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A lumped two-compartment mathematical model of respiratory mechanics incorporating gas exchange and pulmonary circulation is utilized to analyze the effects of square, descending and ascending inspiratory flow waveforms during mechanical ventilation. The effects on alveolar volume variation, alveolar pressure, airway pressure, gas exchange rate, and expired gas species concentration are evaluated. Advantages in ventilation employing a certain inspiratory flow profile are offset by corresponding reduction in perfusion rates, leading to marginal effects on net gas exchange rates. The descending profile provides better CO2 exchange, whereas the ascending profile is more advantageous for O2 exchange. Regional disparities in airway/lung properties create maldistribution of ventilation and a concomitant inequality in regional alveolar gas composition and gas exchange rates. When minute ventilation is maintained constant, for identical time constant disparities, inequalities in compliance yield pronounced effects on net gas exchange rates at low frequencies, whereas the adverse effects of inequalities in resistance are more pronounced at higher frequencies. Reduction in expiratory air flow (via increased airway resistance) reduces the magnitude of upstroke slope of capnogram and oxigram time courses without significantly affecting end-tidal expired gas compositions, whereas alterations in mechanical factors that result in increased gas exchanges rates yield increases in CO2 and decreases in O2 end-tidal composition values. The model provides a template for assessing the dynamics of cardiopulmonary interactions during mechanical ventilation by combining concurrent descriptions of ventilation, capillary perfusion, and gas exchange.

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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 CO2 concentrations 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.

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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.

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Experimental and clinical use of the intravascular oxygenator (IVOX), an intravenacaval gas exchange device, in acute respiratory failure yielded a CO2 transfer of 40-70 ml/min (approximately 30% of adult CO2 production) at normocapnia. Although significant, this rate of CO2 removal is not clinically useful. To maximize CO2 transfer, given the same gas exchange properties and structure design of the IVOX, the authors analyzed the effects of permissive hypercapnia (stepwise increase in arterial blood pCO2 up to 100 mmHg) and active blood mixing (with an intraaortic balloon pump) on different sizes of IVOX (sizes 7, 8, and 9 mm, surface area 0.21, 0.32, and 0.41 m2, respectively) using a previously established ex vivo circuit to model the human vena cava. The CO2 net transfer coefficient (KCO2) was averaged for all sizes and applied to extrapolate the surface area requirements under different pCO2 and with active blood mixing. Results showed that KCO2 increased in a linear relationship with blood flow. Increases in blood flow and blood pCO2 further increase CO2 removal and decrease surface area requirements. For blood flow at 4.0 L/min, the membrane surface area required for 150 ml/min CO2 removal at blood pCO2 of 40 mmHg is 1.76 m2, but can be decreased to 0.47 m2 at blood pCO2 of 80 mmHg, and further to 0.42 m2 with additional active blood mixing. A 0.42 m2 surface area is associated with an O2 transfer of 80 ml/min without and 107 ml/min with active blood mixing. It is concluded that CO2 removal by IVOX alone is limited by insufficient surface area and the resistance in the blood-surface boundary layer. The combination of permissive hypercapnia, adequate blood flow, and active blood mixing can substantially improve CO2 removal and can therefore achieve clinically significant CO2 removal by intravenacaval gas exchange devices during severe respiratory failure.

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The intravenacaval oxygenator and carbon dioxide removal device (IVOX) conceived by Mortensen at CardioPulmonics is a diffusion-limited device capable of removing 30% of CO2 production of an adult at normocapnia with minimal reduction in ventilator requirements. Through mathematical modeling, an ex vivo venovenous bypass circuit to model the vena cava and animal models of severe smoke inhalation injury, the practice of permissive hypercapnia has been established to enhance CO2 removal by IVOX. By allowing the blood PCO2 to rise gradually, the CO2 excretion by IVOX can be linearly increased in a 1:1 relationship. Experimental and clinical studies have shown that CO2 removal by IVOX increased from 30-40 ml/min at normal blood PCO2 to 80-90 ml/min at PCO2 of 90 mm Hg. In addition, IVOX with permissive hypercapnia allowed a significant reduction in minute ventilation and peak airway pressure. Design changes could also improve the performance of IVOX. Increased surface area and mixing with more fibers and crimping in new prototypes of IVOX significantly increased CO2 removal and oxygen transfer. Active mixing in the blood to decrease the boundary layer resistance can further enhance gas exchange of IVOX. In conclusion, gas exchange by the current design of IVOX is limited, and improvements in design are needed for it to become a more clinically applicable device. Permissive hypercapnia can significantly enhance CO2 removal by IVOX as well as significantly reduce ventilator requirements.

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A mathematical model of an intravascular hollow-fiber gas-exchange device, called IVOX, has been developed using a Krogh cylinder-like approach with a repeating unit structure comprised of a single fiber with gas flowing through its lumen surrounded by a coaxial cylinder of blood flowing in the opposite direction. Species mass balances on O2 and CO2 result in a nonlinear coupled set of convective-diffusion parabolic partial differential equations that are solved numerically using an alternating-direction implicit finite-difference method. Computed results indicated the presence of a large resistance to gas transport on the external (blood) side of the hollow-fiber exchanger. Increasing gas flow through the device favored CO2 removal from but not O2 addition to blood. Increasing blood flow over the device favored both CO2 removal as well as O2 addition. The rate of CO2 removal increased linearly with the transmural PCO2 gradient imposed across the device. The effect of fiber crimping on blood phase mass transfer resistance was evaluated indirectly by varying species blood diffusivity. Computed results indicated that CO2 excretion by IVOX can be significantly enhanced with improved bulk mixing of vena caval blood around the IVOX fibers.

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Initial studies have shown that the intravascular oxygenator and carbon dioxide removal device (IVOX, Cardiopulmonics, Inc., Salt Lake City, UT) removes approximately 30% of VCO2. After noting increased CO2 removal with increased venous CO2, we developed a conceptual analytical model based on data obtained from patients and laboratory experiments. Increasing the CO2 gradient across the hollow fiber membranes of IVOX increases the operating efficiency of the device. Using the patient management technique of permissive hypercapnia (limiting tidal volumes, respiratory rates, and airway pressures) serves to increase the CO2 gradient across the membrane. The conceptual analytical model predicts that a PaCO2 of 75-80 mm Hg is required to obtain a CO2 gradient that results in IVOX CO2 removal of approximately 90-100 ml CO2/min. This technique may allow a broader application of both permissive hypercapnia and IVOX in acute respiratory failure.

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A framework using material balances in metabolic pathways to study cellular metabolism is examined and the results are discussed. Rate measurements on extracellular compounds alone were found to be not always sufficient to validate proposed unique intracellular mechanisms. The conditions to delineate among candidate mechanisms based solely on extracellular measurements are established. The number of half reactions comprising the reaction network is found to be an important parameter.