Reduced order modeling of passive and quasi-active dendrites for nervous system simulation

Accurate neuron models at the level of the single cell are composed of dendrites described by a large number of compartments. The network-level simulation of complex nervous systems requires highly compact yet accurate single neuron models. We present a systematic, numerically efficient and stable model order reduction approach to reduce the complexity of large dendrites by orders of magnitude. The resulting reduced dendrite models match the impedances of the full model within the frequency range of biological signals and reproduce the original action potential output waveforms.     

A system model for investigating passive electrical properties of neurons.

Passive membrane properties of neurons, characterized by a linear voltage response to constant current stimulation, were investigated by busing a system model approach. This approach utilizes the derived expression for the input impedance of a network, which simulates the passive properties of neurons, to correlate measured intracellular recordings with the response of network models. In this study, the input impedances of different network configurations and of dentate granule neurons, were derived as a function of the network elements and were validated with computer simulations. The parameters of the system model, which are the values of the network elements, were estimated using an optimization strategy. The system model provides for better estimation of the network elements than the previously described signal model, due to its explicit nature. In contrast, the signal model is an implicit function of the network elements which requires intermediate steps to estimate some of the passive properties.     

Lipid peroxidation reduction and hippocampal and cortical neurons protection against ischemic damage in animal model using Stellaria media

This study was aimed to determine the neuroprotective influence of Stellaria media in terms of restoring normal state of the rat’s hippocampus and cortex after oxidative insult caused by in vitro ischemia and reperfusion. Cell viability and membrane integrity were assessed using MTT and lactate dehydrogenase (LDH) assay, respectively. Ischemic insult was introduced in the rat brain’s hippocampal and cortical slivers by exposing oxygen and glucose deficiency (OGD) for 2 h, followed by 1 h of re-perfusion. Cellular oxidative stress levels were quantified by incorporating 2?,7?-dichlorofluorescein diacetate fluorescent probes. Additionally, the lipid peroxidation was assessed using TBARS assay. Findings revealed significant neuroprotection against OGD-induced mitochondrial impairment at 40 µg/mL of S. media in rat’s hippocampal and cortical slices. The LDH levels were decreased significantly (P < 0.001) during pre-incubation and reoxygenation periods using varied concentrations of S. media extract. Cellular oxidative stress levels results showed significant (P < 0.001) reduction in dichlorofluorescein fluorescence in slices homogenate of hippocampus and cortex using S. media extract. The lipid peroxidation assay results showed decreased (P < 0.01) levels of malondialdehyde in liver tissues of treated rats treated (200 mg/kg body weight) when compared to the ischemic animal. In summary, findings clearly indicated the neuroprotective effects of extract against in vitro ischemia in brain hippocampal and cortex slivers. S. media could undoubtedly be utilized as a healing agent in preventing neuronal cells’ loss during is chemic-reperfusion process.     

Interaction of amygdalar neurons of active and passive rabbits in negative emotional situations

Interaction of basal and central nuclear neurons of amygdala was studied by plotting histograms of crosscorrelation in passive and active rabbits exposed to emotionally significant stimuli. The behavior of animals was studied in the open field, light-dark test and during presentation of emotionally significant stimuli. Rabbits of different typological groups applied a certain behavioral strategy in a variety of behavioral tests. Intergroup differences were revealed in the interaction of neighboring cells of amygdala. Passive rabbits (as comparied to active rabbits) demonstrated more excitatory connections and less inhibitory connections with the latency from 50 to 150 ms. Interactions with the delta1-range and theta2-range frequencies in passive animals were more rarely observed. The asymmetry of the interhemispheric neuronal interaction in amygdala with the right dominance was revealed in passive but not active animals. The results testify that amygdala is involved in the choice of behavioral strategy, and the level of its activation is higher in passive animals.     

A nonlinear model of passive muscle viscosity

The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.     

Mechanical properties of passive myocardium: experiment and mathematical model

We present here a 3D mathematical model of rheological properties of a morphofunctional unit of myocardium as example of biological tissue. The model consists of longitudinal and transverse elastic elements and inclined viscoelastic elements connected pivotally without friction. The parameters of viscosity and elasticity of the structural elements of the model do not depend on the magnitude of deformation. The model adequately describes nonlinear viscoelastic behavior of isolated samples of passive myocardium both in static condition and under dynamic loading. The simulation data fit the experiment very well both for intact rat papillary muscle and for a decellularized specimen.     

A validated model of passive muscle in compression

A better characterisation of soft tissues is required to improve the accuracy of human body models used, amongst other applications, for virtual crash modelling. This paper presents a theoretical model and the results of an experimental procedure to characterise the quasi-static, compressive behaviour of skeletal muscle in three dimensions. Uniaxial, unconstrained compression experiments have been conducted on aged and fresh animal muscle samples oriented at various angles from the fibre direction. A transversely isotropic hyperelastic model and a model using the theory of transverse isotropy and strain dependent Young's moduli (SYM) have been fitted to the experimental data. Results show that the hyperelastic model does not adequately fit the data in all directions of testing. In contrast, the SYM gives a good fit to the experimental data in both the fibre and cross-fibre direction, up to 30% strain for aged samples. The model also yields good prediction of muscle behaviour at 45° from the fibre direction. Fresh samples show a different behaviour than aged tissues at 45° from the fibre direction. However, the SYM is able to capture this difference and gives a good fit to the experimental data in the fibre, the cross-fibre and at 45° from the fibre direction. The model also yields good prediction of muscle behaviour when compressed at 30° and 60° from the fibre direction. The effect of the time of test after death has also been investigated. Significant stiffening of muscle behaviour is noted a few hours after death of the subject.     

The choice of animal model and reduction

Careful choice of the animal model is essential, if research is to be conducted efficiently, by using the minimum number of animals in order to provide the maximum amount of information. Inbred strains of rodents provide an excellent way of controlling and investigating genetic variation in characters of interest and in response to experimental treatments. Outbred stocks, in which genetic and non-genetic factors are inextricably mixed, are much less suitable, because random and uncontrolled genetic variation tends to obscure any treatment responses. In some cases, the use of inbred strains has led to major advances in scientific understanding. The specific example given here is in the understanding of host-parasite relationships but, more generally, inbred strains have been of critical importance in research which has resulted in the award of at least 17 Nobel prizes. And yet, despite the extensive literature on the properties and scientific value of inbred strains, many scientists continue to use outbred stocks in the mistaken belief that the use of such animals will, in some mysterious way, make their research more applicable to humans. There is really no evidence that this is so, and there is much evidence that the use of inbred strains has been highly successful in many disciplines.     

The effect of pulsed microwaves on passive electrical properties and interspike intervals of snail neurons

The effects of pulsed microwaves (2.45 GHz, 10 μs, 100 pps, SAR: 81.5 kW/kg peak, 81.5 W/kg average) on membrane input resistance and action potential (AP) interval statistics were studied in spontaneously active ganglion neurons of land snails (Helix aspersa), at strictly constant temperature (20.8±.07°C worst case). Statistical comparison with sham-irradiated neurons revealed a significant increase in the mean input resistance of neurons exposed to pulsed microwaves (P ? .05 ). Pulsed microwaves had no visible effect on mean AP firing rate; this observation was confirmed by analysis of interspike intervals (ISIs). Using an integrator model for spontaneously active neurons, we found the net input current to be more variable in neurons exposed to pulsed microwaves. The mean input current was not affected. The standard deviation of ISIs and the autocorrelation of the input current were marginally affected, but these changes were not consistent across neurons. Although the observed effects were less obvious than those reported in other studies, they represent evidence of a direct interaction between neurons and pulsed microwaves, in the absence of macroscopic temperature changes. The data do not suggest a single, specific mechanism for such interaction. © 1993 Wiley-Liss, Inc.     

Qualitative validation of the reduction from two reciprocally coupled neurons to one self-coupled neuron in a respiratory network model

The pre-Bötzinger complex of the mammalian brainstem is a heterogeneous neuronal network, and individual neurons within the network have varying strengths of the persistent sodium and calcium-activated nonspecific cationic currents. Individually, these currents have been the focus of modeling efforts. Previously, Dunmyre et al. (J Comput Neurosci 1–24, 2011) proposed a model and studied the interactions of these currents within one self-coupled neuron. In this work, I consider two identical, reciprocally coupled model neurons and validate the reduction to the self-coupled case. I find that all of the dynamics of the two model neuron network and the regions of parameter space where these distinct dynamics are found are qualitatively preserved in the reduction to the self-coupled case.     

Low dimensional model of bursting neurons

A computationally efficient, biophysically-based model of neuronal behavior is presented; it incorporates ion channel dynamics in its two fast ion channels while preserving simplicity by representing only one slow ion current. The model equations are shown to provide a wide array of physiological dynamics in terms of spiking patterns, bursting, subthreshold oscillations, and chaotic firing. Despite its simplicity, the model is capable of simulating an extensive range of spiking patterns. Several common neuronal behaviors observed in vivo are demonstrated by varying model parameters. These behaviors are classified into dynamical classes using phase diagrams whose boundaries in parameter space prove to be accurately delineated by linear stability analysis. This simple model is suitable for use in large scale simulations involving neural field theory or neuronal networks.     

Effects of neurotensin on active and passive avoidance performance in rats with lesions of serotoninergic neurons

After a lesion of serotoninergic neurons performed by administration of 5.7-dihydroxytriptamine into the dorsal raphe nucleus, effects of neurotensin microinjections into the substantia nigra on rat behavior were investigated. Serotoninergic lesions resulted in enhanced fear of rats manifested as an increase in the number of intersignal avoidance reactions and intensification of escape reactions. Neurotensin microinjections into the substantia nigra diminished the neurotoxin action thus increasing the adaptive character of defensive behavior of rats with deficit of functions of serotonin neurons.     

Mathematical-technical model of passive and active vibrations of the basilar membrane]

On the basis of the physiological measurements made by v. Békésy and Johnstone, we developed a mathematical model to describe passive and active displacement patterns of the basilar membrane. Approximation of the model functions to the measured values is achieved with the aid of the linear least squares method. Using frequency mapping, the distribution of the basilar membrane displacement is presented in three-dimensional graphic form. The resulting application possibilities of this approach, for example, to electronic simulation of inner ear functions and speech processing systems, are discussed.     

Differences in activity of hippocampal and neocortical neurons in active and passive rabbits in negative emotional situations

Activities of individual hippocampal (CA1 area) and neocortical parietal-temporal neurons were compared in active and passive rabbits in negative emotional situations during emotionally significant stimuli by plotting histograms of autocorrelations. As compared to passive animals, in active rabbits, the mean firing rate of hippocampal neurons was higher, bursting and periodic oscillations of discharges occurred more frequently. Oscillation periods in the theta 1 band (6.0-9.0 Hz) appeared more frequently (in the baseline state and active exploratory or defensive reactions), whereas those in the theta 2 band (4.0-5.9 Nz), on the contrary, were infrequently observed (during freezing). The greatest changes in activity ofhippocampal neurons were observed during active locomotor responses of active rabbits. Intergroup differences in neocortical neuronal activities were less pronounced than in hippocampus. The results indicate that individual typological features in behaviour of animals appear in negative emotional situations and are reflected in activity of activity ofhippocampal (area CA1) and to lesser extent parietal-temporal neocortical neurons. The results suggest different activation levels of the septohippocampal system of active and passive rabbits and possible differences in the afferent input to the CA1 field.     

Role of corticosterone on the development of passive electrical properties of cultured chick embryo neurons

We worked with neuronal cells of chick embryo cultures. The cells were obtained from 7 days-old embryos and cultured for 12 days. The experimental group was submitted to a single dose of corticosterone during the first 48 hours of culture. We measured the membrane resting potential at different external potassium concentrations, as well as the passive electrical properties of the membrane, resistance, time constant and capacitance. We found that the control cells develop progressively their potassium permeability and the electrical properties of the membrane until reaching values in this parameters that were similar to those found in adult cells. Corticosterone application induced a significant enhancement in these parameters in 3 and 6 days-old cultures as compared with the control cultures. These results suggest that glucocorticoids accelerate the differentiation process of the neurons in culture when applied at very early stages of development. We discuss the possible mechanisms involved in this action.     

Threshold model for clustered firing of neurons

Two probabilistic threshold models for burst activity of cortical neurons are proposed. In model I every input impulse increases the summed effect of previous input impulses by one unit. The decay of the summed effect takes place in discrete steps of one unit. A response occurs on arrival of an input impulse, when a threshold value is attained.Although after a response the summed effect is not reset to zero, it cannot exceed the threshold either. The distribution of intervals can be resolved in two components, one for long and one for short intervals. In model II intervals of the short component are terminated by a multiple response instead of one response.     

Mechanical properties of the passive myocardium: experiment and a mathematical model

A three-dimensional mathematical model of the rheological properties of a morphofunctional unit of the myocardium has been constructed, which consists of transversal and longitudinal elastic elements and tilted viscoelastic elements hinged without friction. The parameters of the viscosity and elasticity of structural elements of the model do not depend on the deformation value. The model makes it possible to adequately describe the features of the viscoelastic behavior of isolated samples of the passive myocardium and of the myocardium under longitudinal strain. A good agreement between the calculated and experimental data for an intact preparation of the rat myocardium and a preparation with removed cardiomyocytes has been shown.     

A continuous-binding cross-linker model for passive airway smooth muscle

Although the active properties of airway smooth muscle (ASM) have garnered much modeling attention, the passive mechanical properties are not as well studied. In particular, there are important dynamic effects observed in passive ASM, particularly strain-induced fluidization, which have been observed both experimentally and in models; however, to date these models have left an incomplete picture of the biophysical, mechanistic basis for these behaviors. The well-known Huxley cross-bridge model has for many years successfully described many of the active behaviors of smooth muscle using sliding filament theory; here, we propose to extend this theory to passive biological soft tissue, particularly ASM, using as a basis the attachment and detachment of cross-linker proteins at a continuum of cross-linker binding sites. The resulting mathematical model exhibits strain-induced fluidization, as well as several types of force recovery, at the same time suggesting a new mechanistic basis for the behavior. The model is validated by comparison to new data from experimental preparations of rat tracheal airway smooth muscle. Furthermore, experiments in noncontractile tissue show qualitatively similar behavior, suggesting support for the protein-filament theory as a biomechanical basis for the behavior.