DIFFUSION PRINCIPLES IN BIOLOGICAL SYSTEMS
Sele£ted Dellnltlons •
Diffusion: It is defined as a mass transfer of individual molecules of a substance caused by random molecular motion. It is associated with a driving force such as the concentration gradient.
•
Flux: It is defined as number of atoms diffusing across the unit area per unit time
•
Fick's first law or diffusion: It states that rate of diffusion across a surface is proportional to the concentration gradient and to the area of the surface
•
Fick's second law or diffusion: It states that the rate of change of diffusant concentration with time at a definite location in unit time.
•
Steady state: A system is said to be in steady state when concentration profile does not change with time.
•
Dlf'fusant: It is a substance that can diffuse through something.
•
Sink condition: It is the state in which concentration in receptor compartment is maintained at lower level compared to its concentration in donor compartment.
3. 1 INTRODUCTION Diffusion is defined as a mass transfer of individual molecules of a substance caused by random molecular motion and associated with a driving force such as the concentration gradient. Diffusion is a time-dependent process. The movement is based on the kinetic energy (velocity), the charge and the mass of molecules. A number of drugs are absorbed by passive diffusion process. The passage of drug molecule across a cell membrane from high concentration region to lower concentration region is called passive diffusion. But Some drugs or nutrients have low partition coefficient i.e. poor absorption through gastrointestinal tract. In this case, a special absorption mechanism is developed. This special mechanism is known as active transport.
fV
46
Physical Pharmaceutics-J
Low Concentration
High Concentration
Figure 3.1: Diffusion process The diffusion phenomenon
applied in pharmaceutical
sciences include
1.
Release of drug from dosage form is diffusion dependent.
2.
Estimation of molecular weight of the polymers. Prediction of Absorption and elimination of drug molecules in living system.
3.
3.2 LAWS OF DIFFUSION 3.2.1 Fick
s first Law of diffusion
Diffusion occurs in response to a concentration
gradient expressed as
J=-D(~~) Where
D is Diffusion coefficient of penetrant (cm2/sec) de is change in concentration dx is change in distance( cm)
of material (g/cm')
(eq 3.1)
Diffusion Principles in Biological Systems
47
FluxJ
•
Gradient
= dC/dx
Position, X Figure 3.2: Fick's first law
The flux is rate of mass transfer through a unit cross section of barrier in unit time J = dM
(eq 3.2)
Sdt Where dM is change in mass of material (g) S is barrier surface area, cm2 dt is change in time, sec
The negative sign in equation 3.1 indicates decrease in the concentration while flux is always a positive quantity.
3.2.2 Fick
S second law
An equation for mass transport that emphasizes the change in concentration with time at a definite location in unit time is known as Fick's second law. The relationship is expressed as dC dt
=
2
-dJ dx
_ D(d C) dx?
(eq 3.3)
Fick' first law gives the flux (or rate of diffusion through unit area) in the steady state of flow. The econd law refers in general to a change in concentration of diffusant with time at any distance, x (i.e., a nonsteady state of flow). The diffu ion coefficient changes as the properties of the system change. At higher temperature , the diffu ion coefficient is larger because the molecules have more thermal movement. The
W
Physical Pharmaceutics-/
diffusion coefficient is also related to the viscosity of the solution. The higher the diffusion coefficient, the lower the viscosity.
3.3 STEADY STATE DIFFUSION A system is said to be steady state, if mass transfer dC/dt remain constant with time. If condition vary with time, then system is unsteady state. Suppose there are two compartments separated by semipermeable membrane. Consider the diffusant dissolved in a solvent in the left compartment of the chamber (donor compartment). The solvent alone is placed on the right side of the barrier (receptor compartment). The solute or penetrant diffuses through the central barrier of the solution to the solvent side (donor to receptor compartment). In diffusion experiments, the solution in the receptor compartment is constantly removed and replaced with fresh solvent to keep the concentration at a low level. This is referred to as "sink conditions,". Membrane
ÂŤ"--
Flow of solvent to maintain sink conditions Figure 3.3: steady state diffusion Originally, the diffusant concentration will fall in the left compartment and rise in the right compartment until the system comes to equilibrium. After some time the concentration of diffusant in the solutions at the left and right of the barrier becomes constant. At that time dC -D d2C -= =0 dt dx?
(eq 3.4)
Diffusion Principles in Biological Systems
49
3.4 MEASUREMENT OF DIFFUSION Franz Diffusion cell are used to measure diffusion. Donor Compartment
Membrane
H C::::==::;:==~
'-~--
Receptor compartment
Water jacket
'-.!!!!~L..-Stirring
bar
Figure 3.4: Franz diffusion cell The Franz Cell apparatus consists of two primary chambers separated by a membrane. Although animal skin can be used as the membrane, human skin is preferred. The donor chamber consist of known concentration of solute. The receptor chamber contain fluid from which samples are taken at regular interval for analysis. The chamber is maintained at constant temperature of 37°C. When experiment starts, the solute from donor chamber diffuses through membrane into receptor chamber. In receptor chamber solution is periodically removed for analysis via sampling port. The test determine amount of diffusant that has permeated the membrane at each time point. The solution of receptor chamber is replaced with new solution after each sampling.
3.5 DIFFUSION CONTROLLED RELEASESYSTEMS The most conventional oral dosage form, such as tablets and capsules, are formulated to release the active drug immediately after oral administration. In the formulation of conventional pharmaceuticals, no deliberate effort is made to modify the rate of release of the drug. But Sustained and controlled release of a drug from a tablet has been obtained by incorporating the drug in an insoluble matrix or slow dissolving material such as plastic, resin, wax, and fatty alcohol. It is of two type :
W
50
Physical Pharmaceutics-I
3.5.1 Reservoir Devices <Laminated Matrix Devices)
Drug
--'11
Polymer
---'Ill
......,,1,
.â&#x20AC;˘.
Jrl ~
Figure 3.5: Reservoir Devices In this case, the water-insoluble polymer material encloses a drug core. The drug parunons into a membrane and exchanges with the surrounding fluid caused by diffusion. The drug will enter the membrane diffuse to periphery and exchange with surrounding media. The release drug from a reservoir device follows Fick's first law of diffusion. -Ddc J=-(eq3.5) dx Where, J = flux, amount/area-time D = diffusion coefficient of drug in the polymer, area/time dc/dx = change in concentration with respect to polymer distance. The release rate of drug from reservior device depends on polymer content in coating and thickness of coating.
3.5.2 Matrix Devices or Monolithic device:
Polymer Drug
Figure 3.6: Matrix system In this, solid drug is dispersed or distributed in a insoluble matrix. In the matrix model, the outer layer of the drug is exposed to the bathing solution in which it is first dissolved. Then, the drug diffuses out of the matrix. This process continues with the interface between the bath solution and the solid drug moves towards the interior. In this system the drug is equally dissolved or
Diffusion Principles in Biological Systems
51
dispersed in the polymer matrix. For monolithic devices the system geometry strongly affects the resulting drug release profile.
3.6 MATHEMATICAL
MODELS OF DRUG RELEASE
The release profile from the microcapsules depends on the nature of the polymer used in the preparation as well as on the nature of the active drug The drug release was confined to any of the order such as zero order or flrst order processes. (1) One indication of mechanism can be obtained using a plot of log of cumulative percentage of drug remaining in the matrix against time. First order release would be linear as predicted by following equation. ' Log C= Log Co---
Kt 2.303
(eq 3.6)
C = Amount of drug left in the matrix Co = Initial amount of drug in the matrix K = First order rate constant, (time -1) t = time, either in hours or minutes (2) Zero order release can be predicted by cumulative %drug release vs time and given by Q=~+~. ~3~ (3) For the monolithic dispersion, the mathematical model is more complicated. Higuchi developed a simple mathematical equation. Thus, the overall release depends on (a) the rate at which the dissolution fluid enters the wall of the microcapsules, (b) the rate at which the drug dissolves in the dissolving liquid, and (c) the rate at which the dissolved drug disperses from the urface. The kinetics of such drug release follows the Higuchi equation which is written as D Q= [ ,/' (2A
+
E
Cs) Cs t
]"2
(eq 3.8)
Q = Weight in grams of drug released per unit surface area. D = Diffusion co-efficient of drug in the release medium. e = Porosity of the matrix. Cs = Solubility of drug in the microcapsule expressed as gmlrnl. A = Total concentration of drug in matrix r =Tortuosity of the matrix t = Time The assumption made in the Higuchi equation is as : (i) A pseudo steady state is maintained during release, (ii) A Âť Cs i.e., excess solute is present, (ill) Drug particles are much smaller than tho e in the matrix, (iv) The diffusion coefficient remains constant and (v) there is no interaction between the drug and the matrix occurs.
;pJ
52
Physical Pharmaceutics-I
The equation is usually reduced to, Q = Ktll2
(eq 3.9)
Therefore a plot of amount of drug released verses the square root of time should be linear if the drug release from the matrix is diffusion controlled. (4) Precisely, to know the exact mechanism of drug release, Korsemeyer used a simple empirical equation to describe the general solute release behavior from control release polymer matrices. The equation is (eq 3.10)
M( = fraction of drug release Ma K = Kinetic rate constant t = Release time. n = Diffusional exponent for drug release.
The value of 'n' gives an indication of the drug release mechanism. For the non-Fickian release, the value 'n' is between 0.5 and 1.0, whereas in the case of Fickian diffusion, n ~ 0.5 Application of Diffusion: 1. Release of drug from dosage form is diffusion controlled 2. Diffusion process is used to predict molecular weight of polymer 3. The absorption of drug through skin or Gastrointestinal tract and further diffusion of drug into tissue and their excretion predicted through diffusion studies.
REVIEW QUESTIONS SUBJECTIVE PART VERY SHORT ANSWER QUESTIONS 1.
Define diffusion. Answer- It is defined as a mass tran fer of individual molecules of a substance caused by random molecular motion. It is associated with a driving force such as the concentration gradient.
2.
Define sink condition. Answer- It is the state in which concentration in receptor compartment is maintained at lower level compared to its concentration in donor compartment.
Diffusion Principles in Biological Systems
3.
53
Define nux. Answer- Flux is defined as number of atoms diffusing across the unit area per unit time Write Hlguchi equation. Answer-
Q
=
[D â&#x201A;ŹI T (2A
.E
Cs) Cs
t]ll2
Define steady state Answer- A system is said to be in steady state when concentration profile does not change with time.
HORT ANSWER QUESTIONS 1.
The diffusion coefficient changes as temperature
change. Why?
Answer- Because At higher temperatures, the diffusion coefficient is larger because the molecules have more thermal movement 2.
Write the application of diffusion In pharmacy. Answer- Release of drug from dosage form is diffusion controlled. Diffusion process is used to predict molecular weight of polymer. The absorption of drug through skin or Gastrointestinal tract and further diffusion of drug into tissue and their excretion predicted through diffusion studies.
3.
Write 2 application of Fick's first law of diffuusion in pharmacy Answer- I. This law is suitable to understand the drug diffusion phenomenon across the membrane. 2. This law is also applicable for development of sustained and controlled release system.
4.
Define active transport
and passive diffusion.
LONG ANSWER QUESTIONS I. Write short note on a. Fick's first law of diffusion Refer article 3.2.1 b. Franz diffusion cell Refer article 3.4 2. Write in detail about diffusion controlled release system Refer article 3.5 3.Explain various mathematical model used to evaluate drug release. Refer article 3.6 4.Write short note on a. Steady state diffusion Refer article 3.3 b. Fick's second law of diffusion Refer article 3.2.2
W
54
Physical Pharmaceutics-I
OBJECTIVE PART MULTIPLE 1.
2.
3.
4.
S.
Fick's law is used for study of a. Dissolution rate b. Disintegration rate c. Dissociation rate d. Diffusion rate Diffusion is measured by a. Franz cell b. Voltameter c. Rotating basket apparatus d. Paddle apparatus The mass transfer of molecules In a substance from higher concentration a. Diffusion b.
Osmosis
c. d. The a. b. c. d. The a.
Active Transport Passive transport "n" in Korsemeyer equation ( Mt / Ma = Kt" ) indicates Fraction of drug release Rate constant Diffusional exponent for drug release Release time. unit of diffusion coefficient is cm2 Si cm2 S-I cm2 S-2
b.
6.
7.
8.
CHOICE QUESTIONS
to lower concentration
c. d. cm' S2 The unit of flux J is a. moles m-2 S-I b. atoms m2 c. moles m? S-I d. moles m' S-I Fick's first law of diffusion is applicable under a. steady state conditions of mass flow b. non-steady state conditions c. steady as well as non-steady state conditions d. none of the above The rate of diffusion according to Fick's flrst law of diffusion is proportional a. concentration gradient b. area of the surface c. Both a and b d. one of the above
to the
ANSWERS l.d
2.a
3.a
4.c
5b
6.a
7.a
8.c
is