Mathematical model for a point-of-care sensor for measuring carbon dioxide in blood

A point-of-Care (POC) pCO2 device is a small electrochemical sensor for determining the partial pressure of dissolved carbon dioxide in blood samples from patients. A mathematical model is developed to predict the voltage response in a pCO2 sensor when it is subjected to different CO2 concentrations in a calibration fluid and in blood samples or control fluids. The model consists of partial differential equation (PDE) material balances for species in the membrane and electrolyte and an algebraic equation relating surface concentrations to voltage. The model considers diffusion of species due to concentration gradients in vertical and radial directions and also reactions in the electrolyte and at the Au electrode. Influential model parameters are identified using estimability analysis and two parameters are fitted using industrial data. The model provides reliable predictions of the dynamic sensor voltage response. Sensor design parameters are varied to study the influence of the electrolyte concentration and sensor geometry on the voltage response, revealing that the most influential parameters are the amount of water in the electrolyte during the sensor operation and the buffer concentration in the electrolyte formulation.