The aim of this study is to develop and validate a distributed model of the systemic arterial tree, coupled to a heart model and including a detailed description of the cerebral arteries. No model has been developed so far that offers a physiologically relevant coupling to the heart and includes the entire cerebral arterial tree.

The 1D forms of the continuity and momentum equations are applied over tapered arterial segments. The intimal shear stress is modeled using the Womersley theory. A non-linear viscoelastic constitutive law for the arterial wall is considered. The arterial tree is coupled to the heart, which is modeled using the time varying elastance model. All distal vessels are terminated with three-element windkessel. Coronary arteries are modeled assuming a systolic flow impediment dependent on the varying elastance of the ventricles. The systemic arterial tree dimensions and properties were taken from literature and extended to include the cerebral arterial tree obtained from real patient scans. To validate model predictions, we performed noninvasive measurements of pressure (applanation tonometry) and flow (ultrasound and MRI) waves in volunteers.

The model predicts pressure and flow waves which are in good qualitative agreement with in-vivo measurements, especially for the shape and wave details, where all features are reproduced in a rather faithful manner. The results obtained validate the model predictions of pressure and flow in central arteries as well as in major arteries of the brain, reinforcing thus the general applicability of the 1D model to the entire systemic and cerebral circulation.