Investigation of the plaque morphology effect on changes of pulsatile blood flow in a stenosed curved artery induced by an external magnetic field
Introduction
During the last few decades, the use of a magnetic field for medical applications has significantly increased. These applications include MRI machines [1,2], magnetic devices for cell separation [3,4], treatment of tumors using hyperthermia [5], adjusting blood flow during surgery, stem cell delivery [6], and magnetic drug targeting (MDT) [[7], [8], [9], [10], [11]]. In all these applications, since the blood is a biomagnetic fluid, it responds to the presence of the magnetic field.
Biomagnetic fluids are found in living organisms, and they react to magnetic fields [12]. The sensitivity of the blood to a magnetic field is due to the presence of hemoglobin. If the blood is deoxygenated, there are chains of Fe++ inside the deoxyhemoglobin that give the blood paramagnetic property [13]. However, when the hemoglobin binds to oxygen, blood becomes oxygenated, behaving as a diamagnetic substance [14]. Measurements have been performed to estimate the magnetic susceptibility of blood, indicating and for deoxygenated and oxygenated blood, respectively [4].
When blood is exposed to an external magnetic field, it experiences the Lorentz force and the magnetization force, which are studied using the principles of magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD), respectively [15]. Employing these rules, researchers can study the effects induced by a magnetic field on the blood flow. Such investigations can be used to select a safe magnetic field for medical applications, such as MDT.
MDT is a new and efficient treatment method [16]. In this method, therapeutic agents are attached to the magnetic particles and they are then steered to a target region with the help of an external magnetic field [17]. The advantages of this method include increasing the concentration of the drug around the target tissue, reducing the side effects of the drug, and improving the treatment efficiency [18]. A safe magnetic field affects the blood in an acceptable range so as not to damage the arteries and the organs of the body; hence, it can be utilized in the MDT technique.
Some of the studies that have investigated the effect of magnetic field on biomagnetic fluids, especially blood, will be reviewed in this section. These studies are classified into four categories based on geometry, i.e., simple geometry, stenosed geometry, flexible geometry, and porous geometry.
Haik et al. [19] and Akar et al. [20] are among those who have experimentally and numerically studied the effect of magnetic field on blood flow in simple geometries. Haik et al. investigated the effect of magnetic field on human blood. Their results indicated that the blood flow rate decreased when it was subjected to a high magnetic field due to an increase in the apparent viscosity. Accordingly, they proposed an experimental correlation for the blood viscosity [19]. Akar et al. studied the influence of magnetic field on the blood flow in a 90-degree horizontal vessel. The blood was considered in both oxygenated and deoxygenated states. The results showed that a magnetic field had a greater effect on high-curvature vessels than low-curvature ones [20].
Studying the blood flow behavior in the stenosed arteries is critical since atherosclerotic plaque formation and rupture have been among the major causes of death during the recent centuries [21,22]. Plaques narrow and harden the arteries and reduce the supply of oxygen and nutrition to the organs. The influence of magnetic field on the blood flow in such occluded arteries is a valuable topic since it provides useful information for therapeutic methods, such as MDT.
Tzirtzilakis analyzed the blood flow through a stenosed channel in the presence of a steady localized magnetic field. The results revealed that a vortex appeared near the magnetic field position, which became larger when the intensity of the field was increased. They also concluded that the effect of magnetic field on the blood flow is considerable even in moderate degree of stenosis [23]. Kenjeres considered the blood flow in a realistic occluded artery influenced by a strong magnetic field. Both Lorentz and magnetization forces were considered in this study [24].
Mustapha et al. investigated the effect of a uniform transverse magnetic field on the blood flow through an artery with irregular-shaped multiple stenoses using MHD principles. They controlled the flow separation by exerting a magnetic field [25]. Varshney et al. evaluated an artery with multiple stenosis, showing that a sufficient magnetic field could cause problems because of the backflow [26]. Srinivasacharya and Madhava Rao considered the blood as a couple stress fluid and investigated the effect of magnetic field on the fluid through a bifurcated artery with mild stenosis [27].
Alshare and Tashtoush investigated the effect of magnetic field on the pulsatile blood flow in an artery with multiple stenoses. They considered different types of blood, including healthy, diabetic, and anemic blood. They observed that applying a magnetic field would increase the pressure drop [28]. Ponalagusamy and Priyadharshini used the Herschel-Bulkley non-Newtonian model to simulate the pulsatile blood flow in a porous bifurcated artery with stenosis in the presence of a magnetic field [29].
Javadzadegan et al. studied the influence of different intensities of magnetic field on the blood flow in a realistic atherosclerotic coronary artery. The results revealed that the MWSS and the length of the recirculation zone were reduced by applying a magnetic field [30]. Sadeghi et al. studied the effect of magnetic field on the pulsatile blood flow in an elastic stenosed artery. The results revealed that the influence of magnetic field on a single stenosis was more significant than its impact on a double stenosis, concluding that the influence increased as the percentage of stenosis decreased [31].
The effect of geometry flexibility is another important parameter that has been studied by researchers. Misra and Shit studied the influence of magnetic field on the blood flow in an elastic artery. They showed that the blood pressure and flow rate could be controlled by applying a sufficiently-high magnetic field [32]. Aminfar et al. investigated the effect of a non-uniform magnetic field on ferrofluid (blood and 3 vol%Fe3O4) in a tube with an elastic segment. The results indicated that the tube became narrower and wider when applying a positive and negative magnetic field, respectively. Moreover, the tube deformation increased when the magnitude of the gradients increased [33]. Chapal Hossain et al. examined the effect of magnetic field on the blood flow containing magnetic particles in a realistic deformable bifurcation [34].
The porosity of the vessels is also known as an influential parameter. Alimohamadi and Imani analyzed the effect of magnetic field on the blood flow in an aneurysm artery containing porous media [35]. Sinha studied the MHD blood flow in a stretchable porous artery. The results revealed that the velocity of blood could be controlled by adjusting the intensity of the magnetic field. This result is useful for surgeons who want to keep the blood flow at a desirable rate [36]. Tripathi and Sharma added a heat source to an inclined porous artery in the presence of a magnetic field. In their study, the viscosity of blood was supposed to vary radially with the hematocrit [37].
Some researchers first studied the effect of magnetic field on the blood flow, and they then investigated targeted drug delivery using the identified safe magnetic field. Larimi et al. used FHD principles to analyze the blood flow behavior in a bifurcation vessel exposed to an external magnetic field. Sharp changes in WSS were observed near the magnetic field, which increased by applying a field with a greater intensity [38]. Bose and Banerjee studied the MDT method in an aortic bifurcation with stenosis. They used FHD and MHD principles to study the blood flow behavior in the presence of a magnetic field, while they also identified the suitable strength of the magnetic field [15]. For more information on the applications of MHD, other studies can be consulted [[39], [40], [41]].
The literature review revealed that most studies have focused on the effect of magnetic field on the blood flow in straight vessels, and a few have paid attention to curved vessels with stenosis. To the best of our knowledge, among those who have investigated the curved arteries, the effect of plaque morphology on blood flow changes, applied by a magnetic field, has not been studied. Therefore, the current study explores the effect of an external magnetic field on the blood flow in a three-dimensional stenosed curved artery with emphasis on plaque morphology. Blood is considered a non-Newtonian fluid, and pulsatile velocity and pressure are applied in the inlet and outlet of the artery. The effect of different parameters, such as the magnetic susceptibility of blood in oxygenated and deoxygenated states, the magnetic field strength, and the morphology of the stenosis, including the occlusion percentage and the chord length, are studied. This study aims to identify a safe magnetic field for such a stenosed artery that has no significant effect on the blood hemodynamics.
Section snippets
Governing equations
The governing equations of the fluid field include the continuity and momentum equations. Some assumptions can be applied in the simulation to simplify these equations. These assumptions are as follows:
- •
The fluid flow is incompressible, laminar, transient, and three-dimensional.
- •
Blood is considered a non-Newtonian fluid, which is simulated by the Carreau model.
- •
The Lorentz force is negligible compared to the magnetization force; hence, the FHD principles are used to investigate the effect of
Numerical solution method
ANSYS-FLUENT 17.2, which is a finite volume solver, was used to discretize and solve the continuity and momentum equations. Diffusion and convection terms were discretized using the second-order upwind scheme. The coupling between the velocity and the pressure was performed using the SIMPLE algorithm. To obtain an accurate solution, the residual values of the governing equations were set to 10−6.
Results and discussion
In the MDT method, an external magnetic field is used to move magnetic particles to the target zone. However, the applied magnetic field also affects the blood flow. Therefore, it is necessary to choose a safe field that does not strongly influence the blood flow. This study aims to investigate the effect of magnetic field on the pulsatile blood flow in an occluded curved artery. The susceptibility of blood is studied in both deoxygenated and oxygenated forms. The effects of parameters such as
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was supported by the National Research Foundation of Korea grant, which is funded by the Korean government (MSIT) (No. 2020R1A5A8018822).
References (51)
- et al.
Computer-aided detection and diagnosis for prostate cancer based on mono and multi-parametric MRI: a review
Comput. Biol. Med.
(2015) - et al.
Development of magnetic device for cell separation
J. Magn. Magn Mater.
(1999) - et al.
A review on numerical modeling for magnetic nanoparticle hyperthermia: progress and challenges
J. Therm. Biol.
(2020) - et al.
A numerical investigation on the Magnetophoretic-guided stem cells delivery in a bend blood vessel
J. Magn. Magn Mater.
(2020) - et al.
Numerical simulation of magnetic drug targeting to a tumor in the simplified model of the human lung
Comput. Methods Progr. Biomed.
(2019) - et al.
On the magnetic aggregation of Fe3O4 nanoparticles
Comput. Methods Progr. Biomed.
(2021) - et al.
Numerical simulation of magnetic nano drug targeting in patient-specific lower respiratory tract
J. Magn. Magn Mater.
(2018) - et al.
Numerical simulation of magnetic nano drug targeting to atherosclerosis: effect of plaque morphology (stenosis degree and shoulder length)
Comput. Methods Progr. Biomed.
(2020) - et al.
In silico study of patient-specific magnetic drug targeting for a coronary LAD atherosclerotic plaque
Int. J. Pharm.
(2019) - et al.
Magnetic particle capture for biomagnetic fluid flow in stenosed aortic bifurcation considering particle--fluid coupling
J. Magn. Magn Mater.
(2015)
A review of magnet systems for targeted drug delivery
J. Contr. Release
Modeling of magnetic bandages for drug targeting: button vs. Halbach arrays
J. Magn. Magn Mater.
Numerical simulation of magnetic nanoparticle-based drug delivery in presence of atherosclerotic plaques and under the effects of magnetic field
Powder Technol.
Apparent viscosity of human blood in a high static magnetic field
J. Magn. Magn Mater.
A numerical investigation of magnetic field effect on blood flow as biomagnetic fluid in a bend vessel
J. Magn. Magn Mater.
A review study on blood in human coronary artery: numerical approach, Comput
Methods Programs Biomed
Biomagnetic fluid flow in a channel with stenosis
Phys. Nonlinear Phenom.
Numerical analysis of blood flow in realistic arteries subjected to strong non-uniform magnetic fields
Int. J. Heat Fluid Flow
Unsteady magnetohydrodynamic blood flow through irregular multi-stenosed arteries
Comput. Biol. Med.
Computational analysis of magnetic effects on pulsatile flow of couple stress fluid through a bifurcated artery
Comput. Methods Progr. Biomed.
Nonlinear model on pulsatile flow of blood through a porous bifurcated arterial stenosis in the presence of magnetic field and periodic body acceleration
Comput. Methods Progr. Biomed.
Magnetohydrodynamic blood flow in patients with coronary artery disease, Comput
Methods Programs Biomed
Two-phase simulation of non-uniform magnetic field effects on biofluid (blood) with magnetic nanoparticles through a collapsible tube
J. Magn. Magn Mater.
MHD flow and heat transfer of a third order fluid in a porous channel with stretching wall: application to hemodynamics
Alexandria Eng. J.
Numerical simulation of magnetic nanoparticles targeting in a bifurcation vessel
J. Magn. Magn Mater.
Cited by (13)
Targeted delivery of therapeutic agents in a healthy and stenosed patient-specific carotid artery using an external magnetic field
2023, Journal of Magnetism and Magnetic MaterialsIdentify essential genes based on clustering based synthetic minority oversampling technique
2023, Computers in Biology and MedicineTwo-phase bio-nanofluid flow through a bifurcated artery with magnetic field interaction
2022, International Journal of ThermofluidsCitation Excerpt :Akar et al. [29] noticed that magnetic arena has greater influence on the analysis of the hemodynamic factors including the WSS, and the Reynolds number (Re = 50–150). Teimouri et al. [30] also found that the WSS and the deoxygenated blood pressure are enhanced gradually while applying an external magnetic field. The results of Cherkaoui et al. [31] revealed that with augmentation of the Reynolds number upto 800, the velocity and recirculation vicinity increase reasonably.
Effect of plaque geometry on targeted delivery of stem cells containing magnetic particles in a rigid and elastic curved artery with stenosis
2022, Journal of Magnetism and Magnetic MaterialsCitation Excerpt :The agreement of the results confirms the accuracy of the present numerical model. A magnetic field of Mn = 2.5 was selected as a safe field that does not induce a significant effect on blood flow [47]. This magnetic field was considered as the base field to study the capture efficiency of cells in the following parts.
Fluid-solid interaction analysis of blood flow in the atherosclerotic carotid artery using the Eulerian-Lagrangian approach
2024, Journal of Central South UniversityToward a Mesoscopic Modeling Approach of Magnetohydrodynamic Blood Flow in Pathological Vessels: A Comprehensive Review
2023, Annals of Biomedical Engineering