Dynamic Model Inversion Techniques for Breath-by-Breath Measurement of Carbon Dioxide from Low Bandwidth Sensors

Respiratory CO
₂
measurement (capnography) is an important diagnosis tool that lacks inexpensive and wearable sensors. This paper develops techniques to enable use of inexpensive but slow CO
₂
sensors for breath-by-breath tracking of CO
₂
concentration. This is achieved by mathematically modeling the dynamic response and using model-inversion techniques to predict input CO
₂
concentration from the slowly varying output. Experiments are designed to identify model-dynamics and extract relevant model-parameters for a solid-state room monitoring CO
₂
sensor. A second-order model that accounts for flow through the sensor's filter and casing is found to be accurate in describing the sensor's slow response. The corresponding model-inversion algorithm is however found to be susceptible to noise sources. Techniques to remove spurious noise, while retaining quality of estimate are developed. The resulting estimate is compared with a standard-of-care respiratory CO
₂
analyzer and shown to effectively track variation in breath-by-breath CO
₂
concentration. This methodology is potentially useful for measuring fast-varying inputs to any slow sensor.