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T1, T2, and complex permittivities of hydrogels, paramagnetic salt solutions, and oils at 0.35, 1.5, and 3 Tesla

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Measurements of T1, T2, and complex permittivity for common MRI phantom materials at 0.35, 1.5, and 3 T support specific material recommendations for phantom builders.

desk verdict Useful multi-field phantom-material reference, solid on T1/T2, but the low-frequency permittivity extrapolation needs validation before the recipe tables are used uncritically. read the letter →

arxiv 2608.11117 v1 pith:RAULO5KV submitted 2026-08-11 physics.med-ph cond-mat.mtrl-sci

H Michael Gach , Kerri Prinos , Hannah Sechaga This is my paper · ORCID
classification physics.med-phcond-mat.mtrl-sci
keywords RelaxationtimedielectricstrengthelectricalconductivityMRIphantomliquidshydrogelsparamagneticsaltsoils
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper aims to turn MRI phantom construction into a data-driven choice rather than a literature hunt. It reports T1, T2, and complex permittivity for seven hydrogel or polymer materials, three paramagnetic salt solutions, three oils, and reference liquids at 0.35, 1.5, and 3 T, with 0.55 T interpolations and 7 T extrapolations. The central result is that generic field-strength rules do not always hold: T1 did not rise with field for every material, r1 did not always fall, and several relaxivities were essentially field-independent. The authors recommend sodium alginate, Miller's LB agar, and xanthan gum as hydrogel candidates, Mn(NO3)2 as the strongest relaxer among the salts, and canola, castor, and grapeseed oils as low-dielectric phantoms.

What carries the argument

The machinery is the measurement and fitting protocol: inversion-recovery EPI for T1, CPMG multi-spin-echo for T2, and open-ended coaxial-probe permittivity sweeps run through a Cole-Cole relaxation fit to extract the static dielectric constant $\varepsilon_s$ and static electrical conductivity $\sigma_s$. Linear fits of relaxation rate $R_n = R_{n,0} + r_n[C]$ versus concentration convert raw relaxation times into relaxivities, and a power law $T_1(B_0) = A\,B_0^C$ is used to interpolate 0.55 T and extrapolate 7 T values.

What would settle it

Measure the same samples with a dielectric probe rated below 14 MHz, or with time-domain reflectometry, and compare the independently obtained $\varepsilon_s$ and $\sigma_s$ with the extrapolated values in Tables 3-15; disagreement beyond the reported uncertainties would overturn the permittivity claims. A second check is the paper's own observation in Figure 1 that the 7 T extrapolated $R_1$ at 5% w/w Miller's LB agar falls below the 4% w/w value: measuring $T_1$ at 7 T across all concentrations would show how often the power-law extrapolation fails.

Watch

Extended reading notes

Core claim

The paper's claim is that these measurements form a reliable, internally consistent dataset for common MRI phantom constituents across clinically relevant field strengths, with concentration sweeps wide enough to extract relaxivities and conductivity slopes. On its own terms, the important findings are that T1 decreased with increasing concentration except for PEG; that the T1 and T2 relaxivities of PEG, PVP, sodium polyacrylate, and deionized water did not vary significantly with field strength; that the T2 relaxivities of gelatin and sodium alginate did not vary significantly; and that the common assumption that T1 rises or r1 falls with field strength fails for several samples. The authors further conclude that sodium alginate, Miller's LB agar, and xanthan gum are good hydrogel candidates, Mn(NO3)2 has the highest relaxivities, and all three oils are good low-dielectric (epsilon_s < 10) phantom materials with low conductivities.

Load-bearing premise

The load-bearing premise is that dielectric-probe readings taken down to 14 MHz, far below the probe's rated 200 MHz lower limit, can be extrapolated through a Cole-Cole fit into accurate static dielectric constants and conductivities; the paper's own Figure 1 note says one 7 T relaxation extrapolation is false, which shows the wider extrapolation chain can break.

Editorial extensions

If this is right

  • Concentration-tuning recipes become practical: Mn(NO3)2 changes T1 and T2 at sub-millimolar concentrations, while CuSO4 and NiCl2 need higher concentrations to reach the same relaxation rates.
  • For PEG, PVP, and sodium polyacrylate, the field-independent relaxivities mean a recipe calibrated at one clinical field should transfer to another without re-measurement.
  • The oils' low dielectric constants (epsilon_s < 10) and low conductivities make them suitable for high-field phantom compartments where dielectric artifacts must be minimized.
  • Because conductivity rises linearly with concentration for most hydrogels and salts, RF-heating and SAR phantoms can be tuned by concentration; PEG and PVP are the exceptions.
  • The 0.55 T and 7 T values are offered as starting points, with the paper itself warning that some extrapolations (for example, 5% w/w Miller's LB agar at 7 T) are not trustworthy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the dielectric probe is rated only down to 200 MHz, the 14 MHz and static permittivity values rest on model extrapolation; a direct low-frequency measurement would tell whether the reported $\varepsilon_s$ and $\sigma_s$ are accurate.
  • The paper characterizes single or duplex materials only, so combined phantoms (gel plus paramagnetic salt) may behave differently since electrolytes can affect gelling; combined recipes need direct validation before adoption.
  • If the field independence of PEG, PVP, and sodium polyacrylate relaxivities extends beyond 3 T, those polymers could become transferable phantom standards at ultra-high field, but the 7 T numbers here are extrapolations, not measurements.
  • A natural test is to build a multi-compartment phantom from the recommended materials and image it at 0.55 T and 7 T; those results would extend or correct the interpolation and extrapolation tables.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports T1, T2, and complex permittivity measurements for a panel of MRI phantom constituents—seven hydrogels, three paramagnetic salt solutions, and three oils—at 0.35, 1.5, and 3 T, with concentrations varied per material. T1 and T2 were acquired with standard IR-EPI and CPMG sequences at the three field strengths and fitted to monoexponential models; relaxivities are obtained from linear concentration fits. Complex permittivities were measured with coaxial dielectric probes over roughly 14 MHz to 1–1.5 GHz and fitted to a Cole-Cole model to extract static dielectric constants and static conductivities. The authors use a power law in B0 to interpolate T1 to 0.55 T and extrapolate to 7 T, and they draw practical conclusions about which materials are suitable as MRI phantom components, including that sodium alginate, Miller's LB agar, and xanthan gum are good hydrogel candidates, Mn(NO3)2 has the highest relaxivities, and the three oils are suitable low-dielectric materials.

Significance. If the dataset is reliable, it fills a practical gap: phantom builders currently need to assemble relaxation times, relaxivities, and permittivities from scattered sources or from studies at a single field strength. The paper's direct, multi-field comparison of common, inexpensive, commercially available phantom materials, with reported fit uncertainties, is potentially useful for QA phantom design in MR-guided radiotherapy (0.35 T), clinical imaging (1.5 and 3 T), and low-field/high-field applications. The study is also a useful reminder that simple field-strength scaling assumptions for T1 and relaxivity do not hold for every material; several reported deviations, such as r2 decreasing with field for CuSO4 and r1 rising for NiCl2, are falsifiable observations that can guide future modeling. The T1/T2 measurements are the strongest part because they are direct measurements at the target field strengths, use standard sequences, and include comparisons to earlier work for CuSO4, NiCl2, and sodium alginate.

major comments (3)
  1. [Methods, Permittivities paragraph] The two instrument specification statements are internally inconsistent, and this matters because the low-frequency credibility of the results is at stake. The text first says the Agilent E4991A impedance analyzer has a rated range of 10 MHz to 3 GHz, then later says the 85070E/E5061A network analyzer combination is rated for 200 MHz to 20 GHz. No cross-check between the two configurations on the same samples is reported, so the reader cannot tell which configuration, if any, supports the 14 MHz lower bound claimed for the measurements. Please clarify which analyzer was used for which samples, report the manufacturer's rated frequency range for each configuration, and provide a direct comparison measurement between the two setups over a common frequency band.
  2. [Figure 1 caption and Table 3] The 7 T extrapolation is shown to be nonphysical for Miller's LB agar within the paper itself. The Figure 1 caption notes that the extrapolated R1 at 7 T for 5% w/w is lower than R1 for 4% w/w, so the power-law extrapolation of Eq. (3) reverses the monotonic concentration ordering at 7 T. Since T1 interpolation/extrapolation is presented as a deliverable in the Highlights and is used to compute r1 values, the authors should either restrict the claimed validity of Eq. (3) to the measured range or provide a criterion for when the power-law extrapolation is reliable; as written, the paper acknowledges a counterexample to its own extrapolation procedure for one of the recommended hydrogels.
  3. [Eq. (3) and relaxivity r1 values] The 0.55 T and 7 T r1 values are not independent predictions. Equation (3), with two free parameters A and C, is fitted to exactly three measured field strengths (0.35, 1.5, 3 T), leaving zero degrees of freedom; the 0.55 T interpolation and the 7 T extrapolation are deterministic transformations of the three measured points, and the quoted r1 uncertainties do not propagate the fit uncertainty or the model-form uncertainty. This should be stated explicitly wherever interpolated/extrapolated r1 values appear, and the error bars on those values should be presented as lower bounds or omitted.
minor comments (5)
  1. [Methods, Hydrogels paragraph] Polyethylene glycol 8000 is described with molecular weight 62.07 g/mol, which is the molecular weight of the ethylene glycol monomer, not PEG 8000; the correct nominal molecular weight should be on the order of 8000 g/mol. Please correct the value or the label.
  2. [Abstract and Introduction] The abstract contains an unbalanced parenthesis: 'low dielectric (εs<10) phantoms for high field applications) but with low conductivities.' Please remove the extra closing parenthesis.
  3. [Table 14] For deionized water, the reported T2 values are 2051.72 ms at 0.35 T, 1755.22 ms at 1.5 T, and 2422.19 ms at 3 T; a non-monotonic field dependence of T2 for pure water is unexpected and deserves a brief comment on possible measurement or fitting effects, since T2 of free water is generally expected to be nearly field-independent.
  4. [Tables 3–13] Several table captions state 'measured at room temperature 20°C' while the Methods report 21°C for relaxation and 21.5°C for DC conductivity; please harmonize the temperature notation so readers can reproduce the measurements.
  5. [Data Availability] The Data Availability statement says data may be provided upon request. Given the paper's goal of serving as a reference dataset, depositing the raw T1/T2 fits and permittivity spectra (e.g., in a repository) would substantially increase the utility and verifiability of the tables.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper reports directly measured relaxation and permittivity data, and its interpolations/extrapolations are transparently labeled rather than presented as independent predictions.

full rationale

The paper is a measurement study rather than a derivation. T1 and T2 are acquired directly at 0.35, 1.5, and 3 T with inversion-recovery and CPMG sequences, and the reported values in Tables 3-14 are the fitted outputs of those measurements. The 0.55 T and 7 T values are explicitly produced by fitting Eq. (3) to the three measured field strengths and are labeled as interpolations/extrapolations; the paper even notes in Figure 1 that the Miller's LB agar 7 T extrapolation produces a nonphysical inversion, so it does not hide the fitted nature of these numbers. The complex permittivity analysis uses a standard Cole-Cole fit, and the static conductivity is obtained from the imaginary permittivity via Eq. (4) in a conventional manner; no fitted parameter is renamed as an independent prediction. The only self-citation is reference 23 (Gach 2019), used among several standard references for the Cole-Cole fitting approach; it is not load-bearing because the fitting model, the calibration procedure, and all target values in this paper are independently presented and measured here. The extrapolation of permittivities below the dielectric probe's rated 200 MHz lower bound is a genuine metrological limitation and should be checked against low-frequency instrumentation, but it is an openly stated extrapolation, not a circular step that equates an output with an input. No step in the paper's chain reduces by construction to its own assumptions or to an unverified self-citation, so the circularity score is 0.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper's conclusions rest on a small number of modeling assumptions: a linear concentration model for relaxivity, a power-law field-strength model for extrapolation, and Cole-Cole fits with extrapolation below the rated probe range. These are standard in the phantom literature, but the paper provides no independent validation of the extrapolated dielectric values and one explicit counterexample to the power-law extrapolation.

free parameters (4)
  • Power-law prefactor A and exponent C for T1(B0) interpolation/extrapolation (Eq 3) = not reported per material
    Fitted to the three measured field strengths and used to produce 0.55 T and 7 T T1 values; the paper shows at least one 7 T extrapolation (Miller's LB agar 5% w/w) is non-monotonic and likely false.
  • Linear relaxivity slopes r1 and r2 (Eq 7) = reported in Tables 3-13 per material and field strength
    Central fitted outputs that support claims about concentration dependence and field-strength behavior of relaxivities.
  • Linear permittivity/conductivity slopes a and b and intercepts (Eqs 5-6) = reported in Tables 3-13
    Used to derive static dielectric and conductivity values and their concentration dependence.
  • Cole-Cole model parameters (epsilon_s, relaxation time, width, sigma_s) = static epsilon_s and sigma_s reported; other parameters not shown
    Fit to complex permittivity data from a probe operated partly below its rated 200 MHz floor; static values rely on extrapolation to 14 MHz and below.
assumptions (4)
  • domain assumption T1 follows a power law in field strength, T1(B0)=A B0^C (Eq 3)
    Used for 0.55 T interpolation and 7 T extrapolation; the paper itself notes a non-physical 7 T result for Miller's LB agar (Figure 1 caption), so this assumption fails for at least one sample.
  • domain assumption Relaxation rate is linear in concentration, R_n = R_n0 + r_n [C] (Eq 7)
    Underlies all relaxivity values; deviations from linearity are not tested, and some fits have broad uncertainties (e.g., gelatin r2 at 3 T).
  • domain assumption Cole-Cole model with extrapolation below the probe rated range yields valid static epsilon_s and sigma_s
    Measurements were made from 14 MHz, while the dielectric probe/network analyzer combination is rated for 200 MHz to 20 GHz; static values are extrapolated.
  • domain assumption Single preparation per concentration and single-slice acquisition are representative
    No replicate sample preparations are reported; hydrogel heterogeneity is acknowledged as a source of high variance.

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Cite this review

Pith. "Pith review of T1, T2, and complex permittivities of hydrogels, paramagnetic salt solutions, and oils at 0.35, 1.5, and 3 Tesla." pith.science (2026). https://pith.science/paper/RAULO5KV

@misc{pith2026260811117,
  author       = {Pith},
  title        = {Pith review of: T1, T2, and complex permittivities of hydrogels, paramagnetic salt solutions, and oils at 0.35, 1.5, and 3 Tesla},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RAULO5KV}},
  note         = {Machine review of arXiv:2608.11117}
}
read the original abstract

Approach: The T1, T2, and complex permittivities of candidate MRI phantom constituents (hydrogels, paramagnetic electrolytes, and oils) were measured at different magnetic field strengths and concentrations. Data: T1 decreased with increasing concentration except for PEG. The T1 and T2 relaxivities of polyethylene glycol (PEG), polyvinylpyrrolidone (PVP), sodium polyacrylate, and deionized water did not significantly vary with field strength. The T2 relaxivities of gelatin and sodium alginate did not significantly vary with field strength. All of the hydrogels and paramagnetic electrolyte solutions had high static dielectrics (e.g., {\epsilon}s~70) similar to water. The static electrical conductivities of Miller's LB agar, gelatin, PVA, sodium alginate, sodium polyacrylate, xanthan gum, CuSO4, NiCl2, and Mn(NO3)2 rose with concentration. However, the conductivities of PEG and PVP did not rise with concentration. Conclusions: Sodium polyacrylate, PVP, and PEG hydrogels are challenging for generating consistent phantoms. Sodium alginate, Miller's LB agar, and xanthan gum were good hydrogel candidates. Mn(NO3)2 had the highest relaxivities of the tested samples. All three oils (canola, castor, and grapeseed) are good candidates for low dielectric ({\epsilon}s<10) phantoms for high field applications) but with low conductivities.

Figures

Figures reproduced from arXiv: 2608.11117 by the authors.

Figure 2
Figure 2. The relaxation times, relaxivities, and permittivity measurements for Miller's LB agar are summarized [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 12
Figure 12. The relaxation times, relaxivities, and permittivity measurements for sodium alginate are summarized [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 16
Figure 16. The relaxation times, relaxivities, and permittivity measurements for xanthan gum are summarized in [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figures from the paper (2 more)
Figure 18
Figure 18. Figure 18: The relaxation times, relaxivities, and permittivity measurements for copper sulfate are summarized [PITH_FULL_IMAGE:figures/full_fig_p026_18.png]
Figure 22
Figure 22. Figure 22: The relaxation times, relaxivities, and permittivity measurements for nickel chloride are summarized [PITH_FULL_IMAGE:figures/full_fig_p031_22.png]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.