Random walk simulation of R2-dispersion in foam microstructures

The spin-spin relaxation rate R₂ (=1/T₂) in hydrogel foams measured by use of a multiple spin echo sequence was found to be dependent on the echo time spacing. (Baete and De Deene. Proc. Intl. Soc. Magn. Reson. Med. 15:37, 2007). This property, referred to as R2-dispersion, originates to a large extent from molecular self-diffusion of water within internal field gradients that result from magnetic susceptibility differences between the gel and air phase. Another contribution to the R2 relaxation rate is surface relaxation. Numerical simulations are performed to investigate the relation between the foam microstructure (the mean air bubble radius and standard deviation of the air bubble radius) at one hand and the R2-dispersion at the other hand. The simulated R2-dispersions of gel foam are in agreement with measured R2-dispersions. By correlating the R2-dispersion parameters and simulated microstructure properties a relationship is obtained that enables the mean air bubble size to be derived from measured R2-dispersion curves. The R2-derived mean air bubble size of a hydrogel foam is in agreement with the bubble size measured with X-ray micro-CT. This illustrates the feasibility of using ¹H R₂-dispersion measurements to determine the size of air bubbles in hydrogel foams and of alveoli in lung tissue.