Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs
Abstract
:1. Introduction
2. Methods
2.1. Mathematical Formulation
2.2. Critical Time for the Formation of a Surface Depletion Zone
2.3. Special Case of Planar Drugs
2.4. Numerical Solutions
2.5. Higuchi’s Model
3. Results and Discussion
3.1. Validation of the Model
3.2. Effects of the Drug Shape Factor
3.3. Identification of Constant Release Rate Region
3.4. Evaluation of Possible Deviation by Higuchi Approximation
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
A | drug surface area per volume unit sphere, 1/cm |
Ao | initial drug surface area per volume unit sphere, 1/cm |
C(r,t) | dissolved drug concentration, g/mL |
Ca(r,t) | un-dissolved drug concentration, g/mL |
Cao | initial un-dissolved drug concentration, g/mL |
Cs | solubility of drug in matrix, g/mL |
Ct | initial total drug concentration Ct = Cao + Cs, g/mL |
D | diffusivity of drug in matrix, cm2/s |
G | ratio of diffusion rate to dissolution rate kAoro2/D |
K | ratio of drug solubility to initial total drug concentration Cs/Ct |
k | dissolution rate constant, 1/(cm2·s) |
n | shape factor of a drug particle |
r | radial coordinate from the left of a sphere, cm |
ro | radius of a sphere, cm |
r* | moving front, cm |
t | time, s |
u | unit step function |
Greek symbols | |
φ(η,τ) | dimensionless dissolved concentration C/Ct |
ϕ(η,τ) | dimensionless un-dissolved concentration Ca/Ct |
η | dimensionless radius r/ro |
η* | dimensionless moving front η/ro |
τ | dimensionless time Dt/ |
τc | dimensionless critical time |
τs | dimensionless starting time of constant release rate region |
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K | G | Time Region of Constant Release Rate (τs–τc) | n | Release Rate | Coverage of Constant Release Rate (%) | |
---|---|---|---|---|---|---|
Range | Middle | |||||
1/2 | 10−1 | 0.91–10 | 0 | 5.02 × 10−2–4.97 × 10−2 | 4.97 × 10-2 | 45.77 |
1/2 | 4.84 × 10−2–2.65 × 10−2 | 3.75 × 10-2 | 33.17 | |||
2/3 | 4.78 × 10−2–2.36 × 10−2 | 3.57 × 10−2 | 30.99 | |||
100 | 0.59–1 | 0 | 4.75 × 10−1–4.70 × 10−1 | 4.73 × 10−1 | 20.66 | |
1/2 | 3.77 × 10−1–2.84 × 10−1 | 3.31 × 10−1 | 13.36 | |||
2/3 | 3.54 × 10−1–2.56 × 10−1 | 3.05 × 10−1 | 12.31 | |||
101 | Negligible–0.1 | 0 | - | - | - | |
1/2 | - | - | - | |||
2/3 | - | - | - | |||
1/101 | 10−1 | 0.91–1000 | 0 | 9.94 × 10−4–9.84 × 10−4 | 9.89 × 10−4 | 98.28 |
1/2 | 9.94 × 10−4–5.19 × 10−4 | 7.57 × 10−4 | 73.92 | |||
2/3 | 9.94 × 10−4–4.62 × 10−4 | 7.28 × 10−4 | 69.39 | |||
100 | 0.61–100 | 0 | 9.40 × 10−3–9.30 × 10−3 | 9.35 × 10−3 | 92.60 | |
1/2 | 9.38 × 10−3–5.21 × 10−3 | 7.30 × 10−3 | 71.29 | |||
2/3 | 9.38 × 10−3–4.65 × 10−3 | 7.02 × 10−3 | 67.13 | |||
101 | 0.2–10 | 0 | 6.52 × 10−2–6.46 × 10−2 | 6.49 × 10−2 | 66.88 | |
1/2 | 6.49 × 10−2–4.57 × 10−2 | 5.53 × 10−2 | 53.98 | |||
2/3 | 6.48 × 10−2–4.24 × 10−2 | 5.36 × 10−2 | 51.85 |
G | 100 | 101 | 103 | 105 | |
---|---|---|---|---|---|
K | |||||
1/2 | 32.7 | 13.6 | −4.6 | −4.7 | |
1/11 | 76.0 | 38.4 | 4.3 | −1.1 | |
1/101 | 84.7 | 43.9 | 4.9 | 0.5 |
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Lin, Y.-S.; Tsay, R.-Y. Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs. Pharmaceutics 2020, 12, 582. https://doi.org/10.3390/pharmaceutics12060582
Lin Y-S, Tsay R-Y. Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs. Pharmaceutics. 2020; 12(6):582. https://doi.org/10.3390/pharmaceutics12060582
Chicago/Turabian StyleLin, Yung-Sheng, and Ruey-Yug Tsay. 2020. "Drug Release from a Spherical Matrix: Theoretical Analysis for a Finite Dissolution Rate Affected by Geometric Shape of Dispersed Drugs" Pharmaceutics 12, no. 6: 582. https://doi.org/10.3390/pharmaceutics12060582