Ortho Evra: The Birth Control Patch: Drug Delivery AnalysisOriginal dimensions for meshTimeFluxResults and DiscussionPatch Falling OffAPPENDIX A: Mathematical Statement of the ProblemMesh SchematicBoundary ConditionsInitial ConditionDiffusivityInput ParametersParameterValueATTACHMENTSOrtho Evra: How Effective is the Patch in Women of Varying Weight Peter Kwiatkowski, Jon Auerbach, Brian Clouser, Daniela Di Iorio, CJ MinchoffOrtho Evra: The Birth Control Patch: Drug Delivery Analysis Peter Kwiatkowski, Jon Auerbach, Brian Clouser, Daniela Di Iorio, CJ Minchoff Executive Summary: This study researched the birth control patch, Ortho Evra and the diffusivity of the hormones, ethinyl estradiol and norelogestromin, into the body through the epidermis. We modeled that all of the species that diffused through the epidermis was completely absorbed into the body. We found that our model validated the amounts given by Ortho Evra for drug release. However, many of the constraints and boundary conditions were taken from the Ortho Evra research information. Our study also analyzed the effectiveness of the hormone in women of varying weight, from 120 pounds to 198 pounds. Results indicated that the patch becomes less and less effective with increasing adipose tissue. This increase in adipose tissue results in a decreasing diffusivity value for the epidermis. Our study also researched the effects of incorrect usage of the Ortho Evra patch. We modeled the scenario of the patch falling off after a given time and the continued effectiveness of the drug. Our values imply that if the patch falls off the woman is not protected. The woman must restart the cycle in-order to reach steady state, which provides the needed amount of drug to be effective.Introduction: Our study will explore the mass transfer effects of a birth control patch. The patch is very helpful and has become popular in the world of birth control because it allows the user to have constant protection without a daily pill. This helps prevent one of the major disadvantages of the pill – forgetting to take it. The patch can be placed on multiple parts of the skin and the drugs are then transferred to the blood stream from which they flow throughout the body. The manufacturing company has listed four specific spots to put the patch because of effective drug diffusivity values for those areas: the buttocks, the abdomen, the upper arm, and the upper torso. This study focuses on the only current company that produces a birth control patch, Ortho Evra. The dimensions of the area studied will be approximately the area of the patch, with a small area of skin surrounding it. We will have to construct a tissue layer for the body parts we use and find properties for skin, the drug, and patch In tests it has been found that Ortho Evra is effective in 99 out of 100 women who use the product for the entire year, similar to that of the pill. In the 15 pregnancies found in the study of 3330 women, 5 of the women had a weight greater than 198 pounds. This was found to be statistically significant by the studies. We will model the difference in a woman of 125 pounds against that of a 200-pound individual. The difference will be monitored by adjusting adipose tissue levels in the skin, thus altering diffusivity values. Design Objectives: The goal of our project is to study the drug delivery form Ortho Evra into the bloodstream. We would like to look at what happens in women of varying weight as described in our Introduction.We also wanted to test other problems with incorrect use. Since the patch is placed in four different areas of the body that can be high friction, we wanted to simulate what would happen if the patch fell off after a certain amount of time and whether a woman would still be protected. Geometry, Boundary Conditions We are modeling the diffusion of norelgestromin and ethinyl estradiol from the patch, through the skin and into the blood. We are modeling the square patch as a circle so that we may use axi-symmetric properties to simplify the problem in FIDAP. To get the same area, we approximate the radius of the circular patch to be 2.53 cm. We are also modeling the patch with .5 cm of skin around it to include diffusive spreading out from the edge of the patch. We used .5 cm instead of 1 cm because the skin is so thin that the drugs can’t diffuse out very far before they have diffused into the blood. Figure 1. Schematic of our Patch and Skin Area. As a result, our mesh is almost the same as during preliminary testing. We have reduced the size of the radius from 3.5 cm to 3 cm. Also, we have changed the interval sizes. There are now many more nodes closer to the patch than the blood in order to better capture the diffusion of the drug into the skin. See Fig 2. (attached) for a picture of the mesh.For the solution, we are using the initial blood concentration of norelgestromin as 7 x 10-4 g/m3 and the initial flux at the patch – skin boundary as 8.849 x 10-7 g/m2s. The diffusivity of the skin layer is 5.55 x 10-12 m2/s. The diffusivity of skin has been obtained from speaking with two dermatogists: Michael Saltzman, and Dr. Richard Guy. The initial flux from the patch for ethinyl estradiol is 1.1789 x 10-7 g/m2s. These figures were used in FIDAP to obtain the following information displayed in Figures 3 and 4. The main problem we had in obtaining these solutions was with our dimensions. After changing our problem to non-dimensionalized terms we were able to obtain a proper solution. Our next section will explain how we non-dimensionalized the terms. Non-Dimensionalizing our Problem:Because FIDAP had trouble calculating a solution with such a small diffusivity, we decided to non-dimensionalize our mesh and governing equation. We divided the dimensions of the mesh by 1.2e-3 meters, which is the actual length of the axis. This set the axis to a unit length of 1, but we also had to alter our equations for the time step and flux. Diffusivity is then set to 1 in FIDAP. Original dimensions for mesh Axis: 1.2 e-3 meters Skin (including patch length): 3 e-2 meters Patch length only: 2.5 e-2 meters Non-dimensional mesh dimensions: Axis: 1 Skin: 25 Patch: 20.8333 Time Time = D*Normal Time / L^2 Where normal time for an hour would be 3600 seconds, L = 1.2 e-3 m, D = diffusivity, 1.11 x 10-12 m2/sFlux Flux = Normal flux * L / D Where normal flux = 8.849 x 10-7 g/m2s
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