Quantitative Analysis of Hematopoietic and Leukemic Stem Cell Dynamics in Acute Myeloid Leukemia: A Mathematical Approach

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.