Drug Patch Key Parts and Basic Principles: Scopolamine - Case Study Example

Project Drug Patch Key Parts and Basic Principles: The aim of this project is to devise a drug patch that provides Scopolamine to astronauts who are taking part in NASA’s space shuttle missions. Scopolamine can be described as a Dramamine-like substance that assists in preventing motion sickness. The intention of the drug patch is to supply an adequate Scopolamine concentration for a long period of time-for example a time of 70 hours as per this design report-since the astronauts are expected to be busy people and thus cannot be able to change it frequently. Generally, the drug patch is made up of 3 components namely the backing layer, the drug reservoir, and the membrane. The design of the backing layer is such that it prevents the drug from diffusing outward in the direction that is opposite to the skin. This is to say that the backing layer is impermeable to the drug. At the same time, a dilute solution is held in the drug reservoir, and it is this reservoir that contains the drug. The 3 components are illustrated in figure 1 below. Figure 1. Drug patch components Mass transfer takes place across the membrane due to the existence of a concentration gradient between the human bloodstream and the drug reservoir. This is governed by Fick’s Law. According to Fick’s law, the net diffusion rate of a gas across a fluid membrane is proportional to the difference in partial pressure (Chanson, 2004). As such, mass transfers will take place from regions of higher concentrations to regions of lower concentrations. Once the drug has left the reservoir, it will diffuse into the bloodstream by passing through the membrane and skin as shown in figure 2. The skin and the membrane pose some resistance to the diffusion of the drug into the bloodstream. In this design project, a patch will be designed that works effectively for all skin types that have differing thicknesses and diffusion coefficients by altering the following factors: 1. The diffusion coefficient of the drug in the membrane (D1). 2. The membrane thickness (l1). 3. The Scopolamine concentration in the drug reservoir (Cp). Figure 2: drug diffusion pathway Rigorous Unsteady State Model: The simulator makes the multidimensional unsteady state model of the drug diffusion into the blood simple by applying numerical assumptions and methods. The simulator employs a pseudo-steady state model, with the multidimensional unsteady state assumption comprising of 3 partial differential equations. The three equations are first order in time, and are second order in the directions x and z. The direction y is ignored when driving since it is a representation of the right and left direction of the arm of the astronaut. This direction is assumed to be symmetrical and thus it is ignored. It is also assumed that the drug patch’s backing layer is impermeable and hence there will be no diffusion outward in the negative z direction. As noted above, the unsteady-state model is consistent of 3 Partial Differential Equations that have 3 initial conditions and 12 boundary conditions. By numerically solving these three equations, the concentration profiles evolutions can be obtained. This is because the solution of a partial differential equation is a group of curves called evolutions; Cp(z,t), Ca1(z,t), and Ca2(z,t) which ultimately gives the flux profile Np(z,t), Na1(z,t), and Na2(z,t)(1). The subscripts P, a1 and a2 relate to the locations which are the drug reservoir, the membrane, and the skin of an astronaut respectively. Applying the assumption that the drug only diffuses in the positive z direction, the boundary conditions can be primarily established. Therefore, at the two edges of the patch, we have: On the assumption that the backing material is impermeable, then: In addition, two more boundary conditions are made at the reservoir-membrane interface, and membrane-skin interface as shown in the equations below: Assuming that the drug will be absorbed into the bloodstream at the skin-blood interface instantaneously, the boundary condition below results: The 3 initial conditions can be expressed as follows: 1) For the drug reservoir at time = to  2) For the membrane at time = to  3) For the astronaut’s skin at time = to  According to the first initial condition, the concentration of the drug at the reservoir is at first equal to the initial concentration of scopolamine in the patch, which is as expected unless there was a leak before the diffusion process had taken place. The second and third initial conditions mean that there was no Scopolamine in the membrane and skin at first. Eventually, the diffusion for multidimensional unsteady-state model can be represented by the following partial differential equations: 1) At the drug reservoir: 2) At the membrane: 3) At the astronaut’s skin: Pseudo-Steady State Model and Assumptions: The simulator estimates a pseudo-steady state model that is formed on the basis of a couple of assumptions. These assumptions make simpler the complicated P.D.E.’s, reducing them into ordinary differential equations that are easier to solve. This model illustrates the diffusion process as assuming the shape of several fast established steady-states, rather than an actual unsteady-state model. Each steady state has a period ( (change in time) for which the concentration of Scopolamine is assumed to experience steady-state conditions. Therefore, the concentration at any particular time in this steady-state, and assuming that there is no homogenous reaction, can be represented as below: Where corresponds to the original concentration of scopolamine in the membrane, Δt represents the duration of each assumed steady-state, R is the overall mass transfer resistance of the drug patch and skin to the diffusing Scopolamine, is the thickness of the drug patch, n is the number of assumed steady states, and is the thickness of the drug patch. The overall mass transfer resistance of the drug patch and skin to the diffusing Scopolamine (R) can be represented as the sum of the skin and membrane resistances. Being oriented next to each other, their resistances are additive since they are considered to be in series: Where and represent the respective thickness of the membrane and the skin. At the same time, D1 and D2 represent the respective diffusivities of the membrane and skin. The duration of each steady-state assumption (Δt) can be described by the following relationship as: Where represents the lifetime of the drug patch. Therefore, the molar flux at any given time can be represented as follows: Data Collection Process: The simulator presents a unique random set of data each time a new drug patch design is started from scratch. It gives; a definite flux range that is required to keep up efficient concentration in the astronaut’s body, a lifetime for which the patch has to supply enough scopolamine, and a range of skin thicknesses and diffusivities. Those specific inputs are tabulated in table 1. In addition, the simulator also provides a set of 3 different membrane diffusivities, 3 different membrane thicknesses, and 7 different drug concentrations. In order to save time and eliminate unnecessary runs, a special method was used in designing a successful drug patch that fit all skin types for the required lifetime. The plan was accomplished by starting the project data collection with the fast skin type which was obtained using the upper limit of the provided range for skin diffusivities, along with the minimum value of skin thickness. Then, a combination of membrane diffusivity and thickness, along with the best drug concentration-a concentration that would result in proper drug diffusion into the blood, were entered to obtain a graph of molar flux vs. time. The area under the curve of flux vs. time plot was shaded in orange by the simulator to indicate a sufficient molar flux, i.e. a molar flux that falls in the given permissible range. After carrying out a set of 9 runs on the fast skin type, there were only 4 combinations of membrane diffusivity and thickness obtained, and drug concentration that offered sufficient molar flux during the given period of time. Those four combinations were taken again to perform another 4 runs with the slow skin type. A low skin type is one which has the lowest diffusivity and highest thickness. Out of the 4 combinations, only 3 of them were found to provide a sufficient molar flux for the required lifetime. The 3 combinations that worked for both fast and slow skin types, i.e. the two extremes, will definitely work on all other skin types. Note that both plots were constructed for the optimum patch design parameters which works for all types of skin and hence only one plot of concentration vs. time, and flux vs. time were needed. Discussion/Explanation of Results: The lifetime of the drug patch was presented by the simulator to be 70 hours, while the acceptable flux range was (2.00e-12 to 3.12e-12) mol/cm2s. As mentioned in the process section of data collection process, there were only 3 combinations of membrane diffusivities and thicknesses, and drug concentrations that offered sufficient drug diffusion into the astronauts’ blood for the requisite lifetime. Those combinations will fit all types of skin since they met the requirement of the two extreme values of skin types, i.e. fast and slow skin. Table 2 presents the 3 successful designs along with membrane diffusivity, membrane thickness, and best value of scopolamine concentration. These values may not accurately match with the actual experimental data since the simulator uses a pseudo-steady state approximation to make simple the approach. Therefore, the actual data may deviate from the provided data. Table 2: Successful values of membrane diffusivity (), membrane thickness (), Scopolamine concentration (): Taking membrane material costs and shipping fees into consideration, it would be suggested that the second design is better since it has a very thin membrane. This therefore translates to a lesser requirement on material and shipping costs. References Chanson, H. (2004) Diffusion: Basic Theory. Retrieved on 30 March 2015 from http://staff.civil.uq.edu.au/h.chanson/reprints/b7_chap05.pdf Read More