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Research Papers

# Data-Driven Lossy Tube-Load Modeling of Arterial Tree: In-Human Study

[+] Author and Article Information

Department of Mechanical Engineering,
University of Maryland,
2107B Glenn L. Martin Hall,
College Park, MD 20742

Chang-Sei Kim

Department of Mechanical Engineering,
University of Maryland,
2107B Glenn L. Martin Hall,
College Park, MD 20742
e-mail: cskim75@umd.edu

Nima Fazeli

Department of Mechanical Engineering,
University of Maryland,
2107B Glenn L. Martin Hall,
College Park, MD 20742
e-mail: nfazeli@umd.edu

Barry A. Finegan

Department of Anesthesiology
and Pain Medicine,
University of Alberta,
8120 Clinical Sciences Building,
e-mail: bfinegan@ualberta.ca

M. Sean McMurtry

Department of Medicine (Cardiology),
University of Alberta,
2C2 Walter Mackenzie Centre,
e-mail: mcmurtry@ualberta.edu

Jin-Oh Hahn

Department of Mechanical Engineering,
University of Maryland,
2104C Glenn L. Martin Hall,
College Park, MD 20742
e-mail: jhahn12@umd.edu

By construction, the lossless tube-load model assumes that central aortic mean BP is identical to peripheral mean BP. Thus, the difference in mean BP must be artificially compensated.

For lossless tube-load model, the difference in mean BP was artificially compensated as was done in Eq. (17).

It is noted that the PTT measured as described above is not necessarily the gold-standard value, since it is susceptible to errors due to artifacts and noises in the BP waves. However, PTT so measured is still a reasonably good estimate of the actual PTT, and is thus expected to be correlated well with the PTT parameter $τ*$ in the lossy tube-load model.

1Corresponding author.

Manuscript received March 7, 2014; final manuscript received July 15, 2014; accepted manuscript posted July 28, 2014; published online August 12, 2014. Assoc. Editor: Alison Marsden.

J Biomech Eng 136(10), 101011 (Aug 12, 2014) (7 pages) Paper No: BIO-14-1108; doi: 10.1115/1.4028089 History: Received March 07, 2014; Revised July 15, 2014; Accepted July 28, 2014

## Abstract

In this paper, we present and validate a data-driven method to lossy tube-load modeling of arterial tree in humans. In the proposed method, the lossy tube-load model is fitted to central aortic and peripheral blood pressure (BP) waves in the time domain. For this purpose, we employ a time-domain lossy tube-load model in which the wave propagation constant is formulated to two terms: one responsible for the alteration of wave amplitude and the other for the transport delay. Using the experimental BP data collected from 17 cardiac surgery patients, we showed that the time-domain lossy tube-load model is able to accurately represent the relation between central aortic versus upper-limb and lower-limb BP waves. In addition, the comparison of lossy versus lossless tube-load models revealed that (1) the former outperformed the latter in general with the root-mean-squared errors (RMSE) of 3.1 mm Hg versus 3.5 mm Hg, respectively (p-value < 0.05), and (2) the efficacy of the former over the latter was more clearly observed in case the normalized difference in the mean central aortic versus peripheral BP was large; when the difference was >5% of the underlying mean BP, lossy and lossless models showed the RMSE of 2.7 mm Hg and 3.7 mm Hg, respectively (p-value < 0.05).

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Topics: Stress , Waves , Modeling

## Figures

Fig. 1

Lossy tube-load model of arterial tree. BP waves at the inlet (PI) and the outlet (PO) of the tube consist of the respective forward and backward BP waves (PI = PfI+PbI and PO = PfO+PbO). Both forward and backward BP waves travel with loss and delay, and, thus, PfO(t) = σPfI(t-τ) and PbI(t) = σPbO(t-τ). At the outlet of the tube, forward and backward BP waves are related to each other via the wave reflection constant: PbO(t) = L-1{Γ(s)L[PfO(t)]} where L[·] is the Laplace transformation.

Fig. 2

A representative snapshot of measured peripheral BP versus peripheral BP predicted by the lossy and the lossless tube-load models

Fig. 3

Validity of the lossy tube-load model. (a) PTT measured directly from central aortic and peripheral BP waves versus τ* identified for the tube-load models via Eq. (14). (b) σ measured directly from central aortic and peripheral BP waves versus σ* identified for the lossy tube-load model via Eq. (14). (c) λ3* identified for the tube-load models.

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