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Numerical Study on the Efficiency of Magnetophoresis in Human Vasculature like Conditions

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Mathematical Modelling and Scientific Computing with Applications (ICMMSC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 308))

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Abstract

Magnetic Nanoparticles (MNPs) have been proposed as therapeutic agents for treatment of medical conditions like cancer by using them either as drug carriers to specific locations in the body or as agents for localized heating. For these treatments to be effective, a substantial quantity of MNPs need to reach the target site from the site of injection. However, this may not be the case if blood flow alone is relied on to transport the MNPs as losses to branching blood vessels that lead to transport in directions away from the target site can occur. We have carried out numerical simulations on the flow of a dilute concentration of magnetic particles (MPs), where inter particle interactions can be ignored, in channels that mimic human vasculature like conditions. This has been done using Open Field Operation And Manipulation (OpenFOAM). Blood has been treated as a Newtonian fluid and only laminar flows are considered. The size of channels and direction of flow, which is always towards the target site, mimics the situation in arteries and arterioles. We have only taken into consideration situations where the main channel gives rise to a single daughter channel at different branching angles to the direction of flow. We find that a substantial number of MPs are lost to the daughter channel when the branching angle is less than 45° while a moderate loss is seen for branching angles greater than 45°. Application of an optimum external magnetic field gradient significantly improves the fraction of particles moving towards the target site in the case of branching angles less than 90° and ensures practically no loss for branching angles greater than 90°.

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Acknowledgements

RS would like to thank University Grants Commission (Govt. of India) for her fellowship under the NET—JRF/SRF scheme. The authors are grateful to the organizers of the “International Conference on Mathematical Modelling and Scientific Computing” for providing an opportunity to present this work and interact with experts working in a similar field leading to constructive critical input for this study.

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Authors and Affiliations

  1. Department of Physics, Bangalore University, Bengaluru, 560056, India

    S. Rekha & Sarbari Bhattacharya

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  1. S. Rekha
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  2. Sarbari Bhattacharya
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Correspondence to Sarbari Bhattacharya .

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Editors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India

    Santanu Manna

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, USA

    Biswa Nath Datta

  3. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India

    Sk. Safique Ahmad

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Rekha, S., Bhattacharya, S. (2020). Numerical Study on the Efficiency of Magnetophoresis in Human Vasculature like Conditions. In: Manna, S., Datta, B., Ahmad, S. (eds) Mathematical Modelling and Scientific Computing with Applications. ICMMSC 2018. Springer Proceedings in Mathematics & Statistics, vol 308. Springer, Singapore. https://doi.org/10.1007/978-981-15-1338-1_14

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