Table 1.

Comparison of different growth model equations for data analysis of capsule volume as a function of time based on the AIC method^a

Cell	AIC value by equation
	Sigmoidalb	Gompertzc	Logisticd	Weibulle
1	4,686.4	6,339.5	3,246.9	3,519.1
2	4,526.3	3,777.8	2,370.2	2,909.5
3	10,780.9	5,052.5	3,235.6	6,507.5
4	3,065.8	4,005.6	2,744.9	2,138.5
5	10,110.5	6,818.3	3,864.3	6,527.1
6	13,366.4	7,068.9	3,764.9	9,256.2
7	14,473.0	3,745.8	3,130.7	16,689.4
8	18,695.9	72,989.9	14,740.3	2,043.3
9	3,385.3	6,818.3	3,864.3	6,527.1
10	7,006.7	7,124.1	4,653.7	4,845.9

^aFor details, see reference 32. Based on the AIC model, the equation with the smallest AIC value (showed in italic type) is most likely to be correct.

^bThe sigmoidal growth equation is $Y=Y_{\min \hspace{0.17em}}+\frac{Y_{\max \hspace{0.17em}}-Y_{\min \hspace{0.17em}}}{{1+10}^{(\log \hspace{0.17em}k\hspace{0.17em}-x)}g}$, where y_max and y_min are the maximum and initial volumes, respectively, k is the value of x at halfway between y_min and y_max, and g is the slope.

^cThe Gombertz growth equation is $Y=Y_{\max \hspace{0.17em}}{e}^{{(\ln \hspace{0.17em}{Y}_{\min \hspace{0.17em}}/Y_{\max \hspace{0.17em}})}_{e^{-kx}}}$.

^dThe logistic growth equation is $Y=\frac{Y_{\max \hspace{0.17em}}\times Y_{\min \hspace{0.17em}}}{(Y_{\max \hspace{0.17em}}-Y_{\min \hspace{0.17em}})e^{-kt}\hspace{0.17em}+Y_{\min \hspace{0.17em}}}$.

^eThe Weibull growth equation is $Y=Y_{\max \hspace{0.17em}}-(Y_{\max \hspace{0.17em}}-Y_{\min \hspace{0.17em}})e^{{-1\left(kt\right)}^g}$.