A mathematical model describing the dynamic interaction between the left and the right ventricle over the complete cardiac cycle is presented. The pericardium-bound left and right ventricles are represented as two coupled chambers consisting of the left and right free walls and the interventricular septum. Time-varying pressure-volume relationships characterize the component compliances, and the interaction of these components produces the globally observed ventricular pump properties (total chamber pressure and volume). The model 1) permits the simulation of passive (diastolic) and active (systolic) ventricular interaction, 2) provides temporal profiles of hemodynamic variables (e.g., ventricular pressures, volumes, and flow) that agree well with reported observations, and 3) can be used to examine the effect of the pericardium on ventricular interaction and ventricular mechanics. It can be reduced to equivalency with models previously reported by invoking simplifying assumptions. Furthermore, model-generated "dynamic interaction gains" are employed to quantify the mode and degree of ventricular interaction. The model also yields qualitative predictions of septal and free wall displacements similar to those detected experimentally via M-mode echocardiography. Such analogies may be extended easily to the study of pathophysiological states via appropriate modifications to 1) the pressure-volume characteristics of the component walls (and/or pericardium) and/or 2) the specific time course of activation of the ventricular free wall or the septum. A limited number of examples are included to demonstrate the utility of the model, which may be used as an adjunct to new experimental investigations into ventricular interaction.

A model integrating airway/lung mechanics, pulmonary blood flow, and gas exchange for a normal human subject executing the forced vital capacity (FVC) maneuver is presented. It requires as input the intrapleural pressure measured during the maneuver. Selected model-generated output variables are compared against measured data (flow at the mouth, change in lung volume, and expired O2 and CO2concentrations at the mouth). A nonlinear parameter-estimation algorithm is employed to vary selected sensitive model parameters to obtain reasonable least squares fits to the data. This study indicates that 1) all three components of the respiratory model are necessary to characterize the FVC maneuver; 2) changes in pulmonary blood flow rate are associated with changes in alveolar and intrapleural pressures and affect gas exchange and the time course of expired gas concentrations; and 3) a collapsible midairway segment must be included to match airflow during a forced expiration. Model simulations suggest that the resistances to airflow offered by the collapsible segment and the small airways are significant throughout forced expiration; their combined effect is needed to adequately match the inspiratory and expiratory flow-volume loops. Despite the limitations of this lumped single-compartment model, a remarkable agreement with airflow and expired gas concentration measurements is obtained for normal subjects. Furthermore, the model provides insight into the important dynamic interactions between ventilation and perfusion during the FVC maneuver.

Despite the existence of respiratory mechanics models in the literature, rarely one finds analytical expressions that predict the work of breathing (WOB) associated with natural breathing maneuvers in non-ventilated subjects. In the present study, we develop relations that explicitly identify WOB, based on a proposed nonlinear model of respiratory mechanics. The model partitions airways resistance into three components (upper, middle and small), includes a collapsible airways segment, a viscoelastic element describing lung tissue dynamics and a static chest wall compliance. The individual contribution of these respiratory components on WOB is identified and analyzed. For instance, according to model predictions, during the forced vital capacity (FVC) maneuver, most of the work is expended against dissipative forces, mainly during expiration. In addition, expiratory dissipative work during FVC is almost equally partitioned among the upper airways and the collapsible airways resistances. The former expends work at the beginning of expiration, the latter at the end of expiration. The contribution of the peripheral airways is small. Our predictions are validated against laboratory data collected from volunteer subjects and using the esophageal catheter balloon technique.