Analytical considerations of beam hardening in medical accelerator photon spectra

Beam hardening is a well-known phenomenon for therapeutic accelerator beams passing through matter in narrow beam geometry. This study assesses quanti tatively the magnitude of beam hardening of therapeutic beams in water. A f ormal concept of beam hardening is proposed which is based on the decrease of the mean attenuation coefficient with depth. On the basis of this concep t calculations of beam hardening effects are easily performed by means of a commercial spreadsheet program. Published accelerator spectra and the tabu lated values of attenuation coefficients serve as input for these calculati ons. It is shown that the mean attenuation coefficient starts at depth zero with an almost linear decrease and then slowly levels off to a limit value . A similar behavior is found for the beam hardening coefficient. A physica lly reasonable, semianalytical model is given which fits the data better th an previously published functions. The energy dependence of the initial att enuation coefficient is evaluated and shown. It fits well to published expe rimental data. The initial beam hardening coefficient, however, shows no en ergy dependence. Its mean value (<(eta(0))over bar> approximate to 0.006 cm (-1)) is also in close agreement to the measured data. (C) 1999 American As sociation of Physicists in Medicine. [S0094-2405 (99)02209-9].