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Now let’s discuss Transdermal Delivery of Drugs

1. Drug molecules diffuse across the skin2. enter the systemic circulation3. skin can be a BIG permeability barrier4. best for drugs with high pharmacological activity (potent) and good skin permeability (lipophilic)

Nictoine patch

Stratus corneum majorresistance for drugtransport-15 layers of keratinocytes-space between cells filled with lipid bilayers

3 issues with diffusion of the drug1. diffusion in the device or patch2. diffusion across the SC3. disposition of drug in underlying tissue4. distribution of drug throughout the body (PK)

The rate of transdermal transport of a drug across the stratus corneum, ie. the drug infusion

rate, can be described by an equation similar to Equation 5.82, ie.

drugSCdrugSC0 CSP0CSPI (7.41)

where PSC is the permeability of the drug in the stratus corneum, S is the total surface area of the

transdermal device, and Cdrug is the average concentration of the drug within the transdermal

device. The permeability of a drug across the stratus corneum needs to be measured experimentally

using samples of skin or it can be estimated as discussed in the next section. It is also assumed that

the concentration of the drug at x = SC is zero since the drug is immediately taken up by the blood

supply. The stratus corneum permeability, ie. PSC , is given by an equation similar to Equation 5.83

SC

SCSCSC

KDP

(7.42)

where SC represents the volme fraction of the lipid bilayers through which the drug diffuses, DSC is

the diffusivity of the drug in the lipid bilayer material, and 0xdrug

SC

C

CK

represents the

equilibrium solubility of the drug in the stratus corneum.

Consider the situation shown in Figure 5.10. A drug is uniformly distributed within a

microporous polymeric disc of radius R and thickness L. All

of the surfaces of the disc are coated with an impermeable material except for the surface located at

x = L. Since the drug release occurs over many days or weeks, the rate limiting process for release

of the drug from the polymeric support at x = L is diffusion of the drug through the pores of the

polymeric material. An unsteady solute mass balance over the region from x to x + x shows that

Fick’s second law describes the diffusion of the solute within the polymeric material.

2

2

e x

CD

t

C

(5.59)

The initial concentration of the drug is C0 and the drug concentration at

x = L is zero since the drug is immediately taken up by the surroundings, a process that is much

faster than the diffusion of the drug through the polymeric material. The initial and boundary

conditions may then be written as shown below

IC: t = 0, C(x,t) = C0

BC 1: x = 0, 0xd

Cd (5.60)

BC 2: x = L, C = 0

Boundary condition one expresses the additional fact that the solute cannot diffuse out through the

top surface of the polymeric disc since this surface is coated with an impermeable material.

In Equation 7.41 the value of Cdrug will change with time as the drug is depleted from the device. In the most rigorous case one could use Equation 5.70 to calculate the average concentration of the drug within the device at a given time. One can also assume that the drug concentration within the device is many times larger than the concentration of drug within the stratus corneum thus satisfying BC 2 in Equation 5.60. However, within the transdermal device we can also make the reasonable assumption that the concentration profile of the drug at any time is flat since the device is very thin, and diffusion of the drug out of the device is a very slow process because the bulk of the mass transfer resistance for the drug lies within the stratus corneum.

Combining Equations 5.65and 5.69 then provides the solution for the concentration distribution of

the drug or solute within the polymeric material.

L2

x1n2cose

1n2

1C4t,xC

2e

22

L4

tD1n2n0

(5.70)

Of particular interest would be the flux of drug leaving the polymeric disk, ie. Equation 5.57 at x =

L. After finding dC/dx from the above equation we can solve for the elution flux of the drug given

by the equation below

0n

L4

tD1n2

0e

LxS

2e

22

eL

CD2j (5.71)

The above equation can also be combined with a pharmacokinetic model for drug distribution in

the body to predict how the drug concentration in the body changes with time. This is discussed

later in Chapter 7.

This result is from the previous 2slides

rigorous

Approx.

Assuming the controlling resistance for diffusion of the drug is the SC, thenthe drug concentration within the patch is basically flat and we can write

Therefore, an unsteady mass balance on the amount of drug within the device at any time

may be written as

drugSCdrug

device CPStd

CdV (7.43)

With the initial condition that Cdrug = Cdrug0, the above equation can be integrated to provide the

amount of drug within the transdermal delivery device at any time

t

P

0drugdrugdevice

SC

eCtC

(7.44)

where device = Vdevice /S is the thickness of the transdermal patch.

Equations 7.41 and 7.44 can then be combined with Equation 7.31 to obtain the following

differential equation that describes the continuous infusion of a drug by a transdermal delivery

system

t

P

0drugSCteapparentapparentdevice

SC

eCSPCkVtd

CdV

(7.45)

with the initial condition that at t = 0, C = 0. The above equation may be easily solved using

Laplace transforms (Table 4.5) to give the following equation for the plasma drug concentration as

a function of time

device

SCte

tkt

P

apparent

0drugSC

Pk

ee

V

CSPtC

tedevice

SC

(7.46)

VdC

dtI CL C I V k Capparent plasma apparent te 0 0

device

SCte

tkt

P

apparent

0drugSC

Pk

ee

V

CSPtC

tedevice

SC

(7.46)

Note that if the device is very large, ie. device >> 0 or the stratus corneum permeability is very

small, then the above equation simplifies to the previous result given by Equation 7.32 with I0 =

PSC S Cdrug0.

C tI

k Veo

te apparent

k tte( )

1

Predicting the permeability of the skin or the SC

Useful for preliminary feasibility calculations in the absence of hard data

Potts and Guy (1992) developed a relatively simple model for the stratus corneum

permeability based on the size of the drug molecule (ie. its molecular weight, MW) and its

octanol/water partition coefficient (KO/W). The octanol/water partition coefficient is a commonly

used measure of the lipid solubility of a drug. They assumed that the diffusivity of a drug in the

stratus corneum depends on the molecular weight of the drug as given by the following equation

MW0SCSCSC eDD (7.47)

Substituting the above equation into Equation 7.42 and replacing the equilibrium solubility of the

drug in the lipid bilayers (K) with the octanol/water partition coefficient (KO/W) we obtain

MW

SC

0SC

W/OSC eD

KP

(7.48)

SC

SCSCSC

KDP

After taking the log10 of each side the above equation becomes

MWKlogD

logPlog W/OSC

0SC

SC

(7.49)

where is an adjustable constant added to improve the regression analysis and is expected to be on

the order of unity. Potts and Guy (1992) then performed a regression analysis using the above

equation on a data set of more than 90 drugs for which the stratus corneum permeability is known.

The drugs considered in their data set ranged in molecular weight from 18 to 750 daltons and had

octanol/water partition coefficients, ie. log KO/W, from -3 to +6. The regression analysis found the

values of

and,,D

SC

0SC that best represented the data set. Their regression analysis resulted in

the following equation

MW0061.0Klog71.03.6)seccm(Plog W/O1

SC (7.50)

The above equation can be expected to yield predicted values of PSC that are within several fold of

the actual values of the stratus corneum permeability for a given chemical.

Example 7.2 Estimate the stratus corneum permeability for caffeine. The molecular

weight of caffeine is 194 daltons and its octanol/water partition coefficient, KO/W, is equal

to 1 (Joshi and Raje, 2002).

SOLUTION We use the Potts and Guy equation to estimate the stratus corneum

permeability for caffeine as shown below

1418SC

SC

hrcm10x18.1seccm10x29.3P

483.7194x0061.01log71.03.6Plog

The value reported by Joshi and Raje for the stratus corneum permeabilty of caffeine is 1 x

10-4 cm hr-1 which compares quite well to the value predicted by the Potts and Guy

equation.