Biomathematical modeling and analysis of blood flow in an intracranial aneurysm

Unsteady non-Newtonian blood flow through a tapered overlapping stenosed catheterized vessel

The unsteady flow characteristics of blood in a catheterized overlapping stenosed artery are analyzed in presence of body acceleration and magnetic field. The stenosed arterial segment is modeled as a rigid constricted tube. An improved shape of stenosis in the realm of the formulation of the arterial narrowing caused by atheroma is integrated in the present study. The catheter inside the artery is approximated by a thin rigid tube of small radius while the streaming blood in the artery is characterized by the Carreau model. Employing mild stenosis condition, the governing equation of the flow is derived which is then solving numerically using finite difference scheme. The variation of axial velocity, flow rate, resistance impendence and wall shear stress is shown graphically for various parameters of interest. The flow patterns illustrating the global behavior of blood are also presented.

Rational macromodeling of 1D blood flow in the human cardiovascular system

In this paper, we present a novel rational macromodeling approach for the description of 1D blood flow in the human cardiovascular system, which is suitable for time-domain simulations. Using the analogy of the blood flow propagation problem with transmission lines and considering the hypothesis of linearized Navier-Stokes equations, a frequency-domain rational macromodel for each arterial segment has been built. The poles and the residues of each arterial segment macromodel have been calculated by means of the Vector Fitting technique. Finally, the rational macromodel of the whole cardiovascular system is obtained by properly combining the macromodels of the single arterial segments using an interconnect matrix. The rational form of the proposed cardiovascular model leads to a state-space or electrical circuit model suitable for time-domain analysis. The stability and passivity properties of the global cardiovascular model are discussed to guarantee stable time-domain simulations. The proposed macromodeling approach has been validated by pertinent numerical results. Copyright © 2015 John Wiley & Sons, Ltd.

A MATHEMATICAL MODEL OF BLOOD FLOW IN AN INTRACRANIAL ANEURYSM: ANALYTICAL AND NUMERICAL STUDY

An aneurysm is a local enlargement of the vessel lumen due to the weakening of the wall material. We propose a mathematical model of the pulsatile blood flow through the system consisting of the cerebral artery and an aneurysm. The mathematical model is based on mass and energy conservation laws. It comprises non-linear rheological properties of the aneurysm and artery, and inertial and resistant properties of the blood flow. The model equations are analyzed by the methods of non-linear dynamics and they are solved numerically. Special attention is paid to the flow stability as a function of the aneurysmal and arterial material properties, the mean and oscillating arterial pressure, and the frequency of heart pulsations. The results of the work can be summarized as follows: (i) the model equations are stable at normal physiological conditions and developed aneurysms, (ii) with decreasing of the aneurysmal compliance, the aneurysmal volume pulsations increase and a limit point of flow stability is approached, (iii) the increased amplitude of the pulsatile pressure and the heart frequency cannot lead to flow instabilities.

A proposed parent vessel geometry-based categorization of saccular intracranial aneurysms: computational flow dynamics analysis of the risk factors for lesion rupture

OBJECT

The authors created a simple, broadly applicable classification of saccular intracranial aneurysms into three categories: sidewall (SW), sidewall with branching vessel (SWBV), and endwall (EW) according to the angiographically documented patterns of their parent arteries. Using computational flow dynamics analysis (CFDA) of simple models representing the three aneurysm categories, the authors analyzed geometry-related risk factors such as neck width, parent artery curvature, and angulation of the branching vessels.

METHODS

The authors performed CFDAs of 68 aneurysmal geometric formations documented on angiograms that had been obtained in patients with 45 ruptured and 23 unruptured lesions. In successfully studied CFDA cases, the wall shear stress, blood velocity, and pressure maps were examined and correlated with aneurysm rupture points. Statistical analysis of the cases involving aneurysm rupture revealed a statistically significant correlation between aneurysm depth and both neck size (p < 0.0001) and caliber of draining arteries (p < 0.0001). Wider-necked aneurysms or those with wider-caliber draining vessels were found to be high-flow lesions that tended to rupture at larger sizes. Smaller-necked aneurysms or those with smaller-caliber draining vessels were found to be low-flow lesions that tended to rupture at smaller sizes. The incidence of ruptured aneurysms with an aspect ratio (depth/neck) exceeding 1.6 was 100% in the SW and SWBV categories, whereas the incidence was only 28.75% for the EW aneurysms.

CONCLUSIONS

The application of standardized categories enables the comparison of results for various aneurysms' geometric formations, thus assisting in their management. The proposed classification system may provide a promising means of understanding the natural history of saccular intracranial aneurysms.