Sum rules are used to develop a broad understanding of light-matter interactions through investigations of
universal properties and are applied to specific phenomena to gain insights into the underlying fundamental
processes. We discuss universal properties associated with the third-order nonlinear-optical response and show
how microscopic cascading – where two molecules interact through their hyperpolarizabilities to yield a second
hyperpolarizability – must obey these same universal properties. In addition, we discuss how the sum rules imply
more exotic classes of Hamiltonians and their consistency with physical laws, which may partially explain the
difference between the sum-rule-derived fundamental limits and observations.
Neural activation generates a hemodynamic response to the localized region replenishing nutrients to the area. Changes
in vigilance state have been shown to alter the vascular response where the vascular response is muted during wake
compared to quiet sleep. We tested the saturation thresholds of the neurovascular response in the auditory cortex during
wake and sleep by chronically implanting rats with an EEG electrode, a light emitting diode (LED, 600 nm), and
photodiode to simultaneously measure evoked response potentials (ERPs) and evoked hemodynamic responses. We
stimulated the cortex with a single speaker click delivered at random intervals 2-13 s at varied stimulus intensities
ranging from 45-80 dB. To further test the potential for activity related saturation, we sleep deprived animals for 2, 4, or
6 hours and recorded evoked responses during the first hour recovery period. With increasing stimulus intensity,
integrated ERPs and evoked hemodynamic responses increased; however the hemodynamic response approached
saturation limits at a lower stimulus intensity than the ERP. With longer periods of sleep deprivation, the integrated
ERPs did not change but evoked hemodynamic responses decreased. There may be physical limits in cortical blood
delivery and vascular compliance, and with extended periods of neural activity during wake, vessels may approach these
limits.
Laser diodes (LD) are commonly used for optical neural recordings in chronically recorded animals and humans, primarily due to their brightness and small size. However, noise introduced by LDs may counteract the benefits of brightness when compared to low-noise light-emitting diodes (LEDs). To understand noise sources in optical recordings, we systematically compared instrument and physiological noise profiles in two recording paradigms. A better understanding of noise sources can help improve optical recordings and make them more practical with fewer averages. We stimulated lobster nerves and a rat cortex, then compared the root mean square (RMS) noise and signal-to-noise ratios (SNRs) of data obtained with LED, superluminescent diode (SLD), and LD illumination for different numbers of averages. The LED data exhibited significantly higher SNRs in fewer averages than LD data in all recordings. In the absence of tissue, LED noise increased linearly with intensity, while LD noise increased sharply in the transition to lasing and settled to noise levels significantly higher than the LED's, suggesting that speckle noise contributed to the LD's higher noise and lower SNRs. Our data recommend low coherence and portable light sources for in vivo chronic neural recording applications.
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