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This paper, the second of two parts, presents an analytical model of motion artifacts (MA) in measured pulse signals by a tactile sensor, which contains a deformable microstructure sitting on a substrate. While the tissue-contact-sensor (TCS) stack and the sensor are both treated as a 1DOF (degree-of-freedom) system, tissue–sensor contact joins their mass together to form a 1DOF system with springs and dampers on both sides. MA on the sensor substrate causes baseline drift and time-varying system parameters (TVSP) of the TCS stack simultaneously. An analytical model is developed to mathematically relate baseline drift and TVSP to a measured pulse signal. The numerical calculation is conducted in MATLAB. Baseline drift in a measured pulse signal is much lower than the actual MA in its measurement. As compared to baseline drift, TVSP generates relatively abrupt, small distortion (e.g., 0.2% variation in heart rate and <5% change in pulse amplitude), but it rides on each harmonic of the true pulse signal. Sensor design alters both the deviation of the amplitude and waveform of a measured pulse signal from the true pulse signal and the influence of MA on it.

Motion artifacts (MA) cause great variability in a measured arterial pulse signal, and treatment of MA solely as a baseline drift (BD) fails to eliminate its effect on the measured signal. This paper presents a study on the effect of MA at rest (<0.7 Hz) on measured arterial pulse signals using a microfluidic-based tactile sensor. By taking full account of the dynamic behavior of the transmission path from the true pulse signal in an artery to a measured pulse signal at the sensor, the tissue-contact-sensor (TCS) stack, an analytical model of MA in a measured pulse signal is developed. In this model, the TCS stack is treated as a 1DOF system for its dynamic behavior; MA is quantified as the displacement (i.e., BD) and time-varying system parameters (TVSP) of the TCS stack. The mathematical expression of MA in a measured pulse signal reveals that while BD remains as low-frequency additive noise, TVSP causes time-varying harmonics in a measured pulse signal. Further time-frequency analysis (TFA) of measured pulse signals validates the existence of TVSP and, for the first time, reveals its effect on a measured pulse signal: time-varying amplitude in each harmonic and non-flat harmonic-MA-coupled baseline.