Mathematical modeling in assessing the risk of restenosis after carotid endarterectomy.

Carotid endarterectomy is the main way to combat atherosclerosis of the carotid arteries, which disrupts cerebral circulation. The generally accepted marker of atherogenesis risk are hemodynamic indices associated with near-wall shear stress. The purpose of the work is to conduct a comparative analysis of hemodynamic indices in various carotid bifurcation models. The influence of a virtual change in the geometric shape of the model in order to optimize hemodynamic indices is also being studied. On the basis of computed angiography data, carotid bifurcation models are constructed, in which critical zones of hemodynamic indices are built using computational fluid dynamics. A comparative analysis of the critical zones for different classes of models is carried out. Comparison of averaged indices for critical zones between 'normal' and post-operative groups gave more than 5-x worse results for the latter. The same results for the near-bifurcation parts of the zones give a 25% better result for postoperative models. Virtual 'removal' of insignificant plaques leads to a deterioration of the indices of up to 40% in the places of the plaque's former location. The described method makes it possible to build the indices critical zones and compare them for various types of models. A technique for virtual changing the shape of a vessel (virtual surgery) is proposed. The novelty of the approach lies in the use for comparative analysis both real vessel models and hypothetical 'improved' virtual ones, as well in the proposed division of post-operative model's critical zones into subzones of different genesis.

[Computer modeling of the area of carotid endarterectomy with patches of various forms]. / Sposob komp'yuternogo modelirovaniya zony klassicheskoi karotidnoi endarterektomii s primeneniem zaplat razlichnoi formy.

OBJECTIVE: To describe geometric models of carotid artery bifurcation and computer modeling of carotid endarterectomy (CEA) with patches of various configurations. MATERIAL AND METHODS: The method was demonstrated on a reconstructed model of intact vessel based on preoperative CT of the affected vessel in a certain patient. Blood flow is modeled by computational fluid dynamics using Doppler ultrasound data. Risk factors were assessed considering hemodynamic parameters of vascular wall associated with WSS. RESULTS: We studied hemodynamic results of 10 virtual CEA with patches of various shapes on the example of a reconstructed intact artery in a particular patient. Patch implantation is aimed at prevention of carotid artery narrowing since simple suture without a patch can reduce circumference of the artery by 4-5 mm. This result adversely affects blood flow. On the other hand, too wide a patch creates aneurysm-like deformation of internal carotid artery bulb. It is not optimal due to a large recirculation zone. It was found that patch width approximately equal to 3 mm ensures an optimal hemodynamic result. Deviations from this median value, both upward and downward, impair hemodynamics while the absence of a patch results the worst result. CONCLUSION: The proposed computer modeling technique is able to provide a personalized patch selection for CEA with low risk of restenosis in long-term follow-up period.

[Personalized brain revascularization: computer modeling of the reconstruction zone for carotid endarterectomy]. / Personifitsirovannaya revaskulyarizatsiya golovnogo mozga: metod komp'yuternogo modelirovaniya zony rekonstruktsii dlya provedeniya karotidnoi endarterektomii.

OBJECTIVE: To develop a technique of computer modeling of hemodynamics before conventional CEE. MATERIAL AND METHODS: Classical CEE is performed according to conventional patch technique. Duplex parameters of stenosis and blood flow velocity in the carotid arteries were analyzed by using of a linear transducer 7-7.5 MG (Acuson 128XP scanner, Acuson, USA). Multispiral computed tomography with angiography and subsequent processing of data using the Clear canvas software were performed to visualize the main geometric characteristics of the carotid arteries and features of atherosclerotic plaque. RESULTS: Blood flow hemodynamics is essential in the occurrence of postoperative restenosis. Therefore, computer simulation of blood flow using CFD (Computational Fluid Dynamics) methods based on particular patient's data makes it possible to assess localization of zones with high risk of restenosis. CFD approach implies construction of blood flow parameters at absolutely every point of the vessel considering geometric shape of the vessel and flow characteristics at the entrance and exit from the vessel. Pressure curves at the inlet and outlet are constructed using blood flow velocity curves. Pressure curves are subsequently used in the CFD model. The result of blood flow CFD modeling is non-stationary three-dimensional fields of pressure and velocity in the investigated area. Visual analysis of blood flow dynamics in these fields makes it possible to judge possible problem areas along the blood flow and on the inner wall of the vessel. DISCUSSION: Patch technique of classical CEE is characterized by great risk of parietal thrombosis and hyperproliferation of neointima that explains more frequent development of restenosis. Computer modeling is valuable to consider some important technical aspects in implementation of various surgical techniques for carotid artery reconstruction. CONCLUSION: This result demonstrates an importance of achieving the optimal ratio of the diameter of common, internal and external carotid arteries. Modification of patch based on computer simulation is required for these purposes.

[Computer-assisted simulation of haemodynamic parameters of carotid artery bifurcation after carotid endarterectomy]. / Komp'iuternoe modelirovanie gemodinamicheskikh pokazatelei v bifurkatsii sonnykh arterii posle karotidnoi éndarteréktomii.

Computer-aided simulation appropriately using the method of computational fluid dynamics (CFD) makes it possible to determine the elevated-risk zones of most probable formation of restenosis. The main idea of the method described in our article consists in a possibility of creating by the model of the geometrical shape of the vessel and characteristics of the flow at inlets and outlets the parameters of flow in each point of a vessel. The curves of velocity are used to create the curves of pressure at inlets and outlets, which are used in a CFD model. The resulting from CFD simulation of blood flow are nonstationary three-dimensional fields of pressure and velocity in the area under study. Visual examination of the dynamics of these fields makes it possible to judge about possible problem zones inside the area of flow and on the internal wall of the vessel. This article also presents a clinical case report illustrating the use of this technique.