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Table 1 Used models for cells growth kinetics prediction

From: Optimization of lipids’ ultrasonic extraction and production from Chlorella sp. using response-surface methodology

Model

Expression

Parameters

Equation n°

Logistic

\( X(t)=\frac{X_0\cdot {e}^{\left({\mu}_{\mathrm{max}}\cdot t\right)}}{1-\frac{X_0}{X_{\mathrm{max}}}\cdot \left(1-{e}^{\left({\mu}_{\mathrm{max}}\cdot t\right)}\right)} \)

μmax; Xmax

(1)

Logistic- with-lag

\( X(t)={X}_0+\frac{X_{\mathrm{max}}-{X}_0}{1+{e}^{\left\{\left(\frac{4\cdot {\mu}_{\mathrm{max}}}{X_{\mathrm{max}}-{X}_0}\right)\cdot \left(\lambda -t\right)+2\right\}}} \)

μmax; Xmax; λ

(2)

Modified- Gompertz

\( X(t)={X}_0+\left({X}_{\mathrm{max}}-{X}_0\right)\cdot {e}^{\left\{-{e}^{\left(\frac{\mu_{\mathrm{max}}\cdot {e}^1}{X_{\mathrm{max}}-{X}_0}\right)\cdot \left(\lambda -t\right)+1}\right\}} \)

μmax; Xmax; λ

(3)

  1. X and Xmax refers to the actual (at time t in day) and the maximum cell number, respectively; X0 is the initial cell number at initial time 0 (X0 = 187 cells ∙ mL− 1 in this study); λ: an additional term (day)