The ‘wet mind’: water and functional neuroimaging

Diffusion imaging for therapy response assessment of brain tumor

Advanced imaging provides insight into biophysical, physiologic, metabolic, or functional properties of tissues. Because water mobility is sensitive to cellular homeostasis, cellular density, and microstructural organization, it is considered a valuable tool in the advanced imaging arsenal. This article summarizes diffusion imaging concepts and highlights clinical applications of diffusion MR imaging for oncologic imaging. Diffusion tensor imaging and its derivative maps of diffusion anisotropy allow assessment of tumor compression or destruction of adjacent normal tissue anisotropy and may aid to assess tumor infiltration and aid presurgical planning.

Dynamics in Biological Systems as seen by QENS

Quasielastic incoherent neutron scattering is a well suited and established experimental method to study protein and water dynamics in the picosecond to nanosecond time- and Ångstrom length-scale. Using deuterium labelling either protein or water motions can be selected and brought into focus. Protein and cell water dynamics were separately studied in red blood cells. A consistent picture of cytoplasmic water and protein dynamics in whole cells is emerging from recent experimental results.

Diffusion MR imaging of hypoglycemic encephalopathy

BACKGROUND AND PURPOSE

MR imaging features of HE have not been fully established. The purpose of this study was to determine the topographic distribution and DWI findings of HE.

MATERIALS AND METHODS

We retrospectively evaluated HE MR imaging (n = 11). The topographic distribution of the lesions was evaluated on routine MR imaging, and DWI SI and ADC values were assessed. The ADC value of involved lesions was compared with the noninvolved subcortical WM area by use of the paired t test.

RESULTS

MR images demonstrated bilateral diffusion-restrictive lesions in the posterior limb of the IC (n = 6), cerebral cortex (n = 8), CR (n = 7), CS (n = 9), hippocampus (n = 4), and BG (n = 1). The mean ADC value of lesions was 448.82 +/- 92.34 x 10(-6) mm(2)/s compared with the mean ADC value of noninvolved lesions (837.72 +/- 62.14 x 10(-6) mm(2)/s); this difference was statistically significant (P < .000). The lesions showed complete resolution on follow-up DWI for 6 patients. Three patients with cortical involvement of > or = 2 lobes showed partial recovery or death, but most of the other patients with WM involvement or cortical involvement in only 1 lobe experienced complete recovery.

CONCLUSIONS

The topographic localization of the lesions was the posterior limb of the IC, cerebral cortex, CR, CS, hippocampus, and BG. Most HE lesions probably correspond to areas of reversible cytotoxic edema as seen on DWI, which can predict the prognosis of HE according to the degree of lesion extent.

On high b diffusion imaging in the human brain: ruminations and experimental insights

Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber "tractography" results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,"ruminations," which have been proposed to account for the nonmonoexponentiality to date.

Crossing fibres in tract-based spatial statistics

Voxelwise analysis of white matter properties typically relies on scalar measurements derived, for example, from a tensor model fit to diffusion MRI data. These are spatially matched across subjects prior to statistical modelling. In this paper, we show why and how this can be improved through the use of directionally dependent measurements. In the case where different orientations relate to different fibre populations (e.g., in the presence of crossing fibres), distinguishing and matching those populations of fibres across subjects are important prior to any statistical modelling. It allows one to compare measurements that are related to the same fibres across subjects. We show how this framework applies to the parameters of a crossing fibre model and discuss its implications for voxelwise analysis of the white matter.

A multi-compartmental SE-BOLD interpretation for stimulus-related signal changes in diffusion-weighted functional MRI

A new interpretation is proposed for stimulus-induced signal changes in diffusion-weighted functional MRI. T(2)-weighted spin-echo echo-planar images were acquired at different diffusion-weightings while visual stimulation was presented to human volunteers. The amplitudes of the positive stimulus-correlated response and post-stimulus undershoot (PSU) in the functional time-courses were found to follow different trends as a function of b-value. Data were analysed using a three-compartment signal model, with one compartment being purely vascular and the other two dominated by fast- and slow-diffusing molecules in the brain tissue. The diffusion coefficients of the tissue were assumed to be constant throughout the experiments. It is shown that the stimulus-induced signal changes can be decomposed into independent contributions originating from each of the three compartments. After decomposition, the fast-diffusion phase displays a substantial PSU, while the slow-diffusion phase demonstrates a highly reproducible and stimulus-correlated time-course with minimal undershoot. The decomposed responses are interpreted in terms of the spin-echo blood oxygenation level dependent (SE-BOLD) effect, and it is proposed that the signal produced by fast- and slow-diffusing molecules reflect a sensitivity to susceptibility changes in arteriole/venule- and capillary-sized vessels, respectively. This interpretation suggests that diffusion-weighted SE-BOLD imaging may provide subtle information about the haemodynamic and neuronal responses.

Atomic-scale dynamics inside living cells explored by neutron scattering

Single-particle neutron spectroscopy has contributed important experimental data on molecular dynamics in biological systems. The technique provides information on atomic and molecular motions in macromolecules on the picosecond to the nanosecond time scale, which are essential to biological function. Here, we report on recent neutron measurements performed directly in living cells by using isotope labelling to explore the dynamics of specific cellular components. The paper proposes an integrated view of results on atomic-scale cell water dynamics, internal and global macromolecular motions and solvent isotope effect on macromolecular dynamics. The work established the specific usefulness of the neutron scattering technique to get insight into biologically relevant dynamical features, in particular through comparative measurements. The method developed can now be applied to look for dynamical signatures related to cell characteristics in many different cell types and organelles.

Diffusion-weighted MRI measurements on stroke patients reveal water-exchange mechanisms in sub-acute ischaemic lesions

The aim of this study was to investigate the diffusion time dependence of signal-versus-b curves obtained from diffusion-weighted magnetic resonance imaging (DW-MRI) of sub-acute ischaemic lesions in stroke patients. In this case series study, 16 patients with sub-acute ischaemic stroke were examined with DW-MRI using two different diffusion times (60 and 260 ms). Nine of these patients showed sufficiently large lesions without artefacts to merit further analysis. The signal-versus-b curves from the lesions were plotted and analysed using a two-compartment model including compartmental exchange. To validate the model and to aid the interpretation of the estimated model parameters, Monte Carlo simulations were performed. In eight cases, the plotted signal-versus-b curves, obtained from the lesions, showed a signal-curve split-up when data for the two diffusion times were compared, revealing effects of compartmental water exchange. For one of the patients, parametric maps were generated based on the extracted model parameters. These novel observations suggest that water exchange between different water pools is measurable and thus potentially useful for clinical assessment. The information can improve the understanding of the relationship between the DW-MRI signal intensity and the microstructural properties of the lesions.

Concordant biology underlies discordant imaging findings: diffusivity behaves differently in grey and white matter post acute neurotrauma

BACKGROUND

Cerebral edema is a common sequelum post traumatic brain injury (TBI). Quantification of the apparent diffusion coefficient (ADC) using diffusion tensor imaging (DTI) may help to characterize the pathophysiology of brain swelling.

METHODS

Twenty-two patients with moderate-to-severe TBI underwent magnetic resonance (MR) imaging, including DTI, within five days of injury. The mean ADCs in whole brain white matter, whole brain grey matter and entire brain were calculated and compared to twenty-five controls.

FINDINGS

A significant decrease in the grey matter ADC (p < 0.001), significant increase in the white matter ADC (p < 0.001) and no significant change in the whole brain ADC (p = 0.771) was observed. No significant correlation was found between DTI parameters in any of the three regions of interest (ROI) and GCS, time to scan, intracranial pressure (ICP) before and during the time of the scan, cerebral perfusion pressure at time of scan, or Glasgow Outcome Score (GCS).

CONCLUSIONS

The decrease in ADC seen in the grey matter is consistent with cytotoxic edema. The increase in ADC in the white matter indicates damage that has led to an overall less restricted diffusion. This study assists in the interpretation of the ADC by showing that the acute changes are different in the whole brain white and grey matter ROIs post TBI.

Water-diffusion slowdown in the human visual cortex on visual stimulation precedes vascular responses

We used magnetic resonance imaging (MRI) to investigate the temporal dynamics of changes in water diffusion and blood oxygenation level-dependent (BOLD) responses in the brain cortex of eight subjects undergoing visual stimulation, and compared them with changes of the vascular hemoglobin content (oxygenated, deoxygenated, and total hemoglobin) acquired simultaneously from intrinsic optical recordings (near infrared spectroscopy). The group average rise time for the diffusion MRI signal was statistically significantly shorter than those of the BOLD signal and total hemoglobin content optical signal, which is assumed to be the fastest observable vascular signal. In addition, the group average decay time for the diffusion MRI also was shortest. The overall time courses of the BOLD and optical signals were strongly correlated, but the covariance was weaker with the diffusion MRI response. These results suggest that the observed decrease in water diffusion reflects early events that precede the vascular responses, which could originate from changes in the extravascular tissue.

An intrinsic diffusion response function for analyzing diffusion functional MRI time series

To disentangle the temporal profiles of the diffusion and BOLD components of diffusion-weighted functional MRI (DfMRI) during visual activation, we extracted the raw signal from an anatomically defined volume of interest encompassing the visual cortex of 16 subjects. Under the assumption of a linear, time invariant system we were able to define an intrinsic diffusion response function (DRF) from neural tissue, as a counterpart to the hemodynamic response function (HRF) commonly used in BOLD-fMRI. The shape of the DRF response was found to be very similar to the time courses of optical imaging transmittance signals, thought to originate from local geometric changes in brain tissue at the microscopic scale. The overall DfMRI signal response was modeled as the convolution of the stimulation paradigm time course with a DhRF, which is the sum of the DRF and a fractional HRF resulting from residual tissue T2-BOLD contrast. The contribution of the HRF to the DfMRI signal was found to be 26% at peak amplitude, but the DRF component which has a much steeper onset contributed solely at beginning of the response onset. The suitability of this model over the canonical HRF to process DfMRI data was then demonstrated on datasets acquired in 5 other subjects using a rapid event-related design. Some non-linearities in the responses were observed, mainly after the end of the stimulation.

Aquaporin 4 correlates with apparent diffusion coefficient and hydrocephalus severity in the rat brain: a combined MRI-histological study

Hydrocephalus features include ventricular dilatation and periventricular edema due to transependymal resorption of cerebrospinal fluid (CSF). Aquaporin 4 (AQP4), a water channel protein located at the blood-brain barrier, might facilitate the removal of this excess of water from the parenchyma into the blood. First, we hypothesized a link between AQP4 expression and the severity of hydrocephalus. We further hypothesized that movements of water through AQP4 could affect apparent diffusion coefficient (ADC) measurements. Communicating inflammatory hydrocephalus was induced in 45 rats, and at various stages, magnetic resonance imaging (MRI) was used to measure CSF volume and periventricular ADC, with immunostaining being used to determine periventricular AQP4. We found an up-regulation of periventricular AQP4 in hydrocephalic rats that was strongly correlated with both CSF volume (Pearson=0.87, p<0.00001) and periventricular ADC (Pearson=0.85, p<0.00001). AQP4 were first located on astrocyte endfeet, but later on the whole membrane of astrocytes that became hypertrophic in the most severe and chronic hydrocephalic rats. These results show that AQP4 expression follows an adaptative profile to the severity of hydrocephalus, which is probably a protective response mechanism. They also suggest that ADC, on top of informing about cell sizes and interstitial bulk water, might also indirectly reflect quantitative water channel expression.

Diffusion tensor imaging study of white matter fiber tracts in pediatric bipolar disorder and attention-deficit/hyperactivity disorder

BACKGROUND

To investigate microstructure of white matter fiber tracts in pediatric bipolar disorder (PBD) and attention-deficit/hyperactivity disorder (ADHD).

METHODS

A diffusion tensor imaging (DTI) study was conducted at 3 Tesla on age- and IQ-matched children and adolescents with PBD (n = 13), ADHD (n = 13), and healthy control subjects (HC) (n = 15). Three DTI parameters, fractional anisotropy (FA), apparent diffusion coefficient (ADC), and regional fiber coherence index (r-FCI), were examined in eight fiber tracts: anterior corona radiata (ACR), anterior limb of the internal capsule (ALIC), superior region of the internal capsule (SRI), posterior limb of the internal capsule (PLIC), superior longitudinal fasciculus (SLF), inferior longitudinal fasciculus (ILF), cingulum (CG), and splenium (SP).

RESULTS

Significantly lower FA was observed in ACR in both PBD and ADHD relative to HC. In addition, FA and r-FCI values were significantly lower in ADHD relative to PBD and HC in both the ALIC and the SRI. Further, ADC was significantly greater in ADHD relative to both the PBD and HC in ACR, ALIC, PLIC, SRI, CG, ILF, and SLF.

CONCLUSIONS

Decreased FA in ACR implies an impaired fiber density or reduced myelination in both PBD and ADHD in this prefrontal tract. These abnormalities, together with the reduced fiber coherence, extended to corticobulbar tracts in ADHD. Increased ADC across multiple white matter tracts in ADHD indicates extensive cellular abnormalities with less diffusion restriction in ADHD relative to PBD.

Current trends and challenges in MRI acquisitions to investigate brain function

Functional magnetic resonance imaging (fMRI) studies using the blood oxygenation level dependent (BOLD) response have become a widely used tool for noninvasive assessment of functional organization of the brain. Yet the technique is still fairly new, with many significant challenges remaining. Capitalizing on additional contrast mechanisms available with MRI, several other functional imaging techniques have been developed that potentially provide improved quantification or specificity of neuronal function. This article reviews the challenges and the current state of the art in MRI-based methods of imaging cognitive function.

Dynamic imaging of brain function

In recent years, there have been unprecedented methodological advances in the dynamic imaging of brain activities. Electrophysiological, optical, and magnetic resonance methods now allow mapping of functional activation (or deactivation) by measurement of neural activity (e.g., membrane potential, ion flux, neurotransmitter flux), energy metabolism (e.g., glucose consumption, oxygen consumption, creatine kinase flux), and functional hyperemia (e.g., blood oxygenation, blood flow, blood volume). Properties of the glutamatergic synapse are used to model activities at the nerve terminal and their associated changes in energy demand and blood flow. This approach reveals that each method measures different tissue- and/or cell-specific components with characteristic spatiotemporal resolution. While advantages and disadvantages of different methods are apparent and often used to supersede one another in terms of specificity and/or sensitivity, no particular technique is the optimal dynamic brain imaging method because each method is unique in some respect. Since the demand for energy substrates is a fundamental requirement for function, energy-based methods may allow quantitative dynamic imaging in vivo. However, there are exclusive neurobiological insights gained by combining some of these different dynamic imaging techniques.

Biexponential apparent diffusion coefficients in prostate cancer

PURPOSE

The purpose of this study was to investigate the need for biexponential signal decay modeling for prostate cancer diffusion signal decays with b-factor over an extended b-factor range.

MATERIALS AND METHODS

Ten healthy volunteers and 12 patients with a bulky prostate cancer underwent line scan diffusion-weighted MR imaging in which b-factors from 0 to 3000 s/mm(2) in 16 steps were sampled. The acquired signal decay curves were fit with both monoexponential and biexponential signal decay functions and a statistical comparison between the two fits was performed.

RESULTS

The biexponential model provided a statistically better fit over the monoexponential model on the peripheral zone (PZ), transitional zone (TZ) and prostate cancer. The fast and slow apparent diffusion coefficients (ADCs) in the PZ, TZ and cancer were 2.9+/-0.2, 0.7+/-0.2 x 10(-3) mm(2)/ms (PZ); 2.9+/-0.4, 0.7+/-0.2 x 10(-3) mm(2)/ms (TZ); and 1.7+/-0.4, 0.3+/-0.1 x 10(-3) mm(2)/ms (cancer), respectively. The apparent fractions of the fast diffusion component in the PZ, TZ and cancer were 70+/-10%, 60+/-10% and 50+/-10%, respectively. The fast and slow ADCs of cancer were significantly lower than those of TZ and PZ, and the apparent fraction of the fast diffusion component was significantly smaller in cancer than in PZ.

CONCLUSIONS

Biexponential diffusion decay functions are required for prostate cancer diffusion signal decay curves when sampled over an extended b-factor range, providing additional, unique tissue characterization parameters for prostate cancer.

Biexponential analysis of diffusion-related signal decay in normal human cortical and deep gray matter

Diffusion imaging with high-b factors, high spatial resolution and cerebrospinal fluid signal suppression was performed in order to characterize the biexponential nature of the diffusion-related signal decay with b-factor in normal cortical gray and deep gray matter (GM). Integration of inversion pulses with a line scan diffusion imaging sequence resulted in 91% cerebrospinal fluid signal suppression, permitting accurate measurement of the fast diffusion coefficient in cortical GM (1.142+/-0.106 microm2/ms) and revealing a marked similarity with that found in frontal white matter (WM) (1.155+/-0.046 microm2/ms). The reversal of contrast between GM and WM at low vs high b-factors is shown to be due to a significantly faster slow diffusion coefficient in cortical GM (0.338+/-0.027 microm2/ms) than in frontal WM (0.125+/-0.014 microm2/ms). The same characteristic diffusion differences between GM and WM are observed in other brain tissue structures. The relative component size showed nonsignificant differences among all tissues investigated. Cellular architecture in GM and WM are fundamentally different and may explain the two- to threefold higher slow diffusion coefficient in GM.

Down to atomic-scale intracellular water dynamics

Water constitutes the intracellular matrix in which biological molecules interact. Understanding its dynamic state is a main scientific challenge, which continues to provoke controversy after more than 50 years of study. We measured water dynamics in vivo in the cytoplasm of Escherichia coli by using neutron scattering and isotope labelling. Experimental timescales covered motions from pure water to interfacial water, on an atomic length scale. In contrast to the widespread opinion that water is 'tamed' by macromolecular confinement, the measurements established that water diffusion within the bacteria is similar to that of pure water at physiological temperature.

A model for thermal exchange in axons during action potential propagation

Several experiments have shown that during propagation of the action potential in axons, thermal energy is locally exchanged. In this paper, we use a simple model based on statistical physics to show that an important part of this exchange comes from the physics of the effusion. We evaluate, during the action potential propagation, the variation of internal energy and of the energy associated with the chemical potential of the effusion of water and ions to extract the thermal energy exchanged. The temperature exchanged is then evaluated on the area where the action potential is active. Results give a good correspondence between experimental work and this model, showing that an important part of the thermal energy exchange comes from the statistical cooling power of the effusion.

Simulation and experimental verification of the diffusion in an anisotropic fiber phantom

Diffusion weighted magnetic resonance imaging enables the visualization of fibrous tissues such as brain white matter. The validation of this non-invasive technique requires phantoms with a well-known structure and diffusion behavior. This paper presents anisotropic diffusion phantoms consisting of parallel fibers. The diffusion properties of the fiber phantoms are measured using diffusion weighted magnetic resonance imaging and bulk NMR measurements. To enable quantitative evaluation of the measurements, the diffusion in the interstitial space between fibers is modeled using Monte Carlo simulations of random walkers. The time-dependent apparent diffusion coefficient and kurtosis, quantifying the deviation from a Gaussian diffusion profile, are simulated in 3D geometries of parallel fibers with varying packing geometries and packing densities. The simulated diffusion coefficients are compared to the theory of diffusion in porous media, showing a good agreement. Based on the correspondence between simulations and experimental measurements, the fiber phantoms are shown to be useful for the quantitative validation of diffusion imaging on clinical MRI-scanners.

Human brain mapping: hemodynamic response and electrophysiology

In view of the recent advance in functional neuroimaging, the current status of non-invasive techniques applied for human brain mapping was reviewed by integrating two principles: hemodynamic and electrophysiological, from the viewpoint of clinical neurophysiology. The currently available functional neuroimaging techniques based on hemodynamic principles are functional magnetic resonance imaging (fMRI), positron emission tomography (PET) or single-photon emission computed tomography (SPECT), and near-infrared spectroscopy (NIRS). Electrophysiological techniques include electroencephalography (EEG), magnetoencephalography (MEG), and transcranial magnetic stimulation (TMS). As for the coupling between hemodynamic response and neuronal activity (neurovascular coupling), experimental studies suggest that the hemodynamic response is significantly correlated to neuronal activity, especially local field potential (synaptic activity) rather than spiking activity, within a certain range. The hemodynamic response tends to be more widespread in space and lasts longer in time as compared with the neuronal activity. Since each technique has its own characteristic features especially in terms of spatial and temporal resolution, it is important to adopt the most appropriate technique for solving each specific question, and it is useful to combine two techniques either simultaneously or in separate sessions. As for the multi-modal approach, the combined use of EEG and MEG, EEG and PET, or EEG and fMRI is applied for the simultaneous studies, and for the separate use of two different techniques, the information obtained from fMRI is used for estimating the generator source from EEG or MEG data (fMRI-constrained source estimation). Functional connectivity among different brain areas can be studied by using a single technique such as the EEG coherence or the correlation analysis of fMRI or PET data, or by combining the stimulation technique such as TMS with neuroimaging. Further advance of each technology and improvement in the analysis method will promote the understanding of precise functional specialization and inter-areal coupling, and will contribute to the increased efficacy of rapidly developing physiological treatments of neurological and psychiatric disorders.

Evidence for a vascular contribution to diffusion FMRI at high b value

Recent work has suggested that diffusion-weighted functional magnetic resonance imaging (FMRI) with strong diffusion weighting (high b value) detects neuronal swelling that is directly related to neuronal firing. This would constitute a much more direct measure of brain activity than current methods and represent a major advance in neuroimaging. However, it has not been firmly established that the observed signal changes do not reflect residual vascular effects, which are known to exist at low b value. This study measures the vascular component of diffusion FMRI directly by using hypercapnia, which induces blood flow changes in the absence of a change in neuronal firing. Hypercapnia elicits a similar diffusion FMRI response to a visual stimulus including a rise in percent signal change with increasing b value, which was reported for visual activation. Analysis of the response timing found no evidence for an early response at high b value, which has been reported as evidence for a nonhemodynamic response. These results suggest that a large component of the diffusion FMRI signal at high b value is vascular rather than neuronal.

Bloodless FMRI

Conventional functional magnetic resonance imaging (fMRI) is a blunt tool for studying the nervous system because it measures neural activity only indirectly, by way of hemodynamics and neurovascular coupling. Several alternative, nonhemodynamic functional imaging methods are now being explored. The methods are designed to offer better resolution and neuronal specificity than hemodynamic imaging and, in some cases, might report signals from specific molecules or cell populations. Much progress has concentrated in three areas: diffusion-weighted functional imaging; detection of neuronal electromagnetic fields; and molecular imaging of neural metabolites and signaling species. Here, we review recent developments in these areas. We consider unique advantages and disadvantages of 'bloodless fMRI' approaches, as well as their future prospects as experimental tools in cognitive and systems neuroscience.

Realistic simulations of neuronal activity: a contribution to the debate on direct detection of neuronal currents by MRI

Many efforts have been done in order to preview the properties of the magnetic resonance (MR) signals produced by the neuronal currents using simulations. In this paper, starting with a detailed calculation of the magnetic field produced by the neuronal currents propagating over single hippocampal CA1 pyramidal neurons placed inside a cubic MR voxel of length 1.2 mm, we proceeded on the estimation of the phase and magnitude MR signals. We then extended the results to layers of parallel and synchronous similar neurons and to ensembles of layers, considering different echo times, voxel volumes and neuronal densities. The descriptions of the neurons and of their electrical activity took into account the real neuronal morphologies and the physiology of the neuronal events. Our results concern: (a) the expected time course of the MR signals produced by the neuronal currents in the brain, based on physiological and anatomical properties; (b) the different contributions of post-synaptic potentials and of action potentials to the MR signals; (c) the estimation of the equivalent current dipole and the influence of its orientation with respect to the external magnetic field on the observable MR signal variations; (d) the size of the estimated neuronal current induced phase and magnitude MR signal changes with respect to the echo time, voxel-size and neuronal density. The inclusion of realistic neuronal properties into the simulation introduces new information that can be helpful for the design of MR sequences for the direct detection of neuronal current effects and the testing of bio-electromagnetic models.