The transport and control of physiological fluids and metabolites is critical to human health, yet remain difficult to measure and subsequently quantify. Computational modeling provides a method for simulating dynamics of physiological transport to aid in understanding the bases of both health and disease. This talk will focus on two studies that use systems of ordinary differential equations to model the responses to stimuli in the cardiovascular and respiratory systems. The first study combines a system-level cardiovascular model and nonlinear least squares parameter estimation with data collected during a CO­2 rebreathing challenge to predict changes in blood flow and resistance in vessels supplying the brain. In the second study, a model of the dynamics of quiet non-ventilated breathing in premature infants is used to demonstrate inefficient inhalation stemming from a floppy (highly compliant) chest wall, which has been seen to lead to lung volume loss and chronic lung disease.