Modern and traditional approaches combined into an effective gray-box mathematical model of full-blood acid-base

Mathematical modelling of bicarbonate supplementation and acid-base chemistry in kidney failure patients on hemodialysis

Acid-base regulation by the kidneys is largely missing in end-stage renal disease patients undergoing hemodialysis (HD). Bicarbonate is added to the dialysis fluid during HD to replenish the buffers in the body and neutralize interdialytic acid accumulation. Predicting HD outcomes with mathematical models can help select the optimal patient-specific dialysate composition, but the kinetics of bicarbonate are difficult to quantify, because of the many factors involved in the regulation of the bicarbonate buffer in bodily fluids. We implemented a mathematical model of dissolved CO2 and bicarbonate transport that describes the changes in acid-base equilibrium induced by HD to assess the kinetics of bicarbonate, dissolved CO2, and other buffers not only in plasma but also in erythrocytes, interstitial fluid, and tissue cells; the model also includes respiratory control over the partial pressures of CO2 and oxygen. Clinical data were used to fit the model and identify missing parameters used in theoretical simulations. Our results demonstrate the feasibility of the model in describing the changes to acid-base homeostasis typical of HD, and highlight the importance of respiratory regulation during HD.

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.

Modeling acid-base balance during continuous kidney replacement therapy

Clinical studies have suggested that use of bicarbonate-containing substitution and dialysis fluids during continuous kidney replacement therapy may result in excessive increases in the carbon dioxide concentration of blood; however, the technical parameters governing such changes are unclear. The current work used a mathematical model of acid-base chemistry of blood to predict its composition within and exiting the extracorporeal circuit during continuous veno-venous hemofiltration (CVVH) and continuous veno-venous hemodiafiltration (CVVHDF). Model predictions showed that a total substitution fluid infusion rate of 2 L/h (33% predilution) with a bicarbonate concentration of 32 mEq/L during CVVH at a blood flow rate of 200 mL/min resulted in only modest increases in plasma bicarbonate concentration by 2.0 mEq/L and partial pressure of dissolved carbon dioxide by 4.4 mmHg in blood exiting the extracorporeal circuit. The relative increase in bicarbonate concentration (9.7%) was similar to that in partial pressure of dissolved carbon dioxide (8.2%), resulting in no significant change in plasma pH in the blood exiting the CVVH circuit. The changes in plasma acid-base levels were larger with a higher infusion rate of substitution fluid but smaller with a higher blood flow rate or use of substitution fluid with a lower bicarbonate concentration (22 mEq/L). Under comparable flow conditions and substitution fluid composition, model predicted changes in acid-base levels during CVVHDF were similar, but smaller, than those during CVVH. The described mathematical model can predict the effect of operating conditions on acid-base balance within and exiting the extracorporeal circuit during continuous kidney replacement therapy.