Diffusion of low-energy electrons in tissue-like liquids

The spatial-energetic distribution of low-energy electrons was studied for a source located in a liquid medium simulating biological tissue. A time-independent Boltzmann equation was used to model this distribution microscopically. Ionization was treated as a perturbation to a quasi-elastic collision process between the electron and the medium. A diffusion limit was obtained by using a scale parameter, leading to a sequence of recursive partial differential equations whose solutions, associated with a macroscopic scale, were obtained by numerical approximations. As an application, electron ranges were estimated based on these solutions and then compared with values reported in the open literature based on experimental results and on Monte Carlo calculation. Local dosimetry, i.e., the energy imparted to a volume of a sphere with radius equal to the range of low-energy electrons, of low-energy electrons from internal emitters can benefit by the knowledge of the ranges estimated for biological tissue. Auger electron emitters, for example, have been the object of a number of investigations because of their radiobiological significance.