Abstract
In the modeling of the pulse wave in the systemic arterial tree, it is necessary to truncate small arterial crowns representing the networks of small arteries and arterioles. Appropriate boundary conditions at the truncation points are required to represent wave reflection effects of the truncated arterial crowns. In this work, we provide a systematic method to extract parameters of the three-element Windkessel model from the impedance of a truncated arterial tree or from experimental measurements of the blood pressure and flow rate at the inlet of the truncated arterial crown. In addition, we propose an improved three-element Windkessel model with a complex capacitance to accurately capture the fundamental-frequency time lag of the reflection wave with respect to the incident wave. Through our numerical simulations of blood flow in a single artery and in a large arterial tree, together with the analysis of the modeling error of the pulse wave in large arteries, we show that both a small truncation radius and the complex capacitance in the improved Windkessel model play an important role in reducing the modeling error, defined as the difference in dynamics induced by the structured tree model and the Windkessel models.
Highlights
In traditional Chinese and Greek medicine, the temporal profile of the blood pressure is believed to be an important indicator of the state of human body [1, 2]
To investigate the validity of the Windkessel model (WK) and complex Windkessel model (CWK) boundary conditions as approximations of truncated arterial crowns, we examine the modeling error in the blood pressure and flow rate in large arteries
For the pulsatile flow input and the pulsatile pressure input, the CWK model approximates the structured tree model (ST) model significantly better than the WK model mainly because that the CWK model can accurately capture the fundamental-frequency time lag between the blood pressure and flow rate
Summary
In traditional Chinese and Greek medicine, the temporal profile of the blood pressure is believed to be an important indicator of the state of human body [1, 2]. Information carried by the pulse wave, in particular, the amplitude and the rhythm, has been used in diagnosis of different cardiovascular diseases such as hypertension, atherosclerosis, and stenosis [3,4,5,6]. Physiological experiments and mathematical modeling have been carried out in the study of physiological and mechanic properties related to the blood flow [7,8,9]. One-dimensional models predicting the blood pressure and flow rate in large arteries have been used to predict pulse wave propagation [10,11,12,13,14,15,16,17]. To reduce the complexity in the simulation of the blood flow, it is necessary to truncate the small arterial crowns, PLOS ONE | DOI:10.1371/journal.pone.0128597. To reduce the complexity in the simulation of the blood flow, it is necessary to truncate the small arterial crowns, PLOS ONE | DOI:10.1371/journal.pone.0128597 May 22, 2015
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