Watch the ALZET Osmotic Surgery Implant Video Now let’s discuss Transdermal Delivery of Drugs 1. Drug molecules diffuse across the skin 2. enter the systemic circulation 3. skin can be a BIG permeability barrier 4. best for drugs with high pharmacological activity (poten and good skin permeability (lipophilic) Nictoine patch
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Watch the ALZET Osmotic Surgery Implant Video Now let’s discuss Transdermal Delivery of Drugs
Watch the ALZET Osmotic Surgery Implant Video Now let’s discuss Transdermal Delivery of Drugs 1. Drug molecules diffuse across the skin 2. enter the systemic circulation 3. skin can be a BIG permeability barrier 4. best for drugs with high pharmacological activity (potent) - PowerPoint PPT Presentation
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Watch the ALZET Osmotic Surgery Implant Video
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