A Network Architecture for Bidirectional Neurovascular Coupling in Rat Whisker Barrel Cortex

Abstract

Neurovascular coupling is typically considered as a master-slave relationship between the neurons and the cerebral vessels: the neurons demand energy which the vessels supply in the form of glucose and oxygen. In the recent past, both theoretical and experimental studies have suggested that the neurovascular coupling is a bidirectional system, a loop that includes a feedback signal from the vessels influencing neural firing and plasticity. An integrated model of bidirectionally connected neural network and the vascular network is hence required to understand the relationship between the informational and metabolic aspects of neural dynamics. In this study, we present a computational model of the bidirectional neurovascular system in the whisker barrel cortex and study the effect of such coupling on neural activity and plasticity as manifest in the whisker barrel map formation. In this model, a biologically plausible self-organizing network model of rate coded, dynamic neurons is nourished by a network of vessels modeled using the biophysical properties of blood vessels. The neural layer which is designed to simulate the whisker barrel cortex of rat transmits vasodilatory signals to the vessels. The feedback from the vessels is in the form of available oxygen for oxidative metabolism whose end result is the adenosine triphosphate (ATP) necessary to fuel neural firing. The model captures the effect of the feedback from the vascular network on the neuronal map formation in the whisker barrel model under normal and pathological (Hypoxia and Hypoxia-Ischemia) conditions.

Keywords: bidirectional network model; hypoxia-ischemia; neurovascular coupling; plasticity; whisker barrel cortex.

FIGURE 1

(A) Bidirectional connection between neural and vascular layers. Neurons send afferent vasodilatory signals to vessels and vessels send oxygen back to the neural layer for oxidative phosphorylation. (B) A schematic of the interactions among various quantities involved in neurovascular coupling. Beta (compliance factor of the vessel, β). P, pressure; V, volume; S, saturation of oxygen in the blood; PO₂, partial pressure of oxygen; OE, oxygen extraction; CMRO₂, cerebral metabolic rate of oxygen; W^vn and W^nv, Gaussian weights; ATP, adenosine triphosphate.

FIGURE 2

(A) A schematic of the model. The big pial artery branches to arterioles and they again branch to capillaries to perfuse the neurons. The neurons and vessels interact at the level of these capillaries. (B) LISSOM architecture. The neural unit receives weighted input from an area in the whisker pad (blue dots). It receives excitatory input from the immediate neighboring neural units (green dots) and inhibitory input from long range neural units (red dots). (C) The neurovascular connectivity. Each vessel receives vasodilatory information from an area of neural units (violet dotted circle). Each neural unit receives oxygen from a group of proximal vessels (blue dotted circle). (D) A schematic for complete interactions among the three layers, Input layer (whisker pad), Neural layer (whisker barrel cortex), and blood vessels (capillaries). The only trained weights are from input layer to whisker barrel cortex (dark blue dotted circle).

FIGURE 3

(A) The whisker pad of the rat. Each whisker is addressed using the row (A–E) and the column (0–4). (B) The topographic map formed in whisker barrel cortex. The whiskers are given numbers 1–24 such that, column 0 has whiskers 1–4; column 1 (5–9); column 2 (10–14); column 3 (15–19); column 4 (20–24). In this sheet of 64 × 64 neurons, each neuron is color coded to the index of the whisker to which it responds maximally. The nearby neurons respond to the same whisker forming barrels as can be seen in the figure. (C) The whiskers which are being considered for pathological study is shown in red circle (C1–C3 and D1–D3).

FIGURE 4

Each plot shows the time profile of different hemodynamic variables. The red arrow shows the time of presentation of stimulus. The color bar on the right shows the percentage change in value. (A) The time profile of HbT in the whisker barrel cortex—HbT is maximum at 1.6 s post stimulus presentation. (B) The time profile of HbO in the whisker barrel cortex. Soon after the stimulus, a dip in HbO can be observed at 0.6 s; HbO peaks around 1.6–2 s. (C) The time profile of Hb in the whisker barrel cortex. Soon after the stimulus, a slight peak in Hb can be observed at 0.6 s. Hb follows a continuous dip following that initial peak.

FIGURE 5

(A) Comparison of estimated hemodynamic response at the center of the activated barrel using the model with the experimental results. The dotted line plots the experimental values observed by Devor et al. (2005) and the solid line plots the values obtained from the model. (B) The percentage change in rCBF (red), rCBV (Blue), and CMRO2 (green) when the input of 1 s duration is presented at t = 0.

FIGURE 6

(A) Peak HbT observed 1.8 s post stimulus presentation to C3 whisker, (i) at the center of the barrel corresponding to the whisker (principal barrel) which was stimulated (blue), at the boundary of the principle barrel (green) and very far from the principal barrel (red). (B) The average of peak response of HbT (red) and the average neural activity (blue) around the principal barrel for different stimulus amplitudes. (C) Variation of threshold as a function of available ATP. (D) Observed variation in % drop of ATP around the principal barrel post stimulus presentation (stimulus is given at t = 0 s).

FIGURE 7

(A–D) Topographic map formation around a small area in the whisker barrel cortex under various conditions. (A) When the whiskers are intact, and blood supply is normal. (B) When the C1–C3 whiskers are lesioned, but blood supply is normal. (C) When the whiskers C1–C3 are lesioned and also the blood is hypoxic. (D) When the whiskers C1–C3 are lesioned and also under hypoxia-ischemia condition.

FIGURE 8

(A) Comparison of D/C ratio of experiment (Ranasinghe et al., 2015) and model under the four simulation paradigms. (B) The change in D/C ratio of a lesioned model at various stages of hypoxia-ischemia (blue) and purely ischemic condition (red). (C) The change in D/C ratio of a lesioned model at various percentages of oxygen saturation at the inlet.