Predictive model for stem cell transplantation with suicidal gene construct for the treatment of leukemia: Analytical model for gene therapy of leukemia

Now-a-days hematopoietic stem cell transplantation becomes a routine therapeutic procedure for the treatment of leukemia. However, due to allogenic transplantation, there is incompatibility in HLA matching between donor and recipient that limits the long term success rate in terms of quality of life of the concerned patient. HLA incompatibility has two prongs effects in patients - on one hand transplanted cells can remove leukemic cells from (recipient) patient successfully (graft versus leukemia effect) and on the other hand it produces graft versus host disease. So, hematopoietic stem cell's transplantation with suicidal gene construct is required. With this scheme, transplanted cells can be removed selectively after the removal of leukemic cells, thus graft versus host disease can be prevented. For the assessment of leukemia therapy by this procedure, a time delay based ordinary difference equation systems model is proposed. The model considers three lineages cellular systems of the hematopoietic system and each of the lineages consists of normal cells, drug sensitive and drug resistive cell types. Here, Lyapunov stability analysis is performed to find the optimal therapeutic condition for removal of leukemic cells without generation of graft versus host disease. Rigorous numerical simulations are performed to determine the optimal therapeutic conditions under varying patients' patho-physiological conditions, so that the systems can be settled to a non-leukemic equilibrium point in long run. We hope that the developed computational model helps clinicians to find out the suitability of this therapy according to patients' patho-physiological conditions followed by optimization of the therapeutic schedule.