Pneumotachograph Calibration: Influence of Regularization Methods on Parameter Estimation and the Use of Alternative Calibration Models

New ventilator designs in response to the pandemic would benefit from flow and volume measurements. This work compares approaches to calibrate a pneumotachograph (PTC) with either a polynomial or a non-polynomial mapping function. Bidirectional 3-L manual strokes with a syringe provided fixed-volume digitized segments of signal spanning the range of flow measurement of a 4-orifice PTC. Voltage-to-flow calibration functions, either polynomial or based on an additive square root term, were optimized in the sense of least squared errors between estimated and known volume per stroke, for each direction, inspiratory and expiratory. Calibrations with a regularizing penalization in the objective function, aiming at removing local extrema (maxima/minima) of the calibration curves within the usage range, were compared to the non-regularized versions. Regularized polynomial (3rd to 5th degrees) yielded relative errors on volume from 3.56 to 7.17%, whereas for standard (non-regularized) models the errors ranged from 0.81 to 1.68%; errors with square-root-based curves were an order of magnitude smaller. Although regularization worsened error performance, on the other hand it avoided implausible curve shapes. Robustness, convergence properties, computational and practical matters and requirements for field operation are issues to be probed further.