In recent years, four square-wave modes of pressure-preset mechanical ventilation (PPV) - pressure control, pressure support, inverse ratio, and airway pressure release ventilation - have been introduced to clinical practice. Conceptually, they share important features. Yet, because there remains widespread uncertainty regarding their ventilatory characteristics, efficacy, and appropriate use, the potential range of application is only now being investigated. To construct a unifying mathematical model of PPV, we developed a system of equations for prediction of the major 'outcome' variables of PPV - tidal volume, minute ventilation, auto-positive end-expiratory pressure, mean alveolar pressure, and mechanical work - from the primary clinical 'inputs' from patient (resistance, compliance) and clinician (applied pressure, frequency, inspiratory time fraction). Our analysis revealed distinct bounding limits for the outcome variables of ventilation and pressure and important implications for their clinical determinants. Although simplifying assumptions were required to enable construction of this mathematical analogue of respiratory system behavior, this model provides a firm conceptual framework for understanding the physiological interactions between PPV and the patients they are intended to help.