Connectivity in the cortex is organized at multiple scales 1-5, suggesting that scale-dependent correlated activity is particularly important for understanding the behavior of sensory cortices and their function in stimulus encoding. Here, we analyze the scale-dependent structure of cortical interactions by using maximum entropy models 6-9 to characterize multiple-tetrode recordings from primary visual cortex of anesthetized monkeys (Macaca mulatta). We compare the properties of firing patterns among local clusters of neurons (<300 microns) with neurons separated by larger distances (600-2500 microns). We find that local firing patterns are distinctive: while multi-neuronal firing patterns at larger distances can be predicted by pairwise interactions, patterns within local clusters often show evidence of high-order correlations. Surprisingly, these local correlations are flexible and rapidly reorganized by visual input. While they modestly reduce the amount of information that a cluster conveys, they also modify the format of this information, creating sparser codes by increasing the periods of total quiescence, and concentrating information into briefer periods of common activity. These results imply a hierarchical organization of neuronal correlations: simple pairwise correlations link neurons over scales of tens to hundreds of minicolumns, but on the scale of a few minicolumns, ensembles of neurons form complex subnetworks whose moment-to-moment effective connectivity is dynamically reorganized by the stimulus.

To understand the functional connectivity of neural networks, it is important to develop simple and incisive descriptors of multineuronal firing patterns. Analysis at the pairwise level has proven to be a powerful approach in the retina, but it may not suffice to understand complex cortical networks. Here we address the problem of describing interactions among triplets of neurons. We consider two approaches: an information-geometric measure (Amari, 2001), which we call the "strain," and the Kullback-Leibler divergence. While both approaches can be used to assess whether firing patterns differ from those predicted by a pairwise maximum-entropy model, the strain provides additional information. Specifically, when the observed firing patterns differ from those predicted by a pairwise model, the strain indicates the nature of this difference -whether there is an excess or a deficit of synchrony -while the Kullback-Leibler divergence only indicates the magnitude of the difference. We show that the strain has technical advantages, including ease of calculation of confidence bounds and bias, and robustness to the kinds of spike-sorting errors associated with tetrode recordings.We demonstrate the biological importance of these points via an analysis of multineuronal firing patterns in primary visual cortex. There is a striking scale-dependent behavior of triplet firing patterns: deviations from the pairwise model are substantial when the neurons are within 300 microns of each other, and negligible when they are at a distance of > 600 microns. The strain identifies a consistent pattern to these interactions: when triplet interactions are present, the strain is nearly always negative, indicating that there is less synchrony than would be expected from the pairwise interactions alone.

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The recording radius and spatial selectivity of an extracellular probe are important for interpreting neurophysiological recordings but are rarely measured. Moreover, an analysis of the recording biophysics of multisite probes (e.g., tetrodes) can provide for source characterization and localization of spiking single units, but this capability has remained largely unexploited. Here we address both issues quantitatively. Advancing a tetrode (Ϸ40-m contact separation, tetrahedral geometry) in 5-to 10-m steps, we repeatedly recorded extracellular action potentials (EAPs) of single neurons in the visual cortex. Using measured spatial variation of EAPs, the tetrodes' measured geometry, and a volume conductor model of the cortical tissue, we solved the inverse problem of estimating the location and the size of the equivalent dipole model of the spike generator associated with each neuron. Half of the 61 visual neurons were localized within a radius of Ϸ100 m and 95% within Ϸ130 m around the tetrode tip (i.e., a large fraction was much further than previously thought). Because of the combined angular sensitivity of the tetrode's leads, location uncertainty was less than one-half the cell's distance. We quantified the spatial dependence of the probability of cell isolation, the isolated fraction, and the dependence of the recording radius on probe size and equivalent dipole size. We also reconstructed the spatial configuration of sets of simultaneously recorded neurons to demonstrate the potential use of 3D dipole localization for functional anatomy. Finally, we found that the dipole moment vector, surprisingly, tended to point toward the probe, leading to the interpretation that the equivalent dipole represents a "local lobe" of the dendritic arbor. recording radius; extracellular action potential; multisite recording; inverse problem; equivalent dipole; lead field theory MULTICONTACT RECORDINGS HAVE HIGH YIELD (Blanche et al. 2005;Csicsvari et al. 2003;Eckhorn and Thomas 1993;Gray et al. 1995;McNaughton et al. 1983) (Buzsaki and Kandel 1998;Drake et al. 1988;Henze et al. 2000) show, the shape and size of the extracellular action potential (EAP) waveform depends on the relative position of cell and probe. Thus, these recordings carry spatial information about spike sources that is not available in single electrode records. However, this spatial information is typically not exploited, because extracting it requires solution of an inverse problem, deducing the position and the size of the current source of a spiking neuron from measurements of its EAP at multiple locations.Here, we solve this inverse problem by modeling the spiking neuron with a single current dipole. The choice of a dipole model rests on reasoning presented in detail in a companion paper and its supplemental material (Mechler and Victor 2011). Briefly, although the membrane currents of a spiking neuron constitute a genuinely distributed current source, the resulting extracellular field is well approximated by that of a dipole beyond a minimum distance a...

OBJECTIVELateral lumbar interbody fusion (LLIF) is a useful minimally invasive technique for achieving anterior interbody fusion and preserving or restoring lumbar lordosis. However, achieving circumferential fusion via posterior instrumentation after an LLIF can be challenging, requiring either repositioning the patient or placing pedicle screws in the lateral position. Here, the authors explore an alternative single-position approach: LLIF in the prone lateral (PL) position.METHODSA cadaveric feasibility study was performed using 2 human cadaveric specimens. A retrospective 2-center early clinical series was performed for patients who had undergone a minimally invasive lateral procedure in the prone position between August 2019 and March 2020. Case duration, retractor time, electrophysiological thresholds, implant size, screw accuracy, and complications were recorded. Early postoperative radiographic outcomes were reported.RESULTSA PL LLIF was successfully performed in 2 cadavers without causing injury to a vessel or the bowel. No intraoperative subsidence was observed. In the clinical series, 12 patients underwent attempted PL surgery, although 1 case was converted to standard lateral positioning. Thus, 11 patients successfully underwent PL LLIF (89%) across 14 levels: L2–3 (2 of 14 [14%]), L3–4 (6 of 14 [43%]), and L4–5 (6 of 14 [43%]). For the 11 PL patients, the mean (± SD) age was 61 ± 16 years, mean BMI was 25.8 ± 4.8, and mean retractor time per level was 15 ± 6 minutes with the longest retractor time at L2–3 and the shortest at L4–5. No intraoperative subsidence was noted on routine postoperative imaging.CONCLUSIONSPerforming single-position lateral transpsoas interbody fusion with the patient prone is anatomically feasible, and in an early clinical experience, it appeared safe and reproducible. Prone positioning for a lateral approach presents an exciting opportunity for streamlining surgical access to the lumbar spine and facilitating more efficient surgical solutions with potential clinical and economic advantages.