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The study of solution dynamics is a very fundamental area of research with wide ranging importance from physical chemistry through to the life sciences. A common theme is that the interactions which control the dynamics and organization of solutions are generally very weak. Translational diffusion provides a non-invasive, direct and natural probe of the dynamics and pulsed gradient spin-echo (PGSE) NMR is a convenient means of measuring diffusion. This paper gives a brief introduction to translational diffusion as a probe of solution dynamics and of the PGSE NMR method before presenting some representative examples illustrating the power of diffusion measurements for elucidating the molecular behaviour. The use of PGSE NMR to study solution dynamics and organization is a very active area of research and a very large literature already exists, consequently, the coverage of possible applications and the literature cited here is not comprehensive.

In 1828, a botanist named Robert Brown found that small pollen particles suspended in water migrated in an erratic fashion. Later it was realized that the dance Brown observed was essentially a two-dimensional random walk driven by thermal fluctuations, thus this Brownian motion was more intense at higher temperatures. The pioneering ideas and observations by Brown have inspired people for a long time to think about the fascinating aspects of random walks, and hence of diffusion. In this brief contribution, we consider this topic at complex biological interfaces known as cellular membranes and discuss how the dance of lipids and small molecules can be quantified through experiments and theoretical approaches. Some illustrative examples of diffusion in membrane systems are discussed.

The use of laser-based optical techniques for medical imaging is an attractive alternative to other methods that utilize ionizing radiation. Beside being non-carcinogenic, it is non-invasive, the equipment is transportable, and the methodology can be used to examine properties of soft tissue. However, unlike x-ray photons, optical photons generated in the near-infrared suffer significant amounts of scattering by heterogeneous bodies (e.g., organelles) found in biological tissue. Thus, theory is required to interpret experimental data which appear in the form o spatially or temporally varying light patterns on the skin surface. There is a wide range of parameters over which either diffusion theory or the theory of lattice random walks can be called on to translate optical data into medically significant information embodied in optical parameters of the tissue. We discuss several problems in diffusion theory arising in the analysis of optical measurements, for tissues modeled by a semi-infinite or slab geometry, having either isotropic or anisotropic optical parameters. The measured quantities are related to the intensity of light re-emitted on the tissue surface. A brief discussion is given related to the telegrapher’s equation, which has been suggested as a simple way of incorporating the effects of forward scattering. Mention is made of calculations related to layered media which frequently occur in tissues such as skull and esophagus. Finally, we briefly discuss discrete random walk models for photon migration. These have recently been used to provide parameters conveying information related to the region interrogated by photons constrained to reappear on skin surface.

This chapter presents a brief introduction to the application of diffusion-weighted magnetic resonance imaging (MRI) to in vivo studies. Diffusion-weighted MRI has found application both in the clinic, and in basic neuroscience. In the former situation it is primarily used for the detection of brain lesions, in particular infarcted regions. The ability to follow fibre tracts in white matter via diffusion tensor imaging has also made this methodology of interest to the neurosurgeon wishing to avoid severance of essential fibre tracts, but also of interest to the cognitive neuroscientist exploring anatomical connectivity in the brain. The chapter starts with a brief recap of the theory of diffusionweighted MRI and moves on to examine the two major experimental confounds, eddy currents and bulk motion. Current correction schemes for these problems are touched upon. Diffusion anisotropy is introduced as a potential source of artefacts for lesion detection in white matter, and the diffusion tensor model presented. The chapter concludes with a short introduction to fibre tracking.

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100 keV 10 B+ ions were implanted into poly-(di-n-hexyl silane) in different directions at a fluence of 1x1014 cm-2, and their depth distribution was determined by means of the neutron depth profiling technique. In no case the projectile ions are found to come to rest according to their predicted range profiles. Instead, they are always found to undergo considerable long-range migration. During the irradiation process this motion appears to be radiation-enhanced, and during the subsequent annealing steps one appears to deal with regular thermal diffusion. The implant redistribution is always found to be governed strongly by the self-created damage, insofar as both electronic and nuclear defects in the polymer act as trapping centers. Their population ratio is modified by thermal annealing. The as-implanted redistribution shows a pronounced directional dependence, which essentially is a consequence of the spatial distributions of the electronic and nuclear damage. The changes of the nuclear defect distribution during thermal annealing are studied by a specially developed tomographic method. It is found that boron is preferentially trapped along the irradiation direction, exhibiting quite pronounced prolate (i.e. cigar-like) distributions. This shape is hardly affected by thermal annealing.

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