Iron Transport across Brain Barriers: Model and Numerical Parameter Estimation

Iron is an essential element for brain metabolism. However, its imbalance and accumulation are implicated in the processes featuring neurodegenerative diseases, such as Alzheimer's disease (AD). The brain barrier's system maintains the sensitive homeostasis of iron in the brain. However, the impairment of the mechanisms of iron passage across the brain barrier is not clearly established. A mathematical model is proposed to macroscopically describe the iron exchange between blood and cerebral compartments. Numerical simulations are performed to reproduce biological values of iron levels in physiological and pathological conditions. Moreover, given different scenarios (neurological control and AD patients), a particle swarm optimization (PSO) algorithm is applied to estimate the parameters. This reverse work could be important to allow the understanding of the patient's scenario. The presented mathematical model can therefore guide new experiments, highlighting further dysregulated mechanisms involved in neurodegeneration as well as the novel disease-modifying therapies counteracting the progression of neurodegenerative diseases.