Non-Mono-Exponential Attenuation of Water andN-Acetyl Aspartate Signals Due to Diffusion in Brain Tissue

Abstract

Diffusion measurements were performed on water andN-acetyl aspartate (NAA) molecules in excised brain tissue using a wide range ofb-values (up to 28.3 × 106and 35.8 × 106s cm−2for water and NAA, respectively). The attenuation of the signals of water and NAA due to diffusion was measured at fixed diffusion times (tD). These measurements, in which the echo time (TE) was set to 70 ms, were repeated for several diffusion times ranging from 35 to 305 ms. Signal attenuations were fitted to mono-, bi-, and triexponential functions to obtain the apparent diffusion coefficients (ADCs) of these molecules at each diffusion time. From these experiments the following observations and conclusions were made: (1) Signal attenuation of water and NAA due to diffusion over the entire range ofbvalues examined is not monoexponential and the extracted ADCs depend on the diffusion time; (2) In the case of water the experimental data are best fitted by a triexponential function, while forbvalues up to 1 × 106s cm−2, a biexponential function seems to reproduce the experimental data as well as the triexponential function; (3) If only the low range ofbvalues are fitted (up to 0.5 × 106s cm−2) signal attenuation of water is monoexponential and insensitive totD; (4) Water ADCs decreased with the increase intDbut the relative population of the fast diffusing component increases such that at atDof 305 ms there is nearly a single population; (5) The major fast diffusion component of the water shows only very limited restriction; (6) NAA signal attenuation is biexponential and analysis of the lowb-value range gives only monoexponential decay, but the obtained ADC is sensitive to the diffusion time; (7) The ADCs obtained from fitting the data with a biexponential function decrease as diffusion time increases; (8) The relative population of the slow-diffusing component decreases with increasingtD; (9) Both the fast and the slow diffusing components of NAA show a considerable restriction by what seems to be a nonpermeable barrier from which two compartments, one of 7–8 μm and one of ∼1 μm, were calculated using the Einstein equation. It is suggested that the two compartments represent the NAA in cell bodies and in the intra-axonal space. The effect of the range of thebvalue used in the diffusion experiments on the results is discussed and used to reconcile some of the apparent discrepancies obtained in different experiments concerning water diffusion in brain tissue. The potential of NAA diffusion experiments to probe cellular structure is discussed.