Quantitative evaluation of equation-based model in hypokalemic periodic paralysis condition with bistability

Biomedical Engineering Institute, Chiang Mai University, Thailand

Abstract

Hypokalemia in periodic paralysis (HypoPP) is usually not a straightforward hypokalemic condition. It is mainly characterized by the intercellular shift of potassium between compartments inside human body, not by depletion solely. Several experiments at the cellular level demonstrated the separation of resting membrane potential including the paradoxical depolarization possibly causing clinical manifestation. We analyzed the structural model focusing on the intracellular potassium pool and connected cellular electrophysiology information to the macroscale. Increment of extracellular potassium cannot be simply expected after potassium supplementation for hypokalemic correction which is different from general pharmacokinetics. Searching the bistable solutions from the existing bifurcation in a bounded parameter subset was the newly-introduced strategy for testing the possibility of pushing the solution to one another stable point as the representative of potassium falling or paradoxical hypokalemia instead of adding parameters or terms in the traditional way. Moreover, the continuous trajectories from the model combined with the difference between input and output and the proposed utilization from parameter mapping to alleviate the sudden falling of the solution were demonstrated. The results also supported the pre-existing hypothesis that NaK+-ATPase activation was responsible for this phenomenon.