Corefield Biophysics

Services

Six studies, each with a stated deliverable

We run every study in-house with our own solver, EMVIE. You receive the results, a report and the inputs behind each number.

Trunk with skeleton and an implant lead route drawn as a tube coloured by the tangential incident electric field along it

BodyParts3D, CC BY 4.0

ISO/TS 10974 · Tier 3

MRI RF safety of active implants

Tip heating of your lead for each route and body position, at 1.5 T and 3 T.

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We compute the transfer function of your lead and the incident fields along clinical lead routes in the body, at 1.5 T and 3 T. Together they give the tip heating for each route and body position.

Also offered: local-SAR safety margins for 7 T parallel-transmit head arrays, with Q-matrices and virtual observation points.

You receive: Lead transfer function, incident-field library, tip SAR and temperature rise per route, and the validity limits of the lead model
Standard: ISO/TS 10974, Tier 3
Turnaround: On request

Close-up of a half-wave dipole above layered tissue, its feed line dropping to the averaging cube marked at the surface

IEC/IEEE 62704-1 · 62209-1528

SAR and psSAR near the body

Peak spatial-average SAR over 1 g and 10 g for devices used against the head or body.

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Peak spatial-average SAR over 1 g and 10 g for devices used against the head or body. Before we model your device, we check the set-up on the standard validation dipoles, as a SAR laboratory does in its system check.

You receive: psSAR over 1 g and 10 g per configuration, SAR maps, a grid convergence check and the consensus-dipole check in the same report
Standard: IEC/IEEE 62704-1; system check against the IEC/IEEE 62209-1528 targets
Turnaround: On request

Four by four dipole array above a cut-away block of skin, fat and muscle, with two square averaging areas marked on the skin

IEC/IEEE 63195 · ICNIRP 2020

Power density above 6 GHz

Absorbed power density over 1 cm² and 4 cm² and the skin temperature rise for 5G and millimetre-wave devices.

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Absorbed power density over 1 cm² and 4 cm² and the skin temperature rise for 5G and millimetre-wave devices. We state how much the result changes with the skin model and the averaging definition.

Pictured: a 4 × 4 dipole array at 30 GHz over skin, fat and muscle, with the 1 cm² and 4 cm² averaging areas on the skin.

You receive: Peak absorbed power density over 1 cm² and 4 cm², maps on the skin, the temperature rise and its spread over skin models
Standard: IEC/IEEE 63195; limits of ICNIRP 2020 and IEEE C95.1-2019
Turnaround: On request

Human body between the two loops of an MRI gradient coil, coloured from dark purple to orange by the induced electric field

BodyParts3D, CC BY 4.0

Directive 2013/35/EU · ICNIRP 2010

Low-frequency exposure at work

Electric fields induced in the body by coils and other low-frequency sources, including MRI gradients.

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Electric fields induced in the body by coils and other low-frequency sources, including MRI gradients. For pulsed and non-sinusoidal waveforms we apply the weighted peak method, in the frequency domain and in the time domain.

Pictured: a body between the loops of a gradient coil; the solver computes the induced field in nerves and muscle.

You receive: Exposure index per tissue against the exposure limit values, the 99th percentile over 2 mm cubes, and the weighting filter used, stated with each result
Standard: Directive 2013/35/EU, Annex II; ICNIRP 2010
Turnaround: On request

TI · tES · TMS

Neurostimulation field planning

Electric fields in the brain for temporal-interference, transcranial current and magnetic stimulation.

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Electric fields in the brain for temporal-interference, transcranial current and magnetic stimulation. We compare electrode montages and currents for your target. We also show how much the target field depends on each tissue's conductivity.

You receive: Field maps in the target and outside it, a montage and current proposal, and the sensitivity of the target field to each tissue
Standard: No product standard applies; methods and uncertainty are reported in full
Turnaround: On request

Any of the standards above

Independent second opinion

We rebuild the key cases of another team's study with our own solver and explain every difference.

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You send us a simulation report or the simulation files from another team or tool. We rebuild the key cases with our own solver and explain every difference we find.

You receive: A written review, an independent recomputation of the key numbers, and the issues ranked by their effect on the result
Standard: The standard the original study follows
Turnaround: On request

We offer fixed-price studies, ongoing support during development, and independent reviews. Turnaround depends on the model and the number of cases, so we state it in each proposal.

Capabilities

One verified engine, from quasi-static to millimetre wave

We wrote the solvers we use, and we run them only in-house, for our clients' studies. Every change runs through an automated test suite, and results are bit-identical for any number of CPU threads.

Low frequencyTMS · tES · TI · gradients

MRI RF1.5 T · 3 T · 7 T

SAR835 to 3000 MHz dipoles

Power densityabove 6 GHz

Volume integral equationFinite-difference time domainTransmit arrays and coilsLeads and transfer functionsQuasi-static fieldsBioheat and damageTwo averaging rules from one solveWeighted peak methodAdjoint sensitivitiesCell-scale stimulationHierarchical matrices (H-LU)Head-to-cell coupling

Read more: what each capability coversHide the details

RF

Volume integral equation

GPU-accelerated, octree meshes, and a dispersion correction that removes the bulk part of the grid error at gigahertz frequencies.

RF

Finite-difference time domain

GPU solver with dispersive tissues, thin wires, lumped ports and absorbed power density readouts.

MRI

Transmit arrays and coils

Ported dipole arrays, matching networks, RF shields, birdcages, Q-matrices and virtual observation points.

Implants

Leads and transfer functions

Insulated leads in tissue, reciprocity transfer functions and stored incident-field libraries for Tier 3.

Low frequency

Quasi-static fields

Multigrid electro- and magneto-quasi-static solvers, contact electrodes, anisotropic tissue and field-dependent conductivity.

Thermal

Bioheat and damage

Pennes bioheat with perfusion, pulse trains, blood cooling, vaporisation and Arrhenius tissue damage.

SAR

Two averaging rules from one solve

Cube-averaged SAR over 1 g and 10 g under the IEC/IEEE 62704-1 rule, which allows up to 10 % air in a cube, and under a stricter rule with no air, from the same field.

New · Low frequency

Weighted peak method

Exposure index for pulsed and non-sinusoidal fields against the ICNIRP 2010 limits and the exposure limit values of Directive 2013/35/EU, in the frequency and the time domain.

New · Neurostimulation

Adjoint sensitivities

The gradient of a target-field objective with respect to every tissue conductivity and every electrode current, for about the cost of two field solves. It covers single-pair and temporal-interference stimulation.

New · Cells

Cell-scale stimulation

The membrane response of neurons and other cells in stimulation fields, with the cell, the surrounding fluid and the electrodes coupled in one bidomain boundary-element model. Verified at second order against exact solutions; it reproduces the published bidomain BEM cases. In final testing. More

New · Fast algorithms

Hierarchical matrices (H-LU)

Compressed boundary-element matrices: low-rank far-field blocks by adaptive cross approximation and a factorization in compressed form. 320 000 unknowns factor in 16.7 GB, where the dense matrix would take 819 GB. More

New · Cells

Head-to-cell coupling

The cell model takes its incident field from our own head solution, for example under a TMS coil, instead of a uniform field.

New in the solver · cell scale

Cell-scale stimulation with a bidomain boundary-element solver

How the membrane of a neuron responds to TMS, deep-brain, temporal-interference and electrode fields. The cell, the fluid around it and the electrodes are solved together, so the cell changes the field and the field changes the membrane voltage. The method builds on the bidomain BEM of Czerwonky, Aberra and Gomez (J. Neural Eng., 2024) and Hasan et al. (IEEE J-ERM, 2026). We reproduce their published cases and extend the method in the five ways below.

Three plots comparing bidomain BEM and cable-model thresholds of Hodgkin-Huxley axons. (a) Ratio of BEM to cable threshold for 8-gon and 16-gon cross-sections, approaching the cable line as the polygon is refined. (b) Threshold gap for a straight axon, a bend, Y and T branch points and a soma, falling to zero within the error bars as the mesh is refined. (c) Cable threshold above the BEM threshold by up to about 5.6 percent for a point electrode within 5 to 20 fibre radii, and near zero for the corrected cable. — **When is the classic cable model right?** (a) On a straight axon, the gap between BEM and cable thresholds comes from the polygonal cross-section of the mesh and closes as the polygon is refined. (b) Bends, branch points and the soma agree with the cable within the numerical uncertainty. (c) Near a point electrode the cable model overestimates the threshold, by up to 5.6 % within 5 to 20 fibre radii; our corrected cable (open markers) reproduces the full model to 0.23 % or better down to five radii.

What our solver adds to the published bidomain BEM

Each item is a result of our own runs. The methods paper is in preparation.

Reproduced first

The published cases

The synthetic axon cases of Hasan et al. (two axons and a multi-axon block) are reproduced on meshes of the same size. One result differs: we find no rise of the threshold with packing density in their Fig. 15. Exact solutions for a sphere, a cylinder, a cell with a nucleus and a prolate spheroid converge at second order, and an independent finite-volume solution agrees to 0.005 % or better.

Speed and memory

H-matrix algebra for large cells

Blocks between distant parts of the cell are stored in compressed form. A cell model with 159 058 nodes runs in 12.0 GB of matrices, where a dense solver would need 0.8 TB. Details below.

Robustness

A charge constraint

A closed membrane carries no net charge. The solver enforces this exactly, with one extra row per membrane. That removes the one poorly conditioned mode of the system at low membrane conductance, and leaves the thresholds unchanged.

Realistic neurons

A reconstructed layer 2/3 pyramidal cell

Meshed with 18 635 to 74 659 nodes and compared with a NEURON cable model of the same tree, both with the Hodgkin-Huxley membrane. The 2 to 3.5 % gap reported in the literature appears only on the coarse mesh. Once the mesh converges, the BEM threshold lies 0.7 to 0.8 % below the cable for a field along the apical axis and for a point source, and 2.7 % below it for a transverse field.

In review

Blue Brain ion channels in the membrane

The cell's own channel set (11 channels and the calcium pool of the L2/3 cell) now runs inside the BEM membrane. On a membrane patch, the spike times match NEURON 9.0.2 to within 0.07 to 8.5 µs over five spikes in 40 ms.

Multiscale

Coupling to head models

The cell can take its field from our own head solution instead of a uniform field. In a first test with a figure-8 TMS coil, the local head field changed the threshold of an axon by 0.7 to 8.5 %, with either sign, at six cortical sites.

Two plots. (a) Peak membrane polarization of a passive axon against the gap to a firing neighbour, for the 642-node mesh and a resolved mesh, with the published value as a star near the 642-node curve. (b) Threshold change of the central axon against the volume fill factor for 3 by 3 and 5 by 5 blocks, flat at zero, with the published 13 percent rise as a star. — **Reproducing Hasan et al.** (a) Polarization of a passive axon by a firing neighbour against the gap between them, on their 642-node mesh and on a resolved mesh. (b) Threshold of the central axon of a block against the fill factor. Stars: values read from Hasan et al., IEEE J-ERM 2026.

Two log-log plots of the relative error of the membrane voltage against the mean edge length for a sphere, a cylinder, a cell with a nucleus and a prolate spheroid; all lines follow slope 2, in the steady state and at one time constant. — **Verification against exact solutions.** The error of the membrane voltage falls with the square of the triangle size for every cell shape. (a) Steady state. (b) At one membrane time constant.

Learn how a cell membrane responds to a field Ask about a cell-scale study

New in the solver · fast algorithms

Hierarchical-matrix (H-matrix) acceleration

In a boundary-element model every surface node interacts with every other, so the matrix is dense: memory grows with the square of the node count. Interactions between groups of nodes that are far apart compared with their size are smooth, and a few terms describe them. An H-matrix stores those blocks in this compressed, low-rank form, built by adaptive cross approximation, and keeps only the near field in full. The whole matrix is then factored in compressed form (H-LU).

The block partition. Nodes are sorted into a tree of nearby groups. Blocks between neighbouring groups stay dense; blocks between distant groups are stored as a thin column times a thin row. Schematic, drawn for this site.

16.7GB

320 000 unknowns factored in 2.0 h. The dense matrix alone would take 819 GB.

30–58

Largest block rank after the factorization, bounded from 5 000 to 320 000 unknowns. A HODLR matrix, the format of the earlier cell solver, reaches rank 1 848 at 20 000 unknowns on the same points.

1.04–1.17×

Peak memory of the factorization over its data, because every update is written into existing blocks. The published recursive HODLR setup peaked at about 200 times its compressed matrices: 332.78 GB for 1.66 GB, eight neurons.

2 × 10⁻⁹

Largest difference from the dense solution, relative to the amplitude, on the exact-solution cases at a block tolerance of 10⁻⁶: four orders of magnitude below the discretization error.

Three log-log plots against the number of unknowns. (a) Largest block rank: HODLR rises to about 1 850, the H-matrix stays between 30 and 58. (b) Memory of the matrices: dense LU rises to about 50 GB at 40 000 unknowns, H-LU stays one to two orders lower up to 159 058 unknowns, with the published values as stars. (c) Time per step: dense LU is slowest; H-LU with 1 to 16 threads approaches the published value. — **Measured cost.** (a) Largest block rank on bath-and-axon point sets. (b) Memory kept and (c) time per step for a soma with axons; stars: values reported by Hasan et al. for one and eight neurons. A cell model with 19 658 nodes keeps 1.02 GB of matrices against 12.37 GB dense. The gains are memory, setup time and bounded ranks; we do not claim a faster time step than the published HODLR solver.

Learn what an H-matrix is

Verification

Checked twice, by different methods

We test against exact solutions and published benchmarks, and compute key results with two independent solvers. The record below comes from our own runs.

How close each check comes to its reference

Relative difference, log scale. Further left is closer agreement.

Second, independent solver

8-channel 7 T dipole arraypower and peak 10 g SAR0.3 %

Dipole over flat phantompeak SAR over 1 g and 10 g0.1 %1.2 %

30 GHz dipole over skincase of 11 research groups0.6 %

Spheres and layered bodiespeak 10 g SAR, finest grids2.2 %

Exact or resolved reference

Insulated implant leadtip current, 64 and 128 MHz0.5 %

Plane wave on spheres and layersabsorbed power, 0.9 and 3 GHz1.5 %

Planar dielectric boundaryIEC/IEEE 62704-1, 8.2.2, Fresnel0.06 %

Plane wave at 6 GHz onto musclefinest grid, 0.0625 mm0.04 %

Weighted peak methodclosed-form exposure index5 × 10⁻⁶

Conductivity sensitivity, shellsclosed form, 0.5 mm0.006 %

Finite differences, published study, grid refinement

Adjoint gradients, 1 mm headvs central finite differences2.4 and 3.1 × 10⁻⁷

Pulsed fields, published studyGiaccone 2023, Fig. 40.908 / 0.91 · 1.377 / 1.38

Dipoles and arrays over skin6 to 24 GHz, 0.25 vs 0.125 mmwithin 2.5 %

second solverexact or resolved referencefinite differences, publication, grid

1, 4 and 8 CPU threads: bit-identicalSAR ratios of a published 7 T design: within 0.03IEC/IEEE 62704-1 system check: +4.5 % and +9.6 % of ±10 %

2.1–2.5×less power

Across the 6 GHz boundary. A device that just passes below 6 GHz may emit less than half that power just above it.

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Above 6 GHz the limit changes from peak SAR over 10 g (2 W/kg) to absorbed power density over 4 cm² (20 W/m²). In 95 runs with dipoles, arrays and patch antennas over three skin models, 5 to 15 mm from the skin and 3 to 24 GHz, the second limit allowed 2.1 to 2.5 times less power than the first would have at the same frequency, whatever the source. So a device that just passes below 6 GHz may emit less than half that power just above it.

Read more: the full verification recordHide the full record

Check	Compared with	Agreement	Study
8-channel 7 T dipole array with matching: accepted power, absorbed power, peak 10 g SAR	Second solver (FDTD vs integral equation)	within 0.3 %	7 T safety margins
Insulated implant lead, tip current at 64 and 128 MHz	Resolved axisymmetric reference	within 0.5 %	Implant heating
Dipole over a flat phantom, IEC/IEEE 62704-1 geometry: peak SAR over 1 g and over 10 g	Second solver, both converged at the surface peak	0.1 % and 1.2 %	RF dosimetry
30 GHz dipole over skin, peak absorbed power density, a case computed by 11 research groups	Second solver	within 0.6 %	Millimetre-wave skin
Fractionated dipole of a published 7 T design: SAR ratios (dimensionless)	Published design study	within 0.03	7 T safety margins
Spheres and layered bodies in a plane wave at 0.9 and 3 GHz: total absorbed power, extrapolated to zero cell size	Exact solution	within 1.5 %	RF dosimetry
The same bodies: peak SAR over 10 g on the finest grids	Second solver	within 2.2 %	RF dosimetry
Same case on 1, 4 and 8 CPU threads	Repeated runs	bit-identical	Automated test suite

Code verification to IEC/IEEE 62704-1, and the new methods
Check	Compared with	Result	Study
IEC/IEEE 62704-1, clause 8, automated test suite for our FDTD solver
8.2.2 planar dielectric boundary: TM reflection onto a lossy dielectric, grids of 1 and 0.5 mm	Exact Fresnel coefficient	within 0.06 % order 1.9 to 2.1	Extrapolated value; the error falls with the square of the cell size, as expected
8.3.4 system check: dipole over the flat phantom at 3000 MHz, FDTD on a 1 mm grid, peak SAR over 1 g and 10 g	Target of the standard, ±10 %	+4.5 % and +9.6 %	Inside the tolerance
8.2.1 free-space propagation, 8.3.1 generic dipole, 8.3.2 microstrip	Values and limits of the standard	pass	8.2.1 also has our own lossy-tissue extension: 1 of its 6 checks sits at its 2 % limit
8.2.3 open boundaries: reflection of the absorbing boundary	Our own −40 dB limit; the standard's range is not openly published	pass	Not the standard's number
Adjoint gradients of low-frequency field objectives
Gradient with respect to tissue conductivity, electrode voltage and current, on layered models and a 1 mm head with 3.87 million voxels	Central finite differences of the forward solver	within 2.4 × 10⁻⁷	Relative difference, worst case
Normalised conductivity sensitivity, concentric shells	Closed form	within 1 % from 1.5 mm 0.006 % at 0.5 mm	Grid refinement
Temporal-interference envelope, two channels	Central finite differences	within 3.1 × 10⁻⁷	Relative difference, worst case
Cost of one gradient, 1 mm head	One forward solve	1.66 solves	Finite differences would need 2 solves per tissue
Weighted peak method for pulsed low-frequency fields
Sinusoids, two-tone signals, a rectangular pulse train and a damped sinusoid	Closed-form exposure index	within 5 × 10⁻⁶	Relative difference
Trapezoid and double pulse of a published study: ratio of the frequency-domain to the time-domain index	L. Giaccone, Phys. Med. Biol. 68 (2023) 095001, Fig. 4: 0.91 and 1.38	0.908 and 1.377	Agrees to the two decimals published
Time-domain weighting filter, all eight limit sets of ICNIRP 2010 and the Directive	The 3 dB and 90° tolerance of the ICNIRP 2010 annex	worst 2.85 dB, 70°	Inside the tolerance
Absorbed power density above 6 GHz
Plane wave at 6 GHz onto muscle: power entering the surface, grids of 0.5 to 0.0625 mm	Exact solution	+2.1 % to +0.04 %	The error falls with the square of the cell size
Dipoles and arrays over skin, 6 to 24 GHz: peak SAR and absorbed power density, 0.25 against 0.125 mm grids	Grid refinement	within 2.5 % ratios within 0.4 %	Grid uncertainty of our 95-case sweep

The clause 8 criteria are those of the 2017 edition, as quoted in open sources. The 2026 edition keeps the structure of clause 8. Two items need data the standard does not publish openly, so they are not in the suite: the SAR averaging test with the SAR Star (8.2.4) and the SAM phantom with the generic phone (8.3.3). The feed-point impedance of 8.3.4 is reported but not judged, because the standard does not specify the feed.

The weighted peak method and the adjoint gradients are new in November 2026. Both pass the checks above. They now go through our full test suite before we use them in client studies.

The papers behind these studies are listed under Research once they are submitted.

Verification against measurement

The set-up every SAR laboratory checks itself against

Exact solutions and a second solver show that the equations are solved correctly. The next question is whether the result matches the physical world. Here we compare EMVIE with published measurements and with the reference values that measurement laboratories use, and we say which is which.

Measurement

A quantity measured on a physical set-up, shown with the uncertainty its authors state.

Consensus target

A reference value fixed by an international standard. It was computed and checked by measurement when the standard was written. Every accredited SAR laboratory must reproduce it to within ±10 % in its system check. Matching it shows that EMVIE reproduces the industry's reference set-up; it is not a new measurement.

Case 1 · consensus target

Standard validation dipoles over the flat phantom

On the 2 mm grid, all six dipoles from 835 to 3000 MHz are inside the ±10 % tolerance under both SAR averaging rules.

The system-check set-up, schematic and not to scale. The SAR peak sits at the inner surface of the phantom, above the feed.

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These are the half-wave dipoles and the liquid-filled flat phantom of IEC/IEEE 62209-1528 and IEC/IEEE 62704-1, from 835 to 3000 MHz. EMVIE models each dipole as a fed thin-wire antenna, solves it together with the phantom and scales the result to 1 W forward power.

On the 2 mm grid, all six dipoles are inside the ±10 % tolerance under both SAR averaging rules. Peak SAR over 1 g is within −3.9 to +1.4 % of the target. Over 10 g, the IEC/IEEE 62704-1 rule, which allows up to 10 % air in a cube, gives +2.8 to +6.2 %. A stricter rule with no air in the cube gives −2.1 to +0.3 %.

EMVIE peak SAR relative to the standard targets, 2 mm grid

EMVIE ÷ target − 1. Shaded: the ±10 % band a laboratory's system check must meet.

835 MHz

900 MHz

1800 MHz

1900 MHz

2450 MHz

3000 MHz

1 g, both rules10 g, up to 10 % air10 g, no air

Read more: values per dipole, the 1 mm grid and our findingsHide the values

2 mm grid, per 1 W forward power
Frequency	Peak SAR, 1 g (W/kg) EMVIE / target	Deviation	10 g, up to 10 % air (W/kg) EMVIE / target	Deviation	10 g, no air (W/kg) EMVIE / target	Deviation	Target from
835 MHz	9.62 / 9.56	+0.7 %	6.47 / 6.22	+4.0 %	6.17 / 6.22	−0.7 %	IEC/IEEE 62209-1528 ¹
900 MHz	10.99 / 11.0	−0.1 %	7.27 / 7.07	+2.8 %	6.92 / 7.07	−2.1 %	IEC/IEEE 62704-1
1800 MHz	38.5 / 38.4	+0.3 %	20.8 / 20.1	+3.6 %	19.7 / 20.1	−1.9 %	IEC/IEEE 62209-1528 ¹
1900 MHz	40.1 / 39.7	+1.0 %	21.5 / 20.5	+4.8 %	20.4 / 20.5	−0.6 %	IEC/IEEE 62209-1528 ¹
2450 MHz	53.1 / 52.4	+1.4 %	25.5 / 24.0	+6.2 %	24.1 / 24.0	+0.3 %	IEC/IEEE 62209-1528 ¹
3000 MHz	62.9 / 65.4	−3.9 %	26.7 / 25.3	+5.4 %	25.0 / 25.3	−1.2 %	IEC/IEEE 62704-1

1 mm grid, per 1 W forward power
Frequency	1 g, up to 10 % air	10 g, up to 10 % air	1 g, no air	10 g, no air	Status
900 MHz	+1.5 %	+2.4 %	not run	not run	Inside the tolerance
1900 MHz	+4.1 %	+5.3 %	rerun pending	rerun pending	Inside the tolerance; the no-air values of the first run had a round-off error, since fixed
3000 MHz	+1.3 %	+6.8 %	−0.2 %	+4.4 %	Inside the tolerance; no-air cubes slid to the surface. Not yet grid-converged: the values still rise from 2 to 1 mm, and the 0.5 mm run decides

¹ Values of the standard's target table as quoted in public reference-dipole calibration reports. The 2450 MHz targets are not yet confirmed in a source we have opened. We are checking them, and the dipole lengths at 1800 to 2450 MHz, against the published standard. The lengths we use are within 0.5 mm of commercial validation dipoles.

Resolved finding. On the 1 mm grid at 3000 MHz the no-air rule first read 8.0 % low on 1 g and 6.6 % low on 10 g. The cause was where the cubes sit: a cube centred on a voxel and grown in whole layers stops up to 0.7 mm short of the surface. With the cubes slid continuously until their face touches the surface, the 1 mm values are −0.2 % on 1 g and +4.4 % on 10 g, both inside the ±10 % tolerance. The 2 mm grid has fewer than 10 cells per wavelength in the liquid at 3000 MHz, so its 1 g shortfall is mostly grid resolution.

Phantom size. A larger phantom at 1900 MHz changes peak SAR by less than 0.1 %.

Not compared. The feed-point impedance: the standards do not specify the feed, and two independent solvers depart from the tabulated value by the same amount.

Case 2 · measurement

5G-band validation dipoles, 3.9 to 4.9 GHz

On the 1 mm grid, EMVIE lies 4.8 to 7.7 % below the measurement on 1 g and 5.2 to 9.7 % below on 10 g. Every value is inside the measurement uncertainty.

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An independent laboratory measured the peak SAR of these dipoles to ISO/IEC 17025 procedures. It states an expanded uncertainty of 0.85 dB for 1 g and 0.83 dB for 10 g at k = 2, which allows a result down to 17.8 % and 17.4 % below the measured value. We average with no air in the cube.

On the 1 mm grid, with the no-air cubes slid until their face touches the liquid surface, EMVIE lies 4.8 to 7.7 % below the measurement on 1 g and 5.2 to 9.7 % below on 10 g, at all four frequencies. Every value is inside the measurement uncertainty. With cubes centred on a voxel, the 1 mm values had read 15 to 24 % low, because those cubes stop short of the surface. The 10 g shortfall is largest at 4.6 and 4.9 GHz, where the grid has the fewest cells per wavelength (10.5 and 9.9). That trend is consistent with discretization, but we have not yet shown it is the cause.

EMVIE against the measured peak SAR, 1 mm grid, cubes slid

EMVIE ÷ measured − 1, labelled 1 g · 10 g. Shaded: the measurement uncertainty at k = 2.

3900 MHz−5.9 · −5.8 %

4200 MHz−4.8 · −5.2 %

4600 MHz−6.3 · −9.3 %

4900 MHz−7.7 · −9.7 %

1 g10 gBoth with no air in the cube.

Read more: all values, both gridsHide the values

Frequency	Grid	1 g, EMVIE / measured (W/kg)	Deviation	10 g, EMVIE / measured (W/kg)	Deviation
3900 MHz	1 mm, slid	68.1 / 72.4	−5.9 %	23.7 / 25.2	−5.8 %
4200 MHz	1 mm, slid	65.6 / 68.9	−4.8 %	22.1 / 23.3	−5.2 %
4600 MHz	1 mm, slid	65.3 / 69.7	−6.3 %	20.9 / 23.0	−9.3 %
4900 MHz	1 mm, slid	64.7 / 70.1	−7.7 %	20.0 / 22.1	−9.7 %
3900 MHz	2 mm	64.5 / 72.4	−10.9 %	22.1 / 25.2	−12.5 %
4200 MHz	2 mm	61.8 / 68.9	−10.4 %	20.4 / 23.3	−12.6 %
4600 MHz	2 mm	61.0 / 69.7	−12.5 %	19.1 / 23.0	−17.1 %
4900 MHz	2 mm	60.1 / 70.1	−14.2 %	18.1 / 22.1	−18.0 %

Bounds of the measurement uncertainty, k = 2: −17.8 % for 1 g and −17.4 % for 10 g. The 2 mm rows use cubes centred on a voxel.

Coming next: more measured data, with their uncertainty bands

MeasurementResonant length of insulated wires heated in 1.5 T and 3 T MRI scanners, in the standard gel phantom (openly licensed data).
MeasurementElectric fields recorded inside the human brain during transcranial current stimulation.

Each comparison will appear here whether it passes or not.

What we do not claim. No measurement has yet been made for EMVIE itself. The results above apply to the configurations shown. We are planning a measurement campaign to ASTM F2182 and ISO/TS 10974. Sources: IEC/IEEE 62209-1528:2020; IEC/IEEE 62704-1:2017; A. Christ and N. Kuster, IT'IS Foundation verification report Dipoles001AA201903 on the 3.9 to 4.9 GHz validation dipoles, 2019; L. J. Bardwell Speltz et al., Magn. Reson. Med. 92:1714–1727, 2024; Y. Huang et al., eLife 6:e18834, 2017.

Method

How a study runs

Confidential from the first message: a non-disclosure agreement is in place before any files change hands.

STEP 1

Scope

We agree the exposure, the standard, the metrics and the acceptance question.

STEP 2

Model

Device and anatomy are built from your design data and licensed or supplied human models.

STEP 3

Verify

Grid convergence, a second solver where it matters, and the uncertainty terms that apply.

STEP 4

Report

Results with error bars, the solver version and every input. We keep the study, so we can repeat it exactly on request.

Research

The science behind the services

We write up our methods for peer review. This list shows only papers that are submitted or published.

Low frequencyVoxel-based low-frequency dosimetry with sub-voxel conductances and aggregation multigrid: accuracy and cost from brain stimulation to electrosurgerySubmitted

Further papers on RF dosimetry, 7 T transmit-array safety, implant heating in MRI, millimetre-wave skin exposure and temporal-interference stimulation will appear here once they are submitted.

RF dosimetry7 T transmit arraysImplant heatingmmWave skinTemporal interferenceCellular bidomain BEM

Body between the loops of a gradient coil, coloured by the induced electric field — MRI gradient coil around a whole body, from the submitted paper.

Electrosurgical needle in gel, surrounded by nested temperature-rise surfaces — Electrosurgery: heating around a needle in gel, from the same paper.

Founders

Built by the people who wrote the solvers

The founders develop the EMVIE solvers and carry out every study themselves, from model to report. Select a founder to read the full bio.

Contact

Bring us the exposure question you need answered.

A short description of the device, frequency and standard is enough for a first reply with a proposed scope and a fixed price. A non-disclosure agreement can be in place before you send any files.

info@corefieldbiophysics.com

Write to us

Medical device and implant makers
MRI coil and system developers
Wireless device makers and test laboratories
Neurostimulation developers and research groups
Teams that need an independent check of a simulation

Every exposure result, with its error bars attached.

What we do, and how we check it

Six consulting studies →

Checked twice, by different methods →

Against the laboratory reference →

How a study runs →

Methods written up for peer review →

The people who wrote the solvers →

Six studies, each with a stated deliverable

MRI RF safety of active implants

SAR and psSAR near the body

Power density above 6 GHz

Low-frequency exposure at work

Neurostimulation field planning

Independent second opinion

One verified engine, from quasi-static to millimetre wave

Volume integral equation

Finite-difference time domain

Transmit arrays and coils

Leads and transfer functions

Quasi-static fields

Bioheat and damage

Two averaging rules from one solve

Weighted peak method

Adjoint sensitivities

Cell-scale stimulation

Hierarchical matrices (H-LU)

Head-to-cell coupling

Cell-scale stimulation with a bidomain boundary-element solver

What our solver adds to the published bidomain BEM

The published cases

H-matrix algebra for large cells

A charge constraint

A reconstructed layer 2/3 pyramidal cell

Blue Brain ion channels in the membrane

Coupling to head models

Hierarchical-matrix (H-matrix) acceleration

Checked twice, by different methods

How close each check comes to its reference

The set-up every SAR laboratory checks itself against

Standard validation dipoles over the flat phantom

EMVIE peak SAR relative to the standard targets, 2 mm grid

5G-band validation dipoles, 3.9 to 4.9 GHz

EMVIE against the measured peak SAR, 1 mm grid, cubes slid

Coming next: more measured data, with their uncertainty bands

How a study runs

Scope

Model

Verify

Report

The science behind the services

Built by the people who wrote the solvers

Bring us the exposure question you need answered.

Six consulting studies

Checked twice, by different methods

Against the laboratory reference

How a study runs

Methods written up for peer review

The people who wrote the solvers