Co,.'"Yrlght C IFAC Mode1ina aod Coaual iD BicmMjc:aJ Systdnl, GalvCltm, Teus, USA, 1994
DESIGN OF BIOERODIBLE DEVICES WITH OPTIMAL RELEASE CHARACTERISTICS KYRIACOS ZYGOURAKIS Dept. of Chemical Engineering and Institute of Biosciences and Bioengineering, Rice University, Houston, TX 77251
INTRODUCTION Biodegradable polymer&- have been used for many applications including controlll:rd (or sustained) release of drugs) . orthopedic implants  and disposable plastics . Several studies ~4] have described polymeric systems that can be used to fabricate controlled release devices for spe ..~ific drugs. The design of devices with specific release characteristics, however, requires extensive experimen~ation and the associated large development costs increase the price of the final pharmaceutical products. In two earlier studies [5, 6), we pre:oented a modeling approach that can systematize and ~acilitate the design of controlled release devices with lie sired properties. These studies considered chenlically controlled release devices where particles i)f a bioactive agent (drug) are dispersed in a porour or nonporous bioerodible matrix consisting of a polymer or some other inert material (see Figure 1). When tt'e release device is exposed to an environmental fluil! (solvent), the matrix erodes and previously inaccessible drug particles dissolve releasing the bioactive agent into the solvent phase  . The simulations showed that erosion fronts with tortuous and continuously changing morphology develop in these systems when the drug and the polymer matrix dissolve at different rates [5, 6]. The drug release rates were strongly affected by several chemical and structural properties of the release system such as dissolution rates and the matrix porosity. More recently, G6pferich and Langer  used a similar discrete approach to model the erosion of a copolymer with crystalline areas dispersed in an amorphous phase. Predictions from this model were fit to experimental data for weight loss and erosion front movement. An analysis showed that the model could accurately predict independent parameters such as the evolution of porosity with erosion. The present study extends the applicability of previous discrete models and considers the effect of several parameters (loading, particle dispersion, device geometry and matrix inhomogeneities) on the release characteristics of multicomponent devices.
CELLULAR AUTOMATA MODELS Let us consider a device consisting of M components (e.g . drug(s) , pores and polymer matrix,
or crystalline and amorphous polymer etc.) that erode! when exposed to a suitable solvent. When the varioU! components have low solubilities, surface detachmen is the rate determining step for the erosion processe! occurring at the solid/solvent interfaces. Our analysi! assumes that the dissolution rate Ri of component (i=1,2, ... ,M) is given by Ri = Vi Si where Si is thE solvent/component i interfacial area and Vi is thE intrinSic dissolution rate constant. To solve the problem of dissolving multi component devices, we use model based on cellulal automata and discrete iterations. The evolvin~ structure of multicomponent release systems i~ simulated on rectangular arrays of squarE computational cells. Each cell represents a smal volume that may be (a) empty (pore), (b) occupied b) one of the solid components (i=1,2, ... ,M) or (c) fillec with solvent. Fig. 1 shows a 256x256 cellular arra) mode ling a nonporous device with two solic components. The black areas represent thE component with the largest dissolution rate constant V, (e.g. drug or amorphous polymer), while the gra) areas represent the component that erodes morE .:;Iowly with constant V2. Domains of arbitrary shapE or size can be defined on the initial cellular arrays tc model, for example, drug particles of various shape~ and s:ze, pores and polymer matrix , or crystallinE and QIT1orphous areas [7) . The parameter~ charactE:.rizing two-component devices are the ratio ( of dissolu~on rate constants, the dispersion parametel ~ and the loading A1 defined by
V, A , =-V, + V2
where d is the chara4~teristic length of component . domains, h is the ct:aracteristic length (e .g. sidE length) of the device, anut V1 and V2 are the volume! of components 1 and 2 in ,he device. To start a simulation, each computational cell i~ assigned a "life expectation". This is the time requirec to dissolve this cell if only one of its neighboring cells i~ filled with solvent. Life expectations for cells belongin~ to component i are binomially distributed around thE average value of life expectation for this particulal solid . The initial cellular array is then updated a equally spaced time instants t i where t r = t r- 1 +.1t. I at time t r a solid cell is adjacent to one or more solven cells, then its life expectation is decreased by ar
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