Fig 1.
Overview of the presented study.
A: Simplified schematic illustration of the cellular pathways underlying the NVC. Neuronal signaling activates GABAergic interneurons, pyramidal neurons, and astrocytes by stimulating the influx of Ca2+. Ca2+ facilitates signaling pathways in the different cells. In GABAergic interneurons, Ca2+ promotes nitric oxide (NO) through the upregulation of nitric oxide synthase (NOS). Furthermore, Ca2+ also facilitates the release of different neuropeptides: neuropeptide Y (NPY), vasoactive intestinal peptide (VIP), and somatostatin (SOM). In pyramidal neurons, Ca2+ promotes the synthesis of arachidonic acid (AA) via phospholipase A2 (PLA2), which in turn is metabolized to prostaglandin E2 (PGE2) via cyclooxygenase-2 (COX-2). In astrocytes, arachidonic acid is synthesized via phospholipase D2 (PLD2) and subsequently metabolized into three different vasoactive molecules: PGE2 via cyclooxygenase-1 (COX-1), epoxyeicosatrienoic acid (EET) via cytochrome P450 (CYP) epoxygenase, and 20-Hydroxyeicosatetraenoic acid (20-HETE) via CYP4A. Together these vasoactive messengers act on arterioles and capillaries to modulate the vessel diameters, where the neuronal messengers act primarily on the arterioles, while the astrocytes act on both arterioles and capillaries. B: Overview of commonly used experimental techniques in rodents, primates, and humans, depicted along two axes: the spatial and temporal resolution of what is measured, and how invasive the technique is. C: Comparison of different published models describing the neurovascular coupling (NVC) with regards to different mechanisms. The notations used in the table are: ‘Yes’ on a green background if the model features the stated mechanism, ‘Partly’ on a yellow background if the model has a description that is not fully satisfying, and ‘No’ on a read background if there is no description of the mechanism. As seen, no model exists that can describe every mechanism. D: Overview of the study. We have collected already published experimental data from different species and/or experimental techniques and combined these experimental data with the development of a mathematical model, which builds upon three already published models. E: Preservation of qualitative features between the three species, including an overview of specific features and in which figures these features are visualized.
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.
Fig 3.
Model estimation to experimental data in Section 2.1.1.
Data and simulations for arteriolar (A–C) and venular (D–F) diameter changes in awake mice for three different sensory stimulation lengths: 125 ms (A & D), 10 s (B & E), and 30 s (C & F). Experimental data are replotted versions of data presented in Fig 2C of the original manuscript by Drew et al. [46]. The stimulation lengths are denoted with the black bar in the bottom left portion of each graph. For each graph: experimental data (colored symbols); the uncertainty of the experimental data is presented as the standard error of the mean (SEM) (colored error bars); the best model simulation is seen as a colored solid line; the model uncertainty as a colored semi-transparent overlay. The x-axis represents time in seconds, and the y-axis is the normalized vessel diameter change (Δ%).
Fig 4.
The model explanation for two-peak behavior in Drew data: mechanistic insights to be preserved and translated (Section 2.1.2) [46].
Model simulations for the three stimulus durations: 125 ms (A & E), 10 s (B & F), and 30 s (C & G) are shown. For each stimulus: the dynamic of the neuronal states, pyramidal neurons (NPyr), GABAergic nitric oxide interneurons (NNO), GABAergic neuropeptide Y interneurons (NNPY), (A–C), and the arteriolar response (E–G). For each graph: model simulation (colored lines); stimulus length (black bar). The x-axis represents time in seconds, and the y-axis is the change in neuronal states (A.U) for A–C, and the vasoactive effect on the arteriolar compartment (A.U) for E–G. In D, a simplified overview of the model is given. Here, u1, u2, and u3 are the stimulus input to the model and are applied for 125 ms, 10 s, and 30 s for each respective experimental setting. The relative timing and function of the three arms (PGE2, SMC, NOSMC, and NPYSMC) depicted in this figure is the first mechanistic insight to be translated to the analysis of the other datasets from the other species (Figs 1E and 5–7). Note that the vasoactive effect presented in E-G is expressed from the relative change from the baseline, see Eq 8, and therefore negative values should be interpreted as lower concentration compared to a non-stimulated state.
Fig 5.
Model estimation to experimental data of hemoglobin changes in mice for three different stimulation types (Section 2.1.4).
The experiment features optogenetic (OG) activation of inhibitory (A & D) and excitatory (B & E) neurons, and sensory stimulation (C & F). For each stimuli type, a short stimulus (OG: 100 ms of light (A-B); Sensory: 2 s I) and a long stimulus (OG: 20 s (D-E); Sensory: 20 s (F)) was used. This is denoted with the black bar in the bottom left portion of each graph. The shown experimental data are replotted versions of S5 Fig of the study by Desjardins et al. [48]. For A-F: experimental data consisting of oxygenated hemoglobin (HbO; dark-red symbols), deoxygenated hemoglobin (HbR; light-blue symbols), and total hemoglobin (HbT; green symbols); the uncertainty of the experimental data is presented as the standard error of the mean (SEM) (colored error bars); the best model simulation is seen as colored solid lines corresponding to respective measurement variable; the model uncertainty as colored semi-transparent overlays; the x-axis represents time in seconds, and the y-axis is the change in hemoglobin concentration (μM). G-I: preserved mechanisms i.e., correct relative timing, of the vasoactive effect on the VSM from the different vasoactive substances, nitric oxide (NO), neuropeptide Y (NPY), and prostaglandin E2 (PGE2). J: model predictions (shaded area) and experimental data (mean ± SEM, symbols) of a BOLD response to an identical stimulus is shown in E. The experimental data were extracted from Desjardins et al. 2019 [48].
Fig 6.
Model estimation to experimental data from macaque primates (Section 2.2). We see blood oxygen level dependent (BOLD) (A) and electrophysiological (B) responses in macaques for two variants of a visual task. The visual task was 20 s long, for the positive task, and 21 s, for the negative task, visual stimulation of V1 in the visual cortex (marked with the black bar in the bottom left portion of each graph). In A & B: experimental data (colored “*”-symbols); the uncertainty of the experimental data is presented as the standard error of the mean (SEM) (colored error bars); the best model simulation is seen as colored solid lines corresponding to respective measurement observables. The model uncertainty is seen as the semi-transparent colored areas. The x-axis represents time in seconds, and the y-axis is BOLD signal change (Δ%) for A and local field potential (LFP) expressed as percent change from baseline (Δ%) for B. C-D: translated dynamics and mechanisms regarding the effect on the VSM from the different vasoactive substances: nitric oxide (NO), neuropeptide Y (NPY), and prostaglandin E2 (PGE2) given as arbitrary units (A. U.). E-F: translated dynamics from mice regarding the hemoglobin changes given as arbitrary units (A. U.).
Fig 7.
Model estimation and prediction of MR-based experimental data in humans for different visual stimulation tasks (Section 2.3).
The graph contains data for three different tasks: cerebral blood volume (CBV) (A), blood oxygen level dependent (BOLD) signal (D), and cerebral blood flow (CBF) (E) changes for small flickering checkerboard task, and compartment-specific CBV changes for an excitatory (B) and inhibitory (C) flickering tasks. For each graph, the stimulus duration (30 s) is depicted as the black bar in the bottom left portion of each graph. In A-E: experimental data shown with the measurement uncertainty as the standard error of the mean (SEM) (colored error bars); the best model simulations are seen as colored solid lines corresponding to respective measurement observables; the model uncertainty is depicted as colored semi-transparent overlays; the x-axis represents time in seconds, and the y-axis is the change in fractional (D, E) or percentual change (A–C) of the measurement observables. The model prediction uncertainty of CBF (E) and compartment-specific CBV changes (B, C) is depicted as semi-transparent overlays. The experimental time series are taken from Huber et al. [49]. Translated mechanistic insights are shown for the three arms of vascular control (F, G), hemoglobin dynamics (H, I), and local field potential (LFP) (J, K), for the positive (F, H, J), and negative (G, I, K) BOLD response. F-K are given as arbitrary units (A. U.).
Table 1.
Overview of parameter usage over all experimental setups.