MARIE 2.0: A Perturbation Matrix Based Patient-Specific MRI Field Simulator.

High static field MR scanners can produce human tissue images of astounding clarity, but rely on high frequency electromagnetic radiation that generates complicated in-tissue field patterns that are patient-specific and potentially harmful. Many such scanners use parallel transmitters to better control field patterns, but then adjust the transmitters based on general guidelines rather than optimizing for the specific patient, mostly because computing patient-specific fields was presumed far too slow. It was recently demonstrated that the combination of fast low-resolution tissue mapping and fast voxel-based field simulation can be used to perform a patient-specific MR safety check in minutes. However, the field simulation required several of those minutes, making it too slow to perform the dozens of simulations that would be needed for patient-specific optimization. In this paper we describe a compressed-perturbation-matrix technique that nearly eliminates the computational cost of including complex coils (or coils and shields) in voxel-based field simulation of tissue, thereby reducing simulation time from minutes to seconds. The approach is demonstrated on a wide variety of head+coil and head+coil+shield configurations, using the implementation in MARIE 2.0, the latest version of the open-source MR field simulator MARIE.

A Hybrid Volume-Surface Integral Equation Method for Rapid Electromagnetic Simulations in MRI.

OBJECTIVE: We developed a hybrid volume surface integral equation (VSIE) method based on domain decomposition to perform fast and accurate magnetic resonance imaging (MRI) simulations that include both remote and local conductive elements. METHODS: We separated the conductive surfaces present in MRI setups into two domains and optimized electromagnetic (EM) modeling for each case. Specifically, interactions between the body and EM waves originating from local radiofrequency (RF) coils were modeled with the precorrected fast Fourier transform, whereas the interactions with remote conductive surfaces (RF shield, scanner bore) were modeled with a novel cross tensor train-based algorithm. We compared the hybrid-VSIE with other VSIE methods for realistic MRI simulation setups. RESULTS: The hybrid-VSIE was the only practical method for simulation using 1 mm voxel isotropic resolution (VIR). For 2 mm VIR, our method could be solved at least 23 times faster and required 760 times lower memory than traditional VSIE methods. CONCLUSION: The hybrid-VSIE demonstrated a marked improvement in terms of convergence times of the numerical EM simulation compared to traditional approaches in multiple realistic MRI scenarios. SIGNIFICANCE: The efficiency of the novel hybrid-VSIE method could enable rapid simulations of complex and comprehensive MRI setups.

Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications.

In this work, we propose a method for the compression of the coupling matrix in volume-surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic analysis in magnetic resonance imaging (MRI) applications, for which the coupling matrix models the interactions between the coil and the body. We showed that these effects can be represented as independent interactions between remote elements in 3D tensor formats, and subsequently decomposed with the Tucker model. Our method can work in tandem with the adaptive cross approximation technique to provide fast solutions of VSIE problems. We demonstrated that our compression approaches can enable the use of VSIE matrices of prohibitive memory requirements, by allowing the effective use of modern graphical processing units (GPUs) to accelerate the arising matrix-vector products. This is critical to enable numerical MRI simulations at clinical voxel resolutions in a feasible computation time. In this paper, we demonstrate that the VSIE matrix-vector products needed to calculate the electromagnetic field produced by an MRI coil inside a numerical body model with 1 mm3 voxel resolution, could be performed in ~ 33 seconds in a GPU, after compressing the associated coupling matrix from ~ 80 TB to ~ 43 MB.

A 31-channel integrated "AC/DC" B0 shim and radiofrequency receive array coil for improved 7T MRI.

PURPOSE: To test an integrated "AC/DC" array approach at 7T, where B0 inhomogeneity poses an obstacle for functional imaging, diffusion-weighted MRI, MR spectroscopy, and other applications. METHODS: A close-fitting 7T 31-channel (31-ch) brain array was constructed and tested using combined Rx and ΔB0 shim channels driven by a set of rapidly switchable current amplifiers. The coil was compared to a shape-matched 31-ch reference receive-only array for RF safety, signal-to-noise ratio (SNR), and inter-element noise correlation. We characterize the coil array's ability to provide global and dynamic (slice-optimized) shimming using ΔB0 field maps and echo planar imaging (EPI) acquisitions. RESULTS: The SNR and average noise correlation were similar to the 31-ch reference array. Global and slice-optimized shimming provide 11% and 40% improvements respectively compared to baseline second-order spherical harmonic shimming. Birdcage transmit coil efficiency was similar for the reference and AC/DC array setups. CONCLUSION: Adding ΔB0 shim capability to a 31-ch 7T receive array can significantly boost 7T brain B0 homogeneity without sacrificing the array's rdiofrequency performance, potentially improving ultra-high field neuroimaging applications that are vulnerable to off-resonance effects.

Individualized SAR calculations using computer vision-based MR segmentation and a fast electromagnetic solver.

PURPOSE: We propose a fast, patient-specific workflow for on-line specific absorption rate (SAR) supervision. An individualized electromagnetic model is created while the subject is on the table, followed by rapid SAR estimates for that individual. Our goal is an improved correspondence between the patient and model, reducing reliance on general anatomical body models. METHODS: A 3D fat-water 3T acquisition (~2 minutes) is automatically segmented using a computer vision algorithm (~1 minute) into what we found to be the most important electromagnetic tissue classes: air, bone, fat, and soft tissues. We then compute the individual's EM field exposure and global and local SAR matrices using a fast electromagnetic integral equation solver. We assess the approach in 10 volunteers and compare to the SAR seen in a standard generic body model (Duke). RESULTS: The on-the-table workflow averaged 7'44″. Simulation of the simplified Duke models confirmed that only air, bone, fat, and soft tissue classes are needed to estimate global and local SAR with an error of 6.7% and 2.7%, respectively, compared to the full model. In contrast, our volunteers showed a 16.0% and 20.3% population variability in global and local SAR, respectively, which was mostly underestimated by the Duke model. CONCLUSION: Timely construction and deployment of a patient-specific model is computationally feasible. The benefit of resolving the population heterogeneity compared favorably to the modest modeling error incurred. This suggests that individualized SAR estimates can improve electromagnetic safety in MRI and possibly reduce conservative safety margins that account for patient-model mismatch, especially in non-standard patients.

Magnetic-Resonance-Based Electrical Property Mapping Using Global Maxwell Tomography With an 8-Channel Head Coil at 7 Tesla: A Simulation Study.

OBJECTIVE: Global Maxwell Tomography (GMT) is a recently introduced volumetric technique for noninvasive estimation of electrical properties (EP) from magnetic resonance measurements. Previous work evaluated GMT using ideal radiofrequency (RF) excitations. The aim of this simulation study was to assess GMT performance with a realistic RF coil. METHODS: We designed a transmit-receive RF coil with 8 decoupled channels for 7T head imaging. We calculated the RF transmit field ( B1+) inside heterogeneous head models for different RF shimming approaches, and used them as input for GMT to reconstruct EP for all voxels. RESULTS: Coil tuning/decoupling remained relatively stable when the coil was loaded with different head models. Mean error in EP estimation changed from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] for relative permittivity and conductivity, respectively, when changing head model without re-tuning the coil. Results slightly improved when an SVD-based RF shimming algorithm was applied, in place of excitation with one coil at a time. Despite errors in EP, RF transmit field ( B1+) and absorbed power could be predicted with less than [Formula: see text] error over the entire head. GMT could accurately detect a numerically inserted tumor. CONCLUSION: This work demonstrates that GMT can reliably reconstruct EP in realistic simulated scenarios using a tailored 8-channel RF coil design at 7T. Future work will focus on construction of the coil and optimization of GMT's robustness to noise, to enable in-vivo GMT experiments. SIGNIFICANCE: GMT could provide accurate estimations of tissue EP, which could be used as biomarkers and could enable patient-specific estimation of RF power deposition, which is an unsolved problem for ultra-high-field magnetic resonance imaging.

Noninvasive Estimation of Electrical Properties From Magnetic Resonance Measurements via Global Maxwell Tomography and Match Regularization.

OBJECTIVE: In this paper, we introduce global Maxwell tomography (GMT), a novel volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements. METHODS: GMT relies on a fast volume integral equation solver, MARIE, for the forward path, and a novel regularization method, match regularization, designed specifically for electrical property estimation from noisy measurements. We performed simulations with three different tissue-mimicking numerical phantoms of different complexity, using synthetic transmit sensitivity maps with realistic noise levels as the measurements. We performed an experiment at 7 T using an eight-channel coil and a uniform phantom. RESULTS: We showed that GMT could estimate relative permittivity and conductivity from noisy magnetic resonance measurements with an average error as low as 0.3% and 0.2%, respectively, over the entire volume of the numerical phantom. Voxel resolution did not affect GMT performance and is currently limited only by the memory of the graphics processing unit. In the experiment, GMT could estimate electrical properties within 5% of the values measured with a dielectric probe. CONCLUSION: This work demonstrated the feasibility of GMT with match regularization, suggesting that it could be effective for accurate in vivo electrical property estimation. GMT does not rely on any symmetry assumption for the electromagnetic field, and can be generalized to estimate also the spin magnetization, at the expense of increased computational complexity. SIGNIFICANCE: GMT could provide insight into the distribution of electromagnetic fields inside the body, which represents one of the key ongoing challenges for various diagnostic and therapeutic applications.

Design and implementation of a low-cost, tabletop MRI scanner for education and research prototyping.

While access to a laboratory MRI system is ideal for teaching MR physics as well as many aspects of signal processing, providing multiple MRI scanners can be prohibitively expensive for educational settings. To address this need, we developed a small, low-cost, open-interface tabletop MRI scanner for academic use. We constructed and tested 20 of these scanners for parallel use by teams of 2-3 students in a teaching laboratory. With simplification and down-scaling to a 1 cm FOV, fully-functional scanners were achieved within a budget of $10,000 USD each. The design was successful for teaching MR principles and basic signal processing skills and serves as an accessible testbed for more advanced MR research projects. Customizable GUIs, pulse sequences, and reconstruction code accessible to the students facilitated tailoring the scanner to the needs of laboratory exercise. The scanners have been used by >800 students in 6 different courses and all designs, schematics, sequences, GUIs, and reconstruction code is open-source.

Circulant preconditioning in the volume integral equation method for silicon photonics.

Recently, the volume integral equation (VIE) approach has been proposed as an efficient simulation tool for silicon photonics applications [J. Lightw. Technol.36, 3765 (2018)JLTEDG0733-872410.1109/JLT.2018.2842054]. However, for the high-frequency and strong-contrast problems arising in photonics, the convergence of iterative solvers for the solution of the linear system can be extremely slow. The uniform discretization of the volume integral operator leads to a three-level Toeplitz matrix, which is well suited to preconditioning via its circulant approximation. In this paper, we describe an effective circulant preconditioning strategy based on the multilevel circulant preconditioner of Chan and Olkin [Numer. Algorithms6, 89 (1994)NUALEG1017-139810.1007/BF02149764]. We show that this approach proves ideal in the canonical photonics problem of propagation within a uniform waveguide, in which the flow is unidirectional. For more complex photonics structures, such as Bragg gratings, directional couplers, and disk resonators, we generalize our preconditioning strategy via geometrical partitioning (leading to a block-diagonal circulant preconditioner) and homogenization (for inhomogeneous structures). Finally, we introduce a novel memory reduction technique enabling the preconditioner's memory footprint to remain manageable, even for extremely long structures. The range of numerical results we present demonstrates that the preconditioned VIE is fast and has great utility for the numerical exploration of prototype photonics devices.

Computation of ultimate SAR amplification factors for radiofrequency hyperthermia in non-uniform body models: impact of frequency and tumour location.

PURPOSE: We introduce a method for calculation of the ultimate specific absorption rate (SAR) amplification factors (uSAF) in non-uniform body models. The uSAF is the greatest possible SAF achievable by any hyperthermia (HT) phased array for a given frequency, body model and target heating volume. METHODS: First, we generate a basis-set of solutions to Maxwell's equations inside the body model. We place a large number of electric and magnetic dipoles around the body model and excite them with random amplitudes and phases. We then compute the electric fields created in the body model by these excitations using an ultra-fast volume integral solver called MARIE. We express the field pattern that maximises the SAF in the target tumour as a linear combination of these basis fields and optimise the combination weights so as to maximise SAF (concave problem). We compute the uSAFs in the Duke body models at 10 frequencies in the 20-900 MHz range and for twelve 3 cm-diameter tumours located at various depths in the head and neck. RESULTS: For both shallow and deep tumours, the frequency yielding the greatest uSAF was ∼900 MHz. Since this is the greatest frequency that we simulated, we hypothesise that the globally optimal frequency is actually greater. CONCLUSIONS: The uSAFs computed in this work are very large (40-100 for shallow tumours and 4-17 for deep tumours), indicating that there is a large room for improvement of the current state-of-the-art head and neck HT devices.

The ultimate signal-to-noise ratio in realistic body models.

PURPOSE: We compute the ultimate signal-to-noise ratio (uSNR) and G-factor (uGF) in a realistic head model from 0.5 to 21 Tesla. METHODS: We excite the head model and a uniform sphere with a large number of electric and magnetic dipoles placed at 3 cm from the object. The resulting electromagnetic fields are computed using an ultrafast volume integral solver, which are used as basis functions for the uSNR and uGF computations. RESULTS: Our generalized uSNR calculation shows good convergence in the sphere and the head and is in close agreement with the dyadic Green's function approach in the uniform sphere. In both models, the uSNR versus B0 trend was linear at shallow depths and supralinear at deeper locations. At equivalent positions, the rate of increase of the uSNR with B0 was greater in the sphere than in the head model. The uGFs were lower in the realistic head than in the sphere for acceleration in the anterior-posterior direction, but similar for the left-right direction. CONCLUSION: The uSNR and uGFs are computable in nonuniform body models and provide fundamental performance limits for human imaging with close-fitting MRI array coils. Magn Reson Med 78:1969-1980, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Computational analysis reveals the coupling between bistability and the sign of a feedback loop in a TGF-ß1 activation model.

BACKGROUND: Bistable behaviors are prevalent in cell signaling and can be modeled by ordinary differential equations (ODEs) with kinetic parameters. A bistable switch has recently been found to regulate the activation of transforming growth factor-ß1 (TGF-ß1) in the context of liver fibrosis, and an ordinary differential equation (ODE) model was published showing that the net activation of TGF-ß1 depends on the balance between two antagonistic sub-pathways. RESULTS: Through modeling the effects of perturbations that affect both sub-pathways, we revealed that bistability is coupled with the signs of feedback loops in the model. We extended the model to include calcium and Krüppel-like factor 2 (KLF2), both regulators of Thrombospondin-1 (TSP1) and Plasmin (PLS). Increased levels of extracellular calcium, which alters the TSP1-PLS balance, would cause high levels of TGF-ß1, resembling a fibrotic state. KLF2, which suppresses production of TSP1 and plasminogen activator inhibitor-1 (PAI1), would eradicate bistability and preclude the fibrotic steady-state. Finally, the loop PLS - TGF-ß1 - PAI1 had previously been reported as negative feedback, but the model suggested a stronger indirect effect of PLS down-regulating PAI1 to produce positive (double-negative) feedback in a fibrotic state. Further simulations showed that activation of KLF2 was able to restore negative feedback in the PLS - TGF-ß1 - PAI1 loop. CONCLUSIONS: Using the TGF-ß1 activation model as a case study, we showed that external factors such as calcium or KLF2 can induce or eradicate bistability, accompanied by a switch in the sign of a feedback loop (PLS - TGF-ß1 - PAI1) in the model. The coupling between bistability and positive/negative feedback suggests an alternative way of characterizing a dynamical system and its biological implications.

Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes.

The rate of electric-field-driven transport across ion-selective membranes can exceed the limit predicted by Nernst (the limiting current), and encouraging this "overlimiting" phenomenon can improve efficiency in many electrochemical systems. Overlimiting behavior is the result of electroconvectively induced vortex formation near membrane surfaces, a conclusion supported so far by two-dimensional (2D) theory and numerical simulation, as well as experiments. In this paper we show that the third dimension plays a critical role in overlimiting behavior. In particular, the vortex pattern in shear flow through wider channels is helical rather than planar, a surprising result first observed in three-dimensional (3D) simulation and then verified experimentally. We present a complete experimental and numerical characterization of a device exhibiting this recently discovered 3D electrokinetic instability, and show that the number of parallel helical vortices is a jump-discontinuous function of width, as is the overlimiting current and overlimiting conductance. In addition, we show that overlimiting occurs at lower fields in wider channels, because the associated helical vortices are more readily triggered than the planar vortices associated with narrow channels (effective 2D systems). These unexpected width dependencies arise in realistic electrochemical desalination systems, and have important ramifications for design optimization.

Fast Electromagnetic Analysis of MRI Transmit RF Coils Based on Accelerated Integral Equation Methods.

A fast frequency domain full-wave electromagnetic simulation method is introduced for the analysis of MRI coils loaded with the realistic human body models. The approach is based on integral equation methods decomposed into two domains: 1) the RF coil array and shield, and 2) the human body region where the load is placed. The analysis of multiple coil designs is accelerated by introducing the precomputed magnetic resonance Green functions (MRGFs), which describe how the particular body model used responds to the incident fields from external sources. These MRGFs, which are precomputed once for a given body model, can be combined with any integral equation solver and reused for the analysis of many coil designs. This approach provides a fast, yet comprehensive, analysis of coil designs, including the port S-parameters and the electromagnetic field distribution within the inhomogeneous body. The method solves the full-wave electromagnetic problem for a head array in few minutes, achieving a speed up of over 150 folds with root mean square errors in the electromagnetic field maps smaller than 0.4% when compared to the unaccelerated integral equation-based solver. This enables the characterization of a large number of RF coil designs in a reasonable time, which is a first step toward an automatic optimization of multiple parameters in the design of transmit arrays, as illustrated in this paper, but also receive arrays.

Non-canonical Activation of Akt in Serum-Stimulated Fibroblasts, Revealed by Comparative Modeling of Pathway Dynamics.

The dynamic behaviors of signaling pathways can provide clues to pathway mechanisms. In cancer cells, excessive phosphorylation and activation of the Akt pathway is responsible for cell survival advantages. In normal cells, serum stimulation causes brief peaks of extremely high Akt phosphorylation before reaching a moderate steady-state. Previous modeling assumed this peak and decline behavior (i.e., "overshoot") was due to receptor internalization. In this work, we modeled the dynamics of the overshoot as a tool for gaining insight into Akt pathway function. We built an ordinary differential equation (ODE) model describing pathway activation immediately upstream of Akt phosphorylation at Thr308 (Aktp308). The model was fit to experimental measurements of Aktp308, total Akt, and phosphatidylinositol (3,4,5)-trisphosphate (PIP3), from mouse embryonic fibroblasts with serum stimulation. The canonical Akt activation model (the null hypothesis) was unable to recapitulate the observed delay between the peak of PIP3 (at 2 minutes), and the peak of Aktp308 (at 30-60 minutes). From this we conclude that the peak and decline behavior of Aktp308 is not caused by PIP3 dynamics. Models for alternative hypotheses were constructed by allowing an arbitrary dynamic curve to perturb each of 5 steps of the pathway. All 5 of the alternative models could reproduce the observed delay. To distinguish among the alternatives, simulations suggested which species and timepoints would show strong differences. Time-series experiments with membrane fractionation and PI3K inhibition were performed, and incompatible hypotheses were excluded. We conclude that the peak and decline behavior of Aktp308 is caused by a non-canonical effect that retains Akt at the membrane, and not by receptor internalization. Furthermore, we provide a novel spline-based method for simulating the network implications of an unknown effect, and we demonstrate a process of hypothesis management for guiding efficient experiments.

The self-limiting dynamics of TGF-ß signaling in silico and in vitro, with negative feedback through PPM1A upregulation.

The TGF-ß/Smad signaling system decreases its activity through strong negative regulation. Several molecular mechanisms of negative regulation have been published, but the relative impact of each mechanism on the overall system is unknown. In this work, we used computational and experimental methods to assess multiple negative regulatory effects on Smad signaling in HaCaT cells. Previously reported negative regulatory effects were classified by time-scale: degradation of phosphorylated R-Smad and I-Smad-induced receptor degradation were slow-mode effects, and dephosphorylation of R-Smad was a fast-mode effect. We modeled combinations of these effects, but found no combination capable of explaining the observed dynamics of TGF-ß/Smad signaling. We then proposed a negative feedback loop with upregulation of the phosphatase PPM1A. The resulting model was able to explain the dynamics of Smad signaling, under both short and long exposures to TGF-ß. Consistent with this model, immuno-blots showed PPM1A levels to be significantly increased within 30 min after TGF-ß stimulation. Lastly, our model was able to resolve an apparent contradiction in the published literature, concerning the dynamics of phosphorylated R-Smad degradation. We conclude that the dynamics of Smad negative regulation cannot be explained by the negative regulatory effects that had previously been modeled, and we provide evidence for a new negative feedback loop through PPM1A upregulation. This work shows that tight coupling of computational and experiments approaches can yield improved understanding of complex pathways.

SPEDRE: a web server for estimating rate parameters for cell signaling dynamics in data-rich environments.

Cell signaling pathways and metabolic networks are often modeled using ordinary differential equations (ODEs) to represent the production/consumption of molecular species over time. Regardless whether a model is built de novo or adapted from previous models, there is a need to estimate kinetic rate constants based on time-series experimental measurements of molecular abundance. For data-rich cases such as proteomic measurements of all species, spline-based parameter estimation algorithms have been developed to avoid solving all the ODEs explicitly. We report the development of a web server for a spline-based method. Systematic Parameter Estimation for Data-Rich Environments (SPEDRE) estimates reaction rates for biochemical networks. As input, it takes the connectivity of the network and the concentrations of the molecular species at discrete time points. SPEDRE is intended for large sparse networks, such as signaling cascades with many proteins but few reactions per protein. If data are available for all species in the network, it provides global coverage of the parameter space, at low resolution and with approximate accuracy. The output is an optimized value for each reaction rate parameter, accompanied by a range and bin plot. SPEDRE uses tools from COPASI for pre-processing and post-processing. SPEDRE is a free service at http://LTKLab.org/SPEDRE.

Systematic parameter estimation in data-rich environments for cell signalling dynamics.

MOTIVATION: Computational models of biological signalling networks, based on ordinary differential equations (ODEs), have generated many insights into cellular dynamics, but the model-building process typically requires estimating rate parameters based on experimentally observed concentrations. New proteomic methods can measure concentrations for all molecular species in a pathway; this creates a new opportunity to decompose the optimization of rate parameters. RESULTS: In contrast with conventional parameter estimation methods that minimize the disagreement between simulated and observed concentrations, the SPEDRE method fits spline curves through observed concentration points, estimates derivatives and then matches the derivatives to the production and consumption of each species. This reformulation of the problem permits an extreme decomposition of the high-dimensional optimization into a product of low-dimensional factors, each factor enforcing the equality of one ODE at one time slice. Coarsely discretized solutions to the factors can be computed systematically. Then the discrete solutions are combined using loopy belief propagation, and refined using local optimization. SPEDRE has unique asymptotic behaviour with runtime polynomial in the number of molecules and timepoints, but exponential in the degree of the biochemical network. SPEDRE performance is comparatively evaluated on a novel model of Akt activation dynamics including redox-mediated inactivation of PTEN (phosphatase and tensin homologue). AVAILABILITY AND IMPLEMENTATION: Web service, software and supplementary information are available at www.LtkLab.org/SPEDRE SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Optimizing electrode configuration for electrical impedance measurements of muscle via the finite element method.

Electrical impedance myography (EIM) is a technique for the evaluation of neuromuscular diseases, including amyotrophic lateral sclerosis and muscular dystrophy. In this study, we evaluated how alterations in the size and conductivity of muscle and thickness of subcutaneous fat impact the EIM data, with the aim of identifying an optimized electrode configuration for EIM measurements. Finite element models were developed for the human upper arm based on anatomic data; material properties of the tissues were obtained from rat and published sources. The developed model matched the frequency-dependent character of the data. Of the three major EIM parameters, resistance, reactance, and phase, the reactance was least susceptible to alterations in the subcutaneous fat thickness, regardless of electrode arrangement. For example, a quadrupling of fat thickness resulted in a 375% increase in resistance at 35 kHz but only a 29% reduction in reactance. By further optimizing the electrode configuration, the change in reactance could be reduced to just 0.25%. For a fixed 30 mm distance between the sense electrodes centered between the excitation electrodes, an 80 mm distance between the excitation electrodes was found to provide the best balance, with a less than 1% change in reactance despite a doubling of subcutaneous fat thickness or halving of muscle size. These analyses describe a basic approach for further electrode configuration optimization for EIM.