During this past grant year, we have begun to address several experimental design issues involving drug interaction studies of anti-infective drugs that demonstrate synergy in vitro. The in vivo experiment design problem involves the design of dosing regimens for the two agents that will allow for a reliable estimate of the degree of synergy of the two drugs. We have begun to explore a design criterion based on maximizing the average deviation of the efect from that which would be produced under the assumption of additivity. Implementation of such experimental protocals designed to quantify in vivo synergy requires dose regimen design approaches for controlling uncertain systems. Toward this end our work on stochastic control for dose regimen design has continued with its focus on the development of an open-loop feedback framework based on a population model for the kinetics of the two test drugs. The class of control objectives considered includes target intervals (e.g., maximize the probability that the drug's response at a selected time falls within a specified range) and target regions (e.g., drug response at several times is within a region) control objectives. We have applied some of the approaches and techniques we developed for the stochastic control of purely kinetic systems, together with the sampling-based density approximation techniques, to the problem of dose regimen design for quantifying drug synergy.
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