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.
Cerebral circulation Model Electrical analog Brain
This is a preview of subscription content, log in to check access.
This project was partially supported by a seed grant (project number UOAX1702) from the Science for Technological Innovation programme of National Science Challenge of New Zealand.
Levick JR (2003) An introduction to cardiovascular physiology. Arnold, London.Google Scholar
Ursino M, Lodi CA (1997) A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics. J Appl Physiol 82:1256–1269CrossRefGoogle Scholar
Olufsen MS, Nadim A, Lipsitz LA (2002) Dynamics of cerebral blood flow regulation explained using a lumped parameter model. Am J Physiol Regul Integr Comp Physiol 282:R611–R622CrossRefGoogle Scholar
Alastruey J, Parker KH, Peiro J, Sherwin SJ (2007) Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows. J Biomech 40:1794–1805CrossRefGoogle Scholar
Zagzoule M, Marc-Vergnes JP (1986) A global mathematical model of the cerebral circulation in man. J Biomech 19:1015–1022CrossRefGoogle Scholar
Reymond P, Merenda F, Perren F, Rfenacht D, Stergiopulos N (2009) Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol 297:H208–H222CrossRefGoogle Scholar
Ho H, Mithraratne K, Hunter P (2013) Numerical simulation of blood flow in an anatomically-accurate cerebral venous tree. IEEE Trans Med Imaging 32:85–91CrossRefGoogle Scholar
Alns MS, Isaksen J, Mardal K-A, Romner B, Morgan MK, Ingebrigtsen T (2007) Computation of hemodynamics in the circle of Willis. Stroke 38:2500–2505CrossRefGoogle Scholar
Gao E, Young WL, Pile-Spellman J, Ornstein E, Ma Q (1998) Mathematical considerations for modeling cerebral blood flow autoregulation to systemic arterial pressure. Am J Physiol Heart Circ Physiol 274:H1023–H1031CrossRefGoogle Scholar
Aaslid R, Lindegaard KF, Sorteberg W, Nornes H (1989) Cerebral autoregulation dynamics in humans. Stroke 20:4552CrossRefGoogle Scholar