Investigation of the plaque morphology effect on changes of pulsatile blood flow in a stenosed curved artery induced by an external magnetic field

Highlights

• The effect of magnetic field on pulsatile blood flow in a stenosed curved artery was investigated.

• Both states of oxygenated and deoxygenated blood were considered.

• The occlusion percentage and the chord length of stenosis, as important parameters, were studied.

• A safe magnetic field with no significant effect on blood hemodynamics was presented by analyzing the WSS and the pressure.

Abstract

In a new therapeutic technique, called magnetic drug targeting (MDT), magnetic particles carrying therapeutic agents are directed to the target tissue by applying an external magnetic field. Meanwhile, this magnetic field also affects the blood as a biomagnetic fluid. Therefore, it is necessary to select a magnetic field with an acceptable range of influence on the blood flow. This study investigates the effect of an external magnetic field on the pulsatile blood flow in a stenosed curved artery to identify a safe magnetic field. The effects of a number of parameters, including the magnetic susceptibility of blood in oxygenated and deoxygenated states and the magnetic field strength, were studied. Moreover, the effect of the plaque morphology, including the occlusion percentage and the chord length of the stenosis, on changes in blood flow induced by the magnetic field was investigated. The results show that applying a magnetic field increases the wall shear stress (WSS) and the pressure of the deoxygenated blood. Comparing the wall shear stresses of the deoxygenated and oxygenated blood shows that the effect of magnetic field on the deoxygenated blood is more significant than its effect on the oxygenated blood due to its higher magnetic susceptibility. The study of the stenosis geometry shows that the influence of magnetic field on the blood flow is increased by decreasing the occlusion percentage of the artery. Furthermore, among the evaluated lengths, the 50° chord length results in the highest variation under the influence of the magnetic field. Finally, the magnetic field of Mn = 2.5 can be utilized as a safe field for MDT purposes in such a stenosed curved artery.

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 $+3.5\times {10}^{-6}$ and $-6.6\times {10}^{-7}$ 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.