Exploring the concentration gradient dependency of the ferric ion diffusion effect in MRI-Fricke-infused gel dosimetry

There has been some discussion on ferric ion diffusion in MRI-Fricke-infused gel dosimetry over the past decade. Despite the attention it received, the time scale of the emergence of the dose distribution profile degradation due to ferric ion diffusion remains unresolved. From elementary physics it is known that, on average, ferric ions diffuse a distance of (2Dt)0.5, where D is the ferric ion diffusion coefficient and t is the elapsed diffusion time. The degradation of the ferric ion concentration distribution can be assessed once D and t are determined. This has drawn the attention of previous studies on the measurement of ferric ion diffusion coefficient and its consequence for the temporal evolution of the distribution profile degradation. For example, based on teh (2Dt)0.5 scenario, and on their measured ferric ion diffusion coefficient (1.83x10-2 cm2 h-1), Schulz et al (1990) calculated the effect of ferric ion diffusion on edge sharpness at instances of 0.5, 2, 10 and 24 h for a step-function type concentration distribution. A substantial smear on the sharp edge was observed starting from the earliest 0.5 h elapsed diffusion time. However, results of another study (Olsson et al 1992) demonstrated that the concentration distribution induced profile degradation did not emerge until another 2 h later. This result was obtained with a measured ferric ion diffusion coefficient of 1.91x10-2 cm2 h-1, which was equivalent to Schulz et al. We noted that Olsson et al conducted their experiment using a 14 MeV electron beam as the irradiation source, which produced a much smoother concentration distribution than a step-function one. The disagreement between Olsson et al's result and Schulz et al's result in the first two-hour observation was due to the lage difference in steepness of the concentration distribution. It can be easily seen for the steep, step-function type ferric ion distribution, such as the one examined by Schulz et al, a slight ferric ion diffusion would result in a substantial smear on the sharp edge. On the other hand, if the underlying distribution profile was flat, no profile degradation could be observed regardless of the magntitude of the ferric ion distribution and elapsed diffusion time. It would be interesting to understand the observed ferric diffusion effect as a function of diffusion coefficient, elapsed diffusion time and the concentration distribution gradient for the commonly encountered situations, i.e. those having concentration distribution gradients lying in between the two extreme cases. It is hoped that this letter will resolve some of the confusion in confronting the variation of diffusion time scale reported by studies conducted on different premises. In addition, because all sterotactic radiosurgery procedures generate steep concentration distributions, and because a prolonged MR imaging time for the R1-based Fricke-infused gel dosimetry is inevitable, the application of this dosimetric method should be put under great scrutiny for its dose-measurement accuracy. In such a case, a fast approach (Chu et al 1998) that reduces the MR imaging time from hours to minutes could be employed to reduce the ferric ion diffusion effect. Letter-to-the-editor