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].