Effect of Parameters - Controlled Drug Delivery Systems

1. (EFFECTS OF SYSTEM PARAMETERS)
Rate Controlled Drug Delivery
By: Samarpan Palit,
Re-Edited by: Suraj C.
Al-Ameen College of Pharmacy,

2. Suraj C.
INTRODUCTION
• The mechanistic analysis of controlled release drug delivery reveals that the system (physicochemical) parameters play variable rate limiting roles in controlling the drug release from different types of drug delivery devices.
• Some of them are:
 Polymer solubility (Cp)
 Solution solubility (Cs)
 Partition coefficient (K)
 Polymer diffusivity (Dp)
 Solution diffusivity (Ds)
 Thickness of polymer diffusional path (hp)
 Thickness of Hydrodynamic diffusion layer (hd)
 Drug loading dose (A)
 Surface area.
POLYMER SOLUBILITY (CP)
• In the controlled release of a drug species from either polymer membrane permeation controlled or polymer matrix diffusion controlled drug delivery devices or other rate preprogrammed drug delivery devices, the drug particles are visualized as not being releasable from the device until the drug molecules on the outer most surface layer of a drug particle
 dissociate from their crystal lattice structure,
 dissolve or partition into the surrounding polymer,
 diffuse through it and finally partition into the surrounding medium the drug delivery device.
• This suggests that the solubility of a drug species in a rate controlled polymer membrane or matrix plays a rate controlling role in its release from a polymeric device.
• To release at an appropriate rate the drug adequate polymer solubility:
Q/t = Cp K Dd Dm
KDd hm + Dm hd
• Indicates the release of drug from polymer membrane permeation controlled drug delivery system is directly proportional to polymer solubility.
• In the controlled release of drugs from a polymer matrix diffusion controlled drug delivery system the magnitude Q/t1/2 is a function of square root of polymer solubility Cp1/2.
Q/t1/2 = [(2A – Cp) Cp Dp] ½
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• The difference in polymer solubility is striking.
• Solubility of steroids in silicone polymer can range from 1 to 2μg/ml to as high as 1511.82μg/ml.
• This dramatic difference is much dependent on differences in chemical structure, variation in functional groups and their stereo-chemical configurations.
Ex-
 Addition of one or more hydroxyl groups to position 11, 17 & 21 on progesterone skeleton. The polymer solubility of progesterone in the lipophilic silicone polymer reduced significantly with addition of one -OH group, which varies in the extent of reduction of depending upon the position where OH group is added.
 The polymer solubility of progesterone derivatives is further reduced with the substitution of 2 more OH groups.
 The polymer solubility of can be increased by esterification of these hydrophilic OH groups.
• It is as common practice to include various quantities of finely ground fillers, such as siliceous earth, into silicone elastomers to enforce mechanical strength of elastomers.
• Presence of fillers was reported to increase the polymer solubility of the drugs as result of Langmuir adsorption of drug molecules onto the fillers.
SOLUTION SOLUBILITY (Cs)
• Various studies stated that the release of drugs from controlled devices is truly influenced by its solution solubility.
• As in vivo sink condition is effectively maintained by active hemo-perfusion, in vitro drug release studies should be conducted under perfect sink conditions so the release of drug is controlled solely by delivery system and is not affected by solution solubility factor.
• This can be done by
1. Maintaining drug concentration in bulk close to zero.
2. Making solution solubility much greater than the bulk solution conc. (Cs>>>Cb)
Ex- aqueous solubility of ethnodiol diacetate was increased from 3 to 584 fold by using PEG-400.
• Aqueous solubility varies similar to that of polymer solubility, which is very much dependent upon the difference in their chemical structure, types and physicochemical nature of the functional groups and stereo chemical configuration.
Ex- Esterification of Testosterone reduces aqueous solubility.
• For drugs having very low aqueous solubility like steroids, metronidazole, etc. the solubility can be increased by various pharmaceutical approaches like micelle formation, complexation and co- solvency, without chemical modification of drug molecules. Page | 2

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Ex- Norgestomet and Hydron implants.
• Solubilization of poorly soluble drugs in aqueous solution can be effectively accomplished by using multiple co-solvent systems.
• The apparent solubility of a steroid in various multiple co-solvent system is described by following relation:
1. Binary cosolvent system:
log Cx = log Cw + exfx
2. Ternary cosolvent system:
log Ca,x = log Cw + eafa + exfx
3. Quaternary cosolvent system:
log Ca,b,x = log Cw + eafa + ebfb + exfx
Where, Cs = are the apparent solubility of a steroid in distilled water W.
a, b, x = aqueous solution of various co-solvents
e = slopes for the semi-logarithmic relationship between solubility and the volume fraction f of a specific co-solvent.
f = volume fraction of a specific co-solvent.
PARTITION COEFFICIENT (K)
• The partition coefficient K of a drug for its interfacial partitioning from the surface of a drug delivery device toward an elution medium is defined in equation,
K = Cs / Cp
Where, Cs = solubility in elution solution.
Cp = solubility in polymer composition.
NOTE: Any variation in Cs or Cp will result in an increase or decrease in the magnitude of K value.
• In vitro studies of Norgestomet from silicone capsules show that, by changing the solubility of norgestomet in elution solution, the magnitude of partition coefficient varies, leading to a variation in drug release rate.
Q/t = K Dd Cp
hd
• The magnitude of Q/t values is a linear function of K.
• The effect of K on controlled release of drugs from a matrix type delivery device was reported to be biphasic: both the mechanism and the rate profile of drug release were dependent upon the variation in K. Page | 3

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Ex – controlled release of ethynodiol diacetate from matrix type silicone device.
• When magnitude of K is small, Q versus t profile results and the magnitude of Q/t value increases linearly with increase in K.
• The region is governed by partition controlled process.
• When partition coefficient is increased beyond a critical point (K≈0.5) the matrix controlled mechanism becomes predominant and Q versus t1/2 profile is then observed.
• Between partition control and matrix control regions exists a transition phase.
Ex – controlled release of homologous series of alkyl-p-aminobenzoates from matrix type silicone devices.
Log ttrans = log 3β2 + log 1
α KCs
Where, ttrans is the time at which the drug release profile undergoes transition from partition controlled to matrix controlled process, is inversely proportional to the partition coefficient.
• The effect of alkyl chain length on the magnitude of the partition coefficient is exponential as defined by the equation,
Log Kn = log Ko – nπCH2
Where, Kn = partition coefficient for compound with an alkyl chain length of nπCH2 groups.
Ko = Y intercept at zero carbon number.
πCH2 = slope of log Kn versus n plot.
• The attainment of negative slope results from the fact that as alkyl chain length increases polymer solubility Cp is enhanced at the expense of Cs, leading to reduction in partition coefficient Kn.
• On the other hand, the addition of hydrophilic functional groups, such as hydroxyl groups, to a drug molecule tends to improve the solution solubility at the expense of polymer solubility in a lipophilic polymer.
Ex – effect of addition of hydroxyl groups on the solubility of progesterone in silicone polymer and elution solution.
• There is progressive increase in partition coefficient in response to addition of OH groups to progesterone molecule.
Log KOH = log Kp + nπOH
Where, Kp n KOH are partition coefficients of progesterone and its hydroxyl derivative respectively. Page | 4

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• Positive slope value is obtained because the addition of hydroxyl group improves the hydrophilicity of progesterone and thus improves interfacial partitioning of progesterone molecule from a lipophilic silicone polymer towards the aqueous solution.
POLYMER DIFFUSIVITY (DP)
• The diffusion of small molecules in a polymer structure is an energy activated process in which the diffusant molecules move to a successive series of equilibrium positions when a sufficient amount of energy, called the energy of activation for diffusion Ed, has been acquired by the diffusant and its surrounding polymer matrix, this energy activated diffusion process is described by Arrhenius relationship,
Dp = Do–(Ed / RT)
Where, Do = Temperature independent frequency factor.
Ed = Energy of activation for polymer diffusion.
• For simplicity of model calculation, the energy of activation is visualized as involving only 2 neighboring polymer chains that have moved apart to permit the passage of diffusant molecules.
• The molecular motions that lead to this activated state are assumed to involve;
i. Bending of polymer chains to make room for the diffusing molecule.
ii. The intermolecular repulsion from their neighboring polymer chains and simultaneously the intramolecular resistance from the rigid bond distances and bond angles within the molecule.
• The energy of activation for polymer diffusion Ed is thus the sum of energy of intramolecular bending Eb and energy of intermolecular repulsion Er.
Ed = Eb + Er
• The results of model calculation indicated that the magnitude of Eb is very high for short segment polymer chain, but decrease as polymer chain becomes longer.
• On the other hand Er increase as polymer chain becomes longer.
• The self-diffusion coefficient of liquid silicone polymers with varying molecular weights can be determined by nuclear magnetic resonance spin-echo technique.
Ex: It was found that the magnitude of self-diffusion coefficient of silicone polymers decreases remarkably as the length of the linear dimethylpolysiloxane is increased.
• The model calculation and diffusion measurements emphasizes the critical importance of molecular diameter of the diffusant in determining the magnitude of its polymer diffusivity, in such cases, the polymer diffusivity of the diffusant molecule is inversely related to the cube root of its molecular weight. Page | 5

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• The magnitude of polymer diffusivity Dp is also dependent upon the type of functional group and their stereo-chemical position in diffusant.
• The factors affecting polymer diffusivity are
1. CROSS LINKING :
 Polymer diffusivity decrease as the cross linking of polymer increases.
 Addition of cross linking agent results in the cross linkage of some polymer chains, which lead to a reduction in mobility of the polymer chain and consequently a decrease in porosity (ε) and increase in tortuosity (θ) for the diffusion of drug molecules in the polymer structure.
 The combination of reduced porosity and increased tortuosity resulted in reduction in polymer diffusivity.
Dp = D ε/θ
2. EFFECT OF CRYSTALINITY :
 It is known that low-density polyethylene (LDPE) has a high degree of side chain branching than high-density polyethylene (HDPE).
 Therefore, LDPE has a lower degree of crystallinity than HDPE.
 The crystallites act similar to cross linking agent.
 The crystallinity introduces regions of very low diffusion relative to the diffusion in the surrounding amorphous structure, which leads to a significant reduction in gross polymer diffusivity.
3. EFFECT OF FILLERS :
 Fillers are often incorporated into a polymer to enhance mechanical strength.
Ex – very pure and finely ground silica particles are usually added as fillers to silicone elastomers in an amount as high as 20% - 25% to enforce mechanical strengths of elastomers.
 The presence of fillers was reported to affect polymer diffusivity.
 Effect of fillers was noted in matrix diffusion of steroids in silicone elastomers containing silicaseous earth.
Ex – A reduction in polymer diffusivity by 19 – 31% was observed with some steroids.
SOLUTION DIFFUSIVITY (DS)
• The diffusion of solute molecules in a solution medium may be considered to result from the random motion of molecules.
• Under concentration gradient molecules diffuse spontaneously from a region of higher concentration to region of lower concentration until equilibrium is reached.
• Therefore solution diffusivity is given by; Page | 6

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Ds = Do e –(Eh/RT)
Where, Ds = solution diffusivity.
Do = pre exponential factor.
Eh = energy of activation for solution diffusion.
• The solution diffusivities of various chemical classes are ;
alkanes > alcohols > amides > acids > amino acids > di-carboxylic acids.
• The diffusivity of solute in aqueous phase usually decreases as its concentration increases.
• This reduction is frequently related to increase in solution viscosity.
• The effect of viscosity on the solution diffusivity is
D = ω/μ
Where, ω = proportionality constant.
μ = viscosity coefficient.
THICKNESS OF POLYMER DIFFUSIONAL PATH (HP)
• Fick’s law of diffusion essentially governs the controlled release of a drug species from polymer membrane and polymer matrix controlled drug delivery devices.
• The observed difference in their release pattern is a result of time dependence of thickness of their diffusional path length.
• For the polymer membrane controlled reservoir system fabricated from bio-degradable and non- swollen polymers such as silicone elastomers, the HP value is defined by polymer wall with constant thickness that is invariable with time.
• In matrix type device fabricated from non-biodegradable polymers, the thickness of diffusional path in the polymer matrix is defined by drug depletion zone which grows progressively in proportional to the square root of time.
THICKNESS OF HYDRODYNAMIC DIFFUSION LAYER (HD)
• The rate limiting role of hydrodynamic diffusion layer HD in determining drug release profiles can be visualized by considering the device immersed in stationary position in a solution, a stagnant layer is established on the immediate surface of the device.
• The effective thickness of stagnant layer is dependent on the solution diffusivity DS and varies with square root of time.
(HD) nr = ( Π Ds)1/2 t1/2
Where, nr = refers to stationary (non rotationary) state Page | 7

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Π = a constant.
• If the device is forced to rotate at constant speed convection results.
• The convective diffusion of drug molecules to and from surface of the device is much greater than when natural diffusion operates on the stationary device because of concentration gradient.
• The drug release profile Q/t1/2 is a function of variation in thickness of the hydrodynamic diffusion layer on the surface of matrix type device.
• The magnitude of Q/t1/2 decreases as the thickness of hydrodynamic diffusion layer hd increase.
DRUG LOADING DOSE (A)
• In the preparation of drug delivery device various loading dose of drug is incorporated into the device as required for different length of treatment.
• Variation in drug loading dose in matrix type device affects the magnitude of drug release flux Q/t1/2.
• Results suggest that any intention to prolong the duration of medication by incorporating higher dose of therapeutic agent in matrix type device produces a greater value of drug release flux Q/t1/2.
• Rate of drug release from membrane permeation controlled reservoir type polymer device is independent of drug loading dose.
SURFACE AREA
Rate of drug release is dependent upon the surface area of drug delivery device. Both in vivo and in vitro rates of drug release are observed to be dependent upon the surface area of drug delivery device.
REFERENCES
1. Yie.w.Chein, Novel Drug Delivery system, 2010. Page | 8