An analytic probability density for particle size in human mastication

In previous studies the distribution of particles sizes of chewed food has been described by an empirical function. However, at the beginning of the chewing process, when many unbroken food particles are still present in the mixture, this function failed to give a good description. In the present study, formula: were derived to characterize the distribution of chewed food particles by size as a function of the number of chewing cycles. The reduction of food particle sizes was considered to be the composite result of a selection and a breakage process. Both processes were described by simple functions. The probability density P-n+1(x) of finding a particle of size x after n + 1 chewing cycles was computed from P-n(x) by selecting a proportion of particles of size y from P-n to be converted to particles of size x < y by a breakage function. Measures of central tendency-average, median and most probable size-were obtained as a function of the number of chewing cycles. The measures of central tendency characterize the degree of food comminution during the chewing process and so can be used to quantify chewing performance. The comminution of food is described in terms of the selection and breakage functions in a convenient, efficient, analytic way, valid for all phases of the chewing process. (C) 1996 Academic Press Limited