Observer-Based Deconvolution of Deterministic Input in Coprime Multichannel Systems With Its Application to Noninvasive Central Blood Pressure Monitoring

Abstract

Estimating central aortic blood pressure (BP) is important for cardiovascular (CV) health and risk prediction purposes. CV system is a multichannel dynamical system that yields multiple BPs at various body sites in response to central aortic BP. This paper concerns the development and analysis of an observer-based approach to deconvolution of unknown input in a class of coprime multichannel systems applicable to noninvasive estimation of central aortic BP. A multichannel system yields multiple outputs in response to a common input. Hence, the relationship between any pair of two outputs constitutes a hypothetical input-output system with unknown input embedded as a state. The central idea underlying our approach is to derive the unknown input by designing an observer for the hypothetical input-output system. In this paper, we developed an unknown input observer (UIO) for input deconvolution in coprime multichannel systems. We provided a universal design algorithm as well as meaningful physical insights and inherent performance limitations associated with the algorithm. The validity and potential of our approach were illustrated using a case study of estimating central aortic BP waveform from two noninvasively acquired peripheral arterial pulse waveforms. The UIO could reduce the root-mean-squared error (RMSE) associated with the central aortic BP by up to 27.5% and 28.8% against conventional inverse filtering (IF) and peripheral arterial pulse scaling techniques.

Fig. 1

A coprime multichannel linear dynamical system in which a common yet unknown input signal $u\left(z\right)$ generates multiple output signals $y_1\left(z\right)\dots y_N\left(z\right)$

Fig. 2

A hypothetical input–output system derived from a coprime multichannel system by designating its one output signal as input to the hypothetical input–output system and its another output signal as output of the same system

Fig. 3

Observer-based deconvolution of central aortic BP waveform from noninvasive peripheral arterial pulse waveform measurements. The PVRs are made at the upper arm and leg sites using the BP cuffs loaded at a subdiastolic pressure level. These diametric PVR signals are applied to a system identification procedure [20] to derive the channel dynamics associated with (i) the propagation of the BP wave from the aorta to the peripheral arteries and (ii) the propagation and distortion of the peripheral BP waves into the PVR signals at the respective peripheral measurement sites. The UIO designed using the estimated channel dynamics estimates central aortic BP from peripheral PVR signals.

Fig. 4

Representative measurements of (a) PVR signals at an arm and a leg and (b) central aortic BP signal

Fig. 5

Multichannel wave propagation dynamics in the arteries represented by (i) a tube-load model to represent the BP wave propagation in the artery, (ii) a viscoelastic model to represent the characteristics of the arterial wall and the tissues, and (iii) a physics-based model of the BP cuff

Fig. 6

Representative examples of true versus estimated central BP waveforms: (a) an example where UIO-PP shows performance marginally superior to inverse filtering and (b) an example where UIO-PP shows performance largely superior to inverse filtering