# Predicting Drug Release from 3D Printed Oral Medicines Based on the Surface Area to Volume Ratio of Tablet Geometry

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

_{s}≥ 200 mg/mL) [49,50]. Mannitol (Parteck M

^{®}, Merck, Germany) was used as a plasticizer at 10% (w/w) content. Polyvinyl alcohol (84%, PVA, Parteck MXP

^{®}, Merck, Germany) was selected as a polymer. Formulation 2, referred to as the EVA-LD formulation, consisted of 10% (w/w) levodopa (Zhejiang Wild Wind Pharmaceutical, Dongyang, China), and was also a BCS class I API (c

_{s}≥ 12 mg/mL) [51]. As water soluble component, a vinylpyrrolidone-vinyl acetate copolymer (VP-VA) was used (39.5%, Kollidon VA 64

^{®}, BASF, Ludwigshafen, Germany) and 10% mannitol was added as a plasticizer. The matrix consisted of ethylene vinyl acetate (EVA) with a content of 18% vinyl acetate (39.5%, Escorene

^{®}FL 01418, TER Chemicals, Hamburg, Germany). To improve flowability, 1% fumed silica (Aerosil

^{®}200 VV Pharma, Evonik, Germany) was added to both formulations. Formulation 3, referred to as the PVA-PZQ formulation, consisted of 5% (w/w) praziquantel (PZQ, donated from Bayer AG, Leverkusen, Germany) as an API of BCS class II (c

_{s}= 0.4 mg/mL) [52,53,54], declared as poorly water-soluble. As a polymer basis, PVA was chosen with 95% content. All filament formulations were systematically developed to minimize diameter fluctuations of the filaments and to ensure highest printability with the available equipment. The criteria for the drug selection were heat stability and different classifications in the BCS. The melting point of PDM is also the decomposition point at 296–305 °C [20,55,56,57]. LD melts and decomposes at 260–330 °C [58]. PZQ has its melting point already at 140–143 °C but decomposes only at temperatures >400 °C [59,60]. The investigated dose ranges do not correspond to therapeutic dosages and result from the drug loading of the filament and the volume of the objects. The polymer matrix of the first formulation should be water soluble and generate prolonged drug release. PVA fulfils both criteria as the polymer forms a water-soluble hydrocolloid matrix [61]. To test the transferability of the predictive model to other formulations, an inert, non-swelling matrix, EVA, was chosen [62]. To improve the printability and hydrophilicity of the filament, VP-VA was added. PVA was again chosen for transferring the model to the BCS class II drug, for the extended drug release as well as better printability. Thus, variations resulting from the process could be eliminated and the differences clearly attributed to the API.

#### 2.2. Methods

#### 2.2.1. Hot Melt Extrusion

#### 2.2.2. 3D Printing of Tablets

^{®}(Autodesk, San Rafael, CA, USA) and sliced in Simplify3D

^{®}(Simplify3D, Cincinnati, OH, USA) to obtain the desired G-code. The print temperature for the PVA-PDM filaments was set to 185 °C, the bed temperature to 60 °C and the printing speed was 20 mm/s. The printing temperature had to be increased for the EVA-LD formulation, as the filament was very flexible and could not be transported reliably through the nozzle by the conveying wheels in the print head at lower temperatures, as the filament would otherwise wrap around the wheels. To ensure a constant filament-flow through the nozzle, the temperature of the nozzle was set to 220 °C and the printing speed was reduced to 10 mm/s. For the PVA-PZQ formulation, a nozzle temperature of 185 °C could again be used, but the bed temperature had to be increased to 90 °C because the printed objects adhered poorly to the print bed and detached from the bed more often. Therefore, a printing speed of 10 mm/s was also selected here. To obtain high print accuracy, the layer height was set to 0.1 mm and the extrusion width to 0.4 mm using a nozzle with a diameter of 0.4 mm. The infill percentage of the concentric infill was set to 100%.

#### 2.2.3. Dissolution Test

_{s}≥ 200 mg/mL [50]; maximum concentration 0.08 mg/mL) and stirred at 50 rpm at a temperature of 37 ± 0.5 °C. The released API was measured using an UV-Vis spectral photometer (UV-1800 Shimadzu, Japan) at a wavelength of 263 nm. Dissolution testing of the levodopa containing geometries was performed in 1000 mL of degassed 0.1 N hydrochloric acid at pH 1.2 under sink conditions (c

_{s}≥ 12 mg/mL [51]; maximum concentration 0.05 mg/mL) and stirred at 50 rpm at a temperature of 37 ± 0.5 °C. The API release was recorded with the same UV-Vis spectral photometer at a wavelength of 280 nm. The dissolution tests with PZQ were performed in 750 mL of degassed 0.1 N hydrochloric acid at pH 1.2 for the first 120 min and then transferred to 1000 mL phosphate buffer pH 6.8 with 250 mL of degassed 0.2 N tri-sodium phosphate dodecahydrate solution. The temperature was adjusted to 37 ± 0.5 °C. The drug release was measured at a wavelength of 210 nm. The tests were performed under sink conditions (c

_{s}= 0.4 mg/mL [54]; maximum concentration: 0.03 mg/mL). Samples were taken every 5 min for the first 30 min, then every 10 min for the next 90 min, followed by sampling in 20 min intervals. After a release time of 240 min, samples were taken every 30 min.

#### 2.2.4. Mathematical Description

#### Release Modeling

_{s}. As soon as these conditions are no longer given, the equation is invalid, since the API is then no longer dispersed but dissolved. The application of this equation is limited to 60% of the released API [70].

#### Prediction

#### Comparison of the Dissolution Profiles

#### 2.2.5. Characterization of the Printed Tablets

## 3. Results

#### 3.1. Characterization of the Printed Tablets

#### 3.2. Drug Release from Dosage Forms with Defined SA/V Ratios

^{−1}, based on changes of the dimensions (Table 3). By keeping the SA/V ratio constant, the dose was varied according to the volume of the objects.

^{−1}released 80% of the API in 100 min, the geometries with a SA/V ratio of 1.5 mm

^{−1}released 80% in 60 min and with a SA/V ratio of 2 mm

^{−1}, 80% API was released in 45 min. The dosages varied by a factor of 7.5 for the SA/V ratio of 2 mm

^{−1}, by a factor of 4.5 for the SA/V ratio of 1.5 mm

^{−1}and by a factor of 3.4 for the ratio of 1 mm

^{− 1}.

^{−1}was 61 ± 3 min, with a SA/V ratio of 1.5 mm

^{−1}35 ± 2 min and with a SA/V ratio of 2 mm

^{−1}25 ± 1 min across all designs. The similarity of the curves was evaluated with the similarity factor (Equation (10)). The cylinder was used as a reference for each SA/V group. The f

_{2}-values are above 50 in each group and show that the curves are similar to each other.

#### 3.3. Correlation between MDT and SA/V Ratio

^{−1}was chosen as minimum and 6.0 mm

^{−1}as maximum. The obtained data is shown in Figure 3a.

^{2}: 0.9977). The linear equation of the regression was used to predict the MDT of 3D printed tablets with different SA/V ratios. The predictions were made exemplarily for four different SA/V ratios not used for the regression model and compared with the experimentally determined MDT of the corresponding printed geometries (Table 4).

^{−1}were printed, and the MDT was calculated from the obtained dissolution data (Figure 4).

^{2}: 0.9819).

^{2}: 0.9953).

^{−1}, the drug was released from the PVA-PDM matrix with a MDT of 35.58 ± 1.87 min, from the PVA-PZQ matrix with a MDT of 45.49 ± 3.27 min and from the EVA-LD matrix with a MDT of 111.07 ± 18.37 min. Despite the different behaviour of the matrix systems, the solubility properties of the APIs and the resulting differences in MDT, a correlation of the SA/V ratio and the MDT can be established for all three tested formulations. With the help of this correlation, the release time of an existing geometry with a given SA/V ratio can be predicted without having to waste material and perform dissolution tests. Similarly, the required SA/V ratio can be predicted for a desired MDT and the corresponding geometry can be designed and printed on this basis.

#### 3.4. Modeling and Prediction of Release Profiles

^{2}values of the fits were compared to evaluate the fit quality (Table 7). According to the Korsmeyer–Peppas model (KMP), the drug release from the PVA formulations follows an anomalous transport (diffusion constant n = 0.7 (PDM), n = 0.8 (PZQ), Table 2). Since anomalous transport can be described with different models (Equations (3) and (5)–(8)), only these equations were used to fit the data of the PVA formulations. For the EVA-LD formulation, n = 0.55 was obtained. This indicates a release according to square-root-of-t kinetic. This profile is often described with the Higuchi equation (Equation (4)). Additionally, the generally applicable Weibull equation (Equation (8)) as well as the Peppas Sahlin equation (Equation (3)) were used to fit the release profiles of the EVA formulation.

_{1}and k

_{2}were determined (Table 8). For the PVA-PDM formulation, an average diffusion exponent of n = 0.79 was obtained, and for the EVA-LD formulation, an average diffusion exponent of n = 0.66 was obtained. The constants k

_{1}and k

_{2}were plotted in a graph as a function of the SA/V ratio. A linear correlation between k and the SA/V ratio was obtained by a log-transformation of both axes (Figure 7).

_{1}and k

_{2}can be determined for arbitrarily selected SA/V ratios. If these calculated values are inserted into the Peppas Sahlin equation with the diffusion exponent n = 0.79, a concentration curve of the released API can be calculated for the specific time points. These calculations were performed exemplarily for the four different SA/V ratios not used for the model creation. The graphs comparing the experimental data points with the prediction curve are shown in Figure 8.

^{−1}with a RMSEP of 0.56% and 0.9 mm

^{−1}with a RMSEP of 0.74%. For the SA/V ratio of 2.3 mm

^{−1}, the prediction above 70% API release underestimated the experimental data points, which results in a RMSEP of 2.85%. If only the release data points up to 70% released API are included, the RMSEP was 1.70%. Predicting the SA/V ratio of 4.7 mm

^{−1}resulted in a RMSEP of 3.41%. If the prediction is only made up to 70% API release, the RMSEP is 1.18%, but only three time points are compared due to the quick drug release. Apparently, the predictions represent the experimental values better for smaller SA/V ratios because multiple time points can be considered and therefore the curves are not as sensitive to changes in k values. Nevertheless, the prediction approximated the experimental release curves well, especially in the early phase of drug release.

_{1}and k

_{2}were plotted in a graph as a function of the SA/V ratio. A linear correlation between k and the SA/V ratio was obtained by a log-transformation of both values (Figure 9). Using this relation and the resulting linear regression, k

_{1}and k

_{2}can be determined for arbitrarily selected SA/V ratios. These calculations were exemplarily for the three different SA/V ratios, the MDT was already predicted in Section 3.2. The resulting graphs comparing the experimental data points with the prediction curve are shown in Figure 10.

^{−1}, the RMSEP value was 1.60% and for the SA/V ratio of 1.73 mm

^{−1}, the RMSEP value was 1.95%. The RMSEP for the SA/V ratio 4.67 mm

^{−1}results in a value of 3.42%. Again, the experimental data of the smaller SA//V ratios can be predicted better by the model, nevertheless, the prediction of higher SA/V ratios is still close to experimental data. The data implies that the developed prediction model also works for this formulation with an inert matrix.

^{−1}is 2.5%, for 1.83 mm

^{−1}3.6%, for 2.3 mm

^{−1}2.1% and for 4.67 mm

^{−1}1.0%. The predicted value of the curve deviates from the experiment by 2.3% on average, which can be considered acceptable.

## 4. Discussion

^{2}: 0.999). Again, the linear relationship between the logarithmised constants and the SA/V ratio was used to calculate dissolution predictions. With an average deviation of 2% from the predicted to the experimentally determined release profile, it can be stated that dissolution curves of dosage forms with a poorly water-soluble API can also be modeled.

## 5. Conclusions

## Supplementary Materials

^{−1}(n ≥ 3, x ± s), Table S2: Physical characterization of the printed tablets for the correlation generation with the PDM-PVA formulation (n ≥ 3, x ± s), Table S3: Physical characterization of the printed tablets for the correlation generation with the LD-EVA formulation (n ≥ 3, x ± s), Table S4: Physical characterization of the printed tablets for the correlation generation with the PZQ-PVA formulation (n ≥ 3, x ± s), Table S5: Physical characterization of the printed tablets for the prediction validation with the PDM-PVA formulation (n ≥ 3, x ± s), Table S6: Physical characterization of the printed tablets for the prediction validation with the LD-EVA formulation (n ≥ 3, x ± s), Table S7: Physical characterization of the printed tablets for the prediction validation with the PZQ-PVA formulation (n ≥ 3, x ± s).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Designed geometries (from left to right): cube 1 (Q1), cube 2 (Q2), cube 3 (Q3), hollow cylinder (HC), cylinder (C) and pyramid (P). Upper image: CAD-Design, lower image: printed geometries of SA/V ratio 1.5 mm

^{−1}.

**Figure 2.**PDM-release curves of the geometries printed with SA/V ratios of 1, 1.5, 2 mm

^{−1}(n = 6; x ± s).

**Figure 3.**Correlation of MDT and SA/V ratio for the PVA-PDM formulation (

**a**) and linearized version (

**b**) (n ≥ 3; x ± s).

**Figure 4.**Correlation of MDT and SA/V ratio for the EVA-LD formulation (

**a**) and linearized version (

**b**) (n ≥ 3; x ± s).

**Figure 5.**Correlation of MDT and SA/V ratio for the PVA-PZQ formulation (

**a**) and linearized version (

**b**) (n ≥ 3; x ± s).

**Figure 6.**Experimental release data points (black cuboids) and predicted release curve (red line) calculated with Peppas Sahlin (PVA-PDM formulation (

**a**); EVA-LD formulation (

**b**)) and Weibull function (PVA-PZQ formulation (

**c**)).

**Figure 7.**Correlation of the constants k

_{1}and k

_{2}of the Peppas Sahlin equation with the SA/V ratio for the PVA-PDM formulation.

**Figure 8.**Predicted PDM release profiles vs. experimental results for SA/V ratio 0.9 mm

^{−1}, 1.6 mm

^{−1}, 2.3 mm

^{−1}and 4.67 mm

^{− 1}of the PVA-PDM formulation.

**Figure 9.**Correlation of the constants k

_{1}and k

_{2}of the Peppas Sahlin equation with the SA/V ratio for the EVA-LD formulation.

**Figure 10.**Predicted levodopa release vs. experimental levodopa release for SA/V ratios of 1.73 mm

^{−1}, 1.89 mm

^{−1}and 4.67 mm

^{−1}of the EVA-LD formulation.

**Figure 11.**Correlation of the constants a and b of the Weibull function with the SA/V ratio for the PVA-PZQ formulation.

**Figure 12.**Predicted PZQ release vs. experimental PZQ release for SA/V ratios of 1.3 mm

^{−1}, 1.83 mm

^{−1}, 2.3 mm

^{−1}and 4.67 mm

^{−1}of the PVA-PZQ formulation.

**Table 1.**Extrusion settings (temperature profile and screw configuration) for the used formulations.

Temperature Profile in Zone 2–10/°C | |||||||||
---|---|---|---|---|---|---|---|---|---|

Zone/- | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

PVA-PDM formulation/°C | 30 | 100 | 180 | 180 | 180 | 180 | 180 | 195 | 195 |

PVA-PZQ formulation/°C | 21 | 31 | 78 | 180 | 180 | 180 | 180 | 180 | 190 |

EVA-LD formulation/°C | 25 | 28 | 78 | 130 | 140 | 155 | 155 | 120 | 100 |

Screw Configuration (Die–Gear) | |||||||||

PVA/EVA formulation | die-10 CE 1 L/D-KZ: 5 × 60°-3 × 30°-5 CE 1 L/D-KZ: 4 × 90°-5 × 60°-3 × 30°-10 CE 1 L/D-2 CE 3/2 L/D-gear | ||||||||

CE = conveying element, KZ = kneading zone |

n | |||
---|---|---|---|

Thin Film | Cylinder | Sphere | Drug Release Mechanism |

0.50 | 0.45 | 0.43 | Fickian diffusion |

0.50 < n < 1.00 | 0.45 < n < 0.89 | 0.43 < n < 0.85 | Anomalous transport |

1.00 | 0.89 | 0.85 | Case-II transport |

**Table 3.**Characteristics of the printed geometries including the calculated MDT of the PVA-PDM formulation.

SA/V 1 mm^{−1} | ||||||
---|---|---|---|---|---|---|

Form | SA/mm^{2} | V/mm^{3} | SA/V/mm^{−1} | API/mg | MDT/min | f_{2} Value |

Q1 | 606.00 | 585.00 | 1.00 | 35.97 | 56.95 | 77.51 |

Q2 | 256.00 | 256.00 | 1.00 | 15.60 | 62.91 | 87.92 |

Q3 | 250.00 | 250.00 | 1.00 | 15.66 | 65.65 | 73.88 |

HC | 667.59 | 667.59 | 1.00 | 41.34 | 56.84 | 71.87 |

C | 201.06 | 201.06 | 1.00 | 12.29 | 60.67 | Reference |

P | 273.05 | 265.97 | 1.03 | 16.25 | 64.30 | 82.89 |

SA/V 1.5 mm^{−1} | ||||||

Form | SA/mm^{2} | V/mm^{3} | SA/V/mm^{−1} | API/mg | MDT/min | f_{2} Value |

Q1 | 546.00 | 360.00 | 1.52 | 21.74 | 32.81 | 78.20 |

Q2 | 192.00 | 128.00 | 1.50 | 8.00 | 35.67 | 92.54 |

Q3 | 166.00 | 110.00 | 1.51 | 6.92 | 38.07 | 73.19 |

HC | 301.59 | 201.06 | 1.50 | 13.54 | 33.83 | 90.82 |

C | 150.80 | 100.53 | 1.50 | 6.19 | 34.80 | Reference |

P | 121.92 | 80.10 | 1.52 | 4.85 | 36.92 | 75.40 |

SA/V 2 mm^{−1} | ||||||

Form | SA/mm^{2} | V/mm^{3} | SA/V/mm^{−1} | API/mg | MDT/min | f_{2} Value |

Q1 | 516.00 | 247.50 | 2.08 | 15.04 | 22.98 | 66.45 |

Q2 | 169.60 | 83.20 | 2.04 | 5.21 | 25.70 | 96.55 |

Q3 | 142.00 | 70.00 | 2.03 | 4.43 | 24.90 | 91.95 |

HC | 201.06 | 100.50 | 2.00 | 6.87 | 25.02 | 92.37 |

C | 133.20 | 65.35 | 2.04 | 3.92 | 25.14 | Reference |

P | 66.02 | 32.24 | 2.05 | 1.99 | 24.86 | 75.79 |

**Table 4.**Comparison of MDT: predicted vs. experimental data of the PVA-PDM formulation (n ≥ 3; x ± s).

SA/V Ratio/mm^{−1} | MDT Prediction/min | MDT Experiment/min | RMSEP/min |
---|---|---|---|

0.90 | 71.70 | 74.06 ± 11.45 | 2.36 |

1.60 | 33.83 | 31.04 ± 2.20 | 2.79 |

2.30 | 21.07 | 16.65 ± 0.46 | 4.42 |

4.67 | 8.36 | 6.93 ± 0.71 | 1.43 |

**Table 5.**Comparison of MDT: predicted vs. experimental data of the EVA-LD formulation (n ≥ 3; x ± s).

SA/V Ratio/mm^{−1} | MDT Prediction/min | MDT Experiment/min | RMSEP/min |
---|---|---|---|

1.73 | 82.25 | 78.79 ± 7.24 | 3.46 |

1.89 | 70.74 | 62.60 ± 5.90 | 8.14 |

4.67 | 15.13 | 14.40 ± 0.77 | 0.73 |

**Table 6.**Comparison of MDT: predicted vs. experimental data of the PVA-PZQ formulation (n ≥ 3; x ± s).

SA/V Ratio/mm^{−1} | MDT Prediction/min | MDT Experiment/min | RMSEP/min |
---|---|---|---|

1.30 | 54.42 | 55.91 ± 1.11 | 1.49 |

1.83 | 36.79 | 38.73 ± 1.07 | 1.94 |

2.30 | 28.32 | 27.88 ± 2.23 | 0.44 |

4.67 | 12.58 | 12.16 ± 0.96 | 0.42 |

PVA-PDM Formulation | ||||||
---|---|---|---|---|---|---|

SA/V mm ^{−1} | KMP | Hixson | Peppas Sahlin n = 0.79 | Hopfenberg | Lapidus + Lordi | Weibull |

0.8 | 0.9837 | 0.9951 | 0.9991 | 0.9837 | 0.9837 | 0.1240 |

1.0 | 0.9971 | 0.9969 | 0.9989 | 0.9971 | 0.9971 | 0.1620 |

1.5 | 0.9981 | 0.9964 | 0.9995 | 0.9981 | 0.9981 | 0.2575 |

2.0 | 0.9966 | 0.9961 | 0.9996 | 0.9966 | 0.9966 | 0.9919 |

2.5 | 0.9783 | 0.9975 | 0.9978 | 0.9783 | 0.9783 | 0.9957 |

3.3 | 0.9982 | 0.9951 | 0.9997 | 0.9982 | 0.9982 | 0.9955 |

4.0 | 0.9949 | 0.9964 | 0.9995 | 0.9949 | 0.9949 | 0.9971 |

5.0 | 0.9931 | 0.9987 | 0.9999 | 0.9931 | 0.9931 | 0.9994 |

6.0 | 0.9970 | 0.9987 | 0.9999 | 0.9970 | 0.9970 | 0.9997 |

PVA-PZQ Formulation | ||||||

SA/Vmm^{−1} | KMP | Hixson | Peppas Sahlinn= 1.1 | Hopfenberg | Lapidus + Lordi | Weibull |

0.8 | 0.9680 | 0.9922 | 0.9980 | 0.9680 | 0.9680 | 0.9993 |

1.0 | 0.9870 | 0.9832 | 0.9953 | 0.9870 | 0.9870 | 0.9972 |

1.5 | 0.9765 | 0.9727 | 0.9890 | 0.9765 | 0.9765 | 0.9976 |

2.0 | 0.9663 | 0.9646 | 0.9667 | 0.9663 | 0.9663 | 0.9973 |

2.5 | 0.9819 | 0.9292 | 0.9932 | 0.9819 | 0.9819 | 0.9963 |

3.3 | 0.9350 | 0.9408 | 0.9807 | 0.9350 | 0.9350 | 0.9980 |

4.0 | 0.9331 | 0.9361 | 0.9877 | 0.9331 | 0.9331 | 0.9975 |

5.0 | 0.9143 | 0.9787 | 0.9823 | 0.9143 | 0.9143 | 0.9994 |

6.0 | 0.9429 | 0.9299 | 0.9888 | 0.9429 | 0.9429 | 0.9992 |

EVA-LD Formulation | ||||||

SA/Vmm^{−1} | KMP | Weibull | Peppas Sahlinn= 0.66 | Higuchi | ||

0.9 | 0.9941 | 0.9986 | 0.9808 | 0.8760 | ||

1.1 | 0.9910 | 0.9936 | 0.9853 | 0.9304 | ||

1.5 | 0.9961 | 0.9961 | 0.9981 | 0.9945 | ||

1.7 | 0.9925 | 0.9884 | 0.9966 | 0.9880 | ||

1.9 | 0.9949 | 0.9894 | 0.9989 | 0.9941 | ||

2.5 | 0.9724 | 0.9979 | 0.9993 | 0.9282 | ||

4.0 | 0.9979 | 0.9928 | 0.9934 | 0.9730 | ||

5.0 | 0.9970 | 0.9944 | 0.9956 | 0.9583 | ||

6.0 | 0.9974 | 0.9946 | 0.9957 | 0.9600 |

PVA−PDM Formulation | |||||
---|---|---|---|---|---|

SA/V | k_{1} | k_{2} | ln(SA/V) | ln(k_{1}) | ln(k_{2}) |

0.8 | 1.986 | 0.010 | −0.223 | 0.686 | −4.608 |

1.0 | 2.516 | 0.011 | 0.000 | 0.923 | −4.549 |

1.5 | 3.920 | 0.027 | 0.405 | 1.366 | −3.626 |

2.0 | 5.561 | 0.067 | 0.693 | 1.716 | −2.704 |

2.5 | 7.362 | 0.135 | 0.916 | 1.996 | −2.001 |

3.3 | 11.555 | 0.258 | 1.203 | 2.447 | −1.353 |

4.0 | 15.459 | 0.545 | 1.386 | 2.738 | −0.608 |

5.0 | 16.888 | 0.713 | 1.609 | 2.827 | −0.338 |

6.0 | 20.856 | 1.069 | 1.792 | 3.038 | 0.066 |

EVA−LD Formulation | |||||

SA/V | k_{1} | k_{2} | ln(SA/V) | ln(k_{1}) | ln(k_{2}) |

0.9 | 1.952 | 0.010 | −0.105 | 0.669 | −4.614 |

1.1 | 2.286 | 0.014 | 0.065 | 0.827 | −4.282 |

1.5 | 3.115 | 0.020 | 0.405 | 1.136 | −3.928 |

1.7 | 4.087 | 0.031 | 0.513 | 1.408 | −3.465 |

1.9 | 5.009 | 0.053 | 0.626 | 1.611 | −2.944 |

2.5 | 7.636 | 0.153 | 0.916 | 2.033 | −1.876 |

4.0 | 10.374 | 0.279 | 1.386 | 2.339 | −1.277 |

5.0 | 14.444 | 0.540 | 1.609 | 2.670 | −0.617 |

6.0 | 16.816 | 0.727 | 1.792 | 2.822 | −0.319 |

PVA-PZQ Formulation | |||||
---|---|---|---|---|---|

SA/V | a | b | ln(SA/V) | ln(a) | ln(b) |

0.8 | 105.0 | 1.38 | −0.223 | 4.654 | 0.322 |

1.0 | 81.0 | 1.45 | 0.000 | 4.394 | 0.372 |

1.5 | 52.0 | 1.63 | 0.405 | 3.951 | 0.489 |

2.0 | 38.0 | 1.80 | 0.693 | 3.638 | 0.588 |

2.5 | 31.5 | 1.91 | 0.916 | 3.450 | 0.647 |

3.3 | 20.8 | 2.05 | 1.194 | 3.035 | 0.718 |

4.0 | 17.1 | 2.15 | 1.386 | 2.836 | 0.765 |

5.0 | 11.5 | 2.29 | 1.609 | 2.442 | 0.829 |

6.0 | 11.2 | 2.40 | 1.792 | 2.414 | 0.875 |

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**MDPI and ACS Style**

Windolf, H.; Chamberlain, R.; Quodbach, J.
Predicting Drug Release from 3D Printed Oral Medicines Based on the Surface Area to Volume Ratio of Tablet Geometry. *Pharmaceutics* **2021**, *13*, 1453.
https://doi.org/10.3390/pharmaceutics13091453

**AMA Style**

Windolf H, Chamberlain R, Quodbach J.
Predicting Drug Release from 3D Printed Oral Medicines Based on the Surface Area to Volume Ratio of Tablet Geometry. *Pharmaceutics*. 2021; 13(9):1453.
https://doi.org/10.3390/pharmaceutics13091453

**Chicago/Turabian Style**

Windolf, Hellen, Rebecca Chamberlain, and Julian Quodbach.
2021. "Predicting Drug Release from 3D Printed Oral Medicines Based on the Surface Area to Volume Ratio of Tablet Geometry" *Pharmaceutics* 13, no. 9: 1453.
https://doi.org/10.3390/pharmaceutics13091453