When Motion Sickness
Can’t Wait
Decreasing the Response Time of
The Transdermal Scopolamine Patch
Written by :
Robert Hung
Yodit Sheido
Meera Tandon
Cornell University
BEE 453: Computer Aided Engineering for Biomedical Processes
Professor Ashim K. Datta
May 6, 2005
When Motion Sickness Can’t Wait
Table of Contents
1.0 Executive Summary…………………………………………………………………3
2.0 Introduction and Design Objectives……………………………………………….4
2.1 Introduction – Motion Sickness………………………………………………4
2.2 Scopolamine Drug Mechanism……………………………………………….4
2.3 Motion Sickness Medication………………………………………………….4
2.4 Transderm Scop Patch System………………………………………………..5
2.5 Design Objectives…………………………………………………………….5
2.6 Problem Schematic…………………………………………………………...6
2.7 Problem Assumptions………………………………………………………...6
3.0 Results and Discussion………………………………………………………………7
3.1 Design Objective I- Modeling Diffusion……………………………………..7
3.2 Design Objective II – Decreasing the Response Time………………………13
3.3 Mesh Convergence Analysis…………………………………………………18
3.4 Sensitivity Analysis………………………………………………………….20
4.0 Conclusions and Design Recommendations………………………………………21
4.1 Conclusions…………………………………………………………………..21
4.1.1. Design Objective I………………………………………………...21
4.1.2 Design Objective II………………………………………………...21
4.2 Model Improvements.………………………………………………………..22
4.3 Design Requirements………………………………………………………...23
Appendix A……………………………………………………………………………...24
Appendix B……………………………………………………………………………...33
Appendix C……………………………………………………………………………...40
Appendix D……………………………………………………………………………...46
51
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52
1.0 Executive Summary
Motion sickness is a common ailment afflicting travelers in all forms of transportation. The
Transderm Scop company markets a transdermal patch which prevents motion sickness for
extended travel, by slowly delivering the drug scopolamine over three days. The patch is
advertised as having a four hour response time, meaning it takes four hours prior to travel to
relieve the symptoms of motion sickness. Our first design objective was to model the diffusion
of scopolamine through the patch and into the skin using FIDAP to measure a response time.
Our second objective was to alter the design of the current patch to accelerate the effects of the
drug. In order to achieve the second objective we considered two options: altering the polymer
membranes and adding additional scopolamine to the adhesive layer of the patch. Our results
indicate that the time required, by the current patch, to prevent motion sickness is less than the
company advertises. We also found that changing polymers does not affect the response time;
however, increasing the amount of drug in the adhesive decreases the response time by half an
hour. The mesh convergence and sensitivity analysis we conducted confirm our conclusion that
the original polymer coupled with additional scopolamine in the adhesive layer is best suited for
decreasing response time of the Transderm Scop patch.
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2.0 Introduction and Design Objectives
2.1 Introduction – Motion Sickness
When we move, many of our senses are interacting collaboratively to create our three
dimensional world. Motion sickness can occur when our eyes and ears are sending conflicting
messages to the brain about our movement and direction. This illness frequently arises during
sea, air or car travel when our body experiences acceleration in varying directions. Symptoms of
motion sickness, which include dizziness, headaches, sweating, nausea and vomiting, are
temporary and usually last the duration of the trip. To prevent these unpleasant symptoms,
various over-the-counter and prescription drugs are available for those who suffer.
2.2 Scopolamine Drug Mechanism
Motion sickness occurs when we are receiving steady visual images but are experiencing an
imbalance in the fluid of our ears. When this occurs, the vestibular nerve in the ear sends the
neurotransmitter, Acetylcholine, to the vomiting center in the brain, making us feel sick.
Scopolamine, the active ingredient in many motion sickness medications, works to prevent
motion sickness by blocking our vomiting reflex. The drug acts as a receptor antagonist,
blocking Acetylcholine from binding and sending a signal to vomit.
2.3 Motion Sickness Medications
Motion sickness pills, such as over-the-counter drugs like Dramamine and Benadryl, take thirty
minutes to an hour to be activated after being administered. These short term medications are
effective for only five hours. Longer trips may require the use of a prescription medication such
as the Transderm Scop patch, which activates after four hours, and remains effective for three
days. This small circular patch is applied to the hairless area behind one ear and gradually
delivers 1.0mg of scopolamine over a three day period (72 hrs). The patch is shown below. This
is the product that we will focus on in our project.
Figure 1: Transderm Scop patch for motion sickness
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2.4 Transderm Scop Patch System
Initially, scopolamine is stored in both the drug reservoir (0.08 mg/mm3) and adhesive layer
(0.04 mg/mm3) of the patch. Scopolamine from the drug reservoir travels through a microporous
polypropylene membrane, which controls the rate of delivery of the drug. After scopolamine
travels through the membrane, it passes through the adhesive, which holds the patch to the skin
and delivers some drug directly to the skin, without a rate limiting layer. The drug is finally
absorbed into the body through the epidermis where it diffuses into dermis of the inner ear (See
Figure 2).
Figure 2: Scopolamine Diffusion through Patch to Skin
* Notice an initial concentration of drug both in the drug reservoir and adhesive layer
2.5 Design Objectives
We have two primary design objectives. Our first one is to model the diffusion of scopolamine
through each of the layers of the patch and into the dermis layer using FIDAP. With this model,
we will calculate the response time for our patch system, that is we will calculate how long it
will take the drug to be effective at relieving motion sickness. In addition, the current patch has
a microporous polypropylene membrane, which yields a four hour response time. Our second
objective is to decrease the response time of the current patch system, for people who cannot
wait four hours prior to their already extensive travel time. We are attempting to do so by
modeling the patch with two other microporous membranes, namely, polyethylene and
polyisobutylene, which would be compatible with the transdermal patch.
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2.6 Problem Schematic
We are modeling the diffusion of scopolamine from the drug reservoir and adhesive layers into
the dermis layer of the skin using Fick’s Law of Diffusion. We are representing the patch and
skin as an axis-symmetric cylinder, in order to simplify our design (See Figure 3).
Figure 3: Model of the patch and skin as an axis-symmetric cylinder
2.7 Problem Assumptions
In order to fulfill our design objective we had to make the following major assumptions:
1. Axisymmetric 2-D geometry
2. Blood immediately removes concentration from skin at the dermis-blood interface
3. No metabolic/consumption reaction within patch and skin.
4. Patch application of 72hrs
5. Response time of Transderm Scop is 4 hours
6. Diffusivity coefficients are constant within each layer
7. Skin dermis layer much thicker than skin epidermis layer
8. Patch application region occupies very small area of overall skin surface
9. Membrane matrix layer is the rate-limiting layer in the patch
10. Epidermis is the rate-limiting layer in the skin
11. Negligible loss of drug on the adhesive lining when applying the patch to skin surface
12. Diffusion coefficient in drug reservoir is equal to the diffusion coefficient in adhesive
layer
13. Fixed temperature, isothermal system
When Motion Sickness Can’t Wait
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3.0 Results and Discussion
3.1 Design Objective I – Modeling Diffusion
For our first design objective, we wanted to ensure that we could accurately model the diffusion
of scopolamine through our current polypropylene patch-skin system in FIDAP. We then
wanted to use our model to calculate the Transderm Scop patch’s response time, that is, how
long it needs to be applied before it is effective at relieving motion sickness. The company says
it yields a 4 hour response time and is active for 72 hours.
Initially, there is scopolamine present in both the drug reservoir and adhesive layers of the patch.
As can be seen in Figure 4, at the initial time, there is only a concentration of drug in the drug
reservoir (red region) and the adhesive layer (green region) of the patch.
Figure 4: Polypropylene patch-skin system at t = 0 hrs
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During the initial patch application time, we expected that scopolamine would slowly diffuse out
of the drug reservoir, due to the rate limiting microporous polypropylene membrane. On the
other hand, we expected that scopolamine would quickly diffuse out of the adhesive layer and
into the skin in the initial hours, because there is no rate-limiting layer there (besides the
epidermis itself).
Therefore, we predicted to see a gradual decline in concentration of the drug in the reservoir, and
a rather quick decline in the adhesive layer during the first few application hours. These
expected trends were confirmed by our FIDAP plots, which showed the concentration of
scopolamine decreasing from the initial concentration over the 72 hours (Figures 5-6).
Figure 5: Concentration of scopolamine decreasing in the drug reservoir over 72 hrs
When Motion Sickness Can’t Wait
Figure 6: Concentration of scopolamine decreasing in the adhesive layer over 72 hrs
58
When Motion Sickness Can’t Wait
59
As can be seen in the species contour plot below, once the patch has been applied for four hours,
some scopolamine has diffused from the drug reservoir and adhesive layers and into the
polypropylene membrane, epidermis, and dermis. A concentration of scopolamine has entered
dermis layer, which can be carried away by the blood to treat motion sickness.
Figure 7: Concentration of drug in polypropylene patch-skin system at t = 4 hrs
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60
After 72 hours, the expected patch application time, most of the drug has diffused out of the drug
reservoir and has been delivered to the body through the blood. The patch can no longer deliver
an effective concentration of scopolamine to treat motion sickness.
Figure 8: Concentration of drug in polypropylene patch-skin system at t = 72 hrs
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Once we saw that our concentration trends seemed to accurately resemble what should happen
over 72 hours of patch application, we wanted to calculate a response time for the current patch
system in order to compare it back to clinical data. A response time is achieved when an
adequate concentration of drug has entered the blood. Since our design did not model blood
flow, we analyzed the flux out of the dermis and into the blood, across the “dermis-blood
interface,” to track the progress of the drug entering the circulatory system over 72 hours. Since
72 hours is the application time for the polypropylene patch system, we used the flux value at
this time as the “minimum effective flux” required to relieve motion sickness. This is the flux
that must be maintained in order for the drug to remain affective. We plotted our flux results
over 72 hours and placed a red-dashed line to show where the minimum effective flux lies
(Figure 9). Any flux below this line is not effective enough to relieve motion sickness.
Flux across the Dermis-Blood Interface over 72 Hours
1.40E-10
1.20E-10
Flux (mg/mm^2*s)
1.00E-10
8.00E-11
5.34*10-11 mg/mm2s
6.00E-11
Minimum Effective Flux Line
4.00E-11
2.00E-11
0.00E+00
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
Time (Hours)
Figure 9: Calculating the response time for the polypropylene patch system using the flux
value at t = 72 hrs
According to the graph above, the flux across the dermis-blood interface increases rapidly over
the first few application hours. Our results show that an effective flux (5.34*10-11 mg/mm2s) is
reached at approximately 2.7 hours, where the flux line first crosses the red line. Since the patch
company advertises that the patch is effective at approximately 4 hours, we believe that our
approximation using flux values is adequate, varying only by 1hr and 18min. So, according to
our results, the current patch yields a response time of 2.7 hours.
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62
3.2 Design Objective II – Decreasing the Response Time
Our second design objective was to decrease the response time of the Transderm Scop patch,
which uses a polypropylene microporous membrane to limit drug delivery. We initially hoped to
achieve this decreased response time by using a polyethylene or polyisobutylene membrane, both
of which have higher diffusivity values than polypropylene. We also attempted to achieve our
objective by adding more scopolamine into the adhesive layer of our polypropylene patch
system.
Decreasing the response time by varying the membrane:
Since Transderm Scop advertises an antiemetic response time of 4 hours, we analyzed the flux
values through dermis-blood interface of the three patch systems at this time. As can be seen in
Figure 10, the polypropylene patch yields the smallest flux value at 4 hours, that is, it is
delivering the least amount of drug at that time. The other two patches have higher flux values at
4 hours due to their higher diffusivity values.
Flux across the Dermis-Blood Interface at 4 hours
1.80E-10
1.60E-10
1.40E-10
Flux (mg/mm^2*s)
1.20E-10
D = 0.1
1.00E-10
D = 0.01
8.00E-11
Polypropylene
Polyisobutylene
Polyethylene
D = 0.001
6.00E-11
4.00E-11
2.00E-11
0.00E+00
Membranes
Figure 10: Flux across dermis-blood interface of 3 patch systems at 4 hours
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63
We then plotted the flux values across the dermis-blood interface for each patch system to
compare their response times. The advertised response time for the polypropylene patch is 4
hours, so we used the flux value for this patch at this time as the “minimum effective flux”
(1.01*10-10 mg/mm2s) required to relieve motion sickness. This is the pink dashed line in the
graph below (Figure 11). Any flux value below this line is not sufficient at relieving motion
sickness.
Flux Through Dermis-Blood Interface Over 72 Hours
3.00E-10
Flux (mg/(mm^2*s)
2.50E-10
2.00E-10
Polypropylene
Polyisobutylene
Polyethylene
1.50E-10
1.00E-10
Minimum Effective Flux Line
1.01*10-10 mg/mm2s
5.00E-11
0.00E+00
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
Time (Hours)
Figure 11: Calculating the response times for the polyisobutylene and polyethylene patch
systems using the flux value for the polypropylene patch at the researched response time of
t = 4 hrs
We had expected that the polypropylene patch system would last the longest due to its small
diffusivity value. These results, though, show that the current patch is only effective for
approximately 32 hours, and that the other patch systems last for approximately 40 hours. We
did not think that these results were very accurate and that the error was due to using the
advertised response time for the Transderm Scop patch. So we decided that in order to stay
consistent with our design, we needed to use our calculated response time (2.7 hrs) and effective
flux for the polypropylene patch (See Design Objective I) instead of the company’s response
time (4 hrs).
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64
In our Design Objective I, we calculated the response time for the polypropylene patch system to
be approximately 2.7 hours with an effective flux of 5.34*10-11 mg/mm2s. Using this response
time and flux, we generated a new “minimum effective flux line,” the red dashed line on the flux
vs. time plot (Figure 12).
Flux Through Dermis-Blood Interface Over 72 Hours
3.00E-10
Flux (mg/(mm^2*s)
2.50E-10
2.00E-10
Polypropylene
Polyisobutylene
Polyethylene
1.50E-10
1.00E-10
5.00E-11
Minimum Effective Flux Line
0.00E+00
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
Time (Hours)
Figure 12: Calculating the response times for the polyisobutylene and polyethylene patch
systems using the flux value for the polypropylene patch at the calculated response time of
t = 2.7 hrs
As can be seen in the figure above, all three patch systems’ flux values grow rapidly to the reddashed line at approximately the same time. That is, all three systems yield very similar
response times.
Membranes:
Polypropylene (D = 0.001)
Polyisobutylene (D = 0.01)
Polyethylene
(D = 0.1)
Response Time:
2.7 hrs = 2 hrs 42 min
2.6 hrs = 2 hrs 36 min
2.3 hrs = 2 hrs 18 min
Table 1: Patch response times
Using the alternative patch system did not decrease our response time significantly. The
polyethylene patch, for instance, which has the highest diffusivity, would only save a user 22
When Motion Sickness Can’t Wait
65
minutes in comparison to the current patch. We would have like to have designed a patch would
save users even more time than this.
Additionally, as can be seen in Figure 12, only the polypropylene patch lasts a full 72 hours. The
polyisobutylene and polyethylene patches only last for approximately 60 hours. This is seen
where the flux lines cross the red-dashed line. As a result, changing the patch membrane only
seems to decrease the patch application time, which is not favorable.
Decreasing the response time by varying the concentration in the adhesive:
Because we were not able to achieve a significantly decreased response time by altering the
patch’s microporous membrane, we decided to add 50% more scopolamine into the adhesive
layer of the patch. This addition is feasible because the adhesive layer is as thick as the drug
reservoir of the patch. As we saw in Figure 6, the concentration of scopolamine leaving the
adhesive decreases rapidly in the first few hours, because it is not limited by a microporous
membrane like the drug reservoir is. We expected that this concentration would decrease even
more rapidly with the addition of a greater concentration of scopolamine into the adhesive, and
that this could help decrease the response time for the drug.
After increasing the drug concentration in the adhesive of our polypropylene patch from 0.04
mg/mm3 to 0.06 mg/mm3 we plotted the flux values over 72 hours again to determine the
response time.
Flux Through Dermis-Blood Interface over 72 Hours
2.00E-10
1.80E-10
1.60E-10
Flux (mg/mm^2*s)
1.40E-10
1.20E-10
Polypropylene w/ added
concentration in adhesive
Polypropylene
1.00E-10
8.00E-11
6.00E-11
4.00E-11
2.00E-11
0.00E+00
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
Time (Hours)
Figure 13: Calculating the response times for the patch system with the added
concentration in the adhesive using the flux value for the polypropylene patch at the
calculated response time of t = 2.7 hrs
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Patch Systems:
Response Time:
Original Polypropylene
2.7 hrs = 2 hrs 42 min
Polypropylene w/added concentration in the 2.2 hrs = 2 hrs 12 min
adhesive
Table 2: Patch response times
As can be seen in Figure 13 and the data in Table 2, adding 50% more concentration into the
adhesive layer, decreases our response time by 30 minutes. Additionally, this new patch system
is effective for the full 72 hours, because the polypropylene membrane is being used.
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3.3 Mesh Convergence Analysis
In order to ensure the precision of our results, we conducted a mesh convergence analysis. We
analyzed five successive meshes and increased the number of nodal points over 300% from our
original mesh. Below we compare our original mesh (Figure 14) to our finest mesh (Figure 15).
It is apparent that the finer mesh has significantly more elements.
Figure 14: Original mesh with ~8,000 nodal points
Figure 15: Finest mesh with ~41,000 nodal points
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We generated the following chart, using the flux values attained at the dermis-blood interface
using a successively finer mesh. We plotted flux values as a percentage of the finest mesh
against the number of nodal points.
N = Number of Nodal Points, and F 
FluxatN
* 100
FluxatN  41334
Node: 41334
Plot of " F" against "N"
101
99
F (%)
97
95
93
91
89
87
85
0
10000
20000
30000
40000
50000
N
Figure 16: Sensitivity Plot for the Various Meshes
As can be seen for the chart above, the fourth and fifth meshes converge to the same value. We
used the fourth mesh for our results. Therefore, this convergence tells us that our results for the
flux through the dermis-blood interface are not dependent on our mesh.
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3.4 Sensitivity Analysis
The researched values for the diffusivities of each of the polymer membranes were given in
ranges, as shown in Table 3.
Membrane
Inputted Values
Diffusivity Ranges
Polypropylene
0.001
0.0005 to 0.005
Polyisobutylene
0.01
0.005 to 0.05
Polyethylene
0.1
0.05 to 0.5
Table 3: Diffusivity ranges for the polymer membranes used in the patch designs
For our model and results, we chose a specific diffusivity value from the ranges for each of the
membranes. Therefore, it was critical to conduct a sensitivity analysis of the diffusivities for
each membrane to see how sensitive our results were to the ranging values. We plotted the flux
values for each of the polymer membranes taking into account their diffusivity ranges, as shown
in Figure 17.
Diffusivity Sensitivity Analysis
Flux Values at 4 hours (mg/mm^2*s)
1.80E-10
1.60E-10
1.40E-10
1.20E-10
Polypropylene
1.00E-10
Polyisobutylene
8.00E-11
Polyethylene
6.00E-11
4.00E-11
2.00E-11
0.00E+00
0
0.02
0.04
0.06
0.08
0.1
0.12
Diffusivity Ranges (non-dimensionalized)
Figure 17: The effect on the flux value through the dermis-blood interface at 4 hours due to
the diffusivity ranges for each polymer membrane
As can be seen in the figure above, the polypropylene and polyethylene systems were not
affected significantly by the diffusivity range. On the other hand, the polyisobutylene flux value
did seem significantly affected by the range. However, these varying flux values do not alter our
final conclusion. The flux values for polyisobutylene are still smaller than polyethylene, which
did not yield a notably decreased response time. Additionally, the polyisolbutylene diffusivity
range will only grant us a patch with an application time which is less than 72 hours.
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4.0 Conclusion and Design Recommendations
4.1 Conclusions
Our goal in this project was two-fold. We sought to model the diffusion of scopolamine through
the patch-skin system and compare the simulated response time to the response time advertised
by the company. We then sought to decrease the response time by first changing the polymer
membranes and second, adding concentration to the adhesive layer.
4.1.1 Conclusion- Design Objective I
The first design objective was satisfied using the polypropylene membrane. Since our schematic
does not include blood we calculated flux values instead of concentration over the patch lifetime
(See Fig.9). We used the final flux value (at 72 hours) as a standard to determine when the patch
initially reached the effective flux value. According to the company the patch remains effective
for 72 hours, therefore we assumed that the flux at 72 hours is sufficient to alleviate motion
sickness. According to this assumption and our data the polypropylene patch only requires 2.7
hours to prevent motion sickness. Although the calculated response time does not coincide with
the company’s claim it is within acceptable bounds.
4.1.2 Conclusion – Design Objective II
The second design objective is contingent upon the first. Since the original polypropylene patch
yields a response time of 2.7 hours, the remaining alternatives, changing the polymers and
adding concentration, must yield response times which are significantly reduced. Table 1
compares the response times of the three polymers and satisfies our second design objective,
indicating that polyethylene has a faster response time. However, the difference between the
response times of the polymer membranes is insignificant. The differences are measured in
minutes which are minor because the patch lifetimes are measured in hours and days. The
decrease in response time satisfies our design objective but it does warrant a change in the patch.
More importantly, both the polyethylene and polyisobutylene patches fall below the effective
flux after 60 hours and shorten the patch application time. In order to efficiently satisfy our
second design objective we will use the polypropylene membrane in the patch.
The second method we used to decrease the response time was to increase the concentration in
the adhesive by fifty percent. The data indicates that the response time is decreased by 30
minutes. This data is significant due to the lifetime of the patch, Figure 13 indicates that the
patch is still effective for the full 72 hours. Therefore we conclude that polypropylene coupled
with the additional scopolamine is the best polymer and adhesive combination for the
transdermal scopolamine patch because it yields the fastest response time.
Using our simulation the microporous polypropylene membrane yields a 2.7 hour response time
and has a lifetime which is unparalleled by the other polymers, polyisobutylene and
polyethylene. Our findings also indicate that increasing the concentration will significantly
reduce the response time and maintain the same patch application time.
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4.2 Model Improvements
Diffusivity values were vital to our project, however, it proved to be quite difficult to obtain
these properties. Since these values are protected trade secrets we were only privy to diffusivity
ranges. Using theses ranges we then compared the values to diffusivity values of smaller
molecules through the polymers. This comparison provided us with estimates of the actual
diffusivity values. Finding exact diffusivity values of scopolamine through the polymers would
increase the accuracy of our model and improve the results we obtained.
One major assumption we made throughout the project was that the blood was continually
removing scopolamine from the dermis. We made this assumption because we did not model
blood in our schematic. Modeling blood would be a useful improvement for the problem because
we would then be able to calculate concentration in the blood itself. This would eliminate the
need for using flux values which only determine the concentration gradient at the dermis-blood
interface instead of the concentration in the blood. Modeling blood flow would also require us to
use a reaction term. Since scopolamine is an inhibitor which must be metabolized, the reaction
term would allow us to determine how quickly it used in the body and how efficiently
scopolamine is replaced with each polymer membrane.
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4.3 Design Recommendations
Our conclusion that polypropylene coupled with extra adhesive is the best polymer membrane
for the patch is further supported by price and health analyses. Although polyethylene and
polyisobutylene do decrease the response time, polypropylene offers advantages which the other
two polymers do not.
Polymers are plastics which must be made from crude oil. The different types of plastics from
which these polymers are made create significant differences in price. Using price data obtained
from Plastics Exchange we compared the cost of each polymer by weight.
Polymer Membrane
Polypropylene
Price Range ( $ / lb)
$0.04
Polyisobutylene
$0.45
Polyethylene
$0.05
Table : Cost Comparison
The above table shows that polypropylene is also the most cost efficient patch. The price
differences affect manufacturing and marketing cost and will create an added cost for the
consumer which may prove to be detrimental for the company. Aside from the added cost from
the consumer the increased price is not balanced by significant changes in response time. The
cost benefit is another reason polypropylene is an effective polymer membrane for this patch.
The next consideration is the health of the individual wearing the patch. Although our goal is to
increase the response time we do not want to allow scopolamine to enter the blood stream too
quickly. This was our initial concern with the increase of .concentration in the adhesive layer.
The rapid entry of scopolamine into the circulatory system can cause undesirable side effects
such as, inhibition of sweating, pupillary dilation and a slight slowing of the heart beat. These
symptoms can occur with as little as 0.5 mg of scopolamine. Since the patch we model has 1.0
mg of scopolamine in the drug reservoir alone and a total of 1.75 mg in the patch –system with
the added scopolamine, side effects were a concern with both the polyisobutylene and
polyethylene membranes. Their high diffusivities increased concentration within the blood thus
increasing the possibility for inducing side effects. Since we did want to increase the frequency
of side effects we concluded that polypropylene served as the best rate limiting membrane. The
polypropylene along with added scopolamine is best suited for continually releasing the drug
without allowing a high level to enter the circulatory system, thus decreasing the incidences of
side effects.
When Motion Sickness Can’t Wait
APPENDIX A:
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When Motion Sickness Can’t Wait
Mathematical Statement of the Problem
I.
Geometry: 2D-Axisymmetric Patch-Skin system
Fig. A1: Geometry and Boundary Conditions
Refer to section A III for entity names
II.
Boundary Conditions and Initial Conditions
* Boundary Conditions – refer to Fig A1.
* Initial Conditions:
C(t=0) at the drug reservoir = 0.08 mg/mm3
C(t=0) at the adhesive layer = 0.04 mg/mm3
74
When Motion Sickness Can’t Wait
III.
75
Entity Names
Fig. A2: Assigned entity names to different interfaces and compartments
We used this 2-D axis-symmetric geometry to model all three patch-skin systems for
polypropylene, polyethylene, and polyisobutylene. For software simulation purposes, we divided
up the geometry into separate compartments in order to define the behavior at each of the
entities.
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IV. Governing Equation:
  2c
c  u v w 
 2c
 2c
  DS  2 
   

t  x y z 
y 2
z 2
 x

  rA

Since we are modeling diffusion through the axis-symmetric system and there are no
convective or reaction terms, the governing equation in cylindrical coordinates becomes
 1   c S   2 c s
c S
 DS 
r
 2
t
 r r  r  z
CS
t
DS
r
z



= concentration of scopolamine
= time
= diffusivity constant of scopolamine
= distance in the radial direction
= distance in the axial direction
We also need to non-dimensionalize our governing equation since values for variables are
so small.




R c
1 r  
 2c


2
D t  r   R  r  
z


 
    
R
 R
R
2
When Motion Sickness Can’t Wait
V.
a.
Input Parameters:
List of parameters as well as the techniques to non-dimensionalize these
values:
PARAMETERS
NON-DIMENSIONALIZED EQUALS
r
r
R
z
z
R
t
Dt
R2
c
c  ci
c  c
Dlayer (diffusivity in the different layers)
Dlayer
Dreservoir
Fig A2. Parameters of simulation
77
When Motion Sickness Can’t Wait
Diffusivity Coefficients
DRESERVOIR
DIFFUSIVITY
NON-
COEFFICIENT
DIMENSIONALIZED
[CM2/S]
DIFFUSIVITY
1* 10 -7
1
Free Patents
Online, 1981
DPOLYPROPYLENE
1* 10 -10
0.001
Free Patents
Online, 1990
DPOLYETHYLENE
1* 10 -8
0.1
Estimated
interpolations
(Park, 1997)
DPOLYISOBUTYLENE
1* 10 -9
0.01
Estimated
interpolations
(Park, 1997)
DADHESIVE
1* 10 -7
1
Free Patents
Online, 1981
DEPIDERMIS
1.45 * 10 -9
.0145
Johnson et al,
1997
DDERMIS
5.8 * 10 -7
5.8
Johnson et al,
1997
Fig A3. Diffusion Coefficients dimensionalized and nondimensionalized
78
When Motion Sickness Can’t Wait
Time
TIME (SECONDS)
NON-DIMENSIONALIZED TIME
tINITIAL
0
0
tFINAL
72 hours = 259200 sec
0.003636
tSTEP
60 sec
8.416 * 10 -7
max no. of steps
4320
4320 (fixed; not time dependent)
Fig A4. Inputted time parameters (dimensional and non-dimensional forms)
79
When Motion Sickness Can’t Wait
80
Concentration
Concentration values were not non-dimensionalized because if they were, we would attain a
zero initial concentration of the drug in the drug reservoir—no diffusion would occur
between the drug reservoir and the adhesive layer. Therefore, we kept the initial
concentration values in mg/mm3.
Layer
Drug Reservoir
Adhesive
Concentration [mg/mm3]
0.08
0.04
Fig A5. Inputted initial concentrations
When Motion Sickness Can’t Wait
Non-Dimensionalized Vertices
Sample calculation: x =
z
r
and y =
R
R
R= 26.7mm
This procedure was repeated for the remaining fourteen vertices (See Fig. A1)
The second vertex:
R
ORIGINAL
NON-
DISTANCES
DIMENSIONALIZED
[MM]
DISTANCES
0
0
Free Patents
Online, 1977
Z
8.92
0.334
Free Patents
Online, 1977
Fig A6: Non-dimensionalized vertices
81
When Motion Sickness Can’t Wait
APPENDIX B:
82
When Motion Sickness Can’t Wait
83
Problem Statement:
PROB (AXI-, ISOT, NOMO, TRAN, LINE, FIXE, NEWT, INCO, SPEC = 1.0)
The problem was defined in PRESTO as:
AXI-
ISOTNOMOTRANLINEFIXENEWTINCOSPEC = 1.0
Axis-symmetric; The axis is taken at the center
of the patch and extended throughout the
different layers of the skin
Isothermal; Simulation at fixed temperature; no
heat equation
Momentum is not considered; no convective
terms
Transient problem; not steady state
No second derivative (convective) term in GE
Geometry has fixed surfaces
Fluid is Newtonian
Drug is incompressible
Scopolamine is the species analyzed; Thus
only 1 species
When Motion Sickness Can’t Wait
84
Solution Statement:
EXEC (NEWJ)
SOLU (S.S. = 50, VELC = 0.100000000000E-02, RESC = 0.100000000000E-01,
SCHA = 0.000000000000E+00, ACCF = 0.000000000000E+00)
For our solution, FIDAP performed successive substitutions to solve for each time step
with a maximum number of 50 interations per time step. The ‘newjob’ parameter in the
execution command informs FIDAP that this is a new problem.
S.S = 50
ACCF = 0
50 iterations per time step
Acceleration of solver set at zero
When Motion Sickness Can’t Wait
85
Time Integration:
TIME (BACK, FIXE, TSTA = 0.000000000000E+00, TEND = 0.363600000000E-02,
DT = 0.840000000000E-06, NSTE = 4320)
BACK
FIXE
TSTA = 0
TEND = 0.3636E-02
DT = 0.84E-06
NSTE = 4320
time integration is set backwards; more stable
t+Δt
fixed time steps
starting time at t=0
ending time at t=0.3636E-02 or 72 hours
time step = 0.84E-06; first increment of 60 sec
total number of time steps = 4320
When Motion Sickness Can’t Wait
86
Plot of element mesh
Fig B1. Mesh of complete system used to simulate results based on mesh convergence
analysis.
Mesh of the complete system is depicted here where fine meshes are used in the membrane,
epidermis, and the initial distance of skin in the radial direction that is beyond the patch
application region.
When Motion Sickness Can’t Wait
87
Fig B2. Mesh of patch and skin beneath the patch used to simulate results based on
mesh convergence analysis
The mesh shown here illustrates the different layers of the patch and the epidermis and
dermis layer underneath the patch. A fine mesh was used in the membrane layer and the
epidermis layer since these two layers are the rate-limiting. A graded mesh was implemented
at the dermis layer since the changes in concentration become less significant with increasing
penetration depth of the dermis.
When Motion Sickness Can’t Wait
88
Fig B3. Mesh of skin not below the patch used to simulate results based on mesh
convergence analysis
Mesh illustrates skin extended beyond the patch. Again, a fine mesh was used for the
epidermis layer because it is rate-limiting. A graded mesh was used in the radial direction
since the changes in this direction are not significant.
When Motion Sickness Can’t Wait
APPENDIX C
89
When Motion Sickness Can’t Wait
90
Fig C1: Contour of diffusion of scopolamine through polyethylene at 72 hours (patch
removal time) Flux across “skinbottom1” = Flux across the interface of the dermis and
the blood at 4 hours = 0.4290311 * 10-3 units
When Motion Sickness Can’t Wait
91
Fig C2: Contour of diffusion of scopolamine through polyisobutylene at 72 hours (patch
removal time) Flux across “skinbottom1” = Flux across the interface of the dermis
and the blood at 4 hours = 0.3210603*10-3
When Motion Sickness Can’t Wait
Fig C3. Line plot at node = 5258 (drug membrane)
92
When Motion Sickness Can’t Wait
Fig C4. Line plot at node = 7498 (epidermis)
93
When Motion Sickness Can’t Wait
Fig C5. Line plot at node = 24368 (dermis)
94
When Motion Sickness Can’t Wait
APPENDIX D
95
When Motion Sickness Can’t Wait
96
References
1. Park, Kinam.1997. Controlled Drug Delivery. ACS Professional Reference Book,
Washington D.C.
2. Johnson et al. 1997. Evaluation of Solute Permeation through Stratus Corneum: Lateral
Bilayer Diffusion as the Primary Transport Mechanism. Department of Chemical
Engineering, Massachusetts Institute of Technology, Cambridge, MA.
3. Novartis (2005). “Transderm Scop”. Retrieved March 29, 2005 from
http://www.transdermscop.com
4. Free Patents Online (1977). “Bandage for transdermally administering scopolamine to
prevent nausea”. Retrieved March 25, 2005 from
http://www.freepatentsonline.com/4031894.html
5. Free Patents Online (1981). “Therapeutic system for administering drugs to the skin”.
Retrieved March 25, 2005 from http://www.freepatentsonline.com/4286592.html
6. Free Patents Online (1990). “Diffusion matrix for transdermal drug administration and
transdermal drug delivery devices”. Retrieved March 25, 2005 from
http://www.freepatentsonline.com/4911916.html
7. Transderm Scop PPI (2002). “Transderm Scop”. Retrieved March 26, 2005 from
http://www.rxpalace.com/tscopppi.htm
8. Fischer Science (2001). “Winek’s Drug and Chemical Blood Level Data 2001”.
Retrieved April 2, 2005 from
https://fscimage.fishersci.com/webimages_FSC/downloads/winek.pdf
9. Drugs.com (2005). “Transderm Scop Transdermal Therapeutic System”. Retrieved April
2, 2005 from
http://www.drugs.com/PDR/Transderm_Scop_Transdermal_Therapeutic_System.htm
10. Plastics Molding and Fabricating (2003). “Feature: Market Update”. Retrieved April 2,
2005 from http://www.plasticsmachining.com/magazine/2003-7/TthePlasticExch.html
11. ICIS-LOR (2004). “Polypropylene (USA) Price Report”. Retrieved April 2, 2005 from
http://www.icislor.com/il_shared/Samples/SubPage144.asp