A Hybrid 0D–1D Model for Cerebral Circulation and Cerebral Arteries

Abstract

In this paper we present a hybrid 0D–1D model for the cerebral circulation and blood flow in large cerebral arteries. The 0D model contains the electrical analog circuit running from the aorta to the circle of Willis (CoW), and the venous network from the superior sagittal sinus (SSS) to the superior vena cava (SVC). To simulate the cerebral autoregulation, the vascular bed between the arterial and venous networks is implemented using an inductor/resistor couple. An artificial pulsatile pressure waveform includes the normal (∼100 mmHg), hypotensive (∼50 mmHg) and hypertensive (∼150 mmHg) phases. A 1D model is used to numerically solve the 1D Navier–Stokes equations coupled with an empirical arterial wall equation. The 1D model is then applied to the internal carotid, middle and anterior cerebral arteries (ICA, MCA and ACA) in the CoW, with the simulation results from the 0D model as boundary conditions. With this hybrid 0D–1D approach, we show that: (a) the cerebral flow may regain a normal flow rate value (∼600 mL/min) within several cardiac cycles; (b) an incomplete CoW can substantially affect the flow distribution in CoW; and (c) the flow rates in the MCA, ACA and PCA alter in response to the cerebral regulation. In conclusion a hybrid 0D–1D model for the cerebral blood flow is proposed, which can potentially be used for the cerebral flow modelling of different age groups or under different vascular diseases.

Appendix

The electrical circuit of the 0D model is quite large. The diameters and lengths of the arteries and veins and their nominal resistance value in the circuit are listed in Table 2. The diagram of the posterior circulation is shown in Fig. 7 to illustrate the design of the posterior circulation and venous return.

Fig. 7

Diagram for the circuit of the posterior circulation

Table 2 Nominal diameter and length of blood vessels and corresponding resistance in the model