Mathematical modeling of bone marrow – peripheral blood dynamics in the disease state based on current emerging paradigms, part I

• Recent emerging hypotheses about cancer stem cells (CSCs) are discussed and placed within a mathematical modeling context.
• New model highlighting the CSC paradigm is used to study cell behavior in the bone marrow (BM) and peripheral blood (PB).
• Three steady states are predicted; a trivial steady state, an axial equilibrium state, and a steady state of coexistence.
• The axial equilibrium exhibiting complete malignant dominance in the BM and PB is found as most persistent steady state.
• Main factors driving malignancy: mutation, abnormal cell replication and release of malignant cells from the BM to the PB.

Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow – peripheral blood architecture.