Analytical calculation of boron-10 dosage in cell nucleus for neutron capture therapy

The following measures of physical effects in a spherical cell nucleus, resulting from heavy charged particles caused by thermal neutron reactions in tissue, were evaluated by analytical calculation: (1) the absorbed energy in a cell nucleus, (2) the number of particles hitting and/or passing through a cell nucleus, (3) the integrated particle track length in a cell nucleus, and (4) absorbed energy distribution in tissue. Quantities (1) to (3) can be used as physical indices, similar to neutron fluence, to express the biological effect of neutrons. In the calculation, the interference of the adjacent cell nuclei was taken into account for the difference in the particle production rate between a cell nucleus and cytoplasm. To simplify the calculation of complicated analytical equations, a computer program with five input parameters was prepared. From calculations with various values of these parameters, for example, the absorbed energy in a cell nucleus was generally shown to be sensitive to changes of particle range, range-LET relation, and the radius of the cell nucleus. The calculation was performed for typical cells, and it was found that the distribution of 10B within a cell is one of most important factors for estimating the absorbed dose in the cell nucleus. The selective lethal effect of 10B, which is most advantageous in neutron capture therapy, was estimated quantitatively by defining the boron selective dose ratio (BSDR)