Characterization of the behaviour of dissociated neurons exposed to dielectrophoretic forces

The behaviour of cortical rat neurons exposed to dielectrophoretic forces is investigated by varying the amplitude and frequency of the applied field. The number of neurons trapped in the center of a planar quadrupole micro-electrode structure is determined for two different amplitudes (3 V and 5 V) and six different frequencies in the range from 1 MHz to 18 MHz. A contradictory trend is found for the yield of trapped neurons for the two amplitudes as a function of the frequency

Fractal homogenization of multiscale interface problems

Inspired by continuum mechanical contact problems with geological fault networks, we consider elliptic second order differential equations with jump conditions on a sequence of multiscale networks of interfaces with a finite number of non-separating scales. Our aim is to derive and analyze a description of the asymptotic limit of infinitely many scales in order to quantify the effect of resolving the network only up to some finite number of interfaces and to consider all further effects as homogeneous. As classical homogenization techniques are not suited for this kind of geometrical setting, we suggest a new concept, called fractal homogenization, to derive and analyze an asymptotic limit problem from a corresponding sequence of finite-scale interface problems. We provide an intuitive characterization of the corresponding fractal solution space in terms of generalized jumps and gradients together with continuous embeddings into L2 and Hs, s<1/2. We show existence and uniqueness of the solution of the asymptotic limit problem and exponential convergence of the approximating finite-scale solutions. Computational experiments involving a related numerical homogenization technique illustrate our theoretical findings

Trapping cortical rat neurons

Cortical rat neurons were trapped by dielectrophoresis (DEP). Experimental data were compared with theoretically deduced relationships. The neuron was represented by a single-shell model. A planar quadrupole electrode structure was used for the creation of a nonuniform field. The electrode structure was modeled as four point charges. The experimental data did almost completely fit the theoretical yield/time relationship. The theoretical yield/amplitude relationship, however, did only apply for a restricted amount of frequencies. The experimental frequency behaviour (i.e., the DEP-spectrum) did not apply to the theory. A difference in neuronal physiological state can produce different DEP-spectra. For two frequencies (10 kHz and 14 MHz) adhesion to the substrate and outgrowth of the neurons was investigate

Dielectrophoretic trapping of dissociated fetal cortical rat neurons

Recording and stimulating neuronal activity at multiple sites can be realized with planar microelectrode arrays. Efficient use of such arrays requires each site to be covered by at least one neuron. By application of dielectrophoresis (DEP), neurons can be trapped onto these sites. This study investigates negative dielectrophoretic trapping of fetal cortical rat neurons. A planar quadrupole microelectrode structure was used for the creation of a nonuniform electric field. The field was varied in amplitude (1, 3, and 5 V) and frequency (10 kHz-50 MHz). Experimental results were compared with a theoretical model to investigate the yield (the number of neurons trapped in the center of the electrode structure) with respect to time, amplitude and frequency of the field. The yield was a function of time1/3 according to theory. However, unlike the model predicted, an amplitude-dependent frequency behavior was present and unexpected peaks occurred in the DEP-spectra above 1 MHz. Gain/phase measurements showed a rather unpredictable behavior of the electrode plate above 1 MHz, and temperature measurement showed that heating of the medium influenced the trapping effect, especially for larger amplitudes and higher frequencie

Increased bradykinesia in Parkinson’s disease with increased movement complexity: elbow flexion-extension movements

The present research investigates factors contributing to bradykinesia in the control of simple and complex voluntary limb movement in Parkinson’s disease (PD) patients. The functional scheme of the basal ganglia (BG)–thalamocortical circuit was described by a mathematical model based on the mean firing rates of BG nuclei. PD was simulated as a reduction in dopamine levels, and a loss of functional segregation between two competing motor modules. In order to compare model simulations with performed movements, flexion and extension at the elbow joint is taken as a test case. Results indicated that loss of segregation contributed to bradykinesia due to interference between competing modules and a reduced ability to suppress unwanted movements. Additionally, excessive neurotransmitter depletion is predicted as a possible mechanism for the increased difficulty in performing complex movements. The simulation results showed that the model is in qualitative agreement with the results from movement experiments on PD patients and healthy subjects. Furthermore, based on changes in the firing rate of BG nuclei, the model demonstrated that the effective mechanism of Deep Brain Stimulation (DBS) in STN may result from stimulation induced inhibition of STN, partial synaptic failure of efferent projections, or excitation of inhibitory afferent axons even though the underlying methods of action may be quite different for the different mechanisms

The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps

We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional $p$-Laplace operator. Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Laplace operator to the continuous fractional Laplace operator

Measuring activity of the subthalamic nucleus in acute slices using multi electrode arrays

The symptoms of Parkinson’s disease (a.o.: tremor, rigidity) can be suppressed by electrical stimulation of the basal ganglia. The most common target nucleus of this so called Deep Brain Stimulation (DBS) is the subthalamic nucleus (STN). Good clinical results are obtained by the application of pulses of 200 s, 1-3 V amplitude at a constant rate of about 130 Hz. However, the mechanism(s) responsible for the clinical improvements are not yet elucidated.\ud The use of acute brain slices as a model is widely used, despite the inevitable loss of many connections. Accurate (i.e. subthreshold) measurements of single neuron and multiple neuron (up to ~3, for practical reasons) membrane potentials are obtained by patch-clamp technique. We propose to use arrays of microelectrodes in slice recordings of STN. We present here our first results