DISSOLUTION AND MECHANISM OF DRUG RELEASE

VARIOUS MECHANISM OF DISSOLUTION WITH MATHEMATICAL MODELS AND THERE USES IN VARIOUS DOSAGE FORM.

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ASSIGNMENT
ON
“MECHANISM OF DISSOLUTION’’


Submitted by
ASHISH KUMAR MISHRA
Roll No: MPH/10008/2018
Submitted to
Dr. SANDEEP KUMAR SINGH






DEPARTMENT OF PHARMACEUTICAL SCIENCES & TECHNOLOGY
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI -835215
2018

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INDEX




S.No. Contents Page
No.
1) Introduction 1
2) Dissolution Mechanism Theories 2-6
3) Carstensen scheme for dissolution 7
4) Mathematical Model for Dissolution 8-16
5 References 17

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INTRODUCTION
Dissolution is a key prerequisite parameter for any orally administered drug to be systemically
effective. Initially dissolution test was introduced to characterize the release profile of low
solubility (<1%) drugs in aqueous media, but now the emphasis is to adopt dissolution test in
monograph of all solid dosage form. Various dissolution experiments as performed by Noyes
and Whitney, Nernst and Brunner, Hixson and Crowell, Danckwert et.al and the
mechanism of dissolution proposed by them help to establish whether the drug can become
available for absorption in terms of being in solution at the site of absorption .In vitro
dissolution has become recognized as important element in drug development in several
theories/kinetics models which describe their release profile .Various mathematical models as
given by Weibull, Hixon-Crowell, Higuchi, Korsmeyers-Peppas, Baker-Lonsdale,
Hopfenberg help in better understanding of drug release from various formulation such as
tablets, capsules, suspension, polymeric film, transdermal patch etc. Drug release testing
is routinely used to predict how formulations or drug products are expected to perform in
patients. With evolution and advances in dissolution testing technology dissolution testing has
emerged as a more valuable tool apart from quality control to much more valuable areas such
as guide to formulation development, assess product quality, monitoring manufacturing
process, in vivo performance of solid oral dosage form, as a surrogate measure for
bioequivalence studies and to provide biowaivers .The kind of drug, its polymeric form,
crystallinity, particle size, solubility and amount in solid dosage form can influence the
release kinetics .

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❖ Dissolution can be defined as a physiochemical process by which a solid substance
enters the solvent phase to yield a solution. Or the transfer of molecules or ions from a
solid state into a solution.

Fig. 1: Disintegration, deaggregation, and dissolution stages as a drug leaves a
tablet or granular matrix. (From J. G. Wagner, Biopharmaceutics and Relevant
Pharmacokinetics)
I. DISSOLUTION MECHANISM THEORIES
The dissolution of a solid in a liquid may be regarded as being composed of two consecutive
stages.
1. Interfacial reaction: Interfacial reaction that results in the liberation of solute molecules
from the solid phase. This involves a phase change, so that molecules of solid become
molecules of solute in the solvent. The solution in contact with the solid will be saturated
(Cs, concentration of the saturated solution). Dissolution involves the replacement of
crystal molecules by solvent molecules.

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Fig 2. Diagram of boundary layers and concentration change
surrounding a dissolving particle.
2. Diffusion through boundary layer: The solute molecules must migrate through the
boundary layers surrounding the crystal to the bulk of the solution, at which time its
concentration will be C.
❖ Dissolution Theories:
1) Diffusion limited theory or Film theory.
2) Reaction Limited Model.
3) Interfacial Barrier Model.
4) Danckwert model.
1. Diffusion limited theory or Film theory.
The rate of diffusion as described by Fick’s Law of diffusion expressed as
dC/dt = k ∆C … (1)
where, k is rate constant (s
-1
) and C is concentration of solid in solution at any point at
time t.

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In 1897 Noyes and Whitney found that the dissolution rate (dC/dt), is a linear function of
difference between the bulk concentration (Cb) and time t, and the saturation solubility (Cs).
Noyes and Whitney equation:
dCb/dt = kd (Cs - Cb) … (2)
kd is the dissolution constant.
In 1904 Nernst and Brunner showed that kd is a composite constant being proportion to
diffusion coefficient D and the surface area of the dissolving body, S. Thus equation (2) was
modified and know as the Nernst and Brunner equation.
dCb/dt = DS (Cs-Cb) / Vh … (3)
where, h designates the thickness of the hydrodynamic layer and V is the volume of the
dissolution medium.

Fig 3. Diffusion layer model for drug dissolution.
In 1931, Hixon and Crowell make the equation (2) applicable to dissolving compact objects
by expressing the surface (S) of equation (3) with respect to weight (w). By this consideration

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Eq (2) when integrated yields Hixson and Crowell or Cubic root law which related time to
cubic root of weight:
wo
1/3
- w
1/3
= k2t … (4)
where, wo is the initial weight, w is the final weight and k2 is the constant.
According to the above equations dissolution rate depends on a small fluid ‘layer’ called the
hydrodynamic boundary adhering closely to the surface of a solid particle that is to be
dissolved.

Fig 4: Dissolution of a drug from a solid matrix, showing the stagnant diffusion
layer between the dosage form surface and the bulk solution.

Note: - The diffusion limited model has been exclusively based on experiments in rotating or
stationary disk apparatus or flow through cell under well-defined hydrodynamic condition.

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Limitation:
Departures from diffusion layer models is reported in powder dissolution experiments in USP
paddle apparatus and in gastrointestinal studies.

2. Reaction Limited Model:
Diffusion mechanism based in Interfacial transport is called Rate limited model.
In this model solubility (Cs) is a result of chemical equilibrium. Dissolution is
considered to be a reaction between the undissolved species and the dissolution media
molecules. The rate of reaction is therefore driven by concentration of the undissolved
species and the solubility is considered to be concentration when reaction equilibrium
is reached. This approach could be applied for surfactant facilitated dissolution of
drugs. Interfacial barrier and Danckwert model are the two approach which can
considers in reaction limited models.

3. Interfacial barrier model or limited solvation theory
In 1909 Wilderman proposed the interfacial barrier theory. According to his theory
interfacial transport rather than the diffusion through the film is the limiting step.
According to this model an intermediate concentration can exist at the interface as a
result of solvation mechanism and is a function of solubility rather than diffusion. The
rate of Dissolution (G) that is controlled by the Interfacial reaction is expressed as:
G = K (Cs – Cb ) … (5)
Where, K is the effective interfacial transport constant.

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4. Danckwert Model

Fig 5: Danckert model for Drug dissolution
In 1951 Danckwert Model appeared according to which constantly renewed
macroscopic packets of solvents (eddies) reaches the solid a surface and absorb the
molecule of solute delivering them to the bulk solution.
dC/dt = A (Cs – Cb )√γD/V … (6)
Where, γ is the rate of surface renewal.

❖ Carstensen scheme for dissolution:
The physical characteristics of the dosage form, the wettability of the dosage unit, the
penetration ability of the dissolution medium, the swelling process, the disintegration,
and the deaggregation of the dosage forms are a few of the factors that influence the
dissolution characteristics of drugs. Carstensen proposed a scheme incorporating the
following sequence:
1. Initial mechanical lag.
2. Wetting of the dosage form.
3. Penetration of the dissolution medium into the dosage form.
4. Disintegration

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5. Deaggregation of the dosage form and dislodgement of the granules.
6. Dissolution and occlusion of some particles of the drug.

Fig 6: The S-shaped dissolution curve of solid dosage forms.
Carstensen explained that the wetting of the solid dosage form surface controls the
liquid access to the solid surface which is the limiting factor in dissolution process. The
speed of wetting directly depends on the surface tension at the interface (interfacial
tension) and upon the contact angle between the solid surface and the liquid.

II. MATHEMATICAL MODELS FOR DISSOLUTION:
The various Mathematical models/kinetics for dissolution are:
1) Zero order kinetics
2) First order kinetics
3) Weibull model
4) Higuchi model
5) Korsmeyer–Peppas model

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6) Baker–Lonsdale model
7) Hopfenberg model
8) Other release parameters

1) Zero order kinetics
Drug dissolution from pharmaceutical dosage forms that do not disaggregate and
release the drug slowly (assuming that area does not change and no equilibrium
conditions are obtained) can be represented by the following equation:
W0 – Wt = Kt … (7)
Where, Wo is the initial amount of drug in pharmaceutical dosage form, Wt is the
amount of drug in the pharmaceutical dosage from at time t and K is a proportionality
constant.
Dividing equation (7) by Wo and simplify we get
ft = Kot … (8)
Where, ft = 1- (Wt / Wo) and f represents the fraction of drug dissolved in time t and
Ko is the apparent dissolution rate or zero order are constant.
The following equation can be simplified as
Qt = Qo +Kot … (9)
Where Qt is the amount of dissolved drug in time t, Qo is the initial amount of drug
in the solution and Ko is zero order rate constant.
➢ Graphic of drug dissolved fraction vs time will be linear.

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Uses:
This relation can be used to describe the drug dissolution of several types of modified
release pharmaceutical dosage forms, as in the case of some transdermal systems,
matrix tablets with low soluble drugs, coated forms, osmotic systems, etc.

2) First order kinetics:
First proposed by Gibaldi and Feldman in (1967) and later by Wagner in (1969).
This model has been used to describe absorption and elimination of drugs.
The equation for first order kinetics is:
log Qt = log Qo + Kt t/ 2.303 … (10)
where Qt is the amount of drug released in time t, Qo is the initial amount of drug in
the solution and Kt is the first order release constant
➢ Graphics of decimal logarithm of the released amount of drug vs time will be
linear.
Uses:
The pharmaceutical dosage form following this dissolution profile are water soluble
drug in porous matrices (Mulye and Turco, 1995).

3) Weibull model
In 1951 an empirical equation was described by Weibull to the dissolution/release
process which was adapted by Langenbucher in 1972. This equation was
successfully applied to almost all kind of dissolution curve. When applied to drug

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dissolution or release from pharmaceutical dosage form, the Weibull equation
express the accumulated fraction of drug m, in solution at time t, by:
m = 1- exp [ - (t – Ti)
b
/ a … (11)
Where, a defines the time scale of the process. The location parameter, Ti represent
the lag time before the onset of the dissolution or release and in most cases will be
zero. The shape parameter b characterizes the curve as either exponential b= 1 or
b>1 for sigmoid, S shaped or b<1 for parabolic shape.
The equation can be rearranged as:
log [ -ln (1 – m)] = b log (t – Ti) -log a … (12)
The pharmaceutical system following this model, the logarithm of the dissolved
amount of drug versus the logarithm of time plot will be linear
Limitation:
1)There is not any kinetic fundament and could only describe, but does not
adequately characterize, the dissolution kinetic properties of the drug,
2)There is not any single parameter related with the intrinsic dissolution rate of the
drug.
3) Tt is of limited use for establishing in vivo/ in vitro correlations.
4) Higuchi Model
Higuchi (1961, 1963) developed several theoretical models to study the release of
water soluble and low soluble drugs incorporated in semi-solid and/or solid.
Mathematical expressions were obtained for drug particles dispersed in a uniform matrix
behaving as the diffusion media. To study the dissolution from a planar system having
a homogeneous matrix, the relation obtained was the following:
ft = Q =√ D (2C – Cs) Cst … (13)

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Where Q is the amount of the drug released in time t per unit area, C is the drug initial
concentration, Cs is the drug solubility in the matrix media and D is the diffusivity of
the drug molecule (diffusion constant) in the matrix substance.
➢ This relation was first proposed by Higuchi to describe dissolution of drugs in
suspension from ointment bases.

Fig 7: Release of drug from homogeneous and granular matrix dosage forms. (a)
Drug eluted from a homogeneous polymer matrix. (b) Drug leached from a
heterogeneous or granular matrix. (c) Schematic of the solid matrix and its receding
boundary as drug diffuses from the dosage form.

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Final equation:
Q =√tDCs (2C – Cs) … (14)
➢ This relation is valid during all the time, except when the total depletion of the
drug in the therapeutic system is achieved.
Higuchi model for drug release from spherical homogenous matrix system and
planer or spherical system having a granular heterogenous matrix.
ft = Q = √Dɛ (2C - ɛCs)Cst … (15)
Where, Q is the amount of drug released in time t by surface unity, C is the initial
concentration of the drug, ɛ is the matrix porosity, τ is the tortuosity factor of the
capillary system, C is the drug solubility in the matrix / excipient media and D the
diffusion constant of the drug molecules in that liquid.
➢ These models assume that these systems are neither surface coated nor that
their matrices undergo a significant alteration in the presence of water.
Higuchi (1962) proposed the following equation, for the case in which the drug is
dissolved from a saturated solution (where C is the solution concentration) dispersed
in a porous matrix:
Ft = Q = √2CoɛDt/τ?????? … (16)
Cobby et al. (1974) proposed the following generic, polynomial equation to the
matrix tablets case:
ft = Q = G1Krt
1/2
– G2(Krt
1/2
)
2
+ G3(Krt
1/2
)
3
… (17)
Where, Q is the released amount of drug in time t, Kr is a dissolution constant and
G1, G2 and G3 are shape factors.

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In a general way it is possible to resume the Higuchi model to the following
expression (generally known as the simplified Higuchi model):
Ft =KH t
1/2
… (18)

where KH is the Higuchi dissolution constant.

5. Hixson–Crowell model
Hixson and Crowell (1931) recognizing that the particle regular area is proportional to
the cubic root of its volume, derived an equation that can be described in the following
manner:
Wo -Wt =Kst … (19)
Where, Wo is the initial amount of drug in the pharmaceutical dosage form, Wt is the
remaining amount of drug in the pharmaceutical dosage form at time t and Ks is a
constant incorporating the surface–volume relation.
This expression applies to pharmaceutical dosage form such as Tablets.

6. Korsmeyers – Peppas Model
Korsmeyer et al. (1983) developed a simple, semi-empirical model, relating
exponentially the drug release to the elapsed time (t):
ft = at
n
… (20)
Where, a is a constant incorporating structural and geometric characteristics of the drug
dosage form, n is the release exponent, indicative of the drug release mechanism, and
the function of t is Mt /M ∞ (fractional release of drug).
Mt /M ∞ = at
n
… (21)

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The drug diffusion from a controlled release polymeric system with the form of a
plane sheet, of thickness d can be represented by:
dc/dt = D d
2
c/dx
2
… (22)
Where, D is the drug diffusion coefficient (concentration independent).

Fig 8: Interpretation of diffusional release mechanisms from polymeric films.

7. Baker – Lonsdale model
This model was developed by Baker and Lonsdale (1974) from the Higuchi model and
describes the drug-controlled release from a spherical matrix, being represented by
the following expression:
3/2[1-(1-Mt/M∞)
2/3
– [Mt /M∞] = 3DmCms t /ro
2
Co … (23)
8. Hopfemberg model
The release of drugs from surface-eroding devices with several geometries was
analysed by Hopfenberg who developed a general mathematical equation describing
drugrelease from slabs, spheres and infinite cylinders displaying heterogeneous erosion
(Hopfenberg, 1976; Katzhendler et al., 1997):
[Mt /M∞] = 1- [1- kot/Coao]
n
… (24)
Where, Mt is the amount of drug dissolved in time t, M∞ is the total amount of drug
dissolved when the pharmaceutical dosage form is exhausted Mt /M∞ is the fraction of

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drug dissolved, ko is the erosion rate constant, Co is the initial concentration of drug in
the matrix and ao is the initial radius for a sphere or cylinder or the half-thickness for a
slab. The value of n is 1, 2 and 3 for a slab, cylinder and sphere, respectively.
9. Other release parameters
Other release parameters, such as dissolution time (tx%), assay time (tx min), dissolution
efficacy (ED), difference factor (f1) similarity factor (f2) and Rescigno index (ζ1 and
ζ2) can be used to characterize drug dissolution / release profiles.




Fig 9: Mathematical models used to describe drug dissolution curves.

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REFERENCES
1. Costa,P. Lobo,JMS.,2001.Modeling and comparison of dissolution profiles. European
Journal of Pharmaceutical Science,13,123-133.
2. Aulton,M.E. Dissolution and Solubility. In: Aulton’s pharmaceutics,The design and
Manufacture of Medicine. Aulton,M.E. and Taylor,K.M.G.,(Eds.)4
th

Edition,2013,Elsevier, Edinburgh,20-37.
3. Jain, N.K. Jain,V.,Dissolution. In:The theory and practice of Industrial
Pharmacy.Khar,R.P.,Vyas,S.P.,Ahmad,F.J.,Jain,G.K.,(Eds.) Fourth Edition,2013,CBS
Publisher and Distributors,New Delhi,182-185.
4. Sinko,P.J. and Singh Yashveer.,Martin’s Physical Pharmacy and Pharmaceutical
Science,Sixth Edition,2011,Wolters Kluwer India,Gurgaon,300-310.