Design of pharmaceutical tablet formulation for a low water soluble drug : search for the critical concentration of starch based disintegrant applying percolation theory and F-CAD (Formulation-Computer Aided Design)

The topic of this PhD work is to search the critical concentration of starch based disintegrant applying percolation theory and F-CAD (Formulation-Computer Aided Design) in order to design a pharmaceutical tablet formulation for a low water soluble drug. Critical concentration of maize starch (MS) for a ternary mefenamic acid (MA) tablet formulation with respect to a minimum disintegration time is investigated. Additionally implemented application of F-CAD to compute the disintegration time of MA tablet formulation is presented. This topic is related to push forward the idea of Quality by Design (QbD) of FDA (Food and Drug Administration) / EMEA (European Medicines Agency) / PMDA (Pharmaceuticals and Medical Devices Agency) and the exploration of the design space according to ICH (International Conference of Harmonization) Q8.
The results of this work shows that the application of percolation theory is not limited to binary tablet formulation. The critical concentration of MS described by the renormalized MS concentration, MS/(MS+MA) applying the renormalization technique is always equal 0.198 (dimensionless). Moreover the critical concentration of MS is optimized using the spline approximation with the dataNESIA software. It is leading to a minimum disintegration time at 0.206, dimensionless, renormalized, which is very close to the experimental value of 0.198. According to the percolation theory, a minimum disintegration time corresponds to the formation of a continuous water-conducting cluster through the entire tablet. The critical volume fraction of an ‘infinite cluster’ that water can diffuse through the entire MA tablets are calculated with taking into account for the geometrical considerations between MS and MA particles based on random close packed (RCP) spheres system. The critical volume fraction of MS is calculated by the multiplication of critical concentration of MS and the solid fraction of MA tablets; which is within the range of 0.16 ± 0.01 (v/v). It is concluded that the critical volume fraction for three dimensional lattices is equal to 0.16 ± 0.01 (v/v); which is useful for the calculation of the critical concentration of starch based disintegrant in order to design the pharmaceutical tablet formulation based on scientific approach proposed by ICH Q8 guidance.
In addition, the disintegration behavior in the neighborhood of the percolation threshold is explained mathematically by the basic equation of the percolation theory, yielding a critical exponent q equal to 0.28 ± 0.06 (Quality of fit: r2 = 0.84). This value is close to the critical exponent for three dimensional lattices (q = 0.4). Thus, it is important, within a planned experimental design to optimize the disintegrant to take into account the percolation theory. However it has to be kept in mind that the determination of the percolation threshold and critical exponent does not give an answer about the absolute value of the disintegration time. Dissolution Simulation (DS) module, which is the one of F-CAD based on cellular automata algorithm is used to simulate the disintegration time of a MA tablet. Disintegration time of tablet is assumed as the time elapsed till the water is detected at the geometric center of the virtual tablet. Comparison of experimental disintegration time of MA tablet and computed specific time point for water to reach the geometric center of the tablet by using F-CAD software has been carried out and shown an acceptable correlation (Correlation coefficient: r = 0.81). The detailed evaluation of the data shows that there is still a need for optimization of F-CAD for the calculation of the disintegration time in order to achieve a similar or the same performance like in the prediction of the dissolution profile of a tablet formulation. It is concluded that F-CAD software is the only software so far, which is capable of computing the disintegration time of tablets. The software has a great potential to be improved and to be not only used for the safe prediction of the dissolution profile of a tablet formulation but also for a safe prediction of the disintegration time. Thus, such a software is one of the tools for the substitution of laboratory experiments for the purpose of the design and development of new pharmaceutical solid dosage forms. The replacement of expensive laboratory experiments by in-silico experiments is an important issue to reduce development costs and to comply with the requirements of ICH Q8 exploring the design space with response surface methodology. The results of this thesis show in addition that the application of percolation theory is a must in order to detect percolation thresholds. It is important to know the response surfaces close to the percolation threshold of sensitive tablet properties such as the disintegration time to get information about the robustness of the selected formulation. In this context one has to put the question forward if the application of percolation theory should be an integral part of the guidelines of ICH Q8 exploring the formulation design space.