## 3 Results and Discussion
### Modelling of Release Kinetics  
The release of the active compounds from their matrix structure is controlled by several methods (dissolution, diffusion and swelling). These processes are strongly dependent on the matrix structure. The use of mathematical models to evaluate and to predict the drug release processes can be very helpful. [PERSON] and [PERSON] [61] developed a simple semi-empirical model known as the \"power law\" to describe the fraction of drug release, \(\frac{M_{i}}{M_{\infty}}\), especially from a polymetric matrix, which exhibits a power law dependence on the elapsed time (\(t\)), given by Equation (5) [62]:  
\[\frac{M_{i}}{M_{\infty}}=kt^{n} \tag{5}\]  
where \(\frac{M_{i}}{M_{\infty}}\) is the fractional release of drug at time \(t\), \(M_{\infty}\) is the amount of the drug at the equilibrium state (expressed as the amount of the drug at the beginning of the release process), \(M_{i}\) is the amount of drug at time \(t\), \(k\) is a constant which incorporates the structural and geometrical characteristics of the drug dosage form and \(n\) is the release exponent, which corresponds to the drug release mechanism. The constants \(k\) and \(n\) were obtained from the linear logarithm form of Equation (5). This gives Equation (6):  
\[\ln\left(\frac{M_{t}}{M_{0}}\right)=\ln k+n\ln t \tag{6}\]  
where the values of \(k\) and \(n\) were obtained from the intercepts and gradients of the plots of \(\ln\left(\frac{M_{t}}{M_{0}}\right)\) versus \(\ln t\). This equation model can be used to analyse the release of pharmaceutical dosage forms in the following cases: (i) when the release mechanism is not well-known or (ii) when more than one type of release mechanism is involved [63]. The power law model has been widely used for the portion of the release curve where \(\frac{M_{i}}{M_{\infty}}<0.6\)[64]. In the present paper, the release was well described using this model for the entire drug release profile. According to [PERSON] [25], the value of the release exponent, \(n\), could be used to characterise the different type of release mechanisms, as follows:  
(i) \(n=0.5\) corresponds to the Fickian model (Case I) mechanism and the kinetics for the drug release are characterised by the diffusion process;  
(ii) \(n=1\) corresponds to the non-Fickian model (Case II transport) mechanism. This corresponds to a zero-order release kinetic where the mechanism is governed by the swelling process;  
Figure 15: Dissolution profiles of the tested formulation compared with the reference product. (iii) \(0.5<n<1\) corresponds to the non-Fickian or anomalous transport, in which case the drug release mechanism is governed by the diffusion and swelling processes;  
(iv) \(n>1\) corresponds to the Super Case II model, an extreme form of transport. Table 15 shows the values of \(n\) obtained by applying Equation (6) for all studied formulations (F1 to F19) and for the final tablet formulation in vitro release in LSNa and in the CTAB medium. In the present study, from the values of the correlation coefficient (shown in Table 15), it was observed that the power release law satisfactorily described the release in both media (1% LSNa and 0.4% CTAB) (Figure 16). In the case of 1.0% LSNa dissolution medium, it is interesting to observed that for F7, F11 and F15, the values of \(n\) are close to those of Fickian diffusion (\(n\)= 0.5). In the case of F4, the drug release exponent \(n\) = 0.24, which suggests that in parallel with the diffusion mechanism a significant contribution comes from another mechanism. The non-Fickian Case II transport mechanisms are observed for F3, F8, F9, F10, F13, F14, F16 and F18 which have values of \(n\) closed to 1. For this type of release, the mechanism is by polymer matrix relaxation. F2, F19 and the final formulation are governed by an extreme form of transport since the drug release exponents are higher than 1. Sigmoidal anomalous transport was observed for F12, which had an \(n\) value of 0.62 which is an indication that the release of drug is a controlled by more than one process.