Drux: Drug Release Analysis Framework

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Overview

Drux is a Python-based framework for simulating drug release profiles using mathematical models. It offers a reproducible and extensible platform to model, analyze, and visualize time-dependent drug release behavior, making it ideal for pharmaceutical research and development. By combining simplicity with scientific rigor, Drux provides a robust foundation for quantitative analysis of drug delivery kinetics.

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Installation

PyPI

• Check Python Packaging User Guide
• Run pip install drux==0.2

Source code

• Download Version 0.2 or Latest Source
• Run pip install .

Supported Models

Zero-Order

The Zero-Order model describes a constant rate of drug release over time. According to this model, the cumulative amount of drug released at time $t$ is given by:

$$ M_t = M_0 + k_0 t $$

where:

• $M_t (mg)$ is the cumulative absolute amount of drug released at time $t$.
• $M_0 (mg)$ is the initial amount of drug in the system. $M_0$ defaults to zero in this model.
• $k_0 (\frac{mg}{s})$ is the zero-order release rate constant.

Applications

1. Tablets with extended release
2. Transdermal Patches
3. Implantable Device
4. Intraocular Implants
5. Infusion Systems

First-Order

The first-order drug release model describes a process where the rate of drug release is proportional to the remaining amount of drug in the system. According to this model, the cumulative amount of drug released at time $t$ is given by:

$$ M_t = M_0 (1 - e^{-kt}) $$

where:

• $M_t (mg)$ is the cumulative absolute amount of drug released at time $t$.
• $M_0 (mg)$ is entire releasable amount of drug (the asymptotic maximum).
• $k (\frac{1}{s})$ is the first-order release rate constant.

Applications

1. Immediate-release tablets and capsules
2. Liquid drug formulations (oral solutions, intravenous injections)
3. Controlled-release matrix systems
4. Elastomeric infusion pumps

Higuchi

The Higuchi model describes the release of a drug from a matrix system, where the drug diffuses through a porous medium. The Higuchi equation addressed important aspects of drug transport and release from planar devices. According to this model, the cumulative amount of drug released at time $t$ is given by:

$$ M_t = \sqrt{D(2c_0 - c_s)c_st} $$

where:

• $M_t (\frac{mg}{cm^2})$ is the cumulative absolute amount of drug released at time $t$
• $D ({\frac{cm^2}{s}})$ is the drug diffusivity in the polymer carrier
• $c_0 (\frac{mg}{cm^3})$ is the initial drug concentration (total concentration of drug in the matrix)
• $c_s (\frac{mg}{cm^3})$ is the solubility of the drug in the polymer (carrier)

⚠️ The Higuchi model assumes that $c_0 \ge c_s$

Applications

1. Matrix Tablets
2. Hydrophilic polymer matrices
3. Controlled - Release Microspheres
4. Semisolid Systems
5. Implantable Drug delivery systems

Usage

Zero-Order Model

from drux import ZeroOrderModel
model = ZeroOrderModel(k0=0.1, M0=0)
model.simulate(duration=1000, time_step=10)
model.plot(show=True)

First-Order Model

from drux import FirstOrderModel
model = FirstOrderModel(k=0.003, M0=0.1)
model.simulate(duration=1000, time_step=10)
model.plot(show=True)

Higuchi Model

from drux import HiguchiModel
model = HiguchiModel(D=1e-6, c0=1, cs=0.5)
model.simulate(duration=1000, time_step=10)
model.plot(show=True)

Issues & bug reports

Just fill an issue and describe it. We'll check it ASAP! or send an email to [email protected].

• Please complete the issue template

You can also join our discord server

References

1- T. Higuchi, "Rate of release of medicaments from ointment bases containing drugs in suspension," Journal of Pharmaceutical Sciences, vol. 50, no. 10, pp. 874–875, 1961.

2- D. R. Paul, "Elaborations on the Higuchi model for drug delivery," International Journal of Pharmaceutics, vol. 418, no. 1, pp. 13–17, 2011.

3- R. T. Medarametla, K. V. Gopaiah, J. N. Suresh Kumar, G. Anand Babu, M. Shaggir, G. Raghavendra, D. Naveen Reddy, and B. Venkamma, "Drug Release Kinetics and Mathematical Models," International Journal of Science and Research Methodology, vol. 27, no. 9, pp. 12–19, Sep. 2024.

4- R. Vaju and K. V. Murthy, "Development and validation of new discriminative dissolution method for carvedilol tablets," Indian Journal of Pharmaceutical Sciences, vol. 73, no. 5, pp. 527–536, Sep. 2011.

5- S. Dash, "Kinetic modeling on drug release from controlled drug delivery systems," Acta Poloniae Pharmaceutica, 2010.

6- K. H. Ramteke, P. A. Dighe, A. R. Kharat, S. V. Patil, Mathematical models of drug dissolution: A review, Sch. Acad. J. Pharm., vol. 3, no. 5, pp. 388-396, 2014.

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