A study on the effect of biconvex compact shape factors on prediction of dilution potential from tensile strength–compaction force data of coprocessed diluents

Abstract

Abstract Background The purpose of this research was to compare the effect of shape factors of biconvex compacts on prediction of dilution potential from polynomial regression models of area ratio-mass fraction data of novel α-lactose monohydrate-starch orodispersible diluent (α-LSOD) and StarLac®. Ibuprofen-diluent blends were compacted between 4.98 and 29.89 kN. Given the biconvex round compact dimensions (t = axial thickness, w = central cylinder thickness, and d = diameter), tensile strength was computed as $$\sigma_{{{\text{biconvex}}}} = \Phi \frac{F}{{\pi {\text{d}}t}}$$ σ biconvex = Φ F π d t , where F is the breaking force. The shape factor (Φ) was defined as $$\left[ \frac{t}{2d} \right]^{ - 1} ,\left[ {\frac{0.14t}{d} + \frac{0.36w}{d}} \right]^{ - 1} ,\left[ {10/\left[ {\left( {\frac{2.84t}{d}} \right) - \left( {\frac{0.126t}{w}} \right) + \left( {\frac{3.15w}{d}} \right) + 0.01} \right]} \right]$$ t 2 d - 1 , 0.14 t d + 0.36 w d - 1 , 10 / 2.84 t d - 0.126 t w + 3.15 w d + 0.01 for Podczeck (ΦPz), Shang (ΦSh), and Pitt (ΦPt) models, respectively. Area under the curve (AUC) was obtained by second-order polynomial fitting of the tensile strength–compaction force curve followed by integration of the quadratic regression equation between the two compaction force limits. The AUC of each powder system was normalised with the AUC of ibuprofen-free powder to obtain area ratio (AR). The AR was plotted against mass fraction of ibuprofen, and the curvilinear data was fitted by third-order polynomial fitting. Dilution potential was obtained from the regression equation by back extrapolation to zero area ratio. Results Tukey’s multiple comparison test indicated statistically significant differences between the three shape factors (p < 0.001). The shape factors ΦSh and ΦPt were higher than ΦPz by a factor of 2.4 and 1.2, respectively. The quadratic regression model sufficiently explained the observed relationship between tensile strength and compaction force as indicated by the coefficient of determination whose values ranged between 0.9344 and 0.99843 and 0.93725 and 0.99812 for α-LSOD and Starlac®, respectively. Dilution potential was predicted as $$AR = B_{3} x^{3} + B_{2} x^{2} + B_{1} x + c$$ A R = B 3 x 3 + B 2 x 2 + B 1 x + c , where x and its coefficients are ibuprofen mass fraction and regression constants, respectively. The predicted dilution potential of the three tensile strength models were within a close range of $$\approx 110.93 \pm 1.02$$ ≈ 110.93 ± 1.02 and $$\approx 116.02 \pm 0.62$$ ≈ 116.02 ± 0.62 for both α-LSOD and StarLac®. Conclusions This study suggests the adoption of the simplest Podczeck model given a biconvex round punch tooling and highlights the suitability of polynomial regression to predict dilution capacity from nonlinear area ratio-mass fraction data.