Firing statistics and correlations in spiking neurons: a level-crossing approach

We present a time-dependent level-crossing theory for linear dynamical systems perturbed by colored Gaussian noise. We apply these results to approximate the firing statistics of conductance-based integrate-and-fire neurons receiving excitatory and inhibitory Poissonian inputs. Analytical expressions are obtained for three key quantities characterizing the neuronal response to time-varying inputs: the mean firing rate, the linear response to sinusoidally-modulated inputs, and the pairwise spike-correlation for neurons receiving correlated inputs. The theory yields tractable results that are shown to accurately match numerical simulations, and provides useful tools for the analysis of interconnected neuronal populations

Patient-specific simulation of stent-graft deployment within an abdominal aortic aneurysm

In this study, finite element analysis is used to simulate the surgical deployment procedure of a bifurcated stent-graft on a real patient's arterial geometry. The stent-graft is modeled using realistic constitutive properties for both the stent and most importantly for the graft. The arterial geometry is obtained from pre-operative imaging exam. The obtained results are in good agreement with the post-operative imaging data. As the whole computational time was reduced to less than 2 hours, this study constitutes an essential step towards predictive planning simulations of aneurysmal endovascular surger

Extracting non-linear integrate-and-fire models from experimental data using dynamic I - V curves

The dynamic I-V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current-voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neuron

Experimentally verified parameter sets for modelling heterogeneous neocortical pyramidal-cell populations

Models of neocortical networks are increasingly including the diversity of excitatory and inhibitory neuronal classes. Significant variability in cellular properties are also seen within a nominal neuronal class and this heterogeneity can be expected to influence the population response and information processing in networks. Recent studies have examined the population and network effects of variability in a particular neuronal parameter with some plausibly chosen distribution. However, the empirical variability and covariance seen across multiple parameters are rarely included, partly due to the lack of data on parameter correlations in forms convenient for model construction. To addess this we quantify the heterogeneity within and between the neocortical pyramidal-cell classes in layers 2/3, 4, and the slender-tufted and thick-tufted pyramidal cells of layer 5 using a combination of intracellular recordings, single-neuron modelling and statistical analyses. From the response to both square-pulse and naturalistic fluctuating stimuli, we examined the class-dependent variance and covariance of electrophysiological parameters and identify the role of the h current in generating parameter correlations. A byproduct of the dynamic I-V method we employed is the straightforward extraction of reduced neuron models from experiment. Empirically these models took the refractory exponential integrate-and-fire form and provide an accurate fit to the perisomatic voltage responses of the diverse pyramidal-cell populations when the class-dependent statistics of the model parameters were respected. By quantifying the parameter statistics we obtained an algorithm which generates populations of model neurons, for each of the four pyramidal-cell classes, that adhere to experimentally observed marginal distributions and parameter correlations. As well as providing this tool, which we hope will be of use for exploring the effects of heterogeneity in neocortical networks, we also provide the code for the dynamic I-V method and make the full electrophysiological data set available

Simulation du déploiement d'endoprothèses dans des anévrismes iliaques tortueux

National audienceLe traitement des anévrismes par voie endovasculaire avec pose d'une endoprothèse (EP) est une technique de choix face à la chirurgie ouverte conventionnelle, mais elle reste à fiabiliser. Dans cette étude, une simulation complète par éléments finis de la pose d'EP est proposée afin d'évaluer et comparer les performances mécaniques de cinq dispositifs du marché. Les résultats confirment l'importance de la flexibilité des EPs et offrent une avancée notable dans la simulation de la chirurgie endovasculaire

Patient-specific numerical simulation of stent-graft deployment: Validation on three clinical cases.

International audienceEndovascular repair of abdominal aortic aneurysms faces some adverse outcomes, such as kinks or endoleaks related to incomplete stent apposition, which are difficult to predict and which restrain its use although it is less invasive than open surgery. Finite element simulations could help to predict and anticipate possible complications biomechanically induced, thus enhancing practitioners' stent-graft sizing and surgery planning, and giving indications on patient eligibility to endovascular repair. The purpose of this work is therefore to develop a new numerical methodology to predict stent-graft final deployed shapes after surgery. The simulation process was applied on three clinical cases, using preoperative scans to generate patient-specific vessel models. The marketed devices deployed during the surgery, consisting of a main body and one or more iliac limbs or extensions, were modeled and their deployment inside the corresponding patient aneurysm was simulated. The numerical results were compared to the actual deployed geometry of the stent-grafts after surgery that was extracted from postoperative scans. We observed relevant matching between simulated and actual deployed stent-graft geometries, especially for proximal and distal stents outside the aneurysm sac which are particularly important for practitioners. Stent locations along the vessel centerlines in the three simulations were always within a few millimeters to actual stents locations. This good agreement between numerical results and clinical cases makes finite element simulation very promising for preoperative planning of endovascular repair

Finite Element Analysis of the Mechanical Performances of 8 Marketed Aortic Stent-Grafts

International audiencePurpose: To assess numerically the flexibility and mechanical stresses undergone by stents and fabric of currently manufactured stent-grafts. Methods: Eight marketed stent-graft limbs (Aorfix, Anaconda, Endurant, Excluder, Talent, Zenith Flex, Zenith LP, and Zenith Spiral-Z) were modeled using finite element analysis. A numerical benchmark combining bending up to 180° and pressurization at 150 mmHg of the stent-grafts was performed. Stent-graft flexibility, assessed by the calculation of the luminal reduction rate, maximal stresses in stents, and maximal strains in fabric were assessed. Results: The luminal reduction rate at 90° was ‹<20% except for the Talent stent-graft. The rate at 180° was higher for Z-stented models (Talent, Endurant, Zenith, and Zenith LP; range 39%-78%) than spiral (Aorfix, Excluder, and Zenith Spiral-Z) or circular-stented (Anaconda) devices (range 14%-26%). At 180°, maximal stress was higher for Z-stented stent-grafts (range 370-622 MPa) than spiral or circular-stented endografts (range 177-368 MPa). At 90° and 180°, strains in fabric were low and did not differ significantly among the polyester stent-grafts (range 0.5%-7%), while the expanded polytetrafluoroethylene fabric of the Excluder stent-graft underwent higher strains (range 11%-18%). Conclusion: Stent design strongly influences mechanical performances of aortic stentgrafts. Spiral and circular stents provide greater flexibility, as well as lower stress values than Z-stents, and thus better durability

Dependence of the spike-triggered average voltage on membrane response properties

The spike-triggered average voltage (STV) is an experimentally measurable quantity that is determined by both the membrane response properties and the statistics of the synaptic drive. Here, the form of the STV is modelled for neurons with three distinct types of subthreshold dynamics; passive decay, h-current sag, and damped oscillations. Analytical expressions for the STV are first obtained in the low-noise limit, identifying how the subthreshold dynamics of the cell affect its form. A second result is then derived that captures the power-law behaviour of the STV near the spike threshold

Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves

The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons

Pulse propagation in discrete excitatory networks of integrate-and-fire neurons

We study the propagation of solitary waves in a discrete excitatory network of integrate-and-fire neurons. We show the existence and the stability of a fast wave and a family of slow waves. Fast waves are similar to those already described in continuum networks. Stable slow waves have not been previously reported in purely excitatory networks and their propagation is particular to the discrete nature of the network. The robustness of our results is studied in the presence of noise