Extracorporeal carbon dioxide removal requirements for ultraprotective mechanical ventilation: Mathematical model predictions

The whole-cell kinetic metabolic model of the pH regulation mechanisms in human erythrocytes

Mathematical modeling in recent years helped to obtain answers to questions that were difficult or even impossible to answer experimentally, to predict several unexpected connections in cell metabolism and to understand and importance of certain biochemical reactions. Due to the complexity and variety of processes underlying the mechanisms of intracellular pH (pHi) regulation, mathematical modeling and metabolome analysis are powerful tools for their analysis. In this regard, a mathematical metabolic model for human erythrocytes was created, which combines cellular metabolism with acid-base processes and gas exchange. The model consists of the main metabolic pathways, such as glycolysis, the pentose phosphate pathway, some membrane transport systems, and interactions between hemoglobin and metabolites. The Jacobs-Stewart cycle, which is fundamental in gas exchange and pH regulation, was included to these pathways. The model was created in the COPASI environment, consisted of 85 reactions, the rate of which is based on accurate kinetic equations. The time dependences of reaction flows and metabolite concentrations, as an outcome of calculations, allowed us to reproduce the behaviour of the metabolic system after its disturbance in vitro and to establish the recovery mechanisms or approximation to stationary states. The COPASI simulation environment provides model flexibility by reproducing any experimental design by optimizing direct quantitative comparisons between measured and predicted results. Thus, the procedure of parameters optimization (Parameter Estimation) followed by the solution of the model’s differential equations (Time Course procedure) was used to predict the behaviour of all measured and unmeasured variables over time. The initial intracellular concentrations of CO2, HCO3– in human erythrocytes used for incubation in a phosphate buffer medium were calculated. Changes in CO2, HCO3– content over time were shown. It was established that the regulation of pH in erythrocytes placed in a buffer medium takes place with the participation of two types of processes – fast (takes place in 1.3 s) and slow. It is shown that fast processes are aimed at restoring the intracellular balance between CO2 and HCO3–, slow processes are aimed at establishing the balance of H+ between the cell and the extracellular environment. The role of carbonic anhydrase (CA) and hemoglobin in the processes of pH stabilization is shown and analyzed. The physiological role of the metabolon between band 3 protein (AE1), CA, aquaporin and hemoglobin in maintaining pH homeostasis in the conditions of in vitro experiments are discussed.

Targeting arterial partial pressure of carbon dioxide in acute respiratory distress syndrome patients using extracorporeal carbon dioxide removal

BACKGROUND

A retrospective analysis of SUPERNOVA trial data showed that reductions in tidal volume to ultraprotective levels without significant increases in arterial partial pressure of carbon dioxide (PaCO₂ ) for critically ill, mechanically ventilated patients with acute respiratory distress syndrome (ARDS) depends on the rate of extracorporeal carbon dioxide removal (ECCO₂ R).

METHODS

We used a whole-body mathematical model of acid-base balance to quantify the effect of altering carbon dioxide (CO₂ ) removal rates using different ECCO₂ R devices to achieve target PaCO₂ levels in ARDS patients. Specifically, we predicted the effect of using a new, larger surface area PrismaLung+ device instead of the original PrismaLung device on the results from two multicenter clinical studies in critically ill, mechanically ventilated ARDS patients.

RESULTS

After calibrating model parameters to the clinical study data using the PrismaLung device, model predictions determined optimal extracorporeal blood flow rates for the PrismaLung+ and mechanical ventilation frequencies to obtain target PaCO₂ levels of 45 and 50 mm Hg in mild and moderate ARDS patients treated at a tidal volume of 3.98 ml/kg predicted body weight (PW). Comparable model predictions showed that reductions in tidal volumes below 6 ml/kg PBW may be difficult for acidotic highly severe ARDS patients with acute kidney injury and high CO₂ production rates using a PrismaLung+ device in-series with a continuous venovenous hemofiltration device.

CONCLUSIONS

The described model provides guidance on achieving target PaCO₂ levels in mechanically ventilated ARDS patients using protective and ultraprotective tidal volumes when increasing CO₂ removal rates from ECCO₂ R devices.

Modeling acid-base balance for in-series extracorporeal carbon dioxide removal and continuous venovenous hemofiltration devices

Patients with acute respiratory distress syndrome and acute kidney injury (AKI) treated by kidney replacement therapy may also require treatment with extracorporeal carbon dioxide removal (ECCO₂ R) devices to permit protective or ultraprotective mechanical ventilation. We developed a mathematical model of acid-base balance during extracorporeal therapy using ECCO₂ R and continuous venovenous hemofiltration (CVVH) devices applied in series for the treatment of mechanically ventilated AKI patients. Published data from clinical studies of mechanically ventilated AKI patients treated by CVVH at known infusion rates of substitution fluid without ECCO₂ R were used to adjust the model parameters to fit plasma levels of arterial partial pressure of carbon dioxide (PaCO₂ ), arterial plasma bicarbonate concentration ([HCO₃ ]), and plasma pH (as well as certain other unmeasured physiological variables). The effects of applying ECCO₂ R at an unchanged and a reduced tidal volume on PaCO₂ , [HCO₃ ] and plasma pH were then simulated assuming carbon dioxide removal rates from the ECCO₂ R device measured in the clinical studies. Agreement of such model predictions with clinical data was good whether the ECCO₂ R device was positioned proximal or distal to the CVVH device in the extracorporeal circuit. Although carbon dioxide removal rates from the ECCO₂ R device measured in one previous clinical study were higher when it was placed proximal to the CVVH device, suggesting that such in-series positioning was optimal, the current mathematical model demonstrates that proximal positioning of the ECCO₂ R device also results in lower bicarbonate (and, therefore, total carbon dioxide) removal from the distal CVVH device. Thus, the removal of total carbon dioxide by such extracorporeal circuits is relatively independent of the position of the in-series devices. It is concluded that the described mathematical model has quantitative accuracy; these results suggest that the overall acid-base balance when using ECCO₂ R and CVVH devices in a single extracorporeal circuit will be similar, independent of their in-series position.

Extracorporeal carbon dioxide removal requirements for ultraprotective mechanical ventilation: Mathematical model predictions

Extracorporeal carbon dioxide (CO₂) removal (ECCO₂R) facilitates the use of low tidal volumes during protective or ultraprotective mechanical ventilation when managing patients with acute respiratory distress syndrome (ARDS); however, the rate of ECCO₂R required to avoid hypercapnia remains unclear. We calculated ECCO₂R rate requirements to maintain arterial partial pressure of CO₂ (PaCO₂) at clinically desirable levels in mechanically ventilated ARDS patients using a six‐compartment mathematical model of CO₂ and oxygen (O₂) biochemistry and whole‐body transport with the inclusion of an ECCO₂R device for extracorporeal veno‐venous removal of CO₂. The model assumes steady state conditions. Model compartments were lung capillary blood, arterial blood, venous blood, post‐ECCO₂R venous blood, interstitial fluid and tissue cells, with CO₂ and O₂ distribution within each compartment; biochemistry included equilibrium among bicarbonate and non‐bicarbonate buffers and CO₂ and O₂ binding to hemoglobin to elucidate Bohr and Haldane effects. O₂ consumption and CO₂ production rates were assumed proportional to predicted body weight (PBW) and adjusted to achieve reported arterial partial pressure of O₂ and a PaCO₂ level of 46 mmHg at a tidal volume of 7.6 mL/kg PBW in the absence of an ECCO₂R device based on average data from LUNG SAFE. Model calculations showed that ECCO₂R rates required to achieve mild permissive hypercapnia (PaCO₂ of 46 mmHg) at a ventilation frequency or respiratory rate of 20.8/min during mechanical ventilation increased when tidal volumes decreased from 7.6 to 3 mL/kg PBW. Higher ECCO2R rates were required to achieve normocapnia (PaCO2 of 40 mmHg). Model calculations also showed that required ECCO2R rates were lower when ventilation frequencies were increased from 20.8/min to 26/min. The current mathematical model predicts that ECCO2R rates resulting in clinically desirable PaCO2 levels at tidal volumes of 5‐6 mL/kg PBW can likely be achieved in mechanically ventilated ARDS patients with current technologies; use of ultraprotective tidal volumes (3‐4 mL/kg PBW) may be challenging unless high mechanical ventilation frequencies are used.