A quantitative model for human neurovascular coupling with translated mechanisms from animals
Fig 2
Interaction graph of the model.
A: a simplified overview of the model described in [42]. Two distinct types of cells are described: pyramidal neurons (grey triangle, left) and GABAergic interneurons (divided into nitric oxide (NNO)- and neuropeptide Y (NNPY)-expressing neurons; yellow oval shapes, right). These neurons are connected in a simple relationship, with pyramidal neurons (NPyr) exciting GABAergic neurons, which in turn inhibit the surrounding cells. Reduction of excited neural activity is illustrated as a flux towards ∅, likewise, mass removal from other states is illustrated with a flux towards ∅. Activation of a neuron causes an influx of Ca2+ ions, which is initiated by the electrical stimulation described by u1, u2, and u3 for the respective neurons. In pyramidal neurons, Ca2+ activates phospholipases, which convert phospholipids into arachidonic acid (AA). AA is further metabolized into prostaglandin E2 (PGE2). In NO-expressing interneurons, Ca2+ activates nitric oxide synthase, which triggers the production and release of nitric oxide (NO). In other subtypes of GABAergic interneurons, vesicle-bound vasoactive peptides such as neuropeptide Y (NPY) are expressed. The release of these peptides is facilitated by Ca2+. Vascular smooth muscle (VSM) cells (brown rectangles) enwrap arterioles (left side of the vascular tree) and regulates the arteriolar diameter. PGE2 promotes arteriolar dilation by activation of the prostaglandin EP4 receptor located on the VSM. NO diffuses freely over cellular membranes and acts to increase the production of cyclic guanosine monophosphate, which in turn promotes arteriolar dilation. Lastly, NPY activates the G-protein coupled NPY Y1 receptor (NPY1R) expressed on VSM cells, promoting arteriolar constriction. These three effects on the VSM control the arteriolar diameter and thereby also the volume (VA) and flow of blood (fA,C) through the arterioles. These volume and flow changes are propagated through the capillaries (VC, fC,V) and venules (VV, fout). B: Three-compartment vascular model of blood volumes (VA, VC, VV), pressures, and flows (fin, fA,C, fC,V, fout) corresponding to an analog electrical circuit, as described in [34]. The blood pressure drop corresponds to a voltage drop, the blood flow to an electric current, and the blood volume to electric charge stored in the capacitors. The vessel compliance (C1, C2, C3) plays the role of capacitance, and the vessel resistance (R1, R2, R3) is analogous to electric resistance. The blood pressure difference (Δpr) maintained by the circulatory system corresponds to the electromotive force. C: Oxygen transport model, as described in [43]. The diagram depicts amount of oxygen (niO2, i = {A, C, V, t}), oxygen saturation (SiO2, i = {A, C, V}), oxygenated hemoglobin (HbOi, i = {A, C, V}) and deoxygenated hemoglobin (HbRi, i = {A, C, V}), for each respective compartment (A = arterial, C = capillary, V = venous, t = tissue). Oxygen in tissue can be metabolized, indicated by the cerebral metabolism of O2 (CMRO2) arrow leaving the state. These different models in unison affect the blood oxygenation and blood volume in each respective compartment, which in turn determines the specific compartments contribution (Si, i = {A, C, V, E}) to the BOLD-fMRI signal (grey boxes), where SE is the oxygen saturation of the extravascular tissue.