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## In vivo

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# Predicting the Percutaneous Penetration of Cosmetic Ingredients

## Figures

page 5 of 11

Cmax (ng/ml) = 8.625 e−07 HA + 8.231 e−07 log Koct − 1.22e−06HD − 2.58e−06     Eq. 4

In Eq. 4, n = 10, r = 0.974, F = 37.45, SD = 0.82 and p < 0.001. In this equation and elsewhere, HA is the total number of hydrogen bond acceptor groups on the molecule, log Koct is logarithmically transformed octanol-water partition coefficient, and HD is the total number of hydrogen bond donor groups on the molecule. All predictors had significant (p < 0.05) partial effects in the full model. The inclusion of molecular weight failed to significantly improve the statistics of this equation. Furthermore, no linear correlation could be established between Cmax and MW. The further inclusion of Abraham’s descriptors led to the model in Eq. 5.

Cmax = 6.055 e−07 log Koct + 8.691 e−07 HA + 1.075 e−06 V − 1.91 e−06 E – 2.84 e−06     Eq. 5

In Eq. 5, n = 10, r = 0.989, F = 56.49, SD = 0.75 and p < 0.001. In this equation, V is the McGown characteristic volume in units of (cm3mol-1)/100, and E is the solute excess molar refractivity in units of (cm3mol-1)/10. No collinearity was found between the variables in the model (VIF < 2 for all the variables in both models).

Studentized residuals showed a normal distribution according to Kolmogrov-Smirnov test of normality (p > 0.05); the residual is the difference between the observed and predicted values of Cmax. Its normality has been tested to assure that the standard errors of regression coefficients are not biased and unusual leverage values were not found, which confirms there is no serious outlier influence in the model.