Transdermal drug delivery is a painless, convenient, and potentially effective way to deliver regular doses of many medications. Unfortunately, from the perspective of transdermal technology, the skin is impermeable to all but the smallest of molecules. In particular, the upper layer of skin, known as the stratum corneum, presents the most formidable barrier. If the stratum corneum could be pierced or temporarily made more permeable, this would allow more rapid transmission of larger molecules such as the insulin molecule. One such system for doing this is the so-called PassPort™ system developed by Altea Therapeutics. This system uses a microporator, like the one shown below to literally burn small holes in the stratum corneum.
Because the stratum corneum is well-separated from nerve cells, this burning process is painless and yet at the same time effective for increasing permeability. The PassPort™ system is an example of microelectromechanical systems (MEMS) technology. The heating filaments used in the microporator are made using an etching process similar to that used to manufacture integrated circuits. The individual filaments are only about 500 microns long and 10 microns on a side. Optimal design of the microporator is the subject of this project. Altea Therapeutics would like to have a poration cycle that lasts on order of ten milliseconds. Initial experiments have been with the sample system shown below:
Unfortunately, when too high of a voltage pulse is applied to the structure above, many of the filaments experience thermal runaway, heating rapidly and melting. On the other hand, it is necessary to get the filaments to the desired temperature as rapidly as possible. The balance of these two phenomena is at the heart of the design problem. Given a target temperature versus time profile, how do we design a voltage pulse that avoids thermal runaway, yet meets the target temperature profile as closely as possible?
To model and analyze this problem we will need to understand the coupled domains of heat transfer and electrostatics. The principle phenomena of interest is Joule heating. You might find it useful to review the following papers:
1. A.A. Lacey, Thermal Runaway in a Non-Local Problem Modeling Ohmic Heating, European J. App. Math., 6 (1995), pp. 127.
2. G.A. Kriegsmann, Hot Spot Formation in Microwave Heated Ceramic Fibers, IMA J. App. Math., 59 (1997), pp. 123.
The following text is also useful: