Toward Minimalistic Model of Cellular Volume Dynamics in Neurovascular Unit

Robert Loshkarev and Dmitry Postnov
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Robert Loshkarev: Department of Optics and Biophotonics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia
Dmitry Postnov: Department of Optics and Biophotonics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov, Russia

Mathematics, 2021, vol. 9, issue 19, 1-13

Abstract: The neurovascular unit (NVU) concept denotes cells and their communication mechanisms that autoregulate blood supply in the brain parenchyma. Over the past two decades, it has become clear that besides its primary function, NVU is involved in many important processes associated with maintaining brain health and that altering the proportion of the extracellular space plays a vital role in this. While biologists have studied the process of cells swelling or shrinking, the consequences of the NVU’s operation are not well understood. In addition to direct quantitative modeling of cellular processes in the NVU, there is room for developing a minimalistic mathematical description, similar to how computational neuroscience operates with very simple models of neurons, which, however, capture the main features of dynamics. In this work, we have developed a minimalistic model of cell volumes regulation in the NVU. We based our model on the FitzHugh–Nagumo model with noise excitation and supplemented it with a variable extracellular space volume. We show that such a model acquires new dynamic properties in comparison with the traditional neuron model. To validate our approach, we adjusted the parameters of the minimalistic model so that its behavior fits the dynamics computed using the high-dimensional quantitative and biophysically relevant model. The results show that our model correctly describes the change in cell volume and intercellular space in the NVU.

Keywords: neurovascular unit; extracellular volume; mathematical modeling; cell swelling; bistable-excitable systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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