Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect

Omamoke Ekakitie; Funakpo Isaac; Olugbenro Osinowo; Sylvester Chibueze Izah; Keneke Edwin Dauseye; Bunonyo Wilcox Kubugha

doi:doi:10.11648/j.ajam.20231103.12

Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect

Omamoke Ekakitie, Funakpo Isaac, Olugbenro Osinowo, Sylvester Chibueze Izah, Keneke Edwin Dauseye, Bunonyo Wilcox Kubugha

Published in American Journal of Applied Mathematics (Volume 11, Issue 3)

Received: 14 March 2023 Accepted: 6 April 2023 Published: 20 June 2023

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Abstract

Sickle cell is a disease that affects the growth and life expectancy of a given population infected with this disease. Hence, we carried out a theoretical study on the improvement of blood flow and the morphology effect on red blood cells in sickle cell patient using a mathematical model. This morphological effect on the red blood cell comes as a result of the effect of treatment parameter embedded in the governing equation. The governing dimensional second order partial differential equations was transformed to non-dimensional form and solved analytically using the Frobenius method and solutions was gotten for both the blood momentum, energy and diffusion. The solutions for the flow of the red blood cell and wall shear stress was obtained with the result showing that heat source increase causes an increase in the flow of blood, reducing the shear stress at the wall and increasing the volumetric flow rate. This effect caused an improvement in the sickle shape of the deformed RBC and an improved flow which will reduce the crises experienced in patients with SCD. Finally, the increase in chemical reaction caused an increase in the pulsatile pressure of the sickled blood cell which results to an increase in the blood flow.

Published in	American Journal of Applied Mathematics (Volume 11, Issue 3)
DOI	10.11648/j.ajam.20231103.12
Page(s)	40-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hemoglobin, Pulsatile Pressure, Heat Source, Chemical Reaction, Blood Flow, Wall Shear Stress

References

[1]	Pauling L, Itano HA, Singer SJ et al. Sickle cell anaemia, a molecular disease. Science 1949; 109: 443.
[2]	Wood WG, Weatherall DJ. Haemoglobin synthesis during human foetal development. Nature 1973; 244: 162-165.
[3]	Fogg, B. J. (2017). Persuasive Technology Lab Stanford University https://doi.org cap-tology.stanford.edu.
[4]	David C Rees, Thomas N Williams, Mark T Gladwin, Sickle-cell disease, The Lancet, Volume 376, Issue 9757, 2010, Pages 2018-2031.
[5]	Weatherall, D. J. & Clegg, J. B. (2001). Inherited haemoglobin disorder: an increasing global health problem. Bull World Health Organ. 2001; 79 (8): 704-12. Epub 2001 Oct 24. PMID: 11545326; PMCID: PMC2566499.
[6]	Kwaku Ohene-Frempong, Steven J. Weiner, Lynn A. Sleeper, Scott T. Miller, Stephen Embury, John W. Moohr, Doris L. Wethers, Charles H. Pegelow, Frances M. Gill, the Cooperative Study of Sickle Cell Disease; Cerebrovascular Accidents in Sickle Cell Disease: Rates and Risk Factors. Blood 1998; 91 (1): 288-294. doi: https://doi.org/10.1182/blood.V91.1.288
[7]	Hutchaleelaha, A., Patel, M., Washington, C., Siu, V., Allen, E., Oksenberg, D., Gretler, D. D., Mant, T. & Lehrer-Graiwer, J. (2019). Pharmacokinetics and pharmacodynamics of voxelotor (GBT440) in healthy adults and patients with sickle cell disease. Br J Clin Pharmacol. 2019 Jun; 85 (6): 1290-1302. doi: 10.1111/bcp.13896. Epub, Mar 31. PMID: 30743314; PMCID: PMC6533444.
[8]	Campinho Pedro, Vilfan Andrej, Vermot Julien; Blood Flow Forces in Shaping the Vascular System: A Focus on Endothelial Cell Behavior. Frontiers in Physiology vol. 11, 2020 pages 552.
[9]	Marvin J. Slepian, Jawaad Sheriff, Marcus Hutchinson, Phat Tran, Naing Bajaj, Joe G. N. Garcia, S. Scott Saavedra, Danny Bluestein, Shear-mediated platelet activation in the free flow: Perspectives on the emerging spectrum of cell mechanobiological mechanisms mediating cardiovascular implant thrombosis, Journal of Biomechanics, Volume 50, 2017, Pages 20-25.
[10]	Eldesoky, M. I. (2012). Mathematical Analysis of Unsteady MHD Blood Flow through Parallel Plate Channel with Heat Source. World Journal of Mechanics, 2, 131, 131-137.
[11]	Sen, S. & Chakravarty, S. (2012). Theoretical study on the constricted flow phenomena in arteries. Korea-Australia Rheology Journal, Volume 14, Number 4, page 287-295, DOI: 10.1007/S/3367-012-0035-9.
[12]	Shit, G. C. & Roy, M. (2012). Hydromagnetic Pulsating Flow of Blood in a Constricted Porous Chanel: A Theoretical Study. Proceedings of the World Congress on Engineering, Volume 1.
[13]	Mukesh, K. S., Kuldip, B. & Seema, B. (2012). Pulsatile Unsteady Flow of Blood through Porous Medium in a Stenotic Artery under the Influence of Transverse Magnetic Field. Korea-Australia Rheology Journal, Volume 24, Number 3, pp. 181-189.
[14]	Kumar, A., Chandel, R. S., Shrivastava, R., Shrivastava, K. & Kumar, S. (2016). Mathematical Modelling of blood flow in an inclined tapered artery under MHD effect through porous medium. International Journal of Pure and Applied Mathematical Science, 9 (1), 75-88, ISSN 0972-9828.
[15]	Sinha, A., Misra, J. C. & Shit, G. C. (2016). Effect of heat transfer on unsteady MHD flow of blood in a permeable vessel in the presence of non-uniform heat source. Alexandria Engineering Journal 55, 2023-2033.
[16]	Vincent, M., Eustance, M. & Kennedy, G. K. (2017). Velocity Profiles of Unsteady Blood Flow through an Inclined Circular Tube with Magnetic Field, Journal of Advances in Mathematics and Computer Science, 24 (6): 1-10, JAMCS.36620, ISSN: 2231-0851.
[17]	Sharma, M., Gaur, R. K. & Biswas, P. (2018). Effect of slip parameter on MHD blood flow and heat transfer through a porous medium with variable viscosity. International Journal of engineering sciences and research, 7 (4), DOI: 10.5281/zenodo.1228826, ISSN: 2277-9655.
[18]	Karthikeyan, D. & Jeevitha, G. (2019). Heat and Mass Transfer on MHD Two Phase Blood Flow through a Stenosed Artery with Permeable Wall. International Journal of Innovative Technology and Exploring Engineering (IJITEE), 8 (7), ISSN: 2278-3075.
[19]	Chinedu, N. & Amadi, I. U. (2021). Analytical Solutions of a Non-isothermal Flow in Cylindrical Geometry. Asian Research Journal of Mathematics, 17 (3): 55-76, 2021; doi: 10.9734/ARJOM/2021/v17i330283.
[20]	Hasitha, N. P. G., Suvash, C. S. and YaunTong, G. (2013). Deformation of a Single Red Blood cell in a Microvessel. ANZIAM J. 55 (EMAC2013) pp. C64-C79, 2014.
[21]	Larkin T. J. and Kuchel, W. P. (2006). Mathematical Models of Naturally Morphed Human Erythrocytes: Stomatocytes and Echinocytes. Bulletin of Mathematical Biology DOI 10.1007/s11538-009-99493-8.
[22]	Paul, B. B., Yunlong, S., Yin-Quan, C. and Arthur, C. (2007). Circulation of Sperical Red Blood Cell Deformation in a dual-beam Optical Stretcher. OSA 15 (24).
[23]	Yixiang, D., Dimitrios, P. P., Hung-Yu, C., Sabia, Z. A., Xuejin, L., Ming, D. and George, E. K. (2019). Quantifying Shear-induced Deformation and Detachment of Individual Adherent Sickle Red Blood Cells. Biophysical Journal, 116, page 360-371.
[24]	Ahmat, N. Ahmed, J. J., Ahmed, A., Arbin, N., Ismail, N. B. and Rashad, S. A. (2021). Red Blood Cell Shapes Parameterization Using Partial Differential Equations. Review of International Geographical Education, 11 (4), 842-849, doi: 10.48047/rigeo.11.04.77.

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APA Style

Omamoke Ekakitie, Funakpo Isaac, Olugbenro Osinowo, Sylvester Chibueze Izah, Keneke Edwin Dauseye, et al. (2023). Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect. American Journal of Applied Mathematics, 11(3), 40-51. https://doi.org/10.11648/j.ajam.20231103.12

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ACS Style

Omamoke Ekakitie; Funakpo Isaac; Olugbenro Osinowo; Sylvester Chibueze Izah; Keneke Edwin Dauseye, et al. Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect. Am. J. Appl. Math. 2023, 11(3), 40-51. doi: 10.11648/j.ajam.20231103.12

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AMA Style

Omamoke Ekakitie, Funakpo Isaac, Olugbenro Osinowo, Sylvester Chibueze Izah, Keneke Edwin Dauseye, et al. Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect. Am J Appl Math. 2023;11(3):40-51. doi: 10.11648/j.ajam.20231103.12

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@article{10.11648/j.ajam.20231103.12,
  author = {Omamoke Ekakitie and Funakpo Isaac and Olugbenro Osinowo and Sylvester Chibueze Izah and Keneke Edwin Dauseye and Bunonyo Wilcox Kubugha},
  title = {Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect},
  journal = {American Journal of Applied Mathematics},
  volume = {11},
  number = {3},
  pages = {40-51},
  doi = {10.11648/j.ajam.20231103.12},
  url = {https://doi.org/10.11648/j.ajam.20231103.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20231103.12},
  abstract = {Sickle cell is a disease that affects the growth and life expectancy of a given population infected with this disease. Hence, we carried out a theoretical study on the improvement of blood flow and the morphology effect on red blood cells in sickle cell patient using a mathematical model. This morphological effect on the red blood cell comes as a result of the effect of treatment parameter embedded in the governing equation. The governing dimensional second order partial differential equations was transformed to non-dimensional form and solved analytically using the Frobenius method and solutions was gotten for both the blood momentum, energy and diffusion. The solutions for the flow of the red blood cell and wall shear stress was obtained with the result showing that heat source increase causes an increase in the flow of blood, reducing the shear stress at the wall and increasing the volumetric flow rate. This effect caused an improvement in the sickle shape of the deformed RBC and an improved flow which will reduce the crises experienced in patients with SCD. Finally, the increase in chemical reaction caused an increase in the pulsatile pressure of the sickled blood cell which results to an increase in the blood flow.},
 year = {2023}
}

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TY  - JOUR
T1  - Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect
AU  - Omamoke Ekakitie
AU  - Funakpo Isaac
AU  - Olugbenro Osinowo
AU  - Sylvester Chibueze Izah
AU  - Keneke Edwin Dauseye
AU  - Bunonyo Wilcox Kubugha
Y1  - 2023/06/20
PY  - 2023
N1  - https://doi.org/10.11648/j.ajam.20231103.12
DO  - 10.11648/j.ajam.20231103.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 40
EP  - 51
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20231103.12
AB  - Sickle cell is a disease that affects the growth and life expectancy of a given population infected with this disease. Hence, we carried out a theoretical study on the improvement of blood flow and the morphology effect on red blood cells in sickle cell patient using a mathematical model. This morphological effect on the red blood cell comes as a result of the effect of treatment parameter embedded in the governing equation. The governing dimensional second order partial differential equations was transformed to non-dimensional form and solved analytically using the Frobenius method and solutions was gotten for both the blood momentum, energy and diffusion. The solutions for the flow of the red blood cell and wall shear stress was obtained with the result showing that heat source increase causes an increase in the flow of blood, reducing the shear stress at the wall and increasing the volumetric flow rate. This effect caused an improvement in the sickle shape of the deformed RBC and an improved flow which will reduce the crises experienced in patients with SCD. Finally, the increase in chemical reaction caused an increase in the pulsatile pressure of the sickled blood cell which results to an increase in the blood flow.
VL  - 11
IS  - 3
ER  -

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Author Information

Omamoke Ekakitie

Department of Mathematics, Bayelsa Medical University, Yenagoa, Nigeria
Funakpo Isaac

Department of Mathematics, Bayelsa Medical University, Yenagoa, Nigeria
Olugbenro Osinowo

Department of Medicine and Surgery, Bayelsa Medical University, Yenagoa, Nigeria
Sylvester Chibueze Izah

Department of Microbiology, Bayelsa Medical University, Yenagoa, Nigeria
Keneke Edwin Dauseye

Department of Physics, Bayelsa Medical University, Yenagoa, Nigeria
Bunonyo Wilcox Kubugha

Department of Mathematics, Federal University, Otuoke, Nigeria

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APA Style

Omamoke Ekakitie, Funakpo Isaac, Olugbenro Osinowo, Sylvester Chibueze Izah, Keneke Edwin Dauseye, et al. (2023). Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect. American Journal of Applied Mathematics, 11(3), 40-51. https://doi.org/10.11648/j.ajam.20231103.12

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ACS Style

Omamoke Ekakitie; Funakpo Isaac; Olugbenro Osinowo; Sylvester Chibueze Izah; Keneke Edwin Dauseye, et al. Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect. Am. J. Appl. Math. 2023, 11(3), 40-51. doi: 10.11648/j.ajam.20231103.12

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AMA Style

Omamoke Ekakitie, Funakpo Isaac, Olugbenro Osinowo, Sylvester Chibueze Izah, Keneke Edwin Dauseye, et al. Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect. Am J Appl Math. 2023;11(3):40-51. doi: 10.11648/j.ajam.20231103.12

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@article{10.11648/j.ajam.20231103.12,
  author = {Omamoke Ekakitie and Funakpo Isaac and Olugbenro Osinowo and Sylvester Chibueze Izah and Keneke Edwin Dauseye and Bunonyo Wilcox Kubugha},
  title = {Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect},
  journal = {American Journal of Applied Mathematics},
  volume = {11},
  number = {3},
  pages = {40-51},
  doi = {10.11648/j.ajam.20231103.12},
  url = {https://doi.org/10.11648/j.ajam.20231103.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20231103.12},
  abstract = {Sickle cell is a disease that affects the growth and life expectancy of a given population infected with this disease. Hence, we carried out a theoretical study on the improvement of blood flow and the morphology effect on red blood cells in sickle cell patient using a mathematical model. This morphological effect on the red blood cell comes as a result of the effect of treatment parameter embedded in the governing equation. The governing dimensional second order partial differential equations was transformed to non-dimensional form and solved analytically using the Frobenius method and solutions was gotten for both the blood momentum, energy and diffusion. The solutions for the flow of the red blood cell and wall shear stress was obtained with the result showing that heat source increase causes an increase in the flow of blood, reducing the shear stress at the wall and increasing the volumetric flow rate. This effect caused an improvement in the sickle shape of the deformed RBC and an improved flow which will reduce the crises experienced in patients with SCD. Finally, the increase in chemical reaction caused an increase in the pulsatile pressure of the sickled blood cell which results to an increase in the blood flow.},
 year = {2023}
}

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TY  - JOUR
T1  - Mathematical Modelling for Improved Blood Flow in a Sickle Cell Anaemia Patient with Morphological Effect
AU  - Omamoke Ekakitie
AU  - Funakpo Isaac
AU  - Olugbenro Osinowo
AU  - Sylvester Chibueze Izah
AU  - Keneke Edwin Dauseye
AU  - Bunonyo Wilcox Kubugha
Y1  - 2023/06/20
PY  - 2023
N1  - https://doi.org/10.11648/j.ajam.20231103.12
DO  - 10.11648/j.ajam.20231103.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 40
EP  - 51
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20231103.12
AB  - Sickle cell is a disease that affects the growth and life expectancy of a given population infected with this disease. Hence, we carried out a theoretical study on the improvement of blood flow and the morphology effect on red blood cells in sickle cell patient using a mathematical model. This morphological effect on the red blood cell comes as a result of the effect of treatment parameter embedded in the governing equation. The governing dimensional second order partial differential equations was transformed to non-dimensional form and solved analytically using the Frobenius method and solutions was gotten for both the blood momentum, energy and diffusion. The solutions for the flow of the red blood cell and wall shear stress was obtained with the result showing that heat source increase causes an increase in the flow of blood, reducing the shear stress at the wall and increasing the volumetric flow rate. This effect caused an improvement in the sickle shape of the deformed RBC and an improved flow which will reduce the crises experienced in patients with SCD. Finally, the increase in chemical reaction caused an increase in the pulsatile pressure of the sickled blood cell which results to an increase in the blood flow.
VL  - 11
IS  - 3
ER  -

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