A mathematical model for studying the Red Blood Cell magnetic susceptibility

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.05.014

Protopapas Eleftherios , Vafeas Panayiotis , Hadjinicolaou Maria

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引用次数: 0

Abstract

The susceptibility of the human Red Blood Cells (RBCs) under the action of magnetic fields, either serves as a biomarker in medical tests, e.g.. Magnetic Resonance Imaging, Nuclear Magnetic Resonance, Magnetoencephalography, or it is used in diagnostic and therapeutical processes, e.g.. magnetophoresis for cell sorting. In the present manuscript we provide analytical expressions for the magnetic potential and the magnetic field strength vector, when a magnetic field is applied to a RBC, modeled as a two-layered inverted spheroid. We introduce this way in the model the biconcave shape of the RBC and its structure (membrane and cytocol) in a more realistic representation, as until now, the RBC's shape was considered either as a sphere or a spheroid. The solution inside the RBC is obtained in R-separable form in terms of Legendre functions of the first and of the second kind and cyclic trigonometric functions, by applying appropriate boundary conditions on each layer. Our results reveal a non-uniform magnetic field inside the RBC. Parametric study of the solution, for various values of the physical properties of the RBC, is also provided, demonstrating the diamagnetic or the paramagnetic property of the RBC, which is strongly related to the health condition of the blood. The obtained solution may also serve for the justification of experimental results.

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研究红血球磁感应强度的数学模型

人体红细胞（rbc）在磁场作用下的易感性，可以作为医学试验中的生物标志物，例如：磁共振成像，核磁共振，脑磁图，或用于诊断和治疗过程，例如。用于细胞分选的磁电泳。在目前的手稿中，我们提供了解析表达式的磁势和磁场强度矢量，当一个磁场施加到一个RBC，建模为一个双层倒球体。我们在模型中引入这种方法，使红细胞的双凹形状及其结构（膜和细胞壁）以更真实的形式呈现，因为到目前为止，红细胞的形状被认为是球体或椭球体。通过在每一层上应用适当的边界条件，以r -可分形式用第一类、第二类Legendre函数和循环三角函数得到了RBC内部的解。我们的结果揭示了红细胞内部的非均匀磁场。还提供了溶液的参数研究，用于RBC物理性质的不同值，证明了RBC的抗磁性或顺磁性，这与血液的健康状况密切相关。所得解也可作为实验结果的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.