Single-shell Model Research Articles

Development of Volume Conductor and Source Models to Localize Epileptic Foci

There is increasing interest in mapping and source reconstruction from electrocorticoencephalographic (ECoG) grid data and comparison to surface EEG evaluations of epileptic patients. ECoG mapping onto three-dimensional renderings of the individual cortical anatomy derived from magnetic resonance images and computed tomography (CT) is performed after coregistration of anatomical and functional coordinate systems. Source reconstructions from ECoG and EEG are compared using different source models and realistically shaped volume conductor models. Realistically shaped volume conductor models for EEG source reconstruction are a prerequisite for improved localization accuracy. Individual boundary element method (BEM) models derived from MRI represent the "gold standard" and can approximate isotropic homogeneous head compartments and thus give an improved description of the head shape as compared with classical oversimplifying spherical shell models. Anisotropic volume conduction properties of the bone layer or the white matter fibers can be described by the finite element method (FEM); unfortunately, these models require a huge computational effort and are thus not used in daily applications. To avoid this computational effort, head models derived from an averaged MRI dataset can be used. Highly refined models with a large number of nodes and thus better numerical accuracy can be used by this approach, because the setup is performed only once and the decomposed models or precomputed leadfield matrices are saved for later application. Individual image data are not at all needed, if an overlay of the reconstruction results with the anatomy is not desired. With precomputed leadfield matrices and linear interpolation techniques, at least standardized BEM and FEM volume conductor models derived from averaged MRI datasets can achieve the same computational speed as analytical spherical models. The smoothed cortical envelope is used as a realistically shaped single-shell volume conductor model for ECoG source reconstruction, whereas three-compartment BEM-models are required for EEG. The authors describe how to localize ECoG-grid electrode positions and how to segment the cortical surface from coregistered magnetic resonance and CT images. Landmark-based coregistration is performed using common fiducials in both image modalities. Another more promising automatic approach is based on mutual three-dimensional volume gray-level information. The ECoG electrode positions can be retrieved from three-dimensional CT slices manually using cursors in thresholded images with depth information. Alternatively, the smoothed envelope of the cortical surface segmented from the MRI is used to semiautomatically determine the grid electrode positions by marking the four corners and measuring distances along the smoothed surface. With extended source patches for cortically constrained scans and current density reconstructions, results from ECoG and surface EEG data were compared. Single equivalent dipoles were used to explain the EEG far fields, and results were compared with the original current density distributions explaining the ECoG data. The authors studied the performance of spherical and realistically shaped BEM volume conductor models for EEG and ECoG source reconstruction in spherical and nonspherical parts of the head with simulations and measured epileptic spike data. Only small differences between spherical and realistically shaped models were found in the spherical parts of the head, whereas realistically shaped models are superior to spherical approximations in both single-shell ECoG and three-shell EEG cases in the nonspherical parts, such as the temporal lobe areas. The ECoG near field is more complicated to interpret than the surface EEG far field and cannot be explained in general by simple equivalent dipoles. However, from simulations with realistically shaped volume conductor models and cortically constrained source models, the authors studied how the bone and skin layer act as spatial low pass filters that smooth and simplify the surface EEG maps generated by much more complicated-looking source configurations derived from measured ECoG data.

Dielectric spectroscopy of single cells: time domain analysis using Maxwell's mixture equation

Dielectric spectroscopy is a powerful tool for investigating the dielectric properties of biological particles in suspension. For low volume fractions, the dielectric properties of the particles are related to the measured properties of the suspension by Maxwell's mixture equation. A number of different techniques can be used to measure the dielectric spectrum in the frequency domain or the time domain. In time domain dielectric spectroscopy, data can be converted into the frequency domain using convolution or Fourier transform, prior to data analysis. In this paper, we present a general method for transforming Maxwell's mixture equation from the frequency domain to the time domain allowing analysis of cell dielectric properties directly in the time domain. The derivation is based on the Laplace transform of the single shell model for a spherical particle, and can be extended to the multi-shell model. For a single shelled cell two characteristic relaxation time constants are derived. The results are compared with published analytical models. We show that the original frequency dependent mixture equation can be recovered by Fourier transform back to the frequency domain. As a result, a general relationship for the dielectric response of a mixture of particles is presented which links the frequency and time domains.

Effects of membrane disruption on dielectric properties of biological cells

Disruption of the plasma membrane causes serious changes in the dielectric properties of biological cells. The changes have been simulated with spherical cell models having holes in the plasma membrane. The complex permittivity of a cubic system including a cell model was calculated by a numerical technique based on the three-dimensional finite difference method. For a cell without hole, the complex permittivity showed dielectric relaxation (β-dispersion) as predicted from interfacial polarization theories for the single-shell model. When there is one hole in the membrane, the cell has anisotropic dielectric properties depending on whether the axis through the centres of the hole and the sphere is parallel (the parallel orientation) or perpendicular (the perpendicular orientation) to the electric field direction. In the parallel orientation, dielectric relaxation (called ‘α-dispersion’) appeared at lower frequencies in addition to the β-dispersion, whereas only the β-dispersion was found in the perpendicular orientation. When there were two holes at the opposite poles of the cell, the ‘α-dispersion’ did not appear and the intensity of the β-dispersion decreased with increasing size of the holes. When two holes located in the hemisphere of the cell, however, the ‘α-dispersion’ appeared again. These results suggest that the occurrence of the ‘α-dispersion’ requires either the presence of one hole or the localization of holes.

Nanoscale Dielectrophoretic Spectroscopy of Individual Immobilized Mammalian Blood Cells

Dielectrophoretic force microscopy (DEPFM) and spectroscopy have been performed on individual intact surface-immobilized mammalian red blood cells. Dielectrophoretic force spectra were obtained in situ in ∼125 ms and could be acquired over a region comparable in dimension to the effective diameter of a scanning probe microscopy tip. Good agreement was observed between the measured dielectrophoretic spectra and predictions using a single-shell cell model. In addition to allowing for highly localized dielectric characterization, DEPFM provided a simple means for noncontact imaging of mammalian blood cells under aqueous conditions. These studies demonstrate the feasibility of using DEPFM to monitor localized changes in membrane capacitance in real time with high spatial resolution on immobilized cells, complementing previous studies of mobile whole cells and cell suspensions.

Free vibration of multiwall carbon nanotubes

A multiple-elastic shell model is applied to systematically study free vibration of multiwall carbon nanotubes (MWNTs). Using Flugge [Stresses in Shells (Springer, Berlin, 1960)] equations of elastic shells, vibrational frequencies and associated modes are calculated for MWNTs of innermost radii 5 and 0.65 nm, respectively. The emphasis is placed on the effect of interlayer van der Waals (vdW) interaction on free vibration of MWNTs. Our results show that the interlayer vdW interaction has a crucial effect on radial (R) modes of large-radius MWNTs (e.g., of the innermost radius 5 nm), but is less pronounced for R modes of small-radius MWNTs (e.g., of the innermost radius 0.65 nm), and usually negligible for torsional (T) and longitudinal (L) modes of MWNTs. This is attributed to the fact that the interlayer vdW interaction, characterized by a radius-independent vdW interaction coefficient, depends on radial deflections only, and is dominant only for large-radius MWNTs of lower radial rigidity but less pronounced for small-radius MWNTs of much higher radial rigidity. As a result, the R modes of large-radius MWNTs are typically collective motions of almost all nested tubes, and the R modes of small-radius MWNTs, as well as the T and L modes of MWNTs, are basically vibrations of individual tubes. In particular, an approximate single-shell model is suggested to replace the multiple-shell model in calculating the lowest frequency of R mode of thin MWNTs (defined by the innermost radius-to-thickness ratio not less than 4) with relative errors less than 10%. In addition, the simplified Flugge single equation is adopted to substitute the exact Flugge equations in determining the R-mode frequencies of MWNTs with relative errors less than 10%.

Local Structure of Aluminum in Zeolite Mordenite as Affected by Temperature

The local aluminum structure in zeolite mordenite was studied at temperatures up to 1000 K in a vacuum by Al K-edge X-ray absorption near-edge structure (XANES) spectroscopy. The interatomic aluminum-oxygen distances and the number of coordinating oxygen atoms were determined by Fourier transform analyses of experimental Al K-edge XANES spectra and the fits of the nearest oxygen atoms contributions, using a limited number of variables. The values of fixed parameters for Fourier transform and fit are established from the spectrum of Na-mordenite, considered the reference compound for the studied zeolites H-mordenites, which was also used to test the accuracy and the stability of the determined structural parameters. To reveal the aluminum coordination in H-mordenite at various temperatures, the Fourier transform peak of the coordinating oxygen polyhedron was fitted first with a single-shell model, and the obtained structural information was refined by the fits, on the basis of the most plausible models for the aluminum coordination environment. The choice of such models for each temperature was performed according to the qualitative predictions on the aluminum local atomic structure provided by the preedge data analysis and 27Al magic angle spinning (MAS) NMR experiments. By this method, the presence of sixfold aluminum atoms, aside from the fourfold ones, in H-mordenite at room temperature was revealed quantitatively, and the concentrations of these mixed coordinations were determined; the structural distortion of the oxygen tetrahedron around aluminum in dehydrated H-mordenite at T = 575 K was found to be strong, and the corresponding Al-O distances for this distortion were obtained; for H-mordenite at 985 K, the presence of threefold coordinated aluminum atoms, aside from the fourfold ones, was revealed, and an estimate of the amount of threefold aluminum was given.

The dielectric behaviour of single-shell spherical cells with a dielectric anisotropy in theshell

Recent experiments on cells treated with hydrophobic ions showed that the mobile chargesadsorbed to the plasma membrane contributed significantly to the low-frequency dielectricbehaviour of cells. Due to the different transport properties of the mobile ions along theradial and tangential directions within the membrane, there is a dielectric anisotropy in theplasma membrane. In this work, we adopted a single-shell spherical cell model with anintrinsic dispersion in the membrane, which can be isotropic or anisotropic. We developed adielectric dispersion spectral representation (DDSR) and expressed the Clausius–Mossottifactor in terms of a series of sub-dispersions. This representation enables us to assess theeffects of the permittivities and conductivities in cells. We further assessed the effects of adielectric anisotropy on the dispersion spectrum in the DDSR. To this end, we interpretedthe results as a change in the dispersion strength, as well as a shift of the characteristicfrequency. Moreover, the changes are indeed small and the weak-anisotropy expansion isjustified.

A New Anharmonic Factor and EXAFS Including Anharmonic Contributions

A new anharmonic factor and the extended X-ray absorption fine structure (EXAFS) including anharmonic contributions have been developed based on the cumulant expansion and the single-shell model. Analytical expressions for the anharmonic contributions to the amplitude and to the phase of the EXAFS have been derived. The EXAFS and its parameters contain anharmonic effects at high temperature and approach those of the harmonic model at low temperature. Numerical results for Cu agree well with experiment. Peaks in the Fourier transform of the calculated anharmonic EXAFS for the first shell at 297 K and 703 K agree well with the experimental ones and are shifted significantly compared to those of the harmonic model.

Estimating the subcellular absorption of electric field energy: equations for an ellipsoidal single shell model

An oriented single shell model is used to describe the absorption of electric field energy for a cell of the general ellipsoidal shape exposed to a homogeneous AC-field. A finite element approach allowed us to derive characteristic equations describing the dependence of the field distribution on the cell geometry, the electric properties of the structural media, membrane and bulk solutions, as well as on the field frequency with a subcellular resolution. Finally, equations were derived for the absorption at certain sites of the model. The model allows for the introduction of frequency-dependent cellular media properties. Experimentally, the new cell parameters can be verified by dielectric single-cell spectroscopy.

Degraded axial buckling strain of multiwalled carbon nanotubes due to interlayer slips

A multiple-shell model is presented for infinitesimal axially compressed buckling of a multiwalled carbon nanotube embedded within an elastic matrix. In contrast to an existing single-shell model which treats the entire multiwalled nanotube as a singlelayer elastic shell, the present model assumes that each of the nested concentric tubes is an individual elastic shell and the deflections of all shells are coupled through the van der Waals interaction between adjacent nanotubes. By examining a doublewalled carbon nanotube, it is found that the change in interlayer spacing has a negligible effect on the axial buckling strain provided that the innermost radius is at least a few nanometers. Under this condition, a single equation is derived which determines the deflection of the multiwalled carbon nanotube, and it is shown that infinitesimal axial buckling of a N-walled carbon nanotubes is equivalent to that of a single layer elastic shell whose bending stiffness is approximately N times the effective bending stiffness of a single walled carbon nanotube. As a result, the axial buckling strain of a N-walled carbon nanotube is about 5 N times lower than that predicted by the existing single-shell model. The degraded axial buckling strain is attributed to the interlayer slips between adjacent nanotubes, which represents an essential feature of mechanical behavior of multiwalled carbon nanotubes.

A single-shell model for biological cells extended to account for the dielectric anisotropy of the plasma membrane

For modeling the polarization of biological cells in electric fields and related AC electrokinetical phenomena, such as electrorotation, dielectrophoresis, etc., dielectric isotropy of the plasma membrane and other cellular compartments is usually assumed. However, this traditional assumption is no longer valid in the case of cell membranes containing mobile charges introduced by the adsorbed hydrophobic ions, such as dipicrylamine, tetraphenylborate, etc. Once partitioned into the membrane, the hydrophobic ions can move freely in the plane of the membrane thus increasing the tangential component of membrane conductivity σ mt. On the contrary, only finite charge displacement, i.e. translocation of hydrophobic ions between the two membrane boundaries, can be induced by the field component normal to the plasma membrane plane. This relaxational effect causes a dielectric dispersion (e.g. in the kHz–MHz range) with a marked increase of the radial membrane permittivity ε mr at low field frequencies. In this study we extended the single-shell spherical model of cells in order to account for the dielectrically anisotropic plasma membrane. In contrast to the usual approach, where the plasma membrane permittivity and conductivity are viewed as scalar quantities, these membrane parameters are treated as tensors in the anisotropic membrane model. Calculations based on the new model showed that the tangential conductivity of hydrophobic ions can induce noticeable changes in the low-frequency part of the electrokinetic spectra of cells.

Dielectric Properties of Human Leukocyte Subpopulations Determined by Electrorotation as a Cell Separation Criterion

The separation and purification of human blood cell subpopulations is an essential step in many biomedical applications. New dielectrophoretic fractionation methods have great potential for cell discrimination and manipulation, both for microscale diagnostic applications and for much larger scale clinical problems. To discover whether human leukocyte subpopulations might be separable by such methods, the dielectric characteristics of the four main leukocyte subpopulations, namely, B- and T-lymphocytes, monocytes, and granulocytes, were measured by electrorotation over the frequency range 1 kHz to 120 MHz. The subpopulations were derived from human peripheral blood by magnetically activated cell sorting (MACS) and sheep erythrocyte rosetting methods, and the quality of cell fractions was checked by flow cytometry. Mean specific membrane capacitance values were calculated from the electrorotation data as 10.5 (± 3.1), 12.6 (± 3.5), 15.3 (± 4.3), and 11.0 (± 3.2) mF/m 2 for T- and B-lymphocytes, monocytes, and granulocytes, respectively, according to a single-shell dielectric model. In agreement with earlier findings, these values correlated with the richness of the surface morphologies of the different cell types, as revealed by scanning electron microscopy (SEM). The data reveal that dielectrophoretic cell sorters should have the ability to discriminate between, and to separate, leukocyte subpopulations under appropriate conditions.

A Unified Resistor-Capacitor Model for Impedance, Dielectrophoresis, Electrorotation, and Induced Transmembrane Potential

Dielectric properties of suspended cells are explored by analysis of the frequency-dependent response to electric fields. Impedance (IMP) registers the electric response, and kinetic phenomena like orientation, translation, deformation, or rotation can also be analyzed. All responses can generally be described by a unified theory. This is demonstrated by an RC model for the structural polarizations of biological cells, allowing intuitive comparison of the IMP, dielectrophoresis (DP), and electrorotation (ER) methods. For derivations, cells of prismatic geometry embedded in elementary cubes formed by the external solution were assumed. All geometrical constituents of the model were described by parallel circuits of a capacitor and a resistor. The IMP of the suspension is given by a meshwork of elementary cubes. Each elementary cube was modeled by two branches describing the current flow through and around the cell. To model DP and ER, the external branch was subdivided to obtain a reference potential. Real and imaginary parts of the potential difference of the cell surface and the reference reflect the frequency behavior of DP and ER. The scheme resembles an unbalanced Wheatstone bridge, in which IMP measures the current-voltage behavior of the feed signal and DP and ER are the measuring signal. Model predictions were consistent with IMP, DP, and ER experiments on human red cells, as well as with the frequency dependence of field-induced hemolysis. The influential radius concept is proposed, which allows easy derivation of simplified equations for the characteristic properties of a spherical single-shell model on the basis of the RC model.

Investigation of the Thermodynamic Properties of Anharmonic Crystals with Defects and Influence of Anharmonicity in Exafs by the Moment Method

By the moment method established previously on the basis of the statistical mechanics, the thermodynamic properties of a strongly anharmonic face-centered and body-centered cubic crystal with point defect are considered. The thermal expansion coefficient, the specific heat Cv and Cp, the isothermal and adiabatic compressibility, etc. are calculated. Our calculated results of the thermal expansion coefficient, the specific heat Cv and Cp… of W, Nb, Au and Ag metals at various temperatures agrees well with the measured values. The anharmonic effects in extended X-ray absorption fine structure (EXAFS) in the single-shell model are considered. We have obtained a new formula for anharmonic contribution to the mean square relative displacement. The anharmonicity is proportional to the temperature and enters the phase change of EXAFS. Our calculated results of Debye–Waller factor and phase change in EXAFS of Cu at various temperatures agrees well with the measured values.

Electrorotation of isolated generative and vegetative cells, and of intact pollen grains of Lilium longiflorum.

The dielectric structure of mature pollen of the angiosperm Lilium longiflorum was studied by means of single-cell electrorotation. The use of a microstructured four-electrode chamber allowed the measurements to be performed over a wide range of medium conductivity from 3 to 500 mS m-1. The rotation spectra of hydrated pollen grains exhibited at least three well-resolved peaks in the kHz-MHz frequency range, which obviously arise due to the multilayered structure of pollen grains. The three-shell model can explain the complex rotational behavior of pollen grains in terms of conductivities, permittivities and thicknesses of the following compartments: the exine and intine of the pollen grain wall as well as the membrane and cytoplasm of the vegetative cell. However, the number of unknown parameters (more than 8) was too large to allow unambiguous values to be assigned to any of them. Therefore, to facilitate the evaluation of the pollen grain parameters, additional rotational measurements were made on isolated vegetative and generative cells. The rotation spectra of these cells could be fitted very accurately on the basis of the single-shell model by assuming a dispersion of the cytoplasm. The data on the membrane and cytoplasmic properties of isolated vegetative cells were then used for modeling the rotation spectra of pollen grains. This greatly facilitated the fitting of the theoretical model to the experimental data and allowed the dielectric properties of the major structural units to be determined. The dielectric characterization of pollen is of enormous interest for plant biotechnology, where pollen and isolated germ cells are successfully used for production of transgenic crop and drug plants of economic importance by means of electromanipulation techniques.

Nonuniform Dust Outflow Observed around Infrared Object NML Cygni

Measurements by the U.C. Berkeley Infrared Spatial Interferometer at 11.15 micron have yielded strong evidence for multiple dust shells and/or significant asymmetric dust emission around NML Cyg. New observations reported also include multiple 8-13 micron spectra taken from 1994-1995 and N band (10.2 micron) photometry from 1980-1992. These and past measurements are analyzed and fitted to a model of the dust distribution around NML Cyg. No spherically symmetric single dust shell model is found consistent with both near- and mid-infrared observations. However, a circularly symmetric maximum entropy reconstruction of the 11 micron brightness distribution suggests a double shell model for the dust distribution. Such a model, consisting of a geometrically thin shell of intermediate optical depth ($\tau_{11 micron} \sim 1.9$) plus an outer shell ($\tau_{11 micron} \sim 0.33$), is consistent not only with the 11 micron visibility data, but also with near-infrared speckle measurements, the broadband spectrum, and the 9.7 micron silicate feature. The outer shell, or large scale structure, is revealed only by long-baseline interferometry at 11 micron, being too cold ($\sim$ 400 K) to contribute in the near-infrared and having no unambiguous spectral signature in the mid-infrared. The optical constants of Ossenkopf, Henning, & Mathis (1992) proved superior to the Draine & Lee (1984) constants in fitting the detailed shape of the silicate feature and broadband spectrum for this object. Recent observations of H$_2$O maser emission around NML Cyg by Richards, Yates, & Cohen (1996) are consistent with the location of the two dust shells and provide further evidence for the two-shell model.

Anharmonic Contributions to High-Temperature EXAFS Spectra: Theory and Comparison with Experiment

In this work the anharmonic contributions to the high-temperature EXAFS spectra have been evaluated by considering the anharmonic contributions to the thermal vibrations of atoms and using the single-shell model. The anharmonicity calculated by our new formula is proportional to the temperature and inversely proportional to the distance between the absorbing atom and its neighbour located in a spherical shell which can be considered as the outer shell in the case of particles. The measured EXAFS spectra of Cu at several temperatures have been presented providing its strucuctural informations, among them the atom position of the first shell is different from the one calculated by the harmonic model by 0.05 Å at 700 K and 0.01 Å at 295 K. These measured results agree very well with the ones calculated by present anharimonic theory. This creates a good possibility for extraction of physical parameters from experiment by using our procedure.

Electrorotation of erythrocytes treated with dipicrylamine: mobile charges within the membrane show their "signature" in rotational spectra.

In this study, electrorotation spectra of individual cells (that is, frequency dependence of cell rotation speed) have been proved to yield information not only about the passive electric properties of cell constituents, but also about the presence of mobile charges within the plasma membrane being part of ion carrier transport systems. Experiments on human erythrocytes pretreated with the lipophilic anion dipicrylamine (DPA) gave convincing evidence that these artificial mobile charges adsorbed to the plasma membrane contributed significantly to the rotational spectrum at relatively low conductivity of the external medium (2-5 mS m-1). Theoretical integration of the mobile charge concept into the single-shell model (viewing the cell as a homogenous sphere surrounded by a membrane) led to a set of equations which predicted electrorotational behavior of DPA-treated cells in dependence on medium conductivity. The quantitative data on the partition and the transmembrane translocation rate of the DPA anion extracted from the experimental rotational spectra agreed well with the corresponding literature values.

Dielectric spectroscopy of single human erythrocytes at physiological ionic strength: dispersion of the cytoplasm

Usually dielectrophoretic and electrorotation measurements are carried out at low ionic strength to reduce electrolysis and heat production. Such problems are minimized in microelectrode chambers. In a planar ultramicroelectrode chamber fabricated by semiconductor technology, we were able to measure the dielectric properties of human red blood cells in the frequency range from 2 kHz to 200 MHz up to physiological ion concentrations. At low ionic strength, red cells exhibit a typical electrorotation spectrum with an antifield rotation peak at low frequencies and a cofield rotation peak at higher ones. With increasing medium conductivity, both electrorotational peaks shift toward higher frequencies. The cofield peak becomes antifield for conductivities higher than 0.5 S/m. Because the polarizability of the external medium at these ionic strengths becomes similar to that of the cytoplasm, properties can be measured more sensitively. The critical dielectrophoretic frequencies were also determined. From our measurements, in the wide conductivity range from 2 mS/m to 1.5 S/m we propose a single-shell erythrocyte model. This pictures the cell as an oblate spheroid with a long semiaxis of 3.3 microns and an axial ratio of 1:2. Its membrane exhibits a capacitance of 0.997 x 10(-2) F/m2 and a specific conductance of 480 S/m2. The cytoplasmic parameters, a conductivity of 0.4 S/m at a dielectric constant of 212, disperse around 15 MHz to become 0.535 S/m and 50, respectively. We attribute this cytoplasmic dispersion to hemoglobin and cytoplasmic ion properties. In electrorotation measurements at about 60 MHz, an unexpectedly low rotation speed was observed. Around 180 MHz, the speed increased dramatically. By analysis of the electric chamber circuit properties, we were able to show that these effects are not due to cell polarization but are instead caused by a dramatic increase in the chamber field strength around 180 MHz. Although the chamber exhibits a resonance around 180 MHz, the harmonic content of the square-topped driving signals generates distortions of electrorotational spectra at far lower frequencies. Possible technological applications of chamber resonances are mentioned.

The spectral energy distribution and mass-loss history of IRC + 10420

We present a study of the spectral energy distribution of the peculiar hypergiant IRC + 10420. To this end we have collected published photometry of IRC + 10420 and obtained some new data, in order to construct the spectral energy distribution and fit it with a radiative transfer model. In addition high-quality (CO)-C-12 spectra of the rotational J=1-0, 2-1, 3-2 and 4-3 transitions have been obtained to determine the gas outflow velocity and independently estimate the gas mass-loss rate. The main conclusions from this work are that the photometric changes over the last 20 years indicate that the object has increased in temperature by more than 1000 K and that the spectral energy distribution cannot be fitted with a single-shell model without first including a hot component. This hot component is likely to be a circumstellar disc. Finally, we present evidence that IRC + 10420 is nota post-AGE star.