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Abstract The need for in vitro models that mimic the human brain to replace animal testing and allow high-throughput screening has driven scientists to develop new tools that reproduce tissue-like features on a chip. Three-dimensional (3D) in vitro cultures are emerging as an unmatched platform that preserves the complexity of cell-to-cell connections within a tissue, improves cell survival, and boosts neuronal differentiation. In this context, new and flexible imaging approaches are required to monitor the functional states of 3D networks. Herein, we propose an experimental model based on 3D neuronal networks in an alginate hydrogel, a tunable wide-volume imaging approach, and an efficient denoising algorithm to resolve, down to single cell resolution, the 3D activity of hundreds of neurons expressing the calcium sensor GCaMP6s. Furthermore, we implemented a 3D co-culture system mimicking the contiguous interfaces of distinct brain tissues such as the cortical-hippocampal interface. The analysis of the network activity of single and layered neuronal co-cultures revealed cell-type-specific activities and an organization of neuronal subpopulations that changed in the two culture configurations. Overall, our experimental platform represents a simple, powerful and cost-effective platform for developing and monitoring living 3D layered brain tissue on chip structures with high resolution and high throughput.

Pulmonary metastasectomy has become a well-established procedure for patients with certain types of solid tumors. Patients are usually scheduled for staged lung metastasectomy in case of primary tumor control, the absence of distant non-lung metastases, and when complete resection is achievable. Nodules are removed with precision resection in order to ensure radical resection with minimal margins; this technique permits good oncological results, preserving the surrounding pulmonary parenchyma and causing minimal distortion compared to staplers. When possible, anatomical resections should be avoided since they are not justified by real oncological advantages and, in the majority of cases, sacrifice too much healthy tissue, possibly leading to inoperability in the case of metachronous relapses. Thus, preserving the maximum amount of pulmonary parenchyma is crucial because repeated metastasectomies are possible and frequent, with no theoretical limits to the number of reinterventions. In our multidisciplinary board team, we support the role of pulmonary metastasectomy as a useful curative therapy, with acceptable morbidity and mortality, with indications to be discussed case-by-case.

Background: Congenital Pulmonary Malformations (CPMs) are rare benign lesions potentially causing infective complications and/or malignant transformation, requiring surgery even when asymptomatic. CPMs are rare in adulthood but potentially detected at any age. There is not a consensus on the correct extent of resection in both adults and paediatrics. This retrospective multicentric study aims to identify the appropriate surgical resection to prevent the recurrence of the related respiratory symptoms., Methods: Between 2010 and 2020, a total of 96 patients (adults and pediatrics) underwent surgery for CPMs in 4 centers. A 2:1 propensity score matching (considering sex and lesion side) was performed, identifying 2 groups: 50 patients underwent lobectomy (group A) and 25 sub-lobar resections (group B). Clinical and histopathological characteristics, early and late complications, and symptom recurrence were retrospectively analyzed and compared between the two groups by univariate and multivariate analysis., Results: Patients who underwent lobectomy had a statistically significant lower rate of recurrence (4% vs. 24% of group B, p = 0.014) and a lower rate of intraoperative complications ( p = 0.014). Logistic regression identified sub-lobar resection ( p = 0.040), intra- and post-operative complications ( p = 0.105 and 0.022),and associated developed neoplasm ( p = 0.062) as possible risk factors for symptom recurrence after surgery., Conclusions: Pulmonary lobectomy seems to be the most effective surgical treatment for CPMs, guaranteeing the stable remission of symptoms and a lower rate of intra- and postoperative complications. To our knowledge, this is one of the largest studies comparing lobectomy and sub-lobar resections in patients affected by CPMs, considering the low incidence worldwide.

The development of the hyperspectral remote sensor technology allows the acquisition of images with a very detailed spectral information for each pixel. Because of this, hyperspectral images (HSI) potentially possess larger capabilities in solving many scientific and practical problems in agriculture, biomedical, ecological, geological, hydrological studies. However, their analysis requires developing specialized and fast algorithms for data processing, due the high dimensionality of the data. In this work, we propose a new semi-supervised method for multilabel segmentation of HSI that combines a suitable linear discriminant analysis, a similarity index to compare different spectra, and a random walk based model with a direct label assignment. The user-marked regions are used for the projection of the original high-dimensional feature space to a lower dimensional space, such that the class separation is maximized. This allows to retain in an automatic way the most informative features, lightening the successive computational burden. The part of the random walk is related to a combinatorial Dirichlet problem involving a weighted graph, where the nodes are the projected pixel of the original HSI, and the positive weights depend on the distances between these nodes. We then assign to each pixel of the original image a probability quantifying the likelihood that the pixel (node) belongs to some subregion. The computation of the spectral distance involves both the coordinates in a features space of a pixel and of its neighbors. The final segmentation process is therefore reduced to a suitable optimization problem coupling the probabilities from the random walker computation, and the similarity with respect the initially labeled pixels. We discuss the properties of the new method with experimental results carried on benchmark images.

Image segmentation is an essential but critical component in low level vision, image analysis, pattern recognition, and now in robotic systems. In addition, it is one of the most challenging tasks in image processing and determines the quality of the final results of the image analysis. Colour based segmentation could hence offer more significant extraction of information as compared to intensity or texture based segmentation. In this work, we propose a new local or global method for multi-label segmentation that combines a random walk based model with a direct label assignment computed using a suitable colour distance. Our approach is a semi-automatic image segmentation technique, since it requires user interaction for the initialisation of the segmentation process. The random walk part involves a combinatorial Dirichlet problem for a weighted graph, where the nodes are the pixel of the image, and the positive weights are related to the distances between pixels: in this work we propose a novel colour distance for computing such weights. In the random walker model we assign to each pixel of the image a probability quantifying the likelihood that the node belongs to some subregion. The computation of the colour distance is pursued by employing the coordinates in a colour space (e.g., RGB, XYZ, YCbCr) of a pixel and of the ones in its neighbourhood (e.g., in a 8-neighbourhood). The segmentation process is, therefore, reduced to an optimisation problem coupling the probabilities from the random walker approach, and the similarity with respect the labelled pixels. A further investigation involves an adaptive preprocess strategy using a regression tree for learning suitable weights to be used in the computation of the colour distance. We discuss the properties of the new method also by comparing with standard random walk and k-means approaches. The experimental results carried on the White Blood Cell (WBC) dataset and GrabCut datasets show the remarkable performance of the proposed method in comparison with state-of-the-art methods, such as normalised random walk and normalised lazy random walk, with respect to segmentation quality and computational time. Moreover, it reveals to be very robust with respect to the presence of noise and to the choice of the colourspace.

The first case of Coronavirus Disease 2019 in Italy was detected on February the 20th in Lombardy region. Since that date, Lombardy has been the most affected Italian region by the epidemic, and its healthcare system underwent a severe overload during the outbreak. From a public health point of view, therefore, it is fundamental to provide healthcare services with tools that can reveal possible new health system stress periods with a certain time anticipation, which is the main aim of the present study. Moreover, the sequence of law decrees to face the epidemic and the large amount of news generated in the population feelings of anxiety and suspicion. Considering this whole complex context, it is easily understandable how people "overcrowded" social media with messages dealing with the pandemic, and emergency numbers were overwhelmed by the calls. Thus, in order to find potential predictors of possible new health system overloads, we analysed data both from Twitter and emergency services comparing them to the daily infected time series at a regional level. Particularly, we performed a wavelet analysis in the time-frequency plane, to finely discriminate over time the anticipation capability of the considered potential predictors. In addition, a cross-correlation analysis has been performed to find a synthetic indicator of the time delay between the predictor and the infected time series. Our results show that Twitter data are more related to social and political dynamics, while the emergency calls trends can be further evaluated as a powerful tool to potentially forecast new stress periods. Since we analysed aggregated regional data, and taking into account also the huge geographical heterogeneity of the epidemic spread, a future perspective would be to conduct the same analysis on a more local basis., Competing Interests: The authors have declared that no competing interests exist.

Background: Malignant pleural mesothelioma (MPM) is a rare and aggressive disease of the pleura with a dismal prognosis. Distant metastases most commonly occur in the liver, spleen, and thyroid gland. To our knowledge, ovarian metastases have never been described., Case Description: We describe a case of a woman with recurrent malignant pleural mesothelioma presenting a single ovarian metastasis, surgically resected., Conclusions: This case report highlights the importance of using a complete staging protocol in patients with MPM to improve patient management. A whole-body computed tomography (CT) scan with contrast enhancement and possibly positron emission tomography-CT should be performed to identify any distant metastases before deciding on treatment strategy.

Diffuse optical tomography (DOT) is an emerging imaging technique which uses light for diagnostic purposes in a non-invasive and non-ionizing way. In this paper, we focus on DOT application to female breast screening, where the surface of the breast is illuminated by light sources and the outgoing light is collected on the surface. The comparison of measured light data with the equivalent field obtained from a relevant mathematical model yields the DOT inverse problem whose solution provides an estimate of the optical coefficients of the tissue. These latter, in turn, can be related to clinical markers for cancer detection. The goal of this work is to propose a mathematical and computational approach tailored to the concept of a DOT imaging device able to perform fast and accurate screenings at an affordable cost. Namely, we address two original points about the crucial issue of the solution of the severely ill-conditioned DOT inverse problem: (a) a computational approach based on Green's functions which do not require the exact knowledge of the tissue geometry, proposed here in the declination of the Method of Fundamental Solutions, which allows to enforce correct boundary conditions; (b) the elastic net regularization technique that shares the desirable properties of both the ℓ 2 - and ℓ 1 -norm penalization approaches and opens the possibility for sparsity recognition in the optical coefficients field and refinement procedures., (© 2019 John Wiley & Sons, Ltd.)

Introduction: Malignant diseases are well-known complications after lung transplantation (LT). Among these, inflammatory myofibroblastic tumor (IMT) is a rare neoplasm with a not well-known and often aggressive biological behavior., Material and Methods: We hereby describe 2 cases of cystic fibrosis patients who underwent bilateral sequential LT (BSLT) complicated by IMT., Results: A 26-year-old man presented a right endobronchial lesion 6 months after BSLT. Two consecutive fiber bronchoscopic biopsies showed granulation tissue. For the persistent lesion growth, the patient underwent a transthoracic biopsy showing histologic diagnosis of IMT. Therefore, he underwent to right pneumonectomy that was unfortunately complicated after 6 months with a late bronchopleural fistula and empyema with exitus 6 months later. A 31-year-old woman 1 year after BSLT presented with a left voluminous pleural-parenchymal lesion; the histologic examination after biopsy revealed an IMT. She underwent a removal of the lesion with a macroscopic R0 resection. Histologic, immunophenotypic, and cytogenetic examinations showed a strong overexpression of anaplastic lymphoma kinase requiring biological adjuvant therapies; however, the patient refused it. Four years later, she presented a recurrence treated with debulking procedure and adjuvant radiotherapy. At last follow-up, the patient was alive with stable disease and optimal graft function., Conclusions: Although IMT is a rare complication after lung transplant, to obtain a careful diagnosis, an early and aggressive treatment is mandatory., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

Background: Lung transplantation (LT) is a viable option for a select group of patients with end-stage lung disease. However, infections are a major complication after LT, accounting for significant morbidity and mortality. Several germs may be responsible; multidrug-resistant Gram-negative (MDR-GN) bacteria are emerging. Colistin is widely used in the treatment of these infections and is administered by inhalation and/or parenterally. At our institution, in patients with tracheostomy, colistin is administered by direct instillation in the airway during bronchoscopy. We reviewed a series of patients who underwent LT complicated by postoperative MDR-GN bacterial pulmonary infection., Methods: From January 2015 to May 2017, 26 lung transplants were performed. In the postoperative course, 14 (54%) developed MDR-GN bacterial infection; respiratory specimen culture, blood tests, and chest X-ray were considered. Colistin was the only antibiotic usable. Thirteen patients received intravenous (IV) colistin; in the subgroup of patients with tracheostomy, colistin was instilled directly in the airway, and 6 patients received inhaled colistin., Results: Seven patients needed tracheostomy. Pseudomonas aeruginosa was the predominant infection (86%), with Acinetobacter baumanii seen in 2 cases (14%). An early clinical-laboratory response was observed in 9 patients (64%). White blood cell count and C-reactive protein values improved (P = .02 and P = .001, respectively). A significant reduction in bacterial load was observed on microbiologic bronchoalveolar lavage specimens., Conclusion: Colistin instilled directly in the airway did not show side effects. The combination of IV and inhaled/instilled colistin could be a useful treatment option for MDR-GN infections after LT., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Background: The cerebellar granular layer input stage of cerebellum receives information from tactile and sensory regions of the body. The somatosensory activity in the cerebellar granular layer corresponds to sensory and tactile input has been observed by recording Local Field Potential (LFP) from the Crus-IIa regions of cerebellum in brain slices and in anesthetized animals., Purpose: In this paper, a detailed biophysical model of Wistar rat cerebellum granular layer network model and LFP modelling schemas were used to simulate circuit's evoked response., Methods: Point Source Approximation and Line Source Approximation were used to reconstruct the network LFP. The LFP mechanism in in vitro was validated in network model and generated the in vivo LFP using the same mechanism., Results: The network simulations distinctly displayed the Trigeminal and Cortical (TC) wave components generated by 2 independent bursts implicating the generation of TC waves by 2 independent granule neuron populations. Induced plasticity was simulated to estimate granule neuron activation related population responses. As a prediction, cerebellar dysfunction (ataxia) was also studied using the model. Dysfunction at individual neurons in the network was affected by the population response., Conclusion: Our present study utilizes available knowledge on known mechanisms in a single cell and associates network function to population responses.

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N2a, N2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

The aim of this study was to develop a model exploiting artificial neural networks (ANNs) to correlate dosimetric and clinical variables with late rectal bleeding in prostate cancer patients undergoing radical radiotherapy and to compare the ANN results with those of a standard logistic regression (LR) analysis. 718 men included in the AIROPROS 0102 trial were analyzed. This multicenter protocol was characterized by the prospective evaluation of rectal toxicity, with a minimum follow-up of 36 months. Radiotherapy doses were between 70 and 80 Gy. Information was recorded for comorbidity, previous abdominal surgery, use of drugs and hormonal therapy. For each patient, a rectal dose-volume histogram (DVH) of the whole treatment was recorded and the equivalent uniform dose (EUD) evaluated as an effective descriptor of the whole DVH. Late rectal bleeding of grade ≥ 2 was considered to define positive events in this study (52 of 718 patients). The overall population was split into training and verification sets, both of which were involved in model instruction, and a test set, used to evaluate the predictive power of the model with independent data. Fourfold cross-validation was also used to provide realistic results for the full dataset. The LR was performed on the same data. Five variables were selected to predict late rectal bleeding: EUD, abdominal surgery, presence of hemorrhoids, use of anticoagulants and androgen deprivation. Following a receiver operating characteristic analysis of the independent test set, the areas under the curves (AUCs) were 0.704 and 0.655 for ANN and LR, respectively. When evaluated with cross-validation, the AUC was 0.714 for ANN and 0.636 for LR, which differed at a significance level of p = 0.03. When a practical discrimination threshold was selected, ANN could classify data with sensitivity and specificity both equal to 68.0%, whereas these values were 61.5% for LR. These data provide reasonable evidence that results obtained with ANNs are superior to those achieved with LR when predicting late radiotherapy-related rectal bleeding. The future introduction of patient-related personal characteristics, such as gene expression profiles, might improve the predictive power of statistical classifiers. More refined morphological aspects of the dose distribution, such as dose surface mapping, might also enhance the overall performance of ANN-based predictive models.

Ultrasensitivity, as described by Goldbeter and Koshland, has been considered for a long time as a way to realize bistable switches in biological systems. It is not as well recognized that when ultrasensitivity and reinforcing feedback loops are present in a spatially distributed system such as the cell plasmamembrane, they may induce bistability and spatial separation of the system into distinct signaling phases. Here we suggest that bistability of ultrasensitive signaling pathways in a diffusive environment provides a basic mechanism to realize cell membrane polarity. Cell membrane polarization is a fundamental process implicated in several basic biological phenomena, such as differentiation, proliferation, migration and morphogenesis of unicellular and multicellular organisms. We describe a simple, solvable model of cell membrane polarization based on the coupling of membrane diffusion with bistable enzymatic dynamics. The model can reproduce a broad range of symmetry-breaking events, such as those observed in eukaryotic directional sensing, the apico-basal polarization of epithelium cells, the polarization of budding and mating yeast, and the formation of Ras nanoclusters in several cell types.

The cerebellum input stage has been known to perform combinatorial operations on input signals. In this paper, two types of mathematical models were used to reproduce the role of feed-forward inhibition and computation in the granular layer microcircuitry to investigate spike train processing. A simple spiking model and a biophysically-detailed model of the network were used to study signal recoding in the granular layer and to test observations like center-surround organization and time-window hypothesis in addition to effects of induced plasticity. Simulations suggest that simple neuron models may be used to abstract timing phenomenon in large networks, however detailed models were needed to reconstruct population coding via evoked local field potentials (LFP) and for simulating changes in synaptic plasticity. Our results also indicated that spatio-temporal code of the granular network is mainly controlled by the feed-forward inhibition from the Golgi cell synapses. Spike amplitude and total number of spikes were modulated by LTP and LTD. Reconstructing granular layer evoked-LFP suggests that granular layer propagates the nonlinearities of individual neurons. Simulations indicate that granular layer network operates a robust population code for a wide range of intervals, controlled by the Golgi cell inhibition and is regulated by the post-synaptic excitability.

Aims and Background: The purpose of the study was to develop a general method able to quantify the mutual disposition in the 3D space of critical organs with respect to the target when these structures are designed for a radiotherapy treatment plan. To that end, we introduce the "expansion intersection histogram", a function defined as the intersection between an organ at risk and the target volume, while the target is expanded in 3D., Methods and Study Design: A software was developed to calculate the expansion intersection histogram of anatomical structures exported in a DICOM format from a commercial treatment planning system. A virtual phantom with spherical and cylindrical objects arranged in different dispositions in the 3D space was created for testing the software under known conditions., Results and Conclusions: Expansion intersection histogram computation was tested against reference data derived analytically for spherical volumes, with a resulting maximum error of 0.5%. Specific geometric features derived from the expansion intersection histogram, such as the distance between a selected target and each different ideal volume included in the virtual phantom, well matched the corresponding theoretical expected values. The expansion intersection histogram was evaluated also for the anatomical structures of a real patient. Data show this method as a tool to effectively take into account the mutual disposition of each critical organ with respect to the target, summarized in characteristics of distance, shape and orientation. The expansion intersection histogram method integrates and extends other preexisting modalities for evaluating the geometrical relationships among radiotherapy volumes and could be used to improve planning optimization.

Understanding population activities of underlying neurons reveal emergent behavior as patterns of information flow in neural circuits. Evoked local field potentials (LFPs) arise from complex interactions of spatial distribution of current sources, time dynamics, and spatial distribution of dipoles apart underlying conductive properties of the extracellular medium. We reconstructed LFP to test and parameterize the molecular mechanisms of cellular function with network properties. The sensitivity of LFP to local excitatory and inhibitory connections was tested using two novel techniques. In the first, we used a single granule neuron as a model kernel for reconstructing population activity. The second technique consisted using a detailed network model. LTP and LTD regulating the spatiotemporal pattern of granular layer responses to mossy fiber inputs was studied. The effect of changes in synaptic release probability and modulation in intrinsic excitability of granule cell on LFP was studied. The study revealed cellular function and plasticity were represented in LFP wave revealing the activity of underlying neurons. Changes to single cell properties during LTP and LTD were reflected in the LFP wave suggesting the sparse recoding function of granule neurons as spatial pattern generators. Both modeling approaches generated LFP in vitro (Mapelli and D'Angelo, 2007) and in vivo (Roggeri et al., 2008) waveforms as reported in experiments and predict that the expression mechanisms revealed in vitro can explain the LFP changes associated with LTP and LTD in vivo., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Local field-potentials (LFPs) are generated by neuronal ensembles and contain information about the activity of single neurons. Here, the LFPs of the cerebellar granular layer and their changes during long-term synaptic plasticity (LTP and LTD) were recorded in response to punctate facial stimulation in the rat in vivo. The LFP comprised a trigeminal (T) and a cortical (C) wave. T and C, which derived from independent granule cell clusters, co-varied during LTP and LTD. To extract information about the underlying cellular activities, the LFP was reconstructed using a repetitive convolution (ReConv) of the extracellular potential generated by a detailed multicompartmental model of the granule cell. The mossy fiber input patterns were determined using a Blind Source Separation (BSS) algorithm. The major component of the LFP was generated by the granule cell spike Na(+) current, which caused a powerful sink in the axon initial segment with the source located in the soma and dendrites. Reproducing the LFP changes observed during LTP and LTD required modifications in both release probability and intrinsic excitability at the mossy fiber-granule cells relay. Synaptic plasticity and Golgi cell feed-forward inhibition proved critical for controlling the percentage of active granule cells, which was 11% in standard conditions but ranged from 3% during LTD to 21% during LTP and raised over 50% when inhibition was reduced. The emerging picture is that of independent (but neighboring) trigeminal and cortical channels, in which synaptic plasticity and feed-forward inhibition effectively regulate the number of discharging granule cells and emitted spikes generating "dense" activity clusters in the cerebellar granular layer.

Objective: We investigated the prevalence of nocturnal smoking (NS) in patients with RLS., Methods: One hundred RLS patients living in Emilia-Romagna (Northern Italy) and 100 matched controls, randomly selected from the general population, underwent interviews for the presence of nocturnal smoking and for obsessive-compulsive traits, depression, excessive daytime sleepiness (EDS) and subjective sleep quality., Results: NS was more prevalent in RLS patients than controls (lifetime prevalence: 12% vs. 2%, P=0.012). Patients with NS had more frequently Sleep-Related Eating Disorders (SRED) than patients without NS (83.3% vs. 26.1%, P=0.0002). Pathological and borderline Maudsley Obsessive-Compulsive Inventory (MOCI) values as well as pathological values at the Beck Depression Inventory (BDI) increased from controls to RLS patients without NS to RLS patients with NS (P=0.005 and P=0.01, respectively)., Conclusions: We demonstrate an increased prevalence of NS in patients with RLS, in many cases associated with increased SRED. NS may be associated with psychopathological traits in RLS and may be relevant in the management of RLS patients., (2009 Elsevier B.V. All rights reserved.)

We investigated the prevalence of nocturnal eating (sleep-related eating disorder-SRED or night-eating syndrome-NES) in patients with restless legs syndrome (RLS). One hundred RLS patients living in Emilia-Romagna (Northern Italy) and 100 matched controls randomly selected from the general population received two telephone interviews, and were investigated for socio-demographic characteristics, general health status, and presence of nocturnal eating. Additionally, subjects underwent interviews for psychopathological traits [by means of the Eating Disorder Inventory-2 (EDI-2), the Maudsley Obsessive-Compulsive Inventory (MOCI), the Beck Depression Inventory (BDI)], excessive daytime sleepiness (EDS), and subjective sleep quality. Compared with controls, RLS patients had more frequently pathological MOCI scores (24% versus 10%, P = 0.03), used significantly more drugs for concomitant diseases and had more nocturnal sleep impairment and EDS. SRED was more prevalent in RLS patients than controls (SRED: 33% versus 1%, P < 0.001). Medication use and pathological MOCI scores were more prevalent in RLS patients with SRED than among RLS patients without SRED. Use of dopaminergic or hypnotic drugs for RLS was not correlated with the presence of SRED. We demonstrate an association between RLS and SRED. Prospective studies are needed to establish the mechanisms underlying such association and whether it is causal., ((c) 2009 Movement Disorder Society.)

In most neurons, Na+ channels in the axon are complemented by others localized in the soma and dendrites to ensure spike back-propagation. However, cerebellar granule cells are neurons with simplified architecture in which the dendrites are short and unbranched and a single thin ascending axon travels toward the molecular layer before bifurcating into parallel fibers. Here we show that in cerebellar granule cells, Na+ channels are enriched in the axon, especially in the hillock, but almost absent from soma and dendrites. The impact of this channel distribution on neuronal electroresponsiveness was investigated by multi-compartmental modeling. Numerical simulations indicated that granule cells have a compact electrotonic structure allowing excitatory postsynaptic potentials to diffuse with little attenuation from dendrites to axon. The spike arose almost simultaneously along the whole axonal ascending branch and invaded the hillock the activation of which promoted spike back-propagation with marginal delay (<200 micros) and attenuation (<20 mV) into the somato-dendritic compartment. These properties allow granule cells to perform sub-millisecond coincidence detection of pre- and postsynaptic activity and to rapidly activate Purkinje cells contacted by the axonal ascending branch.

Neurons process information in a highly nonlinear manner, generating oscillations, bursting, and resonance, enhancing responsiveness at preferential frequencies. It has been proposed that slow repolarizing currents could be responsible for both oscillation/burst termination and for high-pass filtering that causes resonance (Hutcheon and Yarom, 2000). However, different mechanisms, including electrotonic effects (Mainen and Sejinowski, 1996), the expression of resurgent currents (Raman and Bean, 1997), and network feedback, may also be important. In this study we report theta-frequency (3-12 Hz) bursting and resonance in rat cerebellar granule cells and show that these neurons express a previously unidentified slow repolarizing K(+) current (I(K-slow)). Our experimental and modeling results indicate that I(K-slow) was necessary for both bursting and resonance. A persistent (and potentially a resurgent) Na(+) current exerted complex amplifying actions on bursting and resonance, whereas electrotonic effects were excluded by the compact structure of the granule cell. Theta-frequency bursting and resonance in granule cells may play an important role in determining synchronization, rhythmicity, and learning in the cerebellum.