Mathematical Modelling of Circulation in Extracranial Brachocephalic Arteries at P Re-Operation Stage in Carotid Endarterectomy

Abstract

Атеросклероз сонных артерий является одной из наиболее частых причин развития ишемических инсультов и выступает этиологическим фактором в 20-30% случаев [1]. Учитывая достаточно высокий периоперационный риск (смерть, острые нарушения мозгового кровотока (ОНМК)), каротидная реваску-ляризация (эндартерэктомия и стентирование) пока-зана только пациентом с тяжелым атеросклеротиче-ским поражением брахиоцефальных артерий (стеноз более 70% при ультразвуковом исследовании или более 50% при ангиографии) [1,2]. Несмотря на тща-тельный отбор пациентов, частота ОНМК при каро-тидной реваскуляризации составляет от 1,5 до 9,0% [1,3] Aim. Hemodynamic shifts in the brain, developing due to carotid surgery (carotid endarterectomy or stenting) might be the cause of perioperation strokes. Assessment for hemodynamic shifts is important. The aim of current study was to develop methodics of cerebral hemodynamics assessment at pre-operation and post-operation periods of carotid endarterectomy. Material and methods. The authors propose a mathematical model for preoperation analysis of hemodynamics changes in extracranial regions of brachiocephalic arteries after carotid endarterctomy. The development of mathematical model was based upon the data from pre-and postsurgery duplex scan and CT-angiography. Results. The results showed good prediction capacity for the shifts in cerebral hemodynamics, using the developed mathematical model.

Mathematical modelling of atherosclerosis

“…Atherosclerotic vascular stenosis with fraction α can be accounted in 1D hemodynamic models via incorporation into the healthy vascular network of a tubular segment with modified cross-sectional area A s = αA 0 . By analogy with (4.12), at the terminal points of this segment one modifies the continuity of the total pressue by adding the Poiseuille pressure drop condition ∆p = R s Q with hydraulic resistance R s ∼ α −2 [32,67,70,75].…”

“…The straightforward clinical application is presurgical assessment of revascularization (by balloon angioplasty and stenting) impact to the postsurgical blood flow [32,67,70,77,84,87,189]. Such assessment provides a basis for patient specific surgery tactics development.…”