It is well known that stress is an unavoidable and potentially harmful fact of life. Indeed mental stress is becoming recognised as a predominant factor behind many illnesses and deaths in industrialised nations. However it is also true that stress hormones, which mediate our physical response to stress, are essential to allow us to meet physical challenges. In times of physical stress they stimulate the heart, increase respiration, shunt blood from internal organs and skin to skeletal muscle, decrease pain, and have a host of other actions that contribute to our ability to engage in sustained physical activity. It is apparent that a better understanding of how the body copes with stress may lead to an improved means of controlling its effects, both in the medical context, such as during infections and operations, and in psychological and social situations. Corticotropin releasing hormone (CRR) is one of the major regulatory hormones linked with the neuroendocrine response to stress. Secreted from CRR-neurons in the hypothalamus, CRR travels to the anterior pituitary, stimulating the secretion of adrenocorticotropic hormone (ACTH) from the corticotroph cell population. Secreted ACTH then initiates the release of adrenal glucocorticoids, which help the body reduce the metabolic demands of stress. Pituitary corticotroph cells generate repetitive action potentials and associated Ca2+ transients in response to CRH. There is indirect evidence suggesting that CRH modulates the voltage sensitivity of the L-type Ca2+ channels embedded in the plasma membrane. A Hodgkin-Huxley type model of this process is constructed which provides insight into the action potential firing frequency, membrane excitability, and bursting activity. Information transfer in a number of endocrine systems occurs through rapid modulation of hormone levels in concentration pulses. The temporal architecture of the endocrine glandular signaling process is believed to convey important biochemical information to the target tissue, and also represents a signature of the responsive endocrine cells. Therefore to understand the endocrine glandular physiology, the time domain structure of hormone release is required. The perifusion apparatus has been used to investigate the hormone stimulated release of hormones. In this system, a liquid medium flowing at a constant rate flows through a pipe over cells, releasing a substance in response to a stimulus in the flowing medium. The temporal concentration profile of this released substance is then measured at some downstream location. However the major drawback of the perifusion system derives from dispersion, molecular diffusion, and mixing of the hormones in the tubing, generating a distortion in the experimentally observed hormone concentration profile. A comprehensive model of the shear dispersion, mixing, and diffusion associated with the mass transport of a material concentration down a pipe is constructed. Computationally efficient mathematical strategies to the concentration deconvolution problem are constructed, allowing an improved interpretation of the underlying secretory events.