**4.7.1 Mechanistic approach**

In this method, the studied property (e.g. BBB permeation) affecting parameters should be extracted from theoretical findings (several processes include in the overall result) and convert to mathematical representations. The provided descriptors depend on their effects (positive or negative, direct or inverse) on desired property should be correlated to the prediction end point and the resulted equation could be used for prediction purposes (Lavenskij et al., 2010).

#### **4.7.2 Statistical approach**

It is so important to exclude insignificant descriptors to prevent over fitting and biased results using a descriptor selection method. The number of descriptors depends on the modelling method. For simple multivariate regression methods, the number of descriptors depends on the number of data points, while for partial least square and principal component analyses methods it is not limited. In addition to the number of the descriptors

Blood Brain Barrier Permeation 21

have effect on BBB permeation. The complexity of BBB permeation encouraged scientists to check non linear methods applicability in this field and some exponential linear equations and neural networks have been successfully developed. Although neural networks provided more accurate predictions in comparison with linear ones, their interpretation and reproducibility are in question and their usefulness for developing universal models which can be applicable for chemists have not been approved yet. In fact the best model for a chemist is a model which is able to answer him/her what is the possible modification for desired property improvement and the un-interpretable models are not able to answer this question. Because of this, using less accurate but well defined models are preferred to

The studies of unbound fraction of the drug in brain (*Kp,uu*) showed that the previously accepted trend of permeation (higher permeation for more lipophilic compounds) which was raised from log*BB* and log*PS* studies are not the same for unbound fraction, and lipophilicity have inverse relation with it. These findings showed that the absolute values for the effective descriptors are not suitable and a balanced range of descriptors should be

In order to check the sensitivity, specificity, prediction capability, reproducibility, error margins and chance correlations for the developed models, some validation statistics should be provided and using these parameters researchers will be able to make decision on selecting or rejecting a model in comparison with others. The details of these parameters and their usefulness for evaluating the model have been reviewed. For classification methods the lower failure in localization of compounds (both positive and negative) is better and for predictive models the higher correlation coefficients (both for training and test sets and cross validation sets), lower prediction errors (less than about 1 log unit deviation and relative mean squared errors less than 0.3)and lower correlation coefficients (e.g. <0.2) for Y randomized data sets are acceptable. These parameters are not absolute and it would be possible to accept a low quality

Using the developed models, some software has been developed in order to calculate the BBB permeation or P-gp binding affinity which can be used for estimation of compound permeation. These predictions are included in the most of the ADME prediction software

The importance of BBB for reaching CNS drugs to their targets and also undesired penetration of non CNS drugs to avoid their CNS side effects are briefly discussed. Short review of measurement methods of drug's penetration to CNS is presented along with a

The molecular and cellular properties of BBB have been reviewed and the role of its compartments in the regulating of drugs and xenobiotics penetration to the brain has been discussed. Working as a regulatory interface BBB is able to work as a physical and physiological barrier which prevents peripheral drugs to penetrate the brain and reduce

summary of computational aspects used for modelling purposes.

complicate but accurate ones.

**4.9 Validation** 

defined for them (Lavenskij et al., 2010).

model in the absence of the better one.

which could be found on internet.

**5. Conclusion** 

**4.10 Prediction using commercial software** 

and their significances, the inter correlation between them should be checked and just one of the highly correlated descriptors should be kept in multiple linear regression methods, while this is not a problem for partial least square or principal component analyses. There are different methods for descriptor selection and more information can be found in the literature. It is better to keep the penetration mechanisms and approved relationships in mind in this step and avoids complete statistical methods.
