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A successfully developed enzyme-based lactate microsensor with rapid response time allows the direct and continuous in vivo measurement of lactic acid concentration with high temporal resolution in brain extracellular fluid. The fluctuations coupled to neuronal activity in extracellular lactate concentration were explored in the dentate gyrus of the hippocampus of the rat brain after electrical stimulation of the perforant pathway. Extracellular glucose and oxygen levels were also detected simultaneously by coimplantation of a fast-response glucose sensor and an oxygen electrode, to provide novel information of trafficking of energy substances in real time related to local neuronal activity. The results first give a comprehensive picture of complementary energy supply and use of lactate and glucose in the intact brain tissue. In response to acute neuronal activation, the brain tissue shifts immediately to significant energy supply by lactate. A local temporary fuel "reservoir" is established behind the blood-brain barrier, evidenced by increased extracellular lactate concentration. The pool can be depleted rapidly, up to 28% in 10-12 s, by massive, acute neuronal use after stimulation and can be replenished in approximately 20 s. Glutamate-stimulated astrocytic glycolysis and the increase of regional blood flow may regulate the lactate concentration of the pool in different time scales to maintain local energy homeostasis.

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A needle‐type electrochemically based microsensor for glucose (110 µm o.d.) is described. This sensor, designed for monitoring transient glucose content changes in response to neural stimuli, has a response time of ∼5 s and has been shown to be free of interference from endogenous electroactive species such as ascorbate, urate, and various neurotransmitters. It exhibits linear response to glucose up to 10 mM. The usefulness of the sensor has been demonstrated by examining the time‐dependent interstitial glucose concentration in the rat hippocampus in response to KCl depolarization and by stimulation of glutamate neurons through a perforant pathway. Simultaneous monitoring of oxygen is also carried out and demonstrates that for both oxygen and glucose there is substantial local depletion of both species and that their pools are replenished by increased regional cerebral blood flow. The transient initial rapid (10–13 s) decrease up to 20–34%, observed on a time scale comparable to that for neurotransmitter release, may be involved in a recently suggested astrocytic uptake for glutamate‐stimulated aerobic glycolysis possibly needed to meet energy homeostasis in brain. These studies demonstrate the importance of microsensors in monitoring transient events linked to neuronal stimulation.

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Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\in(0,1). Assume d\geq2. We prove that the renormalized self-intersection local time\ell=\int_0^T\int_0^t\delta(B_t^H-B_s^H) ds dt -E\biggl(\int_0^T\int_0^t\delta (B_t^H-B_s^H) ds dt\biggr) exists in L^2 if and only if H<3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a result of Yor, we show that in the case 3/4>H\geq\frac{3}{2d}, r(\epsilon)\ell_{\epsilon} converges in distribution to a normal law N(0,T\sigma^2), as \epsilon tends to zero, where \ell_{\epsilon} is an approximation of \ell, defined through (2), and r(\epsilon)=|\log\epsilon|^{-1} if H=3/(2d), and r(\epsilon)=\epsilon^{d-3/(2H)} if 3/(2d)