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Research Papers

# Blind Identification of Two-Channel IIR Systems With Application to Central Cardiovascular Monitoring

[+] Author and Article Information
Jin-Oh Hahn

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139jinoh.hahn@alum.mit.edu

Andrew T. Reisner

Department of Emergency Medicine, Massachusetts General Hospital, Boston, MA 02114areisner@partners.org

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139asada@mit.edu

The decomposability of $P2(z)$ into $D¯1(z)$ and $N¯2(z)$ can be examined exactly in the same way by using $x1(n)≜P1(z)y¯1(n)$ and $u2(n)≜N¯2(z)y¯2(n)$.

This is a trivial condition in the sense that by solving the blind system ID problem we have already assumed that the two-channel IIR dynamics does not have any common poles or zeros.

Note that $b¯n1(1)=bm1(1)$ from Eq. 24 and $deg[N1(z,b1)] if $bm1(1)=0$.

It is easy to show that $p$ identified from Eq. 29 and $q$ identified from Eq. 33 are equivalent up to scale if the regressor signal $φ(n)$ is PE (11). Therefore, the PE condition for the original blind system ID problem (29a) reduces to the PE condition for the least-squares problem 33, which is given by Eq. 34.

The PTT parameters can be approximately determined by measuring the end diastolic or foot-to-foot interval between the aortic BP or BF signal and the peripheral BP signals.

Since the true frequency responses are unknown, their nonparametric transfer function estimates (TFEs) directly obtained from the cross- and input power spectra, $GiTFE(jω)≜σi(jω)/σa(jω)$ for $i=1,2$, were used to represent the true frequency responses, where $σa(jω)$ is the power spectrum of $u(n)$ and $σi(jω)$ is the cross power spectrum of $u(n)$ and $yi(n)$, respectively.

The nominal CV dynamics was obtained by averaging the 20 upper-limb frequency responses, which were identified using the aortic and the radial BP signals for the first 20 segments of the experimental data (which correspond to nominal physiologic states, i.e., $t<300 s$ in Fig. 1).

Since the exact values of $Li$, $i=1,2$ are not available, this paper used $L1=L2=1$ for normalization purposes.

Although this notion of $Δn$ is not strictly true due to the complex effects of the wave reflections on the BP signal morphologies, the rising limb of the BP signal retains its identity reasonably well in that the early part of the BP wave is in general little affected by the wave reflections (1).

J. Dyn. Sys., Meas., Control 131(5), 051009 (Aug 18, 2009) (15 pages) doi:10.1115/1.3155011 History: Received May 02, 2008; Revised April 29, 2009; Published August 18, 2009

## Abstract

This paper presents a new approach to blind identification of a class of two-channel infinite impulse response (IIR) systems with applicability to clinical cardiovascular monitoring. Specifically, this paper deals with a class of two-channel IIR systems describing wave propagation dynamics. For this class of systems, this paper first derives a blind identifiability condition and develops a blind identification algorithm, which is able to determine both the numerator and denominator polynomials of the channel dynamics uniquely. This paper also develops a new input signal deconvolution algorithm that can reconstruct the input signal from the identified two-channel dynamics and the associated two-channel measurements. These methods are applied to identify the pressure wave propagation dynamics in the cardiovascular system and reconstruct the aortic blood pressure and flow signals from blood pressure measurements taken at two distinct extremity locations. Persistent excitation, model identifiability, and asymptotic variance are analyzed to quantify the method’s validity, accuracy, and reliability without employing direct measurement of the aortic blood pressure and flow signals. The experimental results based on 83 data segments obtained from a swine subject illustrate how the cardiovascular dynamics can be identified accurately and reliably, and the aortic blood pressure and flow signals can be stably reconstructed from two distinct peripheral blood pressure signals under diverse physiologic conditions.

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## Figures

Figure 1

A two-channel IIR system

Figure 2

An illustrative wave propagation channel

Figure 3

Linear regression of x2(n) for FIR and IIR dynamics

Figure 4

Separation structure of lower dimensional decomposition problems

Figure 5

Matrix equation for determination of bm−w¯−1,…,b0, ak−w¯−1,…,ak−wk−N, and aY−1

Figure 6

Matrix equation for the design of deconvolution filter

Figure 7

Matrix equation for determination of ak−wk−1,…,ak−(w¯−wk)

Figure 8

Asymmetric T-tube model of a two-channel CV system

Figure 9

Block diagram of CV system from aortic BP to peripheral BP

Figure 10

Time history of key CV variables in the experimental swine data

Figure 11

Identified frequency responses and recovered aortic BP and BF signals at t=710 s. The dashed and solid lines are true and identified/recovered quantities, respectively.

Figure 12

Frequency responses of 83 upper-limb and lower-limb CV dynamics

Figure 13

True versus identified aortic-to-upper-limb pulse transit times

Figure 14

The distinct influences of PTT parameters and polynomial coefficients on the location and the magnitude of the first peak of |Gi(jω)|, i=1,2

Figure 15

Asymptotic STD of G1(jω) and G2(jω) at t=710 s with N=1000, using uncertain and accurate PTT parameters

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