A mathematical model for blood flow in magnetic field

Tzirtzilakis, E. E.

doi:10.1063/1.1978807

Cited by 314 publications

(241 citation statements)

References 34 publications

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“…In this study, for modelling incompressible non-isothermal flows in conjunction with MHD and FHD models, we adopt the mathematical model equations proposed by Tzirtzilakis [7]. The system of governing equations consists of the continuity, momentum and energy equations, thus the mass conservation for incompressible flows can be written in a vector form as…”

Section: Governing Equations In Conjunction With Combined Mhd-fhd Modelsmentioning

confidence: 99%

“…The combination of MHD and FHD models [2,7] described in this Section is not available in the ANSYS-FLUENT commercial software package by default. Therefore, the MHD-FHD model for the governing momentum (10) and energy (11) equations in conjunction with the magnetization (13) and Lorentz force (16) source terms has been implemented in the ANSYS-FLUENT environment with User-Defined Functions (UDFs) in the C programming language.…”

Section: Implementation Of Mhd-fhd Model Equationsmentioning

confidence: 99%

“…The local arrangement of the single wire in the two-dimensional microfluidic channel has been shown in Figure 8. This benchmark problem is a hybridization of the single wire model used by Tzirakis et al [2] and the mathematical model for blood flows and magnetic fields proposed by Tzitzilakis [7]. The magnetization force due to the effect of FHD and the Lorentz force due to the effect of MHD have been taken into account in the momentum equation (10).…”

Section: Single Wire Problemmentioning

confidence: 99%

“…In other words, it also means that the magneticaloric effect of FHD has been neglected in the MHD-FHD set of model equations in conjunction with Newtonian and non-Newtonian fluids, because the blood can be considered as a weak magnetic conductor. The reason for investigating incompressible and non-isothermal MHD-FHD Newtonian and non-Newtonian fluid flows with the hybridization of Tzirakis et al [2] and Tzitzilakis [7] MHD-FHD models is to study further the interaction between the temperature and MHD-FHD fields for non-Newtonian blood flows, because there is a lack of experimental data available in the literature. In addition to this, there is a lack of well-established and reliable numerical benchmark test case available for verification and validation purposes, thus we also focus on the computational fluid dynamics (CFD) aspects of this physical problem.…”

Section: Single Wire Problemmentioning

confidence: 99%

“…For steady-state flows, the governing equations (10)- (11) with MHD and FHD models in conjunction with Newtonian and non-Newtonian fluids can be implemented in an in-house code or in a commercial software environment by using User-Defined Functions. The governing equations of the combination of MHD and FHD models [2,7] described in Section 2 is not available in the ANSYS-FLUENT software package by default, therefore the implementation of a complex multiphysics problem related to MHD and FHD models gives an opportunity to study the strength and limitations of these models from computational aspects. Therefore, it is important to mention from a numerical modelling point-of-view that it has been observed that the presence of the magnetocaloric term of FHD on the right hand side of the temperature equation (3) could lead to numerically unstable and non-physical results when the magnetization vector M is depending on the temperature.…”

Section: Single Wire Problemmentioning

confidence: 99%

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Validation of a Magneto- And Ferro-Hydrodynamic Model for Non-Isothermal Flows in Conjunction With Newtonian and Non-Newtonian Fluids

Könözsy¹,

Scienza²,

Drikakis³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. This work focuses on the validation of a magnetohydrodynamic (MHD) and ferrohydrodynamic (FHD) model for non-isothermal flows in conjunction with Newtonian and nonNewtonian fluids. The importance of this research field is to gain insight into the interaction of non-linear viscous behaviour of blood flow in the presence of MHD and FHD effects, because its biomedical application such as magneto resonance imaging (MRI) is in the centre of research interest. For incompressible flows coupled with MHD and FHD models, the Lorentz force and a Joule heating term appear due to the MHD effects and the magnetization and magnetocaloric terms appear due to the FHD effects in the non-linear momentum and temperature equations, respectively. Tzirtzilakis and Loukopoulos [1] investigated the effects of MHD and FHD for incompressible non-isothermal flows in conjunction with Newtonian fluids in a small rectangular channel. Their model excluded the non-linear viscous behaviour of blood flows considering blood as a Newtonian biofluid. Tzirakis et al. [2,3] modelled the effects of MHD and FHD for incompressible isothermal flows in a circular duct and through a stenosis in conjunction with both Newtonian and non-Newtonian fluids, although their approach neglects the non-isothermal magnetocaloric FHD effects. Due to the fact that there is a lack of experimental data available for non-isothermal and non-Newtonian blood flows in the presence of MHD and FHD effects, therefore the objective of this study is to establish adequate validation test cases in order to assess the reliability of the implemented non-isothermal and non-Newtonian MHD-FHD models. The non-isothermal Hartmann flow has been chosen as a benchmark physical problem to study velocity and temperature distributions for Newtonian fluids and non-Newtonian blood flows in a planar microfluidic channel. In addition to this, the numerical behaviour of an incompressible and non-isothermal non-Newtonian blood flow has been investigated from computational aspects when a dipole-like rotational magnetic field generated by infinite conducting wires. The numerical results are compared to available computational data taken from literature [2].

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Section: Governing Equations In Conjunction With Combined Mhd-fhd Modelsmentioning

confidence: 99%

Section: Implementation Of Mhd-fhd Model Equationsmentioning

confidence: 99%

Section: Single Wire Problemmentioning

confidence: 99%

Section: Single Wire Problemmentioning

confidence: 99%

Section: Single Wire Problemmentioning

confidence: 99%

See 3 more Smart Citations

Validation of a Magneto- And Ferro-Hydrodynamic Model for Non-Isothermal Flows in Conjunction With Newtonian and Non-Newtonian Fluids

Könözsy¹,

Scienza²,

Drikakis³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Transient Neurovascular Interface for Minimally Invasive Neural Recording and Stimulation

Fanelli

Ferlauto

Zollinger

et al. 2021

Adv Materials Technologies

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time, led to the development of treatments for heavily impairing conditions following traumatic injuries, neurodegenerative diseases, or mental disorders. [1] Although the potential impact of neurotechnology is enormous, its clinical use nowadays is still limited. Many devices require invasive surgery, with related high risks that not always overcome the benefits for the patients. A big step in this direction has been the development of neurovascular interfaces which interact with the neural tissue from within blood vessels. Endovascular procedures are considerably less invasive, are routinely performed and allow for short recovery time. [2] Moreover, neurovascular interfaces do not require craniotomies, reducing the risks associated with the surgical procedure (e.g., susceptibility to seizures). These advantages could increase the chance of patients accepting the treatment.Neurovascular interfaces developed so far are wires or catheters used as electrodes. Even though these solutions opened the doors to endovascular neural recording and stimulation, their main limitations were the short-term application and the low spatial resolution. The introduction of stentelectrode arrays (e.g., Stentrode) overcame these issues, [2] and the advantages of this technology have been recently demonstrated in preclinical and clinical trials for brain-computer-interface. [3][4][5][6] Also, seventeen potential medical targets have been identified where intravascular neuromodulation could replace invasive deep brain stimulation protocols. [7] By accessing the internal cerebral vein or the anterior communicating artery, it would be possible to perform minimally invasive neuromodulation for a wide range of neurological disorders such as Parkinson's, Alzheimer's, essential tremor, depression, and obsessive-compulsive disorders. [7] Furthermore, neurovascular interfaces could be as well applied to the peripheral system for pain relief, motor deficits, bladder control, and stimulation of muscles, among others. However, the main drawback of stent-electrode arrays is the metallic scaffold. A conductive substrate for electrodes makes insulation critical and shortcuts frequent. [3] Also, metallic stents could induce a strong inflammatory response, that could reduce the performances of a neural interface. [8][9][10][11] For conventional stent technology, this limitation already led to the development of bioresorbable devices, allowing for a better interaction with the tissue and placement in mechanically solicited areas. [12] Neural interfaces are used to mitigate the burden of traumatic injuries, neurodegenerative diseases, and mental disorders. However, the transient or permanent placement of an interface in close contact with the neural tissue requires invasive surgery, potentially entailing both short-and long-term complications. To tackle this problem, a transient neurovascular interface for neural recording and stimulation is developed. This endovascular array has been fabricated with facile molding techniques using solely polymeric mat...

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Modulation of the shape and speed of a chemical wave in an unstirred Belousov–Zhabotinsky reaction by a rotating magnet

Okano

Kitahata

2012

Bioelectromagnetics

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The objective of this study was to observe whether a rotating magnetic field (RMF) could change the anomalous chemical wave propagation induced by a moderate-intensity gradient static magnetic field (SMF) in an unstirred Belousov-Zhabotinsky (BZ) reaction. The application of the SMF (maximum magnetic flux density = 0.22 T, maximum magnetic flux density gradient = 25.5 T/m, and peak magnetic force product (flux density × gradient) = 4 T(2) /m) accelerated the propagation velocity in a two-dimensional pattern. Characteristic anomalous patterns of the wavefront shape were generated and the patterns were dependent on the SMF distribution. The deformation and increase in the propagation velocity were diminished by the application of an RMF at a rotation rate of 1 rpm for a few minutes. Numerical simulation by means of the time-averaged value of the magnetic flux density gradient or the MF gradient force over one rotation partially supported the experimental observations. These considerations suggest that RMF exposure modulates the chemical wave propagation and that the degree of modulation could be, at least in part, dependent on the time-averaged MF distribution over one rotation. Bioelectromagnetics 34:220-230, 2013. © 2012 Wiley Periodicals, Inc.

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A mathematical model for blood flow in magnetic field

Cited by 314 publications

References 34 publications

Validation of a Magneto- And Ferro-Hydrodynamic Model for Non-Isothermal Flows in Conjunction With Newtonian and Non-Newtonian Fluids

Validation of a Magneto- And Ferro-Hydrodynamic Model for Non-Isothermal Flows in Conjunction With Newtonian and Non-Newtonian Fluids

Transient Neurovascular Interface for Minimally Invasive Neural Recording and Stimulation

Modulation of the shape and speed of a chemical wave in an unstirred Belousov–Zhabotinsky reaction by a rotating magnet

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