Mitigation of sickle cell crises using chaos-based analysis

Abstract

Sickle-cell diseased persons suffer finite pain episodes (luring their lifetime, which are termed sickle cell crises. Using a sickle cell blood flow model, we mathematically demonstrate that the onset of a sickle cell crisis is chaotic. We further show that sickle cell crises may be mitigated by manipulating certain physiological parameters, namely the partial pressure of oxygen at 50% hemoglobin ([mathematical formula]%) and the kinetic dissociation rate of hemoglobin (kub) These physiological parameters control the chaotic nature of sickle cell crises and have the ability to transfer a person from a crisis state to a non-crisis state. We determine that sickle cell crises may only be mitigated within a critical time period (0 </- t </- 2.5hrs) after the onset of a sickle cell crisis. Based on our analysis, we classify three stages of a sickle cell crisis as weak chaos, strong chaos, and hyperchaos; which range from light to intense pain. Drugs may be developed, based on our analysis, to target these physiological parameters and mitigate sickle cell crises at its onset.