Deterministic Parsing Model of the Compound Biological Effectiveness (<i>CBE</i>) Factor for Intracellular ¹⁰Boron Distribution in Boron Neutron Capture Therapy

Abstract

Purpose: In defining the biological effects of the 10 B( n , α ) 7 Li neutron capture reaction, we have previously developed a deterministic parsing model to determine the Compound Biological Effectiveness ( CBE ) factor in Borono-Phenyl-Alanine ( BPA )-mediated Boron Neutron Capture Therapy ( BNCT ). In present paper, we demonstrate that the CBE factor is directly and unambiguously derivable by the new formula for any case of intracellular 10 Boron ( 10 B) distribution, which is founded on this model for tissues and tumor. Method: To determine the CBE factor, we derive the following new calculation formula founded on the deterministic parsing model with three constants, CBE 0 , F , n and the eigen value N th /N max . where, N th and N max are the threshold value of boron concentration of N and saturation boron density in tissues and tumor. In order to determine these constants and the eigen values, iterative calculation technique was employed for the CEB factor and N max data set previously reported. Results and Conclusion: From the iterative calculation results, it is clear that the calculated CBE factor values obtained are almost identical to the original CBE factors and there is a good correlation between the original CBE factors and N th /N max , when CBE 0 , F and n are given as 0.5, 8 and 3, respectively. These constants provide a better understanding of different types of intracellular 10 B distribution.