## Purpose

To compare the effects of shape factors on biconvex compacts tensile strength measurement and their impact thereof on prediction of dilution potential from polynomial regression models of tensile strength-compaction force data of coprocessed diluents with similar deformation physics.

## Methods

Compact of ibuprofen-diluent blends were produced between 4.98 to 29.89 kN in eccentric hydraulic press. Given the biconvex round compact dimensions (*t* = axial thickness, *w* = central cylinder thickness, and *d* = diameter), tensile strength was computed as \({\sigma }_{biconvex}=\mathcal{ }\mathcal{Q}\frac{F}{\pi {d}^{2}}\) where *F*, is the breaking force. The shape factors (\(\mathcal{Q}\)) were defined as \({\left[\frac{t}{2d}\right]}^{-1}\), \({\left[\frac{0.14t}{d}+\frac{0.36w}{d}\right]}^{-1}\), \(\left[10/\left[\left(\frac{2.84t}{d}\right) - \left(\frac{0.126t}{w}\right)+\left(\frac{3.15w}{d}\right)+0.01\right]\right]\) for Podczeck, Shang, and Pitt based models, respectively. Area under the curve (AUC) was obtained by second order polynomial fitting of the tensile strength-compaction force data followed by integration of the quadratic regression equation between the limits 4.98 to 29.89 kN. The AUC of each powder system was normalised with the AUC of ibuprofen-free powder to obtain the area ratio. The area ratio was plotted against mass fraction of ibuprofen, and the curvilinear data was fitted by third degree polynomial fitting, whose regression equation was back extrapolated to zero area ratio to yield dilution potential.

## Results

The polynomial regression model was of the form: \(Area ratio={B}_{3}{x}^{3}+{B}_{2}{x}^{2}+{B}_{1}x\)+c, where *x* is ibuprofen mass fraction, and all the *x* coefficients and c are regression constants. The average predicted ibuprofen mass fractions (of the three independent tensile strength models) at zero area ratio were \(\approx 110.93\pm 1.02\) and \(\approx 116.02\pm 0.62\) for Tablettose100®-Starch-SSG composites and StarLac®, respectively.

## Conclusion

From simplistic view point, dilution potential can reliability be computed from the simple Podzeck model relative to comparatively complex Shang and Pitt models.