Keywords:-

Keywords: Hematopoietic stem cells, Leukemic stem cells, Bone marrow, Growth dynamics, Compartmental modeling, Fractional order derivatives, Self-renewal, Proliferation rates, Cellular differentiation, Acute myeloid leukemia.

Article Content:-

Abstract

This study aims to unravel the growth dynamics of hematopoietic and leukemic stem cells within the bone marrow, viewing them as a complex network of interconnected compartments representing distinct stages of cellular differentiation. Leveraging insights from established models of cancer cell growth, we have undertaken a comprehensive re-examinations and reinterpretation of some classical growth models, subsequently reformulating them into a fractional order derivative-based framework. Employing this innovative approach, we have delved into the intricate interplay between self-renewal and proliferation rates across diverse sub-stages of cellular differentiation. Our investigations illuminate the nuanced regulatory mechanisms governing stem cell dynamics, offering significant insights into the pathophysiology of hematopoietic disorders, notably acute myeloid leukemia.

References:-

References

Akbar, S., Shah, S. R., “DURYSTA” the first biodegradable sustained release implant for the treatment of open-angle glaucoma, International Journal of Frontiers in Biology and Pharmacy Research, 01(02), 1-7, (2021).

Akbar, S., Shah, S. R., “Mathematical Modeling of Blood Flow Dynamics in the Cardiovascular System: Assumptions, Considerations, and Simulation Results”, Journal of Current Medical Research and Opinion, 7(4), 2216-2225, (2024).

Akbar, S., Shah, S. R., “The Effects of Prostaglandin Analogs on Intraocular Pressure (IOP) in Human Eye for Open Angle Glaucoma. International Journal of Innovative Technology and Exploring Engineering, 10 (2), 176-180, (2020).

Anamika, Shah, S. R., “Mathematical and Computational study of blood flow through diseased artery”, International Journal of Computer Science, Vol. 5, (6), pp. 1-6, (2017).

Anamika, Shah, S. R., Anuradha “Bio-Computational analysis of blood flow through two phase artery”, International Journal of Engineering Science and Computing, 7, (6),13397-213401, (2017).

Anamika, Shah, S. R., Kumar, R., “Mathematical Modelling of blood flow through tapered stenosed artery with the suspension of nanoparticles using Jeffrey fluid model”, International journal of development research, 07, No. 06, 13494-13500, (2017).

Anamika, Shah, S. R., Singh A., “Mathematical Modelling Of Blood Flow through Three Layered Stenosed Artery”, International Journal for Research in Applied Science and Engineering Technology, 5, (6), 1-6, (2017).

Anuradha S,, Shah, S. R., Siddiqui, S. U., “Effects of inclined multi-stenoses arteries on blood flow characteristics using bingham plastic fluid”, International Journal for Mathematics, 1, (12), 7-14, (2015).

Anuradha S., Shah, S. R., S.U. Siddiqui, “Mathematical Modeling and Numerical Simulation of Blood Flow through Tapered Artery”, International Journal of Innovative Science, Engineering & Technology, 3, (2), 710-717, (2016).

Anuradha S., Shah, S. R., S.U. Siddiqui, “Performance of blood flow through two phase stenosed artery using Herschel-Bulkley model”, International Journal of Applied And Pure Science and Agriculture, Vol. 2, (2), pp. 228-240, (2016).

Anuradha S., Shah, S. R., Siddiqui, S. U., “Mathematical Modelling and Analysis of Blood Flow through Diseased Blood Vessels”, International Journal of Engineering and Management Research, Vol.5, (6), pp. 366-372, (2015).

Anuradha, S., Shah, S. R., Siddiqui, S. U., “A Mathematical Model to study the similarities of blood fluid models through inclined multi-stenosed artery”, International Journal of Engineering Research and Modern Eduacation, 2, (1), 108-115, (2017).

Arya, D., Shah, S. R., “Human Resource Management Strategies for Improving Educational Outcomes in Bihar, International Journal of Humanities Social Science and Management, 4(4), 955-963, (2024).

Arya, D., Shah, S. R., “Optimizing Educational Outcomes: The Role of Human Resource Management in Jharkhand's Education System, International Journal of Novel Research And Development, 9(8), b51-b57, (2024).

Chaturvedi, P. and Shah, S. R. “Role of crizanlizumab for sicke red cells disease”, International Journal of Biology, Pharmacy and Allied Sciences, 12(3), 1147-1157, (2023).

Chaturvedi, P., Kumar, R., Shah, S. R., “Bio-Mechanical and Bio-Rheological Aspects of Sickle Red Cells in Microcirculation: A Mathematical Modelling Approach, Fluids, 6, 322, 01-15, (2021).

Chaturvedi, P., Shah, S. R., “Mathematical Analysis for the Flow of Sickle Red Blood Cells in Microvessels for Bio Medical Application, Yale Journal of Biology and Medicine, 96 (1), (2023),13-21.

Chaturvedi, P., Shah, S. R., Akbar, S., Kumar, R., “Prospective of Hydroxychloroquine and Zinc with Azithromycin for Nanoparticles Blood Flow in Covid-19 Patients, International Journal of Nanotechnology in Medicine & Engineering, 6 (1), 01-07, (2021).

Datt, M. G., Arya, S., Shah, S. R., “Ayurvedic Approaches To Maintaining Healthy And Narrowed Arteries”, International Journal For Research & Development In Technology, Vol. 21(6), 21-30, (2024).

Geeta, Siddiqui, S. U., Sapna, “Mathematical Modelling of blood flow through catheterized artery under the influence of body acceleration with slip velocity”, Application and applied Mathematics An international journal, 8(2), 481-494, (2013).

Geeta, Siddiqui, S. U., Shah, S. R., “A Biomechanical approach to the effect of body acceleration through stenotic artery”, Applied Mathematics and Computation, Vol. 109(1), pp.27-41, (2015).

Geeta, Siddiqui, S. U., Shah, S. R., “Effect of body acceleration and slip velocity on the pulsatile flow of Casson fluid through stenosed artery”, Advance in applied science research, Vol. 5(3), pp.231-225, (2014).

Geeta, Siddiqui, S. U., Shah, S. R.,“A Mathematical Model for two layered pulsatile blood flow through stenosed arteries”, E-Journal of science and Technology, Vol. 109 (11), pp. 27-41, (2015).

Gupta, P., Akbar, S., Shah, S. R., Alshehri, Mo., Sharma, S. K., and “A Mathematical Study for Promoting Disability Inclusion in Glaucoma: A Comprehensive Approach”, Journal of Disability Research, 3, 1-12, (2024).

Islam S. M. N., Sadique, Mo., Shah, S. R., Sunil Kumar Sharma, , “Effect of Significant Parameters on Squeeze Film Characteristics in Pathological Synovial Joints”, Mathematics (MDPI), 11 (1468) 1-23, (2023).

Jaiswal., K. M., Shabab Akbar and Shah S. R., Mo. Sadique “Exploring capillary-tissue fluid exchange: Insights into red cell deformation in narrow vessels and its clinical implications”, International Journal of Fauna and Biological Studies, 11(3), 4-14, (2024). https://doi.org/10.22271/23940522.2024.v11.i3a.1021.

Kasturia, P., Rohit Kumar Sharma, Purnima Chaturvedi, Ravins Dohre, Shah, S. R.,“Efficacy of venetoclax and azacitidine for targeting leukemic stem cell in acute myeloid leukemia”, International Journal of Biology, Pharmacy and Allied Sciences, 13(6), 3072-3090, (2024). https://doi.org/10.31032/IJBPAS/2024/13.6.8960

Kaur, H., Prithvi Singh, Rubi Solanki, Alvea Tasneem, Simran Suri, Shah, S. R., Ravins Dohare, “Screening of miRNAs as prognostic biomarkers and their associated hub targets across Hepatocellular carcinoma using survival-based bioinformatics approach”, Journal of Genetic Engineering and Biotechnology, 22 (1), 1-10, (2024).

Kumar V., and Shah, S. R., “Mathematical model to study the heat transfer between core and skin”, SRMS, Journal of Mathematical Sciences, 7 (2021), 7-12, (10th March 2024).

Kumar, J. P., Sadique, Mo. Shah, S. R.,, “Mathematical study of blood flow through blood vessels under diseased condition, International Journal of Multidisciplinary Research and Development, 9(6), 2022, pp.31-44.

Kumar, P, Shah, S. R., “A Hydromechanical Perspective to Study the Effect of Body Acceleration through Stenosed Artery”, International journal of mathematical engineering and management sciences, Volume. 6 No. 5, pp. 1381-1390, 2021.

Kumar, R., Shah, S. R., “A mathematical approach to study the blood flow through tapered stenosed artery with the suspension of nanoparticles” Destech Transactions on Engineering and Technology Research, Vol.01, pp. 1-6, (2017).

Kumar, R., Shah, S. R., “Mathematical Modeling of Blood Flow with the Suspension of Nanoparticles Through a Tapered Artery With a Blood Clot”, Frontiers in Nanotechnology, 2, 596475, 1-5, (2020).

Kumar, R., Shah, S. R., “Performance of blood flow with suspension of nanoparticles though tapered stenosed artery for jeffrey fluid model” International Journal of Nanoscience, Vol.17, No.6, pp. 1850004 (1-7), (2018).

Kumar, R., Shah, S. R., “Study of blood flow with suspension of nanoparticles through tapered stenosed artery”, Global Journal of Pure and Applied Mathematics, 13(10), 7387-7399, (2017).

Kumar, V., and Shah, S. R., “Mathematical modelling to study the heat transfer between core and skin”, SRMS, Journal of Mathematical Sciences, 7 (2021), 7-12, (2024).

Kumar, V., Shah, S. R., “A mathematical approach to investigate the temperature distribution on skin surface with sinusoidal heat flux condition, International Journal of Multidisciplinary Research and Development, 9 (5), 2022, 141-146.

Kumar, V., Shah, S. R., “A Mathematical study for heat transfer phenomenological processes in human skin”, International Journal of Mechanical Engineering, 7 (6), 683-692, (2022).

Kumar, V., Shah, S. R., “Thermobiological Mathematical Model for the study of temperature response after cooling effects”, ssrg, International Journal of Applied physics, 9 (2), 7-11, (2022).

Kumari, N., Shah, S. R., “Examining Women's Representation In Disaster Risk Reduction Strategies Across South Asia”, International Journal of Disaster Management, 2(1), 1-3, (2024).

Lenin, J. S., Shah S. R., “Mathematical Analysis of Stem Cell Dynamics in Acute Myeloid Leukemia: Towards Precision Medicine Strategies, International Journal of Science and Research, 13(05), 528-535, (2024).

Mahesh, Arya, S., Shah, S. R., “Optimizing cardiovascular health: ayurvedic insights into blood flow through normal and stenosed arteries, International Journal of AYUSH, 13 (5), 18-35, (2024).

Majhi, L., Sudheer Arya Sapna Ratan Shah, “Exploring Shilajatu's Therapeutic Potential in Diabetes Management: A Comprehensive Study Integrating Ayurvedic Wisdom and Modern Science”, International Journal of Science and Research (IJSR), 13(5), 1374-1380, (2024). https://dx.doi.org/10.21275/SR24522110012.

Mo. Sadique and Shah, S. R., “Mathematical model to study the study the squeeze film characteristics of synovial joints in diseased human knee joint”, World Scientific Annual Review of Biomechanics, 1 (2330004) 1-21, (2023).

Mo., Sadique, Shah, S. R.,, “Mathematical model to study the effect of PRG4, hyaluronic acid and lubricin on squeeze film characteristics of diseased synovial joint”, International Journal of Mechanical Engineering, 7 (6), 2022, pp. 832-848.

Parambath, A. B., Kandankel, P., Shah, S. R., Dynamic Modeling of Cytokine-Dependent Proliferation Rates over Time in Cancer: Insights from Scientific Analysis, Journal of Mathematical Techniques and Computational Mathematics, 3(7), 01-09, (2024).

Purnima C., Shah, S. R., “Assessing the Clinical Outcomes of Voxelotor Treatment in Patients with Sickle Cell Disease”, International Journal of Applied Science and Biotechnology, 12(1), 46-53, (2024).

Sadique, Mo., Shah, S. R.,, “Mathematical study for the synovial fluid flow in Osteoarthritic knee joint, Journal of Engineering and Applied Sciences, 17(2),15-21,(2022).

Sapna, Siddiqui, S. U., “Study of blood flow through a stenosed capillary using Casson’s fluid model”, Ultra Science, International journal of physical sciences, Vol. 16, (2) pp. 133-142, (2004).

Sengar, N., Yadav, P., Shah, S., R., Economic Conditions and Age Profile of Women Domestic Workers in Delhi's Urban Informal Sector, International Journal of Research Publication and Reviews, 15(8),494-500, (2024).

Shabab A., Shah, S. R., “Mathematical Modeling of Blood Flow Dynamics in the Cardiovascular System: Assumptions, Considerations, and Simulation Results”, Journal of Current Medical Research and Opinion, 7(4), 2216-2225, (2024).

Shah, S. R., “A biomechanical approach for the study of deformation of red cells in narrow capillaries”, IJE: Transaction A: Basics, Vol. 25(4), pp.303-313, (2012).

Shah, S. R., “A biomechanical approach for the study of Two-phase blood flow through stenosed artery”, International Journal of research studies in biosciences, 1(2), 24-32, (2013).

Shah, S. R., “A case study of non-Newtonian viscosity of blood through artherosclerotic artery”, The cardiology, Vol.6 (2), pp.11-17, (2011).

Shah, S. R., “A Mathematical Model for the analysis of blood flow through diseased blood vessels under the influence of porous parameter”, Journal of Biosciences and Technology, Vol. 4(6), pp.534-541, (2013).

Shah, S. R., “A mathematical study of blood flow through radially non-symmetric multiple stenosed arteries under the influence of magnetic field”, International Journal of Advanced Research in Biological Sciences. 2 (12), 379-386, (2015).

Shah, S. R., “A mathematical study of blood flow through stenosed artery”, International Journal of Universal Science and Engineering, 1(1), pp.26-37, (2015).

Shah, S. R., “A study of blood flow through multiple atherosclerotic arteries”, International Journal for Mathematics, Vol. 1, (12), pp. 1-6, (2015).

Shah, S. R., “A study of effects of magnetic field on modified Power-law fluid in modeled stenosed artery” Journal of Bioscience and Technology, 1 (4), 187-196, (2010).

Shah, S. R., “An innovative solution for the problem of blood flow through stenosed artery using generalized bingham plastic fluid model”, International Journal of research in applied and natural social sciences, (2013) Vol. 1(3), pp.97-140.

Shah, S. R., “An innovative study for non-Newtonian behavior of blood flow in stenosed artery using Herschel-Bulkely flud”, International Journal of biosiences and biotechnology, Vol. 5(5), pp.233-240, (2013).

Shah, S. R., “Capillary-tissue diffusion phenomena for blood flow through a stenosed artery using herschel-bulkley fluid” International journal of research in Biochemistry and Biophysics, Vol.1 (1) pp.1-8 (2011).

Shah, S. R., “Effect of clopidogrel on blood flow through stenosed artery under diseased condition”, International Journal of Experimental Pharmacology, 4(1), 887-893, (2014).

Shah, S. R., “Effects of Acetylsalicylic Acid on blood flow through an artery under Atherosclerotic condition”, International Journal of Molecular medicine and advances sciences, Vol. 7 (6), pp.19-24, (2011).

Shah, S. R., “Effects of antiplatelet drugs on blood flow through stenosed blood vessels”, Journal of Biomimetics, Biomaterials and Tissue Engineering, 18, 21-27, (2013).

Shah, S. R., “Impact of radially non-symmetric multiple stenoses on blood flow through an artery”, International Journal of Physical and Social Sciences, Vol.1 (3), pp.1-16, (2011).

Shah, S. R., “Mathematical analysis of blood flow through atherosclerotic arterial segment having non-symmetric mild stenosis”. International Journal of Research in Pure and Applied Physics .Vol.1. pp. 1-5, (2011).

Shah, S. R., “Mathematical Study of Blood Flow through Atherosclerotic Artery in the Presence of Porous Effect”, International Journal of Modern Sciences and Engineering Technology, Vol. 2, (12), pp.12-20, (2015).

Shah, S. R., “Non-Newtonian flow of blood through an atherosclerotic artery”, Research journal of applied sciences. Vol.6 (1), pp 76-80, (2011).

Shah, S. R., “Performance modeling and analysis of magnetic field on nutritional transport capillary tissue system using modified Herschel-Bulkely fluid”, International Journal of Advanced research in physical sciences, 1(1), 33-41, (2014).

Shah, S. R., “Performance Study on Capillary-Tissue Diffusion Phenomena for Blood Flow through Stenosed Blood Vessels”, American journal of pharmtech research, Vol. 2(2), pp.695-705, (2012).

Shah, S. R., “Response of blood flow through an atherosclerotic artery in the presence of magnetic field using Bingham plastic fluid” International Journal of Pharmaceutical and Biomedical Research. Vol. 2(3), 96-106, (2011).

Shah, S. R., “Role of Non-Newtonian behavior in blood flow through normal and stenosed artery”, Research journal of Biological sciences, 6(9),453-458, (2011).

Shah, S. R., “Significance of Aspirin on Blood Flow to Prevent Blood Clotting through Inclined Multi-Stenosed Artery”, Letters In Health and Biological Sciences, 2(2), 97-100, (2017).

Shah, S. R., “Study of dispersion of drug in blood flow with the impact of chemical reaction through stenosed artery”, International journal of Biosciences, 21 (3), 2022, 21-29.

Shah, S. R., “Study of modified Casson’s fluid model in modeled normal and stenotic capillary-tissue diffusion phenomena” International journal of computational engineering & management,. 11, 51-57, (2011).

Shah, S. R., Akbar, S., “Mathematical Study for the Outflow of Aqueous Humor and Function in the Eye”, International Journal of Scientific & Engineering Research 11(10), 743-750, (2020).

Shah, S. R., and Anamika, “A mathematical model of blood flow through diseased blood vessel”, International Journal of Emerging Trends and Technology in computer Science, Vol. 6, (3), pp. 282-286, (2017).

Shah, S.R., Clinical influence of hydroxychloroquine with azithromycin on blood flow through blood vessels for the prevention and Treatment of covid-19, International journal of biology, pharmacy and allied science. 2021, 10(7): 2195-2204.

Sharma, S. K., Alshehri, Mo., Priya Gupta and Shah, S. R., “Empowering the visually impaired: Translating Handwritten Digits into Spoken Language with HRNN-GOA and Haralick Features”, Journal of Disability Research, 3, 1-21, (2024).

Siddiqui, S. U., Shah, S. R., "A Physiologic Model for the problem of blood flow through Diseases blood vessels", International journal of advances in Applied Sciences, 5(2), 58-64, (2016).

Siddiqui, S. U., Shah, S. R., “Achievement of Pentoxifylline for Blood Flow through Stenosed Artery”, Journal of Biomimetics, Biomaterials and Tissue Engineering, Vol. 13 pp.81-89, (2012).

Siddiqui, S. U., Shah, S. R., “Two-phase model for the study of blood flow through stenosed artery, International Journal of Pharmacy and Biological Sciences, 1(3), 246-254, (2011).

Siddiqui, S. U., Shah, S. R., Geeta, “A Computational Analysis of a Two-Fluid non-Linear Mathematical model of pulsatile blood flow through Constricted Artery”, E-Journal of science and Technology , Vol. 10(4), pp.65-78, (2015).

Siddiqui, S. U., Shah, S. R.,“A Comparative Study for the Non-Newtonian Behaviour of Blood Flow through Atherosclerotic Arterial Segment”, International Journal of Pharmaceutical Sciences Review and Research, Vol.9 (2), 120-125, (2011).

Siddiqui, S. U., Singh, A., Shah, S. R., “Mathematical Modeling of peristaltic blood flow through a vertical blood vessel using Prandtl fluid model”, International Journal of Mathematics and Computer Research, Vol. 4, (9), pp. 710-717, (2016).

Singh, A., Shah, S. R., “Influence of transverse magnetic field on steady blood flow in a stenosed artery: numerical and analytical insights”, International Journal of Mathematical Archive,15(8), (2024), 1-10.

Singh, S., “A mathematical model for modified Herschel-bulkley fluid in modeled stenosed artery under the effect of magnetic field”, International Journal of Bioengineering and Technology, Vol. 1 (1), pp.37-42. (2010).

Singh, S., “A two-layered model for the analysis of arterial rheology” International Journal of Computer Science and Information Technology, 4, 37-42. (2011).

Singh, S., “Clinical significance of aspirin on blood flow through stenotic blood vessels” Journal of Biomimetics, Biomaterials and Tissue Engineering, 10(17) 24, (2011).

Singh, S., “Effects of shape of stenosis on arterial rheology under the influence of applied magnetic field” International Journal of Biomedical Engineering and Technology, Vol. 6 (3) pp. 286-294, (2011).

Singh, S., “Influence of magnetic field on blood flow through stenosed artery using Casson’s fluid model”, International Journal of BioEngineering, CardioPulmonary Sciences and Technology, Vol. 1, pp. 1-7, (2010).

Singh, S., “Numerical modeling of two-layered micropolar fluid through a normal and stenosed artery”, International journal Engineering, 24 (2), 177-187, (2011).

Singh, S., “Numerical modelling for the modified Power-law fluid in stenotic capillary-tissue diffusion phenomena”, Archives of Applied Science Resaerch, An international peer reviewed journal of applied sciences, 2 (1) 104-112, (2010).

Singh, S., “The effect of Saline Water on viscosity of blood through stenosed blood vessels using Casson’s fluid model”, Journal of Biomimetics, Biomaterials and Tissue Engineering, Vol.9 pp 37-45, (2011).

Singh, S., and Shah, R. R.,“A numerical model for the effect of stenosis shape on blood flow through an artery using power-law fluid”, Advance in applied science research, An international peer reviewed journal of sciences, 1, 66-73, (2010).

Smith, J. A., & Johnson, L. R. (2021). The effects of diabetes on blood rheology: A review. Journal of Diabetes Research, 12(3), 456-467.

Yadav, P., Sengar, N., Shah S. R., “Economic Conditions and Age Profile of Women Domestic Workers in Delhi's Urban Informal Sector”, International Journal of Research Publication and Reviews, 15(8),494-500, (2024).

Yadav, P., Shah S. R., “Female Domestic Laborers In The Urban Informal Economy: A Case Analysis of Delhi, International Research Journal of Modernization in Engineering Technology and Science, 6(8), 216-225 (2024).

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Shah, S., Parambath, A. B., & Arora, K. (2024). Quantitative Analysis of Hematopoietic and Leukemic Stem Cell Dynamics in Acute Myeloid Leukemia: A Mathematical Approach. International Journal Of Mathematics And Computer Research, 12(9), 4422-4435. https://doi.org/10.47191/ijmcr/v12i9.02