Prony Analysis of Left Ventricle Pressure and Volume

Direct measurement of cardiac pressure-volume (PV) relationships is the gold standard for assessment of ventricular hemodynamics, but few innovations have been made to "multi-beat" PV analysis beyond traditional signal processing. The Prony method solves the signal recovery problem with a series of dampened exponentials or sinusoids. It achieves this by extracting the amplitude, frequency, dampening, and phase of each component. Since its inception, application of the Prony method to biologic and medical signal has demonstrated a relative degree of success, as a series of dampened complex sinusoids easily generalizes to multifaceted physiological processes. In cardiovascular physiology, the Prony analysis has been used to determine fatal arrythmia from electrocardiogram signals. However, application of the Prony method to simple left ventricular function based on pressure and volume analysis is absent. We have developed a new pipeline for analysis of pressure volume signals recorded from the left ventricle. We propose fitting pressure-volume data from cardiac catheterization to the Prony method for pole extraction and quantification of the transfer function. We implemented the Prony algorithm using open-source Python packages and analyzed the pressure and volume signals before and after severe hemorrhagic shock, and after resuscitation with stored blood. Each animal (n = 6 per group) underwent a 50% hemorrhage to induce hypovolemic shock, which was maintained for 30 min, and resuscitated with 3-week-old stored RBCs until 90% baseline blood pressure was achieved. Pressure-volume catheterization data used for Prony analysis were 1 s in length, sampled at 1000 Hz, and acquired at the time of hypovolemic shock, 15 and 30 min after induction of hypovolemic shock, and 10, 30, and 60 min after volume resuscitation. We next assessed the complex poles from both pressure and volume waveforms. To quantify deviation from the unit circle, which represents deviation from a Fourier series, we counted the number of poles at least 0.2 radial units away from it. We found a significant decrease in the number of poles after shock (p = 0.0072 vs. baseline) and after resuscitation (p = 0.0091 vs. baseline). No differences were observed in this metric pre and post volume resuscitation (p = 0.2956). We next found a composite transfer function using the Prony fits between the pressure and volume waveforms and found differences in both the magnitude and phase Bode plots at baseline, during shock, and after resuscitation. In summary, our implementation of the Prony analysis shows meaningful physiologic differences after shock and resuscitation and allows for future applications to broader physiological and pathophysiological conditions.