The "inverse problem" solved for a three-dimensional model of the cochlea. III. Brushing-up the solution method.

In two earlier papers [de Boer, J. Acoust. Soc. Am. 98, 896-903 and 904-910 (1995)] the inherent problems of the inverse-solution method in cochlear mechanics were described. The present paper shows results obtained with a more universal solution method. With the new method it is possible to construct a three-dimensional model of the cochlea producing a response that accurately simulates a measured mechanical basilar-membrane response. With earlier methods this could not be done. The inverse solution invariably yields that, with low stimulus levels, the model simulating a viable cochlea must be locally active. For the response of a dead animal a passive model is sufficient. Once more the inherent intricacies and problems of the inverse-solution method are discussed. Conservation of fluid volume leads to the concept of the "virtual stapes velocity." For best results, the input signal to the inverse-solution procedure should be acquired in the form of a "composite cross-correlation spectrum." Inverse analysis can, under certain circumstances, produce aberrant results. In this paper it is shown why the resulting impedance function is the most accurate in the region of the response peak. Therefore, it is unlikely that a passive model would exist of which the response simulates the data obtained from a healthy animal.     

Three-dimensional numerical modeling for global cochlear dynamics

A hybrid analytical-numerical model using Galerkin approximation to variational equations has been developed for predicting global cochlear responses. The formulation provides a flexible framework capable of incorporating morphologically based mechanical models of the cochlear partition and realistic geometry. The framework is applied for a simplified model with an emphasis on application of hybrid methods for three-dimensional modeling. The resulting formulation is modular, where matrices representing fluid and cochlear partition are constructed independently. Computational cost is reduced using two methods, a modal-finite-element method and a boundary element-finite-element method. The first uses a cross-mode expansion of fluid pressure (2.5D model) and the second uses a waveguide Green's-function-based boundary element method (BEM). A novel wave number approach to the boundary element formulation for interior problem results in efficient computation of the finite-element matrix. For the two methods a convergence study is undertaken using a simplified passive structural model of cochlear partition. It is shown that basilar membrane velocity close to best place is influenced by fluid and structural discretization. Cochlear duct pressure fields are also shown demonstrating the 3D nature of pressure near best place.     

The mechanical waveform of the basilar membrane. II. From data to models--and back

Mechanical responses in the basal turn of the guinea-pig cochlea are measured with low-level broad-band noise as the acoustical stimulus [for details see de Boer and Nuttall, J. Acoust. Soc. Am. 101, 3583-3592 (1997)]. Results are interpreted within the framework of a classical three-dimensional model of the cochlea that belongs to a very wide class of nonlinear models. The use of linear-systems analysis for this class of nonlinear models has been justified earlier [de Boer, Audit. Neurosci. 3, 377-388 (1997)]. The data are subjected to inverse analysis with the aim to recover the "effective basilar-membrane impedance." This is a parameter function that, when inserted into the model, produces a model response, the "resynthesized" response, that is similar to the measured response. With present-day solution methods, resynthesis leads back to an almost perfect replica of the original response in the spatial domain. It is demonstrated in this paper that this also applies to the response in the frequency domain and in the time domain. This paper further reports details with regard to geometrical properties of the model employed. Two three-dimensional models are studied; one has its dimensions close to that of the real cochlea, the other is a stylized model which has homogeneous geometry over its length. In spite of the geometric differences the recovered impedance functions are very similar. An impedance function computed for one model can be used in resynthesis of the response in the other one, and this leads to global amplitude deviations between original and resynthesized response functions not exceeding 8 dB. Discrepancies are much larger (particularly in the phase) when a two-dimensional model is compared with a three-dimensional model. It is concluded that a stylized three-dimensional model with homogeneous geometric parameters will give sufficient information in further work on unraveling cochlear function via inverse analysis. In all cases of a sensitive cochlea stimulated by a signal with a stimulus level of 50 dB SPL per octave or less, the resulting basilar-membrane impedance is found to be locally active, that is, the impedance function shows a region where the basilar membrane is able to amplify acoustic power or to reduce dissipation of power by the organ of Corti. Finally, the influence of deliberate errors added to the data is discussed in order to judge the accuracy of the results.     

Calculating Bessel functions with Padé approximants

The solution of the two-body Schrodinger equation with a $\text{C}\text{r}{}^2$ potential is a Bessel function. The asymptotic series in r^?1, which is generated from Schrodinger equation, has a zero radius of convergence. The Padé approximants to the asymptotic series in $\text{1}\text{z}\text{for}\text{J}{}_{\mathrm{v}}\text{(z)}$ converge rigorously for v real. For v imaginary convergence appears to be the same as for v real.     

Characteristic metal-halogen vibrational frequencies of complexes with bivalent metal halides

Studies of the metal-halogen vibrational frequencies of complexes have been numerous and it is apparent that such frequencies are often characteristic of the structure and stoichiometry. The method, although generally applicable, is most valuable where neither ultraviolet spectra nor magnetic moments can be of assistance. The current literature is reviewed with the intention of facilitating the characterization of unknown materials derived from bivalent metal halides.     

Structural and Magnetic Characterisation of Ce@C82

Abstract

We report the structural and magnetic properties of the endohedral metallofullerene Ce@C₈₂. A hexagonal close packing phase [P6₃/mmc [a=11.1544Å, c=18.2256Å] is formed exclusively after vacuum annealing of the solvent precipitated compound. In contrast, sublimed Ce@C₈₂ was found to be dominantly face-centred cubic close packed [Fm-3m; a=15.766Å]. X-ray powder profile calculations revealed that the endohedral cerium atom lies close to 1.8Å from the C₈₂ cage centre in both phases. Hexagonal Ce@C₈₂ has been investigated by magnetic susceptibility measurements. Paramagnetic behaviour is maintained down to 2K attributable to Ce³⁺ ions. Towards lower temperatures, the observed paramagnetic moment falls from the free ion Ce³⁺(μ_eff =2.54μB) value, monotonically approaching 1μB at 2K.     

Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the galilean space

In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G₃. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G₃.     

Lentivirus-mediated transgene delivery to the hippocampus reveals sub-field specific differences in expression

Background  

In the adult hippocampus, the granule cell layer of the dentate gyrus is a heterogeneous structure formed by neurons of different ages, morphologies and electrophysiological properties. Retroviral vectors have been extensively used to transduce cells of the granule cell layer and study their inherent properties in an intact brain environment. In addition, lentivirus-based vectors have been used to deliver transgenes to replicative and non-replicative cells as well, such as post mitotic neurons of the CNS. However, only few studies have been dedicated to address the applicability of these widespread used vectors to hippocampal cells in vivo. Therefore, the aim of this study was to extensively characterize the cell types that are effectively transduced in vivo by VSVg-pseudotyped lentivirus-based vectors in the hippocampus dentate gyrus.