A mathematical model of cellular swelling in Neuromyelitis optica

Neuromyelitis Optica (NMO) is a severe neuro-inflammatory disease of the central nervous system characterized by predominant damage to the optic nerve and of the spinal cord. The pathogenic antibody found in the majority of patients targets the AQP4 channels on astrocytic endfeet and causes the cells to swell. Although, the pathophysiology of the disease is broadly known, there are no specific targeted treatments for this process clinically available nor accurate prognostic markers both during attacks and for predicting long term neuronal damage. This lack is, in part, due to the rarity of the disease and its relatively recent pathogenic clarity. Hence, the ability to mathematically model the progress of the condition to test prospective therapies in silico would be a step forward. This paper combines state of the art models of cellular metabolism and cytotoxic oedema in neurons and astrocytes and augments it with a detailed characterization of water transport across the cellular membrane. In particular, we capture the process of perforation of the cell through the human complement cascade and resulting water and ionic fluxes. Simulating NMO by injecting its antibody and human complement into the extracellular space showed a 25% increase of the astrocytic volume after 12 h from onset. Most of the volume change occurred during the first 30 min of simulation with a peak volume change of 38%. The model was further adapted to simulate the therapeutic potential of CD59. It was found that there is a threshold of CD59 concentration that can prevent the swelling of astrocytes. Since the astrocyte volume changes mostly during the first hour, further experimental work should focus on this time scale to provide data for further model refinement and validation.