This thesis integrates formal language theory with mathematical modeling methods to derive new analytical approaches that are computationally efficient and that facilitate exploration of physiological hypotheses. Two specific circadian and sleep applications are presented that address both direct and inverse modeling approaches: (1) the scheduling of bright light stimuli to affect circadian rhythms and result in optimal predicted performance, and (2) the development of analytic techniques that are applied to plasma cortisol data.

Application 1—Schedule design (direct problem). Formal language methods (lambda calculus, regular languages) and existing mathematical models of circadian rhythms are integrated to facilitate the derivation of an optimal light scheduling algorithm called the Circadian Adjustment Method (CAM). The CAM has been used to generate testable hypotheses regarding circadian phase resetting characteristics and the maintenance of human performance during shifting sleep/wake schedules. The CAM algorithm lighting recommendations are provably optimal light-schedules and result in optimal predicted performance.

Application 2—Cortisol analysis and modeling (indirect problem). A context free language (CFL) representation of hormone pulsatility is defined and used for the development of Hierarchically AdaPtive (HAP) Hormone Analysis. HAP is a data-driven analysis technique that computes traditional hormone analysis parameters (secretion rate, clearance rate, and interpulse interval) from individual time series. HAP is used to perform multi-scale analysis and to generate both a text based description and graph based representation of a cortisol time series. HAP is integrated with statistical and system identification techniques to identify and quantify individual differences in nonlinear changes in cortisol pulsatility.

The thesis proposes new formalisms to enable the integration of experimental specification and data, to formally define physiologically relevant solution space, and to develop efficient algorithms that enable interactive analysis. The scheduling problem aims to provide interventions that ameliorate performance decrements following jet-lag and shift-work schedules. The hormone analysis and modeling problem formally develops a prescriptive, data driven, and extensible data analysis and modeling framework within a non-specific-hormone modeling approach. These new approaches will facilitate the integration of sleep and circadian principles to the scientific community by providing robust analysis techniques that can be applied to scheduling, hormone, and other research problems.