Fig 1.
Main neuro-glio-vascular interactions in a voxel and their link to bimodal LFP-LD recordings.
Arrows represent the interactions between the five compartments of the model: the compartments of pyramidal cells and interneurons provide a representation of the neuronal activity as measured by local field potential (LFP); the astrocytic compartment represents the key role of astrocytes in neurotransmitter (glutamate and GABA) cycling and cerebral blood flow (CBF) dynamics; the vessel compartment involves the CBF dynamics as measured by laser Doppler (LD); the extracellular space represents neurotransmitter exchanges between the other compartments.
Fig 2.
Modeling and experimental recording of neuronal activity.
(A) Variables and relationships of the neural mass model (Table 1 and S1 Table). The input to the model is the activity coming from afferent populations, together with the injection of bicuculline in order to elicit an epileptic activity. The model output is the simulated local field potential (LFP). (B) and (C) Model-data comparison between the neural mass model (black) and LFP recording (light gray) for two isolated discharges. The mean value of p was set to mB = 3.07 and its standard deviation to σp = 0. Magnitudes of the discharges (B) Apeak = 8.14 mV and (C) Apeak = 4.13 mV were obtained with the gain in Eq 2 set to (B) G1 = 965 and (C) G9 = 535.
Table 1.
Parameters values chosen from the experimental literature.
Fig 3.
Modeling of the glutamate and GABA cycles according to the experimental literature.
(A) Main physiological principles of glutamate and GABA cycles are glutamate and GABA releases by pyramidal cells and interneurons respectively, glutamate uptake by astrocytes and GABA uptake by both neurons and astrocytes (S1 File). (B) The glutamate release (solid line) from Eq 9 matches the experimental impulse response (circles) depicted in Fig 4 in [40] for the parameter set {W = 0.59, w1 = 90, w2 = 33}. (C) Comparison between the simulated glutamate uptake from Eq 11 and Michaelis-Menten representations {VM, KM} obtained from the experimental literature and converted to the same unit (Table 1). The Michaelis-Menten representations are numbered according to the experimental literature with 1: {VM = 9.5, KM = 91} for [42]; 2a: {VM = 4.2, KM = 18.6}, 2b: {VM = 4.8, KM = 37}, 2c: {VM = 2, KM = 16} for [44]; 4a: {VM = 6.8, KM = 18.9}, 4b: {VM = 1.5, KM = 54.9} for [45]. Setting parameters of Eq 11 to {Vmg = 5, rg = 0.5, sg = 9} led to a sigmoid function (solid line), which was close to the experimental measures for the usual physiological values of extracellular glutamate concentration (below 10 μM). (D) Comparison between Michaelis-Menten responses of the GABA uptake from Eqs 15 and 16 with {Vm1 = 5, Km1 = 24} for GAT1 transport (neurons, in gray) and {Vm1 = 2, Km1 = 8} for GAT3 transport (astrocytes, in black).
Fig 4.
Temporal simulations of the NVG model.
(A) Simulated LFP for discharges number 1 (with the highest level) and number 9 (with the lowest level) separated by 105 s reproduced bicuculline wash-out as a function of time. (B) Temporal simulation of the resulting extracellular concentration of glutamate GluE was in a good agreement with the temporal dynamics of experimental recordings with a glutamate probe such as those found in Fig 2 in [67]. (C) The resulting extracellular GABA concentration GABAE had a slower dynamics than GluE.
Fig 5.
Modeling cerebral blood flow (CBF) dynamics.
(A) CBF dynamics represented by the variable Fin consist of a neuronal contribution and an astrocytic contribution. (B) Model-data comparison was assessed by the relative error |Fpeak,simu—Fpeak,expe|/Fpeak,expe, where Fpeak,simu is the CBF magnitude collected on the simulations and Fpeak,expe is the CBF magnitude collected on the laser Doppler recording (Materials and Methods). This relative error (in %, coded in grayscale with black for lower values and white for higher values) was represented as a function of the magnitude Apeak of the extracted discharges and the parameter set leading to the magnitude Fpeak,simu. (C) Same as (B) for time tpeak of the main peak (Materials and Methods).