Mathematical Modeling of Topical Drug Delivery in Women’s Health

Our lab focuses on developing and optimizing drug delivery systems for applications in women’s health. In this field, development of drugs and drug delivery systems is hindered by a heavy reliance on empirically derived data, usually obtained from non-standardized, highly variable in vitro and in vivo animal experiments. Further, without a mechanistic understanding of the various phenomena progressing during drug delivery, experiments tend to explore complex parameter spaces blindly and randomly. Deterministic mathematical models can improve the efficiency of this process by informing rational drug and product design. In this work, we were interested in two applications: 1. drug delivery of topically applied anti-HIV microbicides to the female reproductive tract; and 2. Localized intratumoral injections of ethanol-ethyl cellulose mixtures for treatment of cervical lesions. Development of topically applied anti-HIV microbicides to prevent sexual HIV transmission is inefficient, with in vitro and in vivo tests having limited applicability to real product use. This issue is exacerbated by the dependence of drug performance on adherence and drug-administration conditions, which are not tested until clinical trials. Further, the lack of a standardized pharmacodynamic (PD) metric that is dependent on the heterogenous dynamics of viral transport and infection makes it difficult to identify the most promising drug candidates. Here we develop a deterministic mathematical model that incorporates drug pharmacokinetics (PK) and viral transport and dynamics to estimate the probability of infection (POI) as a PD metric that can be computed for a variety of anti-HIV drugs in development. The model reveals key mechanistic insights into the spatiotemporally dependent dynamics of infection in the vaginal mucosa, including susceptibility to infection at different phases in the menstrual cycle. Further, it and can be used as a platform to test novel drugs under several conditions, such as the timing of drug administration relative to the time of HIV exposure. Localized injections of ablative agents, immunotherapeutics and chemotherapeutics have potential for increased therapeutic efficacy against tumors and reduced systemic effects. However, injection outcomes thus far have been largely unsatisfactory, due to unintended leakage of the active pharmaceutical ingredients (APIs) to non-target tissues. Adding a gelling or precipitating agent to the injection can help ameliorate this limitation, by acting to contain the API within the target tissue. One such example is injection of ethanol-ethyl cellulose mixtures. Due to the insolubility of ethyl cellulose in water, this polymer phase-separates in the aqueous tumor environment, forming a fibrous gel that helps contain ethanol, the current ablating agent (and chemotherapeutic drugs in the future), within the boundaries of the tumor. Our collaborators have shown that this strategy can be an effective low-cost treatment strategy for superficial solid tumors, with cervical cancer and cervical dysplasia, and liver cancer, being promising targets. Here we present a mathematical model that enables characterization of the injection process. Our model uses Cahn Hilliard theory to model the phase separation of a precipitating or gelling agent during injection into poroelastic tissue. This theory is linked to the soft mechanics of tissue deformation during the injection, and to mass transport theory for the API. The model predicts key elements of the injection process, including the pressure field, the soft tissue displacement field, the phase constitution of the precipitating or gelling agent in the tissue, and the concentration distribution of the API in the tissue. The model enables us to explore relationships between these elements and fundamental injection and tissue parameters. This can inform design of optimized injection protocols. Select model predictions include that larger injection volumes do not significantly affect cavity volumes but do lead to faster transport of the API to target tumor tissue. However, although higher flow rates lead to larger cavities – in the absence of tissue fracture, and when injected volume is held constant – they also lead to slower delivery of the API into the target tumor tissue. This is due to the shorter injection times. Importantly, concentration distributions of the API are not sensitive to the speeds of precipitation of the precipitating agents or to diffusion coefficients of the API in the dense (gelled) phase of the injectate material. The model presented here enables first-pass exploration of injection parameter space for select tissue types (properties). This can aid in optimization of localized therapeutic injections in a range of applications.