(M1130-06-34) A Mathematical Model as a Tool to Optimize the 3D Printing Design for Tablet Dosage Form

Purpose: Three-dimensional (3D) printing technology used in the pharmaceutical industry is growing as the technology is evolving to create a complex and customized dosage form. The main issue facing researchers in this field is to print a tablet with a targeted dose. Their approaches were to extrude 3D printer feedstock with different drug loading or to use a trial-and-error method where they print different dimensions or different percentage infill to get the targeted tablet weight and dose. This study aimed to develop a mathematical model to optimize the tablet dose by correlating the tablet weight with the 3D printing design without the need to know the density of the 3D printing feedstock. This study was conducted to investigate the applicability of the proposed mathematical model using four different FDM 3D printers.

Methods: Polylactic acid (PLA) filaments were used as the 3D printer feedstock. The average density of PLA is known to be 1.24 g/cm³. A pre-designed cylindrical shape without an upper and lower layer was used as a model for the 3D printed tablet shape with a volume to be calculated using equation 1.
v=πr2h (1)

Where r is the radius of the cylinder and h is its height.

Four different 3D printers were used to perform the same experiment in ten replicates, Prusa i3 MK3S+, and Prusa i3 MK3S (Prusa Research, Prague, Czech Republic), Ultimaker 3 (Ultimaker, Framingham, Massachusetts, USA), and LulzBot TAZ 6 (Fargo Additive Manufacturing Equipment 3D, N Fargo, North Dakota, USA). Line (L) and grid (G) printing patterns were tested to study three different percentage infill (100%, 70%, and 40%), two different wall line widths (0.4 and 0.7 mm), and the default width of each 3D printer (Prusa i3-0.4 mm, Ultimaker-0.35 mm, LulzBot-0.5 mm). For each processing parameter, average weight, relative standard deviation, weight percentage error, and volume percentage error were calculated.

Results: The final mathematical formula as shown in equation 2 was used to control the height, diameter, and density infill of the 3D printed tablet to optimize and maintain the dose was proven to be applicable.
h_pf = b²h_cf / {(b²-(1-P)c²)} (2)

Where h_pf is the height for the unknown; partially filled tablet (Less than 100% infill density), b is the radius of completely filled tablet, h_cf is the height for the reference tablet; completely filled tablet, P is the % infill density that is less than a 100% (70% and 40%), and c is the inner core radius (radius - outer wall width).

The weight percentage error (Figure 1) was minimal in the Prusa i3 MK3S+ (0.002-0.028) as well as the LulzBot printer (0.0004 -0.045). On the other hand, the weight percentage error in both Prusa i3 MK3S (0.019-0.179) and Ultimaker 3 (0.025-0.812) was relatively higher due to error in the printed tablet volume, and mainly due to error in the tablet infill density in which the error itself increase when the percent infill density decreases (Figure 2). Prusa i3 MK3S+ printer showed the best accuracy in printing quality and weight targeting.

The grid printing pattern showed a higher weight percentage error compared to the line pattern due to the fact that it has more space between printed lines, and this error was higher in both Ultimaker and Prusa i3 MK3S compared to Prusa i3 MK3S+ and LulzBot.

It was observed that using a different infill density generally will not affect the accuracy of the printed tablet weight. However, the accuracy of the core infill density may be affected

Conclusion: The developed mathematical model is successfully used to optimize the 3D printed tablet design. Applying this model will give the possibility of controlling the percentage infill, height, and diameter of the 3D printed tablets to get the desired dose. Moreover, 3D printer efficiency plays a major effect on 3D printing precision.

References: 1. Okwuosa, T. C. et al. A Lower Temperature FDM 3D Printing for the Manufacture of Patient-Specific Immediate Release Tablets. Pharm Res 33, 2704–2712 (2016).
2. Ventola, C. L. Medical Applications for 3D Printing: Current and Projected Uses. P T 39, 704–711 (2014).
3. Reddy Dumpa, N., Bandari, S. & A. Repka, M. Novel Gastroretentive Floating Pulsatile Drug Delivery System Produced via Hot-Melt Extrusion and Fused Deposition Modeling 3D Printing. Pharmaceutics 12, 52 (2020).


Figure 1: Weight Percentage Error. a, Prusa i3 MK3S+ Printer. b, LulzBot Printer. c, Prusa i3 MK3S Printer. d, Ultimaker Printer.


Figure 2: Ultimaker printer, a: Weight Percentage Error when there is no wall, b: Percentage error in volume when there is no wall, c: Percentage Error in density when there is no wall.