This paper describes the criteria to be used in the management of persons accidentally exposed to ionizing radiation for predicting whether the stem cell pool damage was reversible or irreversible. This question is of importance. If the damage was reversible, the clinical management may be restricted to symptomatic therapeutic measures (antibiotics, platelet transfusions). If the indicators show that the stem cell damage is irreversible (from a clinical viewpoint) then stem cell transplantation must be considered and performed. A granulocyte computer simulation model is discussed that may be useful in the analysis and evaluation of blood cell regeneration patterns after radiation and transfusion of stem cells from different sources.