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In this work, a parametric study is carried out on carbon fiber-reinforced plastic (CFRP) materials to investigate how the spatially varying fiber distribution influences the measured signal in an eddy current testing (ECT) configuration. The measurement setup was modeled using finite element method, while the fiber distribution is taken into account by an inhomogeneous anisotropic conductivity tensor. The study revealed a trade-off relation between the size of the ECT coil and the maximal dynamic range of the ECT signal, which contributes to the understanding of the connection between the fiber arrangement and the ECT signal and provides an opportunity for optimal ECT coil design. [ABSTRACT FROM AUTHOR]

Electrical stimulation such as transcranial direct current stimulation (tDCS) is widely used to treat neuropsychiatric diseases and neurological disorders. Computational modeling is an important approach to understand the mechanisms underlying tDCS and optimize treatment planning. When applying computational modeling to treatment planning, uncertainties exist due to insufficient conductivity information inside the brain. In this feasibility study, we performed in vivo MR-based conductivity tensor imaging (CTI) experiments on the entire brain to precisely estimate the tissue response to the electrical stimulation. A recent CTI method was applied to obtain low-frequency conductivity tensor images. Subject-specific three-dimensional finite element models (FEMs) of the head were implemented by segmenting anatomical MR images and integrating a conductivity tensor distribution. The electric field and current density of brain tissues following electrical stimulation were calculated using a conductivity tensor-based model and compared to results using an isotropic conductivity model from literature values. The current density by the conductivity tensor was different from the isotropic conductivity model, with an average relative difference |rD| of 52 to 73%, respectively, across two normal volunteers. When applied to two tDCS electrode montages of C3-FP2 and F4-F3, the current density showed a focused distribution with high signal intensity which is consistent with the current flowing from the anode to the cathode electrodes through the white matter. The gray matter tended to carry larger amounts of current densities regardless of directional information. We suggest this CTI-based subject-specific model can provide detailed information on tissue responses for personalized tDCS treatment planning. [ABSTRACT FROM AUTHOR]

Electrical stimulation such as transcranial direct current stimulation (tDCS) is widely used to treat neuropsychiatric diseases and neurological disorders. Computational modeling is an important approach to understand the mechanisms underlying tDCS and optimize treatment planning. When applying computational modeling to treatment planning, uncertainties exist due to insufficient conductivity information inside the brain. In this feasibility study, we performed in vivo MR-based conductivity tensor imaging (CTI) experiments on the entire brain to precisely estimate the tissue response to the electrical stimulation. A recent CTI method was applied to obtain low-frequency conductivity tensor images. Subject-specific three-dimensional finite element models (FEMs) of the head were implemented by segmenting anatomical MR images and integrating a conductivity tensor distribution. The electric field and current density of brain tissues following electrical stimulation were calculated using a conductivity tensor-based model and compared to results using an isotropic conductivity model from literature values. The current density by the conductivity tensor was different from the isotropic conductivity model, with an average relative difference |rD| of 52 to 73%, respectively, across two normal volunteers. When applied to two tDCS electrode montages of C3-FP2 and F4-F3, the current density showed a focused distribution with high signal intensity which is consistent with the current flowing from the anode to the cathode electrodes through the white matter. The gray matter tended to carry larger amounts of current densities regardless of directional information. We suggest this CTI-based subject-specific model can provide detailed information on tissue responses for personalized tDCS treatment planning.

In the review brought to the attention of readers, the results of experimental studies of magneto-optical effects in noble metals are presented. These studies, carried out by both Italian and United States scientists, made it possible to establish a direct relationship between galvanomagnetic and magneto-optical phenomena in the noble metals.

Electrical conductivity at low-frequency is associated with the cell density, fiber direction, and extracellular composition of the biological tissues. Imaging of conductivity distribution inside the human brain can localize the source in EEG measurements and predict current pathways for brain stimulation therapy planning. Human tissues such as white matter and muscles are known to be anisotropic in nature and conductivity changes concerning fiber directions. Since muscle is the most abundant anisotropic tissue in the human body, in vitro and in vivo muscle conductivity tensor assessment has been attempted. In this study, we conducted high-resolution imaging of muscle tissues using recent MR-based conductivity tensor imaging (CTI) to validate its in vivo usefulness. The low- and high-frequency conductivity obtained from the CTI and the in vitro conductivity obtained from the impedance analyzer were compared, and the anisotropy of the tissue was quantified using the anisotropy ratio (AR) to confirm the anisotropy. The application of the CTI method can be found in the evaluation of musculoskeletal microstructure. [ABSTRACT FROM AUTHOR]

Aims: Electric conduction in the atria is direction-dependent, being faster in fibre direction, and possibly heterogeneous due to structural remodelling. Intracardiac recordings of atrial activation may convey such information, but only with high-quality data. The aim of this study was to apply a patient-specific approach to enable such assessment even when data are scarce, noisy, and incomplete.Methods and Results: Contact intracardiac recordings in the left atrium from nine patients who underwent ablation therapy were collected before pulmonary veins isolation and retrospectively included in the study. The Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps (PIEMAP), previously developed, has been used to reconstruct the conductivity tensor from sparse recordings of the activation. Regional fibre direction and conduction velocity were estimated from the fitted conductivity tensor and extensively cross-validated by clustered and sparse data removal. Electrical conductivity was successfully reconstructed in all patients. Cross-validation with respect to the measurements was excellent in seven patients (Pearson correlation r > 0.93) and modest in two patients (r = 0.62 and r = 0.74). Bland-Altman analysis showed a neglectable bias with respect to the measurements and the limit-of-agreement at -22.2 and 23.0 ms. Conduction velocity in the fibre direction was 82 ± 25 cm/s, whereas cross-fibre velocity was 46 ± 7 cm/s. Anisotropic ratio was 1.91±0.16. No significant inter-patient variability was observed. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps correctly predicted activation times in late regions in all patients (r = 0.88) and was robust to a sparser dataset (r = 0.95).Conclusion: Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps offers a novel approach to extrapolate the activation in unmapped regions and to assess conduction properties of the atria. It could be seamlessly integrated into existing electro-anatomic mapping systems. Personalized Inverse Eikonal model from cardiac Electro-Anatomical Maps also enables personalization of cardiac electrophysiology models. [ABSTRACT FROM AUTHOR]

Applications of anisotropic composite materials range from construction composites to electric circuit boards. Anisotropic conductivity is one of the many important measurands for anisotropic composites for identifying misalignment. However, there are only a few nondestructive, noncontact techniques available. Here, we explore waveguide ellipsometry, a new electromagnetic characterization technique, and its application to conductive anisotropic composites. We demonstrate waveguide ellipsometry and discuss the design and implementation of a novel rotation test head on a robotic arm. To validate our technique, we designed and fabricated test wafers with ideal anisotropic composites consisting of gold stripes on materials with varying sheet resistances. The measurements were compared to full-wave simulations with simulated material properties extracted with the help of composite theory and simple circuit analysis. We found a good match between the simulated and measured complex scattering (S-) parameters for all test wafers fabricated with molybdenum disilicide (MoSi2) and gold stripes. Finally, we map the measured S-parameters to simulated S-parameters with help from composite theory and circuit modeling. Broader impacts of microwave ellipsometry include in-line measurement and conductivity imaging of large-scale and 3-D parts for nondestructive evaluation. [ABSTRACT FROM AUTHOR]

Electrical anisotropy is a property of the Earth materials that can be studied through electromagnetic geophysical methods, such as magnetotellurics. It consists of the electrical conductivity changing with the orientation and being mathematically characterized by the conductivity tensor. In order to better understand the conductivity tensor and provide more effective tools for quantitatively analyzing the conductivity tensor of anisotropic structures, three graphical representations for symmetric tensors using ellipsoids, Mohr circles and geometric forms are presented. The ellipsoid representation can be applied to indicate the strength of the anisotropy in different directions. The Mohr circle provides a graphic representation of a tensor as a function of the rotation of the coordinate system. For the geometric forms, one-dimensional (1-D), two-dimensional (2-D) and three-dimensional (3-D) sheet models with given parameters (sizes and resistivities of the constituent prisms), the macroscopic anisotropic conductivity may be calculated using the closed-form mathematical formulas. These three graphical representations have different abilities for revealing information on the conductivity tensor. Four synthetic examples involving uniaxial or biaxial anisotropic conductivity structures are examined in the principal axis coordinate system to investigate the advantages and disadvantages of the graphical displays. [ABSTRACT FROM AUTHOR]

Magnetic resonance conductivity tensor imaging (MRCTI) reconstructs high-resolution anisotropic conductivity images, which are proved to have critical importance in radio-oncological imaging as well as source localization fields. In the MRCTI technique, linearly independent current injections are applied to the region to be imaged and resulting magnetic flux densities are measured using magnetic resonance imaging techniques. In this study, a novel iterative reconstruction algorithm based on a sensitivity matrix approach is proposed and tested using both simulated and experimental measurements. Obtained results show that the proposed technique can reconstruct anisotropic conductivity images with high and position-independent spatial resolution in addition to decreased number of current injection strategies. [ABSTRACT FROM AUTHOR]

Abstract: Heat‐pulse tracers are a promising field method to measure Darcy flux in the hyporheic zone. Interpretation of data collected from such tests typically assumes knowledge of the direction of local Darcy flux (vertical) and relies on simplified heat transport models with one‐dimensional fluid flow and heat transfer. These assumptions are seldom valid due to complex flow geometry, heterogeneity, and the presence of localized heat sources. We derive a set of analytical expressions that obviate the need for these simplifying assumptions, thus substantially improving the capabilities of existing field instruments without requiring additional measurements. These closed‐form solutions account for tensorial nature of heat‐transfer parameters, and are obtained by using Green's functions and rotational coordinate transformations. The approach simplifies data collection, estimates three‐dimensional Darcy flux, relates fluid flow to heat‐transfer properties of the host medium, and can facilitate inverse modeling. Field applications of our solutions and their ramifications for data collection and analysis are discussed. [ABSTRACT FROM AUTHOR]

A canonical relativistic quantization of the electromagnetic field is introduced in the presence of an anisotropic conductor magneto-dielectric medium in a standard way in the Gupta-Bleuler framework. The medium is modeled by a continuum collection of the vector fields and a continuum collection of the antisymmetric tensor fields of the second rank in Minkowski space-time. The collection of vector fields describes the conductivity property of the medium and the collection of antisymmetric tensor fields describes the polarization and the magnetization properties of the medium. The conservation law of the total electric charges, induced in the anisotropic conductor magneto-dielectric medium, is deduced using the antisymmetry conditions imposed on the coupling tensors that couple the electromagnetic field to the medium. Two relativistic covariant constitutive relations for the anisotropic conductor magneto-dielectric medium are obtained. The constitutive relations relate the antisymmetric electric-magnetic polarization tensor field of the medium and the free electric current density four-vector, induced in the medium, to the strength tensor of the electromagnetic field, separately. It is shown that for a homogeneous anisotropic medium the susceptibility tensor of the medium satisfies the Kramers-Kronig relations. Also it is shown that for a homogeneous anisotropic medium the real and imaginary parts of the conductivity tensor of the medium satisfy the Kramers-Kronig relations and a relation other than the Kramers-Kronig relations. [ABSTRACT FROM AUTHOR]

We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising. [ABSTRACT FROM PUBLISHER]

One of the most cited papers in Applied Mechanics is the work of Eshelby from 1957 who showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in an unbounded (in all directions) homogeneous isotropic host would feel uniform strains and stresses when uniform strains or tractions are applied in the far-field. Of specific importance is the uniformity of Eshelby's tensor $\mathbf{S}$ . Following Eshelby's seminal work, a vast literature has been generated using and developing Eshelby's result and ideas, leading to some beautiful mathematics and extremely useful results in a wide range of application areas. In 1961 Eshelby conjectured that for anisotropic materials only ellipsoidal inhomogeneities would lead to such uniform interior fields. Although much progress has been made since then, the quest to prove this conjecture is still not complete; numerous important problems remain open. Following a different approach to that considered by Eshelby, a closely related tensor $\mathbf{P}=\mathbf{S}\mathbf{D}^{0}$ arises, where $\mathbf{D}^{0}$ is the host medium compliance tensor. The tensor $\mathbf{P}$ is associated with Hill and is of course also uniform when ellipsoidal inhomogeneities are embedded in a homogeneous host phase. Two of the most fundamental and useful areas of applications of these tensors are in Newtonian potential problems such as heat conduction, electrostatics, etc. and in the vector problems of elastostatics. Knowledge of the Hill and Eshelby tensors permit a number of interesting aspects to be studied associated with inhomogeneity problems and more generally for inhomogeneous media. Micromechanical methods established mainly over the last half-century have enabled bounds on and predictions of the effective properties of composite media. In many cases such predictions can be explicitly written down in terms of the Hill tensor, or equivalently the Eshelby tensor and can be shown to provide excellent predictions in many cases. Of specific interest is that a number of important limits of the ellipsoidal inhomogeneity can be taken in order to be employed in predictions of the effective properties of, for example, layered media and fibre reinforced composites and also to the cases when voids and cracks are present. In the main, results for the Hill and Eshelby tensors are distributed over a wide range of articles and books, using different notation and terminology and so it is often difficult to extract the necessary information for the tensor that one requires. The case of an anisotropic host phase is also frequently non-trivial due to the requirement of the associated Green's tensor. Here this classical problem is revisited and a large number of results for problems that are felt to be of great utility in a wide range of disciplines are derived or recalled. A scaling argument leads to the derivation of the Eshelby tensor for potential problems where the host phase is at most orthotropic, without the requirement of using the anisotropic Green's function. The Concentration tensor $\boldsymbol{\mathcal{A}}$ linking interior fields to those imposed in the far-field is derived for a wide variety of problems. These results can therefore be used in the various micromechanical schemes. Directly related to the tensors of Eshelby and Hill is the so-called Moment tensor $\mathbf{M}$ . As well as arising in the literature on micromechanics, this tensor is important in the vast area of research associated with inverse problems and specifically with the problem of identifying an object inside some domain given the application of a specific set of boundary conditions. Due to its fundamental importance and direct link to the Eshelby and Hill tensors, here we state the connection between $\mathbf{M}, \mathbf{P}$ and $\mathbf{S}$ in an effort to ensure that the work is of use to as wide a community as possible. Both tensor and matrix formulations are considered and contrasted throughout. Appendices give various details that illustrate the implementation of both approaches. [ABSTRACT FROM AUTHOR]

Objective: Transcranial direct current stimulation (tDCS) is a neuromodulatory technique for neuropsychiatric diseases and neurological disorders. In the tDCS treatment, dc current is injected into the head through a pair of electrodes attached on the scalp over a target region. A current density imaging method is needed to quantitatively visualize the internal current density distribution during the tDCS treatment. Methods: We developed a novel current density image reconstruction algorithm using 1) a subject specific segmented 3-D head model, 2) diffusion tensor data, and 3) magnetic flux density data induced by the tDCS current. We acquired $T_1$ weighted and diffusion tensor images of the head using the MRI scanner before the treatment. During the treatment, we can measure the induced magnetic flux density data using a magnetic resonance electrical impedance tomography (MREIT) pulse sequence. In this paper, the magnetic flux density data were numerically generated. Results: Numerical simulation results show that the proposed method successfully recovers the current density distribution including the effects of the anisotropic, as well as isotropic conductivity values of different tissues in the head. Conclusion: The proposed current density imaging method using DT-MRI and MREIT can reliably recover cross-sectional images of the current density distribution during the tDCS treatment. Significance: Success of the tDCS treatment depends on a precise determination of the induced current density distribution within different anatomical structures of the brain. Quantitative visualization of the current density distribution in the brain will play an important role in understanding the effects of the electrical stimulation. [ABSTRACT FROM PUBLISHER]

Kubo formula was obtained for conductivity tensor of electron gas on the surface of nanotube with superlattice in magnetic field. The high-frequency conductivity tensor components were calculated for quantum and quasiclassical cases. Electromagnetic wave Landau damping areas in the tube were determined. The conductivity tensor components show Aharonov-Bohm type oscillations and de Haas-van Alphen ones. When Fermi energy exceeds the miniband width, beatings are observed in the plot of conductivity vs. the tube parameters. Otherwise, the beatings are absent. [ABSTRACT FROM AUTHOR]

Magnetic resonance conductivity tensor imaging (MRCTI) is an emerging modality which reconstructs images of anisotropic conductivity distribution within a volume conductor. Images are reconstructed based on magnetic flux density distribution induced by an externally applied probing current, together with a resultant surface potential value. The induced magnetic flux density distribution is measured using magnetic resonance current density imaging techniques. In this study, MRCTI data acquisition is experimentally implemented and anisotropic conductivity images of test phantoms are reconstructed using recently proposed MRCTI reconstruction algorithms. [ABSTRACT FROM AUTHOR]

Abstract: In the framework of kinetic approach we develop a theory for light scattering by ellipsoidal metallic nanoparticles whose dimensions are less than those of a free electron path. In this case, the surface of the particle starts to play a dominant role in electron scattering. When the size of the particle decreases below the free electron path at least in one direction, the optical conductivity becomes a tensor quantity, and the diagonal components of this tensor define the half-widths of the plasmon resonances peaks. Thus, the effect of the particles'' shape both on the frequencies of plasmon resonances and on their half-widths is considered. Additionally, the expression for a cross-section of the light scattering by a collection of chaotically oriented spheroidal nanoparticles is obtained and averaged over different directions of particles in the collection. Our results highlight the plasmonic properties of metallic nanospheroids, notably, the spectrum of the light scattering has two peaks at the frequencies of plasmon resonances even if there is no preferential direction in the collection of particles. [Copyright &y& Elsevier]

Abstract: This paper studies the influence of microfracture orientation, shape and conductivity on the effective electrical properties of carbonate formations. The conductivity model of these formations can be presented as a conductive porous matrix in which the oblate spheroids representing microfractures are embedded. The spheroid aspect ratio varies in the range of 10−2–10−4 that corresponds to crack shapes in carbonates. To simulate the effective conductivity of formations with different aligned fracture systems we have used the approach of non-interacting fractures (dilute inclusion concentration). Based on the comparison of the modeling results for the non-interactive approach and effective medium methods we have demonstrated that the first-order equations can be applied for calculating the conductivity tensor for the fracture porosity up to 0.03. If the fracture conductivity is higher than the matrix one (fractures saturated with water of the same or higher conductivity), the first-order expression is introduced for the effective conductivity tensor. In the case when the inclusion conductivity is lower than the matrix one (fractures filled with oil, gas, or sealed by solid phase), the first-order approximation should be applied to the resistivity tensor to provide the similar calculation accuracy in the required fracture-porosity range. We present the results of the effective conductivity simulation for formations with arbitrary oriented fractures, one system of aligned fractures, one system of fractures with normal distribution of orientations along one direction, and three systems of fractures (conductive and resistive) with non-orthogonal orientations. The modeling results demonstrate the feasibility of assessing the fracture parameters (conductivity, orientation, aspect ratio, and concentration) in carbonate formations using borehole measurements of the conductivity tensor. [Copyright &y& Elsevier]

Abstract: We consider the dynamics of a fluid interface in heterogeneous porous media, whose hydraulic properties are uncertain. Modeling hydraulic conductivity as a random field of given statistics allows us to predict the interface dynamics and to estimate the corresponding predictive uncertainty by means of statistical moments. The novelty of our approach to obtaining the interface statistics consists of dynamically mapping the Cartesian coordinate system onto a coordinate system associated with the moving front. This transforms a difficult problem of deriving closure relationships for highly nonlinear stochastic flows with free surfaces into a relatively simple problem of deriving stochastic closures for linear flows in domains with fixed boundaries. We derive a set of deterministic equations for the statistical moments of the interfacial dynamics, which hold in one and two spatial dimensions, and analyze their solutions for one-dimensional flow. [Copyright &y& Elsevier]

Abstract: Electrical conductivity plays a central role in many areas of space science. However, texts and research articles sometimes misquote the conductivity tensor. This highlights the need for authors and researchers to verify the accuracy of this tensor for their chosen coordinate system. This paper presents a new graphical method to analyze the correctness of the conductivity tensor, applicable to any coordinate system. This method also illuminates the physical meaning of the terms in the conductivity tensor, which is often obscured by standard mathematical derivations. [Copyright &y& Elsevier]

Surface electromyographic (EMG) signal modelling is important for signal interpretation, testing of processing algorithms, detection system design and didactic purposes. Various surface EMG signal models have been proposed in the literature. This study focuses on the proposal of a method for modelling surface EMG signals, using either analytical or numerical descriptions of the volume conductor for space-invariant systems, and on the development of advanced models of the volume conductor by numerical approaches, accurately describing the volume conductor geometry and the conductivity, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function has been derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fibre orientation. In some cases (e.g. multi-pinnate muscles), accurate description of the conductivity tensor can be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibres is presented and applied to investigate representatively a bi-pinnate muscle with rectilinear and curvilinear fibres. The study thus proposes an approach for surface EMG signal simulation in space invariant systems, as well as new models of the volume conductor using numerical methods. [ABSTRACT FROM AUTHOR]

Objective: The goal of this project was to develop a quantitative understanding of the volume of axonal tissue directly activated by deep brain stimulation (DBS) of the subthalamic nucleus (STN).Methods: The 3-dimensionally inhomogeneous and anisotropic tissue medium surrounding DBS electrodes complicates our understanding of the electric field and tissue response generated by the stimulation. We developed finite element computer models to address the effects of DBS in a homogeneous isotropic medium, and a medium with tissue conductivity properties derived from human diffusion tensor magnetic resonance data. The second difference of the potential distribution generated in the tissue medium was used as a predictor of the volume of tissue supra-threshold for axonal activation.Results: The model predicts that clinically effective stimulation parameters (−3 V; 0.1 ms; 150 Hz) result in activation of large diameter (5.7 μm) myelinated axons over a volume that spreads outside the borders of the STN. The shape of the activation volume was dependent on the strong dorsal-ventral anisotropy of the internal capsule, and the moderate anterior-posterior anisotropy of the region around zona incerta.Conclusions: Small deviations (∼1 mm) in the electrode position within STN can substantially alter the shape of the activation volume as well as its spread to neighboring structures.Significance: STN DBS represents an effective treatment for medically refractory movement disorders such as Parkinson''s disease. However, stimulation induced side effects such as tetanic muscle contraction, speech disturbance and ocular deviation are not uncommon. Quantitative characterization of the spread of stimulation will aid in the development of techniques to maximize the efficacy of DBS. [Copyright &y& Elsevier]

Roughness and grain effects in nanowires or oxide-embedded damascene ULSI structures are modelled using a pseudo-Monte Carlo carrier particle optics (CPO) method [MRS Advanced Metallization Conference for ULSI applications (AMC 2001) (2002) 371], matching experimental data on aluminum and platinum films and electrodeposited copper wire. Diffuse scatter from rough and specular scatter from uneven geometric surfaces is considered. Diffusive results accord with Sambles and Elsom [J. Phys. F 11 (1981) 647; J. Phys. F 10 (1980) 1487], matching temperature-dependent resistivities in very thin films more closely than Fuchs and Sondheimer [Proc. Cambridge Phil. Soc. 34 (1938) 100; Adv. Phys. 1 (1952) 1]. Grain profile effects improve the model of resistance increase in embedded structures, suggesting directions for improving conduction through enlarged grain cross-section. [Copyright &y& Elsevier]