Dissolution release modeling

1. A
Seminar On
Presented By
KAUSAR SULTHANA
Under the guidance of
Dr.D.KARTHIKEYAN M.Pharm.,Ph.D
DEPARTMENT OF PHARMACEUTICS
DISSOLUTION RELEASE MODELING
SRIKRUPA INSTITUTE OF PHARMACEUTICAL SCIENCES,
VELIKATTA ,SIDDIPET, MEDAK-502277, TELANGANA.
(Affiliated to osmania university)

2. WHAT IS DISSOLUTION?
WHAT IS DISSOLUTION RATE?
• It is defined as the amount of solute
dissolved in a given solvent under standard
conditions of temperature, pH , solvent
composition and constant solid surface area.
• Dissolution is a process in which a solid
substance solubilises in a given solvent i.e
mass transfer from the solid surface to the
liquid phase

3. Drug Dissolution Process

4. MECHANISMS OF DRUG RELEASE
1.) Diffusion method:
Molecules intermingle as a result of their kinetic
energy.
Based on Fick’s first law of diffusion
J= -D(dc/ dx)
where,
J is the amount of drug passing through the
surface per unit time
D is the diffusion coefficient
dc/dx is the concentration gradient

5. 2.) Zero order release
• Zero order refers to the process of constant drug release from a drug delivery device
such as oral osmotic tablets, transdermal systems, matrix tablets with low soluble
drugs
• Drug release from pharmaceutical dosage forms that donot disaggregate and release
the drug slowly can be represented by the following equation
•
• W0 – Wt = K .t ---------- 1---------
• W0 = initial amount of drug in the dosage form.
• Wt = amount of drug in the pharmaceutical dosage form at time t
• K = proportionality constant.
• Dividing this equation by W0 and simplifying
• ft = K0 .t
• where ft = 1-(Wt/W0)
• Ft = fraction of drug dissolved in time t and Ko the zero order release constant.
• A graphic of the drug dissolved fraction versus time will be linear

6. 3.) First order release:
• If the amount of drug Q is decreasing at a rate that is
proportional to he amount of drug Q remaining ,then the rate
of release of drug Q is expressed as
dQ/dt = -k.Q -----------------1
• Where k is the first order rate constant.
• Integration of above equation gives,
• ln Q = -kt + ln Q0 ---------------- 2
• The above equation is aslo expressed as
• Q = Q0 e-kt ------------------------ 3
• Because ln=2.3 log, equation (2) becomes
• log Q = log Q0 + kt/2.303 ---------------------(4)
• This is the first order equation
• A graphic of the logarithm of released amount of drug versus
time will be linear.

7. 4.) Korsmeyer and Peppas model
• Also called as Power law
• To understand the mechanism of drug release and to
compare the release profile differences among these matrix
formulations ,the percent drug released time versus time
were fitted using this equation
Mt / M∞ = k. tn
• Mt / M∞ = percent drug released at time t
• k= constant incorporating structural and geometrical
characteristics of the sustained release device.
• n = release exponential which characterizes mechanism
of drug release

8. THEORIES OF DISSOLUTION
I. Diffusion layer model/Film Theory
II. Danckwert’s model/Penetration or surface
renewal Theory
III. Interfacial barrier model/Double barrier or
Limited solvation theory.

9. I. Diffusion layer model/Film Theory :-
It involves two steps :-
a. Solution of the solid to form stagnant film or
diffusive layer which is saturated with the drug
b. Diffusion of the soluble solute from the stagnant
layer to the bulk of the solution; this is rate
determing step in drug dissolution.

11. DIFFUSION LAYER MODEL/FILM THEORY
Transport of solute into bulk is slower than solvent-solute
interaction

12. Based on Fick’s first law of diffusion:
Where,
dc/dt= dissolution rate of the drug
K= dissolution rate constant
Cs= concentration of drug in stagnant layer
Cb= concentration of drug in the bulk of the
solution at time t

13. Nerst and Brunner modified Noyes-Whitney
equation to:
dC/dt =D.A.Kw/o (Cs –Cb) v.h
dC/dt = dissolution rate of the drug.
D = diffusion coefficient of the drug.
A = surface area of the dissolving solid
Kw/o = water/oil partition coefficient of drug
V = volume of dissolution medium
h = thickness of stagnant layer
(Cs- Cb)= concentration gradient for diffusion of drugs

14. PARAMETERS SYMBOL INFLUENCE ON DRUG
DISSOLUTION
Diffusion coefficient D Greater the value, faster is
the dissolution rate
Surface area of solid A Greater the surface area,
faster the dissolution rate
Water/oil partition
coefficient
Kw/o Higher the value, faster the
dissolution rate
Concentration gradient Cs-Cb Greater the value, faster
the dissolution rate
Thickness of stagnant layer h More the thickness, lesser
is the diffusion and
dissolution rate

15. • Noyes-Whitney equation represents first order
dissolution rate process where (Cb-Cs) acts as the
driving force .
• Dissolution is in non-sink conditions, this is true in
case of in-vitro dissolution in limited dissolution
medium.
• Dissolution slows down as concentration in the
bulk builds up.
• In-vivo dissolution is always faster than in-vitro
dissolution, as Cb=0.
• No concentration build up, hence no retarding
force on dissolution rate.

16. • Cs>>Cb, thus sink conditions are maintained.
• Equation reduces to dC/dt =K

17. IN VITRO-IN VIVO CORRELATIONS
The relation can be improved by:
• Bathing the dissolving solid in fresh solvent.
• Increasing the volume of dissolution fluid.
• Partitioning dissolved drug from aqueous phase
to organic phase.
• Adding water-miscible solvent to the
dissolution fluid.
• Adding adsorbent to remove the dissolved
drug.

18. • Noyes-Whitney equation assumes that the
surface area of the dissolving solid remains
constant which is practically impossible for
dissolving solids.
• To account for particle size decrease and change
in surface area, Hixson and Crowell’s c Equation:
w0
1/3 – w1/3 = k .t
W=mass of drug remaining to be dissolved at
time t
k=dissolution rate constant
W =original mass of the drug

19. Hixon-crowell cube root law
• Hixon Crowell cube root equation for dissolution kinetics is based on assumption that:
a) Dissolution occurs normal to the surface of the solute particles
b) Agitation is uniform all over the exposed surfaces and there is no stagnation.
c) The particle of solute retains its geometric shape
• The particle (sphere) has a radius r and surface area 4Π r2
• Through dissolution the radius is reduced by dr and the infinitesimal
volume of section lost is
• dV = 4Π r2 . dr ------------------(1)
• For N such particles, the volume loss is
• dV = 4N Π r2 dr ----------------------------(2)
• The surface of N particles is
• S = 4 N Π r2 -----------------------------(3)
• Now ,the infinitesimal weight change as represented by he Noyes –
Whitney law ,equation is
• dW = k.S.Cs.dt ---------------------------(4)
• The drugs density is multiplied by the infinitesimal volume change

20. • ρ.dV, can be set equal to dW,
• ρ.dV = k.S.Cs.dt --------------------------- (5)
• Equations (2) and (3) are substituted into equation (5) , to yield
• -4 ρ N Π r2 . dr = 4 N Π r2 . K .Cs .dt -------------(6)
• Equation 6 is divided through by 4 N Π r2 to give
• - ρ . Dr = k Cs.dt -------------------------(7)
• Integration with r = ro at t= 0produces the expression
• r = ro – kCs .t/ ρ -----------------------------(8)
• The radius of spherical particles can be replaced by the weight of
N particles by using the relationship of volume of sphere
• W = N ρ(Π/6)d3 ----------------------------(9)
• Taking cube root of the equation (9) yield,
• W 1/3 = [ N ρ(Π/6)]1/3. d. ----------------------------(10)
• The diameter d from equation (10) ,is substituted for 2r into
equation 8 to give

21. • W0
1/3 - W1/3 =k t ------------------(11)
• Where k = [ N ρ(Π/6)]1/3.2 k Cs/ρ.
• Wo is the original weight of drug
particles .
• Equation (11) is known as Hixson-
Crowell cube root law ,and k is the
cube root dissolution rate constant.

22. Danckwert’s model/Penetration or
surface renewal Theory :-
• Dankwert takes into account the eddies or
packets that are present in the agitated fluid
which reach the solid-liquid interface, absorb
the solute by diffusion and carry it into the
bulk of solution.
• These packets get continuously replaced by
new ones and expose to new solid surface
each time, thus the theory is called as surface
renewal theory.

24. • As the packets are continuously replaced with
new packets of fresh solvent, the concentration
at interface never reaches Cs.
• Since solvent packets are exposed to new solid
surface each time, the theory is also known as
surface renewal theory.

25. • The Danckwert model is expressed by the
equation:
V.dC/dT= dm/dt = A ( Cs-Cb). (ү.D)1/2
Where, m=mass of solid dissolved
y= rate of surface renewal

26. Interfacial barrier model/Double
barrier or Limited solvation theory :-
• The concept of this theory is explained by
following equation-
G = Ki (Cs - Cb)
Where,
G = dissolution rate per unit area,
Ki = effective interfacial transport constant.

27. • In the interfacial barrier model, it is assumed that
the reaction at the solid/liquid interface is not
instantaneous due to a high activation free energy
barrier which has to be surmounted before the
solid can dissolve.
• The rate of diffusion in the static layer is
relatively fast in comparison with the
surmounting of the energy barrier, which
therefore becomes rate limiting in the dissolution

28. Equation : dm/dt = Ki (Cs – Cb)
Where Ki = effective interfacial transport rate

29. CONCLUSION
• The Quantitative interpretation of the values
obtained in dissolution assays is easier using
mathematical equations which describe the release
profile in function of some parameters related with
the pharmaceutical dosage forms
• As dissolution is an important qc procedure, it is
necessary to understand the basic mechanisms and
theories of the process
• Only then its easier to interpret the results and
understand IVIVC

30. REFERENCES
• http://www.technicaljournalsonline.com/
• D.M.Brahmankar, Biopharmaceutics and
pharmacokinetics- A Treatise, Vallabh
Prakashan, pg no. 29-35.
• www.google images.com

31. THANK YOU