Developing bioresorbable polymers for implantable and drug-delivery applications is a complex process. The use of nonlinear modeling tools can reduce tedious and costly experiments and enable the calculation of material composition that will result in the desired resorption profile, according to Dr. Abhay Bulsari of Nonlinear Solutions Oy (Turku, Finland). "Without nonlinear models, there are no good ways that I can think of by which someone could calculate the material composition that would lead to a desired degradation profile," says Bulsari. "Nonlinear modeling reduces development time and costs by a large factor."
The company's technique follows the degradation of polylactide/glycolide polymers, which are typically used in these applications, in terms of several variables including mechanical properties, crystallinity, inherent viscosity, mass loss, and molecular weight, explains Bulsari. "Among these variables, inherent viscosity is used for most of the nonlinear modeling work, since it seems to be the best measure of degradation. "The models we have developed predict the degradation behavior sufficiently accurately and reliably and make it easy for us to calculate the material composition that will result in a desired degradation profile," says Bulsari.
Nonlinear modeling is empirical or semi-empirical modeling, which takes at least some nonlinearities into account, explains Bulsari. "In other words, we try to describe the reality from experimental or production data as best as we can. The degradation dynamics of these polymers/co-polymers are fairly complicated." To characterize these dynamics, linear statistical techniques and physical modeling are not very useful tools, says Bulsari, because the degradation phenomena are not well understood and copious assumptions and simplifications must be made. "Sophisticated nonlinear models are able to predict the loss in strength, mass, and molecular weight relatively well. Consequently, fewer experiments are needed for product development," says Bulsari.
Since its inception in August 1996, Nonlinear Solutions has successfully used this technique on various kinds of materials and processes, from self-compacting concretes and enzymes to zirconium used for nuclear fuel elements. Applying it to polylactides and glycolides was not a stretch, adds Bulsari. In fact, the company has been involved in other medical applications.
Drug-delivery systems made from composites of polydimethylsiloxanes (PDMS) have been the subject of much nonlinear modeling in the last several years, says Bulsari. "This reduces expensive and time-consuming experimentation by a large factor, and speeds up product development. We have very good mathematical tools to determine the design variables—drug load, composition, and dimension variables—from the desired drug delivery profiles, once the nonlinear models are ready."