Aims: In this study we aim to show Proportional-Integral-Derivative (PID) closed loop control implemented in phase space for baseline wandering removal. PID process variable represents continuous set of center points for phase space portraits targeted to shift the fixed point and shifts drive with PID algorithm.
Methods: Optical mappings were performed on isolated rabbit hearts stained with Di-4-ANBDQPQ Vm. Time embedded method was used for phase space transformation, while time delay for embedding was chosen equal to the average action potential rise time across mapped cardiac surface. Centers of phase space portraits were calculated as intersect of lines corresponding to maximal horizontal and vertical ranges for a segment of time domain signal equal to one cycle time. PID parameters are tuned by widely accepted algorithm: first increase P gain until oscillations are observed, increase D gain until oscillations go away, and at last increase I gain to eliminate steady state error. Qualitative effectiveness of the method was compared in time-domain with results obtained with Keiser Window and Equiripple filters.
Results: With the cut-off frequency set at ½ of the pacing cycle length typical SNR ratio for PID method was on average 90% as effective as Keiser and Equiripple filters. PID method exhibited equivalent group delay equal to twice the pacing cycle period, while digital filters group delay required to achieve comparable SNR ratios were three to four times longer than the pacing cycle period. This illustrates one advantage of the PID filtering method.
Conclusions. PID method is a viable tool of baseline wandering removal in phase space. While PID algorithm optimization may seem as a complex task, its advantages are in shorter equivalent filter group delay, and elimination of the optimal cut-off frequency as required for digital filters implementation.