Table 1.

Notation, descriptions, default values, and pointers to definitions or explanations.

Symbol	Descriptive phrase	Default value	More details
dk,D	Dose in the kth fraction, total dose D = Σkdk	dk = 2 Gy, D = 60 Gy	Eqs. 1, 2
K	Number of dose fractions	30	Fig. 2
Tk	Time t of the kth fraction, with T1 = 0.	30 weekdays	Fig. 2
t = 0−	Time just before the first fraction	Slightly less than 0	Fig. 2
t = TK+	Time just after the last fraction	39 days	Fig. 2
t = TK+1	End of recovery period	62 days	Fig. 2
α	Linear quadratic (LQ) parameters	0.3 Gy−1	Eqs. 1, 2
β		α/(10 Gy)	Eqs. 1, 2
S(k)	Average clonogenic cell survival for the kth fraction	Calculated with LQ	Eqs. 1, 2
J(t)	Number of SLCC per niche at time t, a stochastic process with non-negative integer values	Stochastic-logistic with default parameters	Eq. 3
J(0−)	J(t) just before treatment starts	Binomially distributed	Eq. 4
J	Average of J(0−)	10 SLCC per niche	Below Eq. 4
N(t)	Number of nonempty SLCC niches, a stochastic process	Calculated	Above Eq. 5
N	Average of N(t) just before treatment starts	Calculated	Eq. 5 and below
n0	Average initial SLCC number: n0 = NJ	Calculated	Below Eq. 5
C	Carrying capacity (maximum number of SLCC per niche)	20 SLCC
b(j)	Birth rate when a niche contains j SLCC	Calculated from m, σ, and C	Preliminary comments above,
d(j)	“Endogenous” death rate1 when a niche contains j SLCC		Subsection 1E,
m	b1-d1 “Malthusian” rate	ln(2)/(3 days)
σ	d/b ratio	0.5	Eq. 4

¹Applies between fractions, and also after the last fraction before recovery ends.