Modeling the Circle of Willis Using Electrical Analogy Method under both Normal and Pathological Circumstances

M. Abdi, A. Karimi, M. Navidbakhsh, M. A. Rahmati, K. Hassani, A. Razmkon


Background and objective: The circle of Willis (COW) supports adequate blood supply to the brain. The cardiovascular system, in the current study, is modeled using an equivalent electronic system focusing on the COW.

Method: In our previous study we used 42 compartments to model whole car- diovascular system. In the current study, nevertheless, we extended our model by using 63 compartments to model whole CS. Each cardiovascular artery is modeled using electrical elements, including resistor, capacitor, and inductor. The MATLAB Simulink software is used to obtain the left and right ventricles pressure as well as pressure distribution at efferent arteries of the circle of Willis. Firstly, the normal operation of the system is shown and then the stenosis of cerebral arteries is induced in the circuit and, consequently, the effects are studied.

Results: In the normal condition, the difference between pressure distribution of right and left efferent arteries (left and right ACA–A2, left and right MCA, left and right PCA–P2) is calculated to indicate the effect of anatomical difference between left and right sides of supplying arteries of the COW. In stenosis cases, the effect of internal carotid artery occlusion on efferent arteries pressure is investigated. The modeling results are verified by comparing to the clinical observation reported in the literature.

Conclusion: We believe the presented model is a useful tool for representing the normal operation of the cardiovascular system and study of the pathologies.


Artery occlusion; Cardiovascular system; Cerebrovascular system; Collateral vessel; Pressure waveforms

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