the hydrogen bonded belt between the two parts of the dimer could be determined by total line shape analysis for the aromatic protons of the calixarene. The value of 14.3 ± 0.2 kcal mol⁻¹ for the dimeric capsules of 3⁺+PF₆ ⁻ is very similar to the free activation energy found for dimeric capsules of 1 with 4⁺PF₆ ⁻ and 5⁺PF₆ ⁻in C₂D₄Cl₂. It becomes significantly lower, if PF₆ ⁻ is replaced by BF₄ ⁻. We also found that ten times more DMSO is needed to disrupt the capsule 1·3⁺+·1 than the corresponding 1·1 dimer containing benzene as guest. This demonstrates again the importance of the cation–π interactions for the stability of such hydrogen-bonded dimeric capsules.

This review deals with high b‐value q‐space diffusion‐weighted MRI (DW‐MRI) of neuronal tissues. It is well documented that at sufficiently high b‐values (and high q‐values) neuronal water signal decay in diffusion experiments is not mono‐exponential. This implies the existence of more than one apparent diffusing component or evidence for restriction. The assignment of the different apparent diffusing components to real physical entities is not straightforward. However, the apparent slow diffusing component that was found to be restricted to a compartment of a few microns, if originating mainly from a specific pool and if assigned correctly, may potentially be used to obtain more specific MR images with regard to specific pathologies of the CNS. This review examines the utility of analyzing high b‐value diffusion MRS and MRI data using the q‐space approach introduced by Callaghan and by Cory and Garroway. This approach provides displacement probability maps that emphasize, at long diffusion times, the characteristics of the apparent slow diffusing component. Examples from excised spinal cord, where the experimental conditions for which the q‐space analysis of MR diffusion data was developed can be met or approached will be presented. Then examples from human MS patients, where q‐space requirement for the short gradient pulse is clearly violated, are presented. In the excised spinal cord studies, this approach was used to study spinal cord maturation and trauma, and was found to be more sensitive than other conventional methods in following spinal cord degeneration in an experimental model of vascular dementia (VaD). High b‐value q‐space DWI was also recently used to study healthy and MS diseased human brains. This approach was found to be very sensitive to the disease load in MS, compared with other conventional MRI methods, especially in the normal appearing white matter (NAWM) of MS brains. Finally, the potential diagnostic capacity embedded in high b‐value q‐space analyzed diffusion MR images is discussed. The potentials and caveats of this approach are outlined and experimental data are presented that show the effect of violating the short gradient pulse (SGP) approximation on the extracted parameters from the q‐space analysis. Copyright © 2002 John Wiley & Sons, Ltd.

Experimental autoimmune neuritis (EAN) has been studied in rat sciatic nerves by a combination of high b‐value ¹H and ²H double quantum filtered (DQF) diffusion MRS. The signal decays of water in the ¹H and ²H DQF diffusion MRS were found to be not monoexponential and were analyzed using the q‐space approach. The q‐space analysis of the ¹H diffusion data detected two diffusing components, one having broad and the other having narrow displacement profiles. These components were shown to be very sensitive to the progression of EAN disease. The q‐space parameters were found to be abnormal at day 9 postimmunization before the appearance of clinical signs. The assignment of the component with the narrow displacement profile to axonal water has been corroborated by the ²H DQF diffusion MRS results. The displacement and the relative population of this slow and restricted diffusing component followed the processes of demyelination, axonal loss, and remyelination that occur in EAN. The displacements extracted from the slow‐diffusing component with the narrow displacement correlated well with the average size of the axons as deduced from electron microscopy (EM). The component with the broad displacement showed significant changes which were attributed to the formation of endoneurial edema. This observation was also corroborated by the ²H DQF diffusion MRS experiments. It seems, therefore, that q‐space analysis of high b‐values diffusion MRS is a promising new approach for early detection and better characterization of the different pathologies associated with EAN. This study demonstrates the utility of high‐b‐value q‐space diffusion MRS for studying white matter‐associated disorders in general. Magn Reson Med 48:71–81, 2002.

Multiple sclerosis (MS) is an inflammatory disease of the central nervous system (CNS) which affects nearly one million people worldwide, leading to a progressive decline of motor and sensory functions, and permanent disability. High b‐value diffusion‐weighted MR images (b of up to 14000 s/mm²) were acquired from the brains of controls and MS patients. These diffusion MR images, in which signal decay is not monoexponential, were analyzed using the q‐space approach that emphasizes the diffusion characteristics of the slow‐diffusing component. From this analysis, displacement and probability maps were constructed. The computed q‐space analyzed MR images that were compared with conventional T₁, T₂ (fluid attenuated inversion recovery (FLAIR)), and diffusion tensor imaging (DTI) images were found to be sensitive to the pathophysiological state of white matter. The indices used to construct this q‐space analyzed MR maps, provided a pronounced differentiation between normal tissue and tissues classified as MS plaques by the FLAIR images. More importantly, a pronounced differentiation was also observed between tissues classified by the FLAIR MR images as normal‐appearing white matter (NAWM) in the MS brains, which are known to be abnormal, and the respective control tissues. The potential diagnostic capacity of high b‐value diffusion q‐space analyzed MR images is discussed, and experimental data that explains the consequences of using the q‐space approach once the short pulse gradient approximation is violated are presented. Magn Reson Med 47:115–126, 2002.

¹H NMR diffusion experiments performed on the signal of the metabolites in bovine optic nerve showed that the signal decay due to diffusion is bi-exponential with a slow and a fast diffusing component. Diffusion was measured as a function of the diffusion time, and the data were analyzed as a function of b and q values. Bi-exponential fit was used to analyze the data, and the results were compared with the displacement distribution profiles obtained from the q-space analysis of the data. This q-space analysis showed that the fast diffusing component has a broad displacement distribution and appears not to be restricted. On the other hand, the slow diffusing component appears to be highly restricted to milieu in the order of 1–2 µm. The orientation of the sample with respect to the axis for which diffusion was measured affected mainly the relative sizes of the populations of each component, but had only a small effect on the extracted apparent diffusion coefficients. These results from both the b and the q value analyses suggest that the slow diffusing component is related to restricted diffusion of these metabolites in the axonal fibers, while the fast diffusing component represents diffusion of metabolites in cells and along the long axis of the nerve fibers. It is concluded that q-space analysis of metabolite diffusion enables extraction of structural information about the sample, and that the diffusion of the metabolites in optic nerve is dictated mainly by the cellular medium and microstructure of the tissue. Copyright © 1999 John Wiley & Sons, Ltd. apparent diffusion coefficient; diffusion weighted imaging; central nervous system; N-acetyl aspartate; Carr–Purcell–Meiboom–Gill; electron microscopy

Diffusion measurements were performed on the N -acetyl aspartate (NAA) signal in in situ brains (in vivo and post-mortem) and on in vitro brain tissue at 37 °C using wide ranges of b-values (from 0 up to 4.5 × 10⁶ s/cm² and 35.8 × 10⁶ s/cm² for the in vivo and the in vitro cases, respectively). In vivo and in vitro NAA signals attenuation due to diffusion was measured at fixed diffusion times (t_D ). In the in vitro cases the effect of t_D on the apparent diffusion coefficients (ADCs) of NAA was evaluated. From these experiments the following observations and conclusions were made: (1) NAA signal attenuation both in vivo and in vitro is not mono-exponential and could be fitted by bi-exponential fitting function; (2) analysis of the low b-value range only (up to 0.5 × 10⁶ s/cm² ) gives a mono-exponential decay (r = 0.999); (3) in both cases the obtained ADCs are sensitive to the diffusion time; (4) the ADCs of the pre- and post-mortem cases are nearly similar; (5) the ADCs obtained from the bi-exponential fitting function decrease when the diffusion time increases; and (6) both the fast and the slow diffusing components of NAA show a considerable restriction by what seems to be a non-permeable barrier from which two compartments were identified, one having a size of 6–8 μm and the other of ∼1–2 μm in size. It seems conceivable that the two populations identified in the diffusion experiments represent primarily the NAA in the cell body (soma) and in the neurital space (axons and proximal dendrites). © 1998 John Wiley & Sons, Ltd.