Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons

Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude. In similar experiments, frequency dependent SR is found in the reliability of detection of alpha-function inputs under noise, which are more realistic inputs for neurons. A mathematical analysis of the equations reveals that the frequency preference arises from the dynamics of the slow variable. Noise can then transfer the resonance over the firing threshold because of the proximity of the fast subsystem to a Hopf bifurcation point. Our results may have implications for the behavior of thalamic neurons in a network, with noise switching the membrane potential between different resonance modes.     

Vibrational characteristics of bone fracture and fracture repair: application to excised rat femur

BACKGROUND: The vibrational characteristics of any object are directly dependent on the physical properties of that object. Therefore, changing the physical properties of an object will cause the object to adopt changed natural frequencies. A fracture in a bone results in the loss of mechanical stability of the bone. This change in mechanical properties of a bone should result in a change of the resonant frequencies of that bone. A vibrational method for bone evaluation has been introduced. METHOD OF APPROACH: This method uses the radiation force of focused amplitude-modulated ultrasound to exert a vibrating force directly, and remotely, on a bone. The vibration frequency is varied in the range of interest to induce resonances in the bone. The resulting bone motion is recorded and the resonance frequencies are determined. Experiments are conducted on excised rat femurs and resonance frequencies of intact, fractured, and bonded (simulating healed) bones are measured. RESULTS: The experiments demonstrate that changes in the resonance frequency are indicative of bone fracture and healing, i.e., the fractured bone exhibits a lower resonance frequency than the intact bone, and the resonance frequency of the bonded bone approaches that of the intact bone. CONCLUSION: It is concluded that the proposed radiation force method may be used as a remote and noninvasive tool for monitoring bone fracture and healing process, and the use of focused ultrasound enables one to selectively evaluate individual bones.     

Membrane Resonance and Stochastic Resonance Modulate Firing Patterns of Thalamocortical Neurons

We examined the interactions of subthreshold membrane resonance and stochastic resonance using whole-cell patch clamp recordings in thalamocortical neurons of rat brain slices, as well as with a Hodgkin-Huxley-type mathematical model of thalamocortical neurons. The neurons exhibited the subthreshold resonance when stimulated with small amplitude sine wave currents of varying frequency, and stochastic resonance when noise was added to sine wave inputs. Stochastic resonance was manifest as a maximum in signal-to-noise ratio of output response to subthreshold periodic input combined with noise. Stochastic resonance in conjunction with subthreshold resonance resulted in action potential patterns that showed frequency selectivity for periodic inputs. Stochastic resonance was maximal near subthreshold resonance frequency and a high noise level was required for detection of high frequency signals. We speculate that combined membrane and stochastic resonances have physiological utility in coupling synaptic activity to preferred firing frequency and in network synchronization under noise.     

Organ temperature measurement in a microwave oven by resonance frequency shift

An experimental system has been developed that can indirectly measure temperature in a high-intensity microwave field over a broad range of conditions. A RF amplifier connected closed-loop around a high Q cavity oscillates at one of the natural modes of the oven. A bandpass filter selects the mode of interest. As the frozen sample is thawed, an increase in dielectric constant occurs, decreasing the resonance frequency of the cavity. Calibration of the system is performed by measuring the frequency shift for samples whose temperatures are known, Rotation of samples during thawing often causes oscillations of the resonance frequency. These oscillations are generated by asymmetric sample properties and geometry, and hot spots developed during the thaw. Development of a method that would predict hot spot location from these resonance frequency oscillations and permit modulation of the magnetron or sample rotation to minimize thermal runaway is suggested.     

Concentration dependence of IgG-protein A affinity studied by wireless-electrodeless QCM

The binding affinity between human immunoglobulin G (IgG) and protein A was studied by the homebuilt wireless-electrodeless quartz crystal microbalance (QCM). Protein A was immobilized on the electrodeless AT-cut quartz plate of 0.05 mm thick and its fundamental resonance frequency near 34 MHz was measured by a noncontacting manner using a line antenna. The vibrational analysis was performed to ensure higher sensitivity of the electrodeless QCM. A flow-cell system was fabricated to continuously measure the resonance frequency during the injection sequence of the IgG solutions with concentrations of 1-20,000 ng/mL. The exponential frequency changes were recorded to determine the affinity based on the Langmuir kinetics. The equilibrium constant K(A) significantly varied between 6 x 10(6) and 6 x 10(10) M(-1), depending on the IgG concentration, which is attributed to various formations of IgG-protein A complexes.     

A mechanism for the regulation of ligament width based on the resonance frequency of ion concentration waves

A model is developed for a mechanism for the regulation of the width of ligament spaces and of other tissue spaces bounded by calcified surfaces. The proposed mechanism involves the transmission, detection, and retransmission of ion concentration waves by cells located on the calcified surfaces. It is assumed that these cells can use the information regarding ligament width contained in the resonance frequency of the cell-concentration wave system. The assumptions of the proposed mechanism are supported by recent experimental evidence concerning the effect of electrical signals on bone cells, the use of frequency-encoded information by cells, and the production of low frequency K⁺ pulses by osteoblast-like cells. The relation between resonance frequency and ligament width is derived, and the resonance frequencies corresponding to measured ligament widths are shown to occur in the same frequency range as occur in the K⁺ pulses emitted by bone cells. The model suggests definite experimental tests that involve investigating the effect in vitro of ion concentration wave frequency on bone cell activity and hormone receptors.     

Resonance properties of protein solutions according to data from electrical conductance measurements in the frequency range 0.1-10 mHz, obtained by L.A. Lapaev]

Experimental and theoretical results of some studies by L. A Lapaeva are analysed which state that the dependence of electroconductance on the frequency of applied voltage in some globular protein solutions is of a resonance character in the frequency range of 0,1 minus 10 mHz. The evaluation shows that the theory suggested is not applicable for the results obtained at these frequencies. The measurement method of electroconductance applied by L. A. Lapaeva is critisized. The analysis of her results enables a conclusion that is is premature to speak about resonance properties of proteins as of the fact stated.     

Calcium cyclotron resonance and diatom mobility

The hypothesis that movement of biological ions may be predicted by cyclotron resonance theory applied to cell membranes is tested in these experiments. Diatoms (Amphora coffeaeformis) were chosen as the biosystem since they move or don't move, depending on how much calcium is transported across the membrane. The experiments demonstrate that a particular ion (calcium) is apparently moved across the cell membrane in response to the DC and AC values of magnetic flux densities (B) and the frequency derived from the cyclotron resonance theory. A clear resonance is shown and a rather sharp frequency response curve is demonstrated. The experiments also show a dose response as the AC value of the flux density is varied, and that odd harmonics of the basic cyclotron frequency are also effective.     

Electrical Resonance in the θ Frequency Range in Olfactory Amygdala Neurons

The cortical amygdala receives direct olfactory inputs and is thought to participate in processing and learning of biologically relevant olfactory cues. As for other brain structures implicated in learning, the principal neurons of the anterior cortical nucleus (ACo) exhibit intrinsic subthreshold membrane potential oscillations in the θ-frequency range. Here we show that nearly 50% of ACo layer II neurons also display electrical resonance, consisting of selective responsiveness to stimuli of a preferential frequency (2–6 Hz). Their impedance profile resembles an electrical band-pass filter with a peak at the preferred frequency, in contrast to the low-pass filter properties of other neurons. Most ACo resonant neurons displayed frequency preference along the whole subthreshold voltage range. We used pharmacological tools to identify the voltage-dependent conductances implicated in resonance. A hyperpolarization-activated cationic current depending on HCN channels underlies resonance at resting and hyperpolarized potentials; notably, this current also participates in resonance at depolarized subthreshold voltages. KV7/KCNQ K⁺ channels also contribute to resonant behavior at depolarized potentials, but not in all resonant cells. Moreover, resonance was strongly attenuated after blockade of voltage-dependent persistent Na⁺ channels, suggesting an amplifying role. Remarkably, resonant neurons presented a higher firing probability for stimuli of the preferred frequency. To fully understand the mechanisms underlying resonance in these neurons, we developed a comprehensive conductance-based model including the aforementioned and leak conductances, as well as Hodgkin and Huxley-type channels. The model reproduces the resonant impedance profile and our pharmacological results, allowing a quantitative evaluation of the contribution of each conductance to resonance. It also replicates selective spiking at the resonant frequency and allows a prediction of the temperature-dependent shift in resonance frequency. Our results provide a complete characterization of the resonant behavior of olfactory amygdala neurons and shed light on a putative mechanism for network activity coordination in the intact brain.     

NMR in cancer: IX. The concept of cancer treatment by NMR: a preliminary report of high resolution NMR or phosphorus in normal and malignant tissues.

A preliminary study of high resolution P31 nuclear resonance of normal and malignant tissue is reported. Utilization of nuclear resonance in the frequency frame contrasts with the pulsed magnetic resonance studies originally introduced for investigating cancer. Frequency dependent NMR was employed to study cancer with the primary objective of identifying resonant frequencies that could be used to indicate cancer. Such cancer specific frequencies would help circumvent current difficulties in the pulsed resonance diagnosis of cancer and might even have application in therapy.     

Evolution of the frequency spectrum of an extraordinary wave near the upper hybrid resonance in a turbulent plasma

A study is made of the formation of the frequency spectrum of an extraordinary wave during its multiple small-angle scatterings along the path to the upper hybrid resonance, in the upper hybrid resonance region, and behind the conversion point. The formation of the spectrum is investigated both approximately (by the eikonal method) and exactly (in the limit of large-scale plasma density fluctuations responsible for small-angle scattering). It is demonstrated that these two approaches yield the same results in the common range of their applicability. It is shown that, in the vicinity of the upper hybrid resonance, the broadening of the frequency spectrum of a probing wave is proportional to its wavenumber. This circumstance and the predicted amount by which the spectrum broadens make it possible to consider small-angle scattering as one of the main effects responsible for a very large spectrum broadening observed in experiments.     

Spatially Distributed Dendritic Resonance Selectively Filters Synaptic Input

An important task performed by a neuron is the selection of relevant inputs from among thousands of synapses impinging on the dendritic tree. Synaptic plasticity enables this by strenghtening a subset of synapses that are, presumably, functionally relevant to the neuron. A different selection mechanism exploits the resonance of the dendritic membranes to preferentially filter synaptic inputs based on their temporal rates. A widely held view is that a neuron has one resonant frequency and thus can pass through one rate. Here we demonstrate through mathematical analyses and numerical simulations that dendritic resonance is inevitably a spatially distributed property; and therefore the resonance frequency varies along the dendrites, and thus endows neurons with a powerful spatiotemporal selection mechanism that is sensitive both to the dendritic location and the temporal structure of the incoming synaptic inputs.     

Resonance phenomena to rhythmic light stimulation with various intensity and frequency in human EEG

The photoinduced resonance EEG response in the occipital area (O1 and O2) of right-handed men during 12-s intermittent photic stimulation was studied as a function of flash frequency (6, 10, or 16 Hz) and intensity (5 levels from 0.05 to 0.7 J). The EEG power in the narrow band coinciding with stimulation frequency was FFT-extracted in 3-s intervals before, during, and after each stimulation. It was found that increase in flash intensity was accompanied by an enhancement of the resonance EEG response and decrease in time of reaching its maximal value. These changes were to a greater extent characteristic for the right hemisphere. The low-intensity stimulation induced more pronounced resonance effects in the left hemisphere, whereas the high-intensity flashes to a greater extent involved the right hemisphere. The asymmetry of the EEG response to stimulation of the middle intensity was slight, and the time of reaching the maximal level of the resonance activation was about 6-8 s. A relatively high level of the resonance EEG response was observed during stimulation with the frequency of 10 Hz, even in case of its minimal intensity. The most pronounced resonance EEG response was induced in the right occipital area by the high-intensity 16-Hz stimulation. The enhanced sensitivity of the right hemisphere to intensity of flashes is interpreted as an indication of interhemispheric differences in nonspecific adaptive mechanisms of the brain.     

Resonance phenomena in membranes containing ion channels with inactivation

A mathematical model of the ion transport across a membrane containing channel with inactivation has been analysed. Under certain conditions, such a membrane has been shown to behave as a selfoscillating circuit of a very high quality, its own frequency ranging for a variety of natural channels between 10(-1)-10(3) cycles. When exposed to an alternating electric field with a frequency approximating f0, the membrane displays resonance changes in its potential and channel conductivity. The average (over a period of forced oscillations) values of the potential and conductivity also show a resonance type of dependence on the frequency of the external field.     

Resonance phenomenon during wrist pulse-taking: A stochastic simulation,model-based study of the ‘pressing with one finger’ technique

This study analyzed the ‘pressing with one finger’ technique for wrist pulse-taking and explored the identification of internal organs according to the resonance theory in the circulatory system. A five-section discretized-transmission-line model of the distal upper limb was proposed considering the radial artery, the distal positions chi–guan–cun, and the hand vasculature. The transfer function of the model was parameterized in terms of its resonance frequency and respective amplification factor. Rheological and geometrical parameters of the modeled arterial system were used to simulate a sample of 1000 healthy volunteers subjected to wrist pulse-taking examination. The ‘pressing with one finger’ technique was simulated individually at each position by varying the vertical (minor) diameter of the elliptical cross-sectional radial artery from 0% to 99%. The pulse waveform harmonics were calculated in the frequency domain and had their internal organs assigned according to the resonance theory. Compressions in range 0–70% resulted in resonance frequencies around 3–6 Hz (related to the spleen) and amplification factors > 1. Compression in range 70–85% shifted up the resonance frequency of the majority of cases up to 6–8 Hz (related to the heart) and a minority of cases was shifted down to 0–2 Hz. A large decrease in the amplification factor occurred with module values <1. Compressions in range 85–99% increased the resonance frequency to 7–10 Hz (related to the gallbladder) with an even decent amplification factor. These effects were more pronounced in the proximal to distal sequence of positions. Therefore, pressing with one finger amplified specific pulse wave harmonics as a function of depth in all three positions, but it did not explore all harmonics described by the resonance theory.     

Computational simulation of dental implant osseointegration through resonance frequency analysis

The aim of this study is to predict the evolution of the resonance frequency of the bone-implant interface in a dental implant by means of finite element simulation. A phenomenological interface model able to simulate the mechanical effects of the osseointegration process at the bone-implant interface is applied and compared with some experimental results in rabbits. An early stage of slow bone ingrowth, followed by a faster osseointegration phase until final stability is predicted by the simulations. The evolution of the resonance frequency of the implant and surrounding tissues along the simulation period was also obtained, observing a 3-fold increase in the first principal frequency. These findings are in quantitative agreement with the experimental measurements and suggest that the model can be useful to evaluate the influence of mechanical factors such as implant geometry or implant loading on the indirect evaluation of the process of implant osseintegration.     

Statistical measurement of signal transmission in the central nervous system of the crayfish

Summary Transmission of nerve signals in the crayfish brain was studied by means of the transfer function derived from input-output analysis with random stimulation. The transfer function was measured in the form of frequency-response-function and represented by Bode plot. Two classes of the frequency-response-functions were discriminated, corresponding to two types of response patterns evoked by the constant frequency stimuli. The first type had the characteristics of a band pass filter similar to an underdamped resonant circuit. The second one had the characteristics of a phase lag circuit, occasionally, with additional small positive or negative peak at almost the same frequency as the resonance of the first type. A few possibilities for the resonance and the phase lag mechanisms were discussed.     

Broad Tunable Nanoantenna Based on Graphene Log-Periodic Toothed Structure

A log-periodic toothed nanoantenna based on graphene is proposed, and its multi-resonance properties with respect to the variations of the chemical potential are investigated. The field enhancement and radar cross-section of the antenna for different chemical potentials are calculated, and the effect of the chemical potential on the resonance frequency is analyzed. In addition, the dependence of the resonance frequency on the substrate is also discussed. It is shown that large modulation of resonance intensity in log-periodic toothed nanoantenna can be achieved via turning the chemical potential of graphene. The tunability of the resonant frequencies of the antenna can be used to broad tuning of spectral features. The property of tunable multi-resonant field enhancement has great prospect in the field of graphene-based broadband nanoantenna, which can be applied in non-linear spectroscopy, optical sensor, and near-field optical microscopy.     

Voltage dependence of subthreshold resonance frequency in layer II of medial entorhinal cortex

The resonance properties of individual neurons in entorhinal cortex (EC) may contribute to their functional properties in awake, behaving rats. Models propose that entorhinal grid cells could arise from shifts in the intrinsic frequency of neurons caused by changes in membrane potential owing to depolarizing input from neurons coding velocity. To test for potential changes in intrinsic frequency, we measured the resonance properties of neurons at different membrane potentials in neurons in medial and lateral EC. In medial entorhinal neurons, the resonant frequency of individual neurons decreased in a linear manner as the membrane potential was depolarized between -70 and -55 mV. At more hyperpolarized membrane potentials, cells asymptotically approached a maximum resonance frequency. Consistent with the previous studies, near resting potential, the cells of the medial EC possessed a decreasing gradient of resonance frequency along the dorsal to ventral axis, and cells of the lateral EC lacked resonant properties, regardless of membrane potential or position along the medial to lateral axis within lateral EC. Application of 10 μM ZD7288, the H-channel blocker, abolished all resonant properties in MEC cells, and resulted in physiological properties very similar to lateral EC cells. These results on resonant properties show a clear change in frequency response with depolarization that could contribute to the generation of grid cell firing properties in the medial EC.     

The apparent mass of the seated human body: vertical vibration

Apparent mass frequency response functions of the seated human body have been measured with random vibration in the vertical direction at frequencies up to 20 Hz. A group of eight subjects was used to investigate some factors (footrest, backrest, posture, muscle tension, vibration magnitude) that may affect the apparent mass of a person; a group of 60 subjects (24 men, 24 women and 12 children) was used to investigate variability between people. Relative movement between the feet and the seat was found to affect the apparent mass at frequencies below resonance, particularly near zero-frequency. The resonance frequency generally increased with the use of a back rest, an erect posture and, in particular, increased muscle tension; but there was considerable intersubject variability in the changes. The magnitude of the vibration had a consistent effect: the resonance frequency decreased from about 6 to 4 Hz when the magnitude of the vibration was increased from 0.25 to 2.0 ms-2 r.m.s. The apparent masses of all the subjects were remarkably similar when normalized with respect to sitting weight. However, there were statistically significant correlations between apparent mass and some body characteristics (such as weight and age).