Study of cohabitation and interconnection effects on normal and leukaemic stem cells dynamics in acute myeloid leukaemia

Abstract

On the basis of recent studies, understanding the intimate relationship between normal and leukaemic stem cells is very important in leukaemia treatment. The authors' aim in this work is to clarify and assess the effect of coexistence and interconnection phenomenon on the healthy and cancerous stem cell dynamics. To this end, they perform the analysis of two time-delayed stem cell models in acute myeloid leukaemia. The first model is based on decoupled healthy and cancerous stem cell populations (i.e. there is no interaction between cell dynamics) and the second model includes interconnection between both population's dynamics. By using the positivity of both systems, they build new linear functions that permit to derive global stability conditions for each model. Moreover, knowing that most common types of haematological diseases are characterised by the existence of oscillations, they give conditions for the existence of a limit cycle (oscillations) in a particularly interesting healthy situation based on Poincare-Bendixson theorem. The obtained results are simulated and interpreted to be significant in understanding the effect of interconnection and would lead to an improvement in leukaemia treatment.

Dynamical Behavior of Biological Healthy Steady State in Leukemia Using a New Leukemic & Healthy Stem Cells Cohabitation Model with Distributed Delay

“…We then used it to elaborate the conditions that are sufficient and necessary for the global asymptotic stability of the positive healthy steady state; knowing its significant meaning from clinical point of view. This result confirms our previous researches [30], [31] and is explained as follows: if we act on the interconnection mechanism modeled by (18), (19) and (20) in a specific way, we may be able to eradicate LSCs and hence reinforce HSCs. The HSCs reinforcement stabilizes pre-leukemic states as introduced in [14].…”

On Instability and Global Asymptotic Stability of Age-structured Distributed Delay System Describing Pathological Hematopoeisis

“…Thus, it is possible to understand the therapy mechanism based on this observation. • it is common to mix different therapeutic agents (having different activation mechanisms) [26], [24] in chemotherapy in order to eradicate sick cells or inhibit their proliferation [27], [25]. We verified this well known fact, by showing that the extinction of leukemic cells depends on δ i , G i (0) and β i (0) in Theorem III-A-III-B.…”

“…where ϒ i (t) and ψ i (t) are the functions defined in (22) and (25), respectively. If u i−1 (t) = 0, then its derivative along the trajectories of (9) satisfieṡ…”

Poincaré Maps and Aperiodic Oscillations in Leukemic Cell Proliferation Reveal Chaotic Dynamics

“…Previous works by Wolfrom et al, (1994, 2000, 2004) [ 23 , 24 , 25 ], Guerroui et al, (2005) [ 26 ] and Laurent et al, (2010) [ 27 ] has investigated the chaotic dynamics of hepatocellular carcinoma cells as well as bone marrow progenitor cells [ 23 ]. In addition, few works have highlighted the oscillatory nature of leukemic cell proliferation [ 28 ]. Finally, in a previous work we have also reported that we have found evidence of deterministic chaos in leukemia cells in vitro [ 29 ].…”