Validation of a Person Specific 1-D Model of the Systemic Arterial Tree

Abstract

The aim of this study is to validate a personspecific distributed model of the main systemic arterial tree, coupled to a model of the left ventricle of the heart. This model is built and validated with non-invasive measurements on the same person, leading therefore to a coherent set of physiological data. Although previous studies have been done on 1-D model of arterial trees, demonstrating their aptitude of modeling wave propagation, they were mainly based on generic disparate arterial trees and were not able to provide for both a qualitative and quantitative validation. The 1-D form of the fluid equations is applied over each large arterial segment. The systemic arterial tree geometric dimensions are deduced from angio MR, performed with contrast agent injection. A nonlinear viscoelastic constitutive law for the arterial wall is considered. Arterial wall distensibility is based on literature data and adapted to match the specific subject, using traveling time of the waves by ECG referenced tonometry measurements. The intimal shear stress is modeled using the Witzig-Womersley theory. The arterial tree is coupled to the heart, which is modeled using the time varying elastance model. To validate model predictions, we performed non-invasive measurements of pressure and flow waveforms. Pressure was measured using applanation tonometry and flow rate using transcranial ultrasound and PC-MRI. The model predicts pressure and flow waveforms shape and wave features with high qualitative agreement compared to in-vivo measurements. The quantitative aspect of pressure and flow waveforms is also well reproduced. The results obtained let us conclude that an 1-D model based on specific geometric arterial tree is able to predict qualitative and quantitative pressure and flow waveforms in the main systemic circulation.