## Concept of diffusion: Drug release from polymer matrices (Part – II) and MCQs for GPAT, NIPER, Pharmacist and Drug Inspector exam

**Diffusion During Swelling of Matrix – **When water-soluble drugs are entrapped in glassy hydrogels, the release of the drugs engages simultaneously the absorption of water and desorption of drug while the hydrogels swell slowly. Drug release kinetics is governed by the rate of polymer swelling (via solvent diffusion and polymer relaxation) and the rate of drug diffusion. However, in the presence of water soluble drugs in glassy hydrogels, the sorption of water is enhanced at a much faster rate. Thus, drug release kinetics is determined by the polymer relaxation rate and the rate of drug diffusion. The case where polymer relaxation occurs rapidly to water as related to the rate of drug diffusion results in Fickian release kinetics.

**Diffusion in Matrix Erosion – **The diffusion of the drug occurs in polymer materials that are eroded or degraded throughout the entire matrix. The release rate of the drug is given by the Higuchi model:

dM_{t}/dt = √A^{2}DKC_{s}C_{0}/2t (1)

The erosion/degradation of a polymer matrix enhances the rate of drug diffusion due to a decrease in the diffusion path length and/or an increase in the space of the diffusion of the drugs. The rate of diffusion (or diffusivity) increases with time because the polymer chains are cleaved, thus creating a larger space and allowing the drug to diffuse out of the matrix at a faster rate. The mathematical expression for the rate of drug diffusion during erosion/degradation of a polymer matrix is

dM_{t}/dt = √A^{2}D_{0}e^{k}_{0}^{t}KC_{s} C_{0}/2t (2)

**Table no. 1 – Mathematical models for drug release behavior**

S. no. |
Drug release mechanism |
Equation |
Plot |
Delivery system |

1 | Zero-order release | Q = Q_{0} + K_{0}t |
Cumulative % drug release vs time | Osmotic pumps |

2 | First-order release | dC/dt = K(C_{s}-C_{t}) |
log cumulative of % drug remaining vs time |
Tablets, capsules |

3 | Hixson–Crowell cube root law |
Q_{0}^{1/3}-Q_{t}^{1/3} = K_{t} |
Cube root of drug % remaining in matrix vs time | Powder |

4 | Higuchi | Q = [Dɛ/ɽ(2A-ɛC_{s}) C_{s}t]^{0.5} |
Cumulative % drug release vs square root of time |
Drug dispersed in matrix |

5 | Korsmeyer–Peppas model |
M_{t}/M_{͚ }= Kt” |
log cumulative % drug release vs log time |
Swelling hydrogelsn = 0.45 (Fickian diffusion)0.45 < n < 0.89 (non-Fickiandiffusion) n = 0.89 (case II transport) |

** Multiple choice questions:**

**1.When water-soluble drugs are entrapped in glassy hydrogels, the release of the drugs engages simultaneously the absorption of water and desorption of drug while the hydrogels swell slowly.**

a)true

b)false

**2.Drug release kinetics is governed by**

a)rate of polymer swelling

b)rate of drug diffusion

c)only b

d)both of these

**3.In the presence of water soluble drugs in glassy hydrogels, the sorption of water is**

a)enhanced at a much faster rate

b)decreased

c)increased at a very slow rate

d)remains constant

**4.The case where polymer relaxation occurs rapidly to water as related to the rate of drug diffusion results in Fickian release kinetics.**

a)true

b)false

**5.The diffusion of the drug occurs in polymer materials that are eroded or degraded throughout the entire matrix is called**

a)Diffusion During Swelling of Matrix

b)Diffusion in Matrix Erosion

c)both of these

d)none of these

**6.The release rate of the drug in Diffusion in Matrix Erosion is given by**

a)Fickian model

b)Higuchi model

c)Noyes whitney model

d)All of these

**7.Which of the following is Higuchi model equation in Diffusion in Matrix Erosion?**

a)dM_{t}/dt = √A^{2}DKC_{s}C_{0}/2t

b)Q = Q_{0} + K_{0}t

c)dC/dt = K(C_{s}-C_{t})

d)Q_{0}^{1/3}-Q_{t}^{1/3} = K_{t}

**8.The erosion/degradation of a polymer matrix enhances the rate of drug diffusion due to**

a)decrease in the diffusion path length

b)an increase in the space of the diffusion of the drugs

c)both of these

d)only a

**9.The rate of diffusion (or diffusivity) _____ with time because the polymer chains are cleaved, thus creating a larger space and allowing the drug to diffuse out of the matrix at a faster rate.**

a)increase

b)decrease

c)remains same

d)increase then decrease

**10.The mathematical expression for the rate of drug diffusion during erosion/degradation of a polymer matrix is**

a)dM_{t}/dt = √A^{2}DKC_{s}C_{0}/2t

b)Q = Q_{0} + K_{0}t

c)dC/dt = K(C_{s}-C_{t})

d)dM_{t}/dt = √A^{2}D_{0}e^{k}_{0}^{t}KC_{s} C_{0}/2t

**11.Which of the following shows Zero-order release?**

a)Osmotic pumps

b)Tablets

c)capsules

d)Drug dispersed in matrix

**12.Which of the following shows Higuchi release?**

a)Osmotic pumps

b)Tablets

c)capsules

d)Drug dispersed in matrix

**13.Cumulative % drug release vs time plot is obtained in**

a)Zero-order release

b)First-order release

c)Hixson–Crowell cube root law

d)Korsmeyer–Peppas model

**14.dC/dt = K(C _{s}-C_{t}) This is the equation for**

a)Zero-order release

b)First-order release

c)Hixson–Crowell cube root law

d)Korsmeyer–Peppas model

**15.Powders show which of the following drug release?**

a)Zero-order release

b)First-order release

c)Hixson–Crowell cube root law

d)Korsmeyer–Peppas model

**Solutions:**

- a)true
- d)both of these
- a)enhanced at a much faster rate
- a)true
- c)both of these
- b)Higuchi model
- a)dM
_{t}/dt = √A^{2}DKC_{s}C_{0}/2t - c)both of these
- a)increase
- d)dM
_{t}/dt = √A^{2}D_{0}e^{k}_{0}^{t}KC_{s}C_{0}/2t - a)Osmotic pumps
- d)Drug dispersed in matrix
- a)Zero-order release
- b)First-order release
- c)Hixson–Crowell cube root law

**References:**

- Gaurav K. Jain Theory and Practice of Physical Pharmacy, 1st edition 2012 Elsevier, page no. 278.
- Martins Physical Pharmacy, 6th edition 2011, page no. 465-477.

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