System Identification and Frequency Response Techniques for the Design of Controlled Release Drug Delivery Systems

System Identification and Frequency Response Techniques for the Design of Controlled Release Drug Delivery Systems

Timothy Knab, Sam Rothstein, Steven R. Little, and Robert S. Parker

Department of Chemical and Petroleum Engineering

University of Pittsburgh, Pittsburgh, PA 15237

There is great interest in developing truly programmable controlled release systems and, to that end, numerous models have been developed. However most models are not broadly predictive and fewer still allow for direct correlation of release behavior to the controllable physical properties of the device. To address this issue, our group has recently produced a model for well-defined, programmable controlled release in vitro^[1], which to our knowledge, can be applied to more drugs and polymers than systems described to date. However, the current model is limited to an idealized in vitro environment and further work is required to account for the non-ideal in vivo processes that may impact release behavior. Our goal is, for the first time, to extend the current release model to have predictive capabilities in an in vivo environment and systematically determine the most important parameters governing release in vivo. We hypothesize that tissue environment-specific effects, affecting release and transport rates, can be detected in systemic circulation and characterized using system identification techniques, namely frequency response analysis. Using the predictive power of the aforementioned model, we can synthesize particles that yield specific release profiles designed to inform the data-driven analysis.

As a basis for this study, a proof of concept diffusion experiment has been developed. Changes in membrane diffusivities in a simulation of this experiment lead to changes in reservoir concentrations over time, and these differences produce identifiable changes in the frequency response characteristics as evidenced from Bode plots. This type of analysis requires a well-controlled input function -- taken from the mathematical model of controlled release - and an output signals that is easily measurable. For this we use flux, which is easily attainable from an actual experimental measurement of concentration via a derivative relationship. Over a two order of magnitude span in diffusivities these simulations show these plots changing from flat, indicating no lag, (rapid diffusion) to a rapid drop off in the magnitude and phase indicating slow diffusion and equilibration of the second tank.

Experimental studies on the physical realization of the simulated diffusion cell are being compared against the simulated data as a test/validation of the experimental system and the numerical tools. Although the dynamics of diffusion cells are well studied, this system can be extended to be more analogous to in vivo physiology through experimental modifications, such as using an ECM seeded with cells as a barrier to transport or the introduction of a diffusive barrier mimicking the effects of fibroblast encapsulation of foreign microparticles. If successful, this system would provide a design framework for controlled release where exquisite control of the release system can be used to characterize -- and overcome -- potential barriers to drug release. The result is the ability to "pre-program" a microparticle for a desired release profile that results in a specified concentration profile at a location remote to the particle.

The system identification techniques we propose to use require reliable, high resolution tracking of spatially disparate drug or tracker molecule concentrations. To that end, Gadolinium-tetraazacyclododecanetetraacetic acid (Gd-DOTA) is being investigated as a potential tracking agent. Gd-DOTA concentrations at various locations within a system can be directly related to magnetic resonance imaging (MRI) T1 relaxation times. The availability of a non-invasive non-destructive imaging platform facilitates the translation of our tools to spatio-temporal analysis of experimental and in vivo systems. Initial work has focused on the design and release of Gd-DOTA from microparticles and the characterization of the diffusion profile in a polymer gel matrix. Gd-DOTA seems to be capable of coordinating with the microparticle polymer matrix, which, in effect, acts as a ligand and results in extremely delayed release compared to the model-simulated release that neglects this drug-polymer coordination. This is thought to be due to the interplay between intra-microparticle pH and Gd-DOTA charge -- an observation consistent with protein release studies also taking place in our lab. For our techniques to be successful, the effects of pH and charge needed to be included in the current model. We are currently working on a mechanistic description of these effects that will ultimately lead to an even more broadly predictive model for controlled release that can also be used in the development of a model of pre-programmable, controlled release, in vivo.

[1] Rothstein, S. N., Federspiel, W. J., & Little, S. R. (2008). A simple model framework for the prediction of controlled release from bulk eroding polymer matrices. Journal of Materials Chemistry, 18(16), 1873. doi:10.1039/b718277e