A Mathematical Study of Effects of Alzheimer’s Drug Donepezil Hydrochloride on Neuronal Viscoelasticity and Action Potentials

Alzheimer’s disease (AD) is a degenerative disorder characterized by progressive cognitive decline and memory loss. The few contemporary therapies may ease symptoms and/or slow down AD progression but cannot cure the disease. The orally administered AD drug donepezil hydrochloride enhances the availability of acetylcholine that supports cholinergic neurotransmission. In this paper, a generalized Hodgkin-Huxley model is proposed that uses Caputo fractional order temporal derivatives to link action potentials and viscoelasticity of cholinergic receptors. The model provides not only structurally dependent action potentials for health and AD but also a possible mechanism of donepezil effect on action potentials: the binding between the acetylcholine and the receptors preserves the structural fitness of these receptors. In addition, a generalized pharmacokinetic model of donepezil transport to the brain is proposed that incorporates controlled release modalities. Caputo fractional order temporal derivatives are used again to model anomalous drug release. Numerical simulations show how controlled release donepezil recovers the structural integrity of the receptors which further brings the abnormal action potentials due to AD to their healthy state. The results suggest that combining various drug release modalities and dosages may improve treatment effectiveness with donepezil.