🔬 materials science

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

This study characterizes the T1, T2, and complex permittivities of various hydrogels, paramagnetic salt solutions, and oils at 0.35, 1.5, and 3 Tesla to identify optimal materials for constructing MRI phantoms with specific dielectric and relaxivity properties.

Original authors: H Michael Gach, Kerri Prinos, Hannah Sechaga

Published 2026-08-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: H Michael Gach, Kerri Prinos, Hannah Sechaga

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a chef trying to bake the perfect cake, but instead of flour and sugar, your ingredients are invisible waves of energy and magnetic fields. This is the world of MRI (Magnetic Resonance Imaging), a medical superpower that lets doctors see inside the human body without making a single cut. But to make sure the MRI machine is working correctly, scientists need "test cakes" called phantoms. These aren't for eating; they are jars of special liquids and gels that mimic how human tissues react to the machine's magnetic pull.

To understand how these test cakes work, you need to know two main things about the ingredients. First, there's relaxation time. Think of this like a trampoline. When a magnet pushes a proton (a tiny particle in water) onto the trampoline, it bounces. Relaxation time is how long it takes for that proton to stop bouncing and settle back down. Different tissues bounce for different lengths of time, which is how the MRI creates a picture. Second, there's permittivity and conductivity. Imagine the MRI machine is a radio station broadcasting a signal. Some materials, like water, are like a sponge that soaks up the signal and changes its shape (permittivity), while others, like salty water, act like a wire that lets electricity flow through them easily (conductivity). If the test cake doesn't match the real body's "bounce" and "signal-soaking" abilities, the MRI picture could be blurry or wrong. This is why scientists are always hunting for the perfect recipe.

In this study, a team of researchers set out to test a massive buffet of potential phantom ingredients to see which ones make the best "test cakes" for MRI machines of different sizes. They looked at three main groups of ingredients: hydrogels (jiggly, water-filled gels like gelatin), paramagnetic salt solutions (water mixed with special metals like copper or manganese that act like tiny magnets), and oils (like the kind you cook with). They tested these mixtures in three different "kitchens": a small MRI machine at 0.35 Tesla, a standard hospital machine at 1.5 Tesla, and a powerful one at 3 Tesla. They even tried to guess how these ingredients would behave in a super-strong 7 Tesla machine or a tiny 0.55 Tesla one.

The researchers discovered that not all recipes are created equal. Some ingredients, like sodium alginate, Miller's LB agar (a nutrient-rich mix usually for growing bacteria), and xanthan gum, turned out to be excellent candidates. They created stable gels that behaved consistently, making them great for building reliable test cakes. However, other ingredients were a bit of a disaster. Sodium polyacrylate, PVP, and PEG hydrogels were "challenging," meaning they were hard to mix evenly and often resulted in lumpy, inconsistent results that would confuse the MRI machine.

When it came to the salt solutions, the team found a surprising twist. A common rule of thumb in MRI physics is that as you turn up the magnetic power (field strength), the "bounce" time (T1) usually gets longer. But the researchers found that for some of their samples, this rule didn't hold true. For instance, the Mn(NO3)2 (manganese nitrate) solution had the highest "bounciness" (relaxivity) of all the salts they tested, making it a very potent ingredient, but it also showed that the relationship between magnetic strength and bounce time isn't always a straight line. They also noted that while CuSO4 (copper sulfate) and NiCl2 (nickel chloride) worked well, they come with a warning label: they can be toxic or corrosive, so handling them requires care.

For the oils, the results were a clear win for high-power machines. The team tested canola, castor, and grapeseed oils and found they were perfect for high-field MRI (like the 3 Tesla and 7 Tesla machines). Why? Because they have very low "signal-soaking" power (low dielectric constant) and low electrical conductivity. In the world of high-power MRI, this is a superpower because it prevents the signal from getting distorted, much like how a clear window lets light pass through without bending it.

The study also measured exactly how these ingredients changed as they got more concentrated. For example, adding more salt to water generally made it conduct electricity better, but adding more PEG or PVP didn't change the conductivity much at all. They also measured how the "bounce" times changed with concentration, finding that for some gels, the relationship wasn't as predictable as they hoped.

In the end, the paper doesn't declare one single "perfect" ingredient for every situation. Instead, it offers a detailed menu of options. If you need a low-dielectric phantom for a high-power machine, reach for the oils. If you need a gel that mimics soft tissue, sodium alginate or Miller's LB agar are your best bets. But if you try to use PEG or PVP, be prepared for a bumpy ride. The researchers also pointed out that while synthetic polymers are great because they don't rot, the salt solutions are great because they stop bacteria from growing, though they bring their own toxicity risks. By mapping out exactly how these materials behave at different magnetic strengths, the study gives future scientists the tools to bake better, more accurate test cakes, ensuring that the MRI machines in hospitals everywhere are giving us the clearest possible view of the human body.

Technical Summary: T1, T2, and Complex Permittivities of Hydrogels, Paramagnetic Salt Solutions, and Oils at 0.35, 1.5, and 3 Tesla

Problem Statement
Magnetic Resonance Imaging (MRI) quality assurance (QA) relies heavily on phantoms to validate system performance. While commercial phantoms exist, they are often cost-prohibitive for facilities with limited funding, necessitating the use of home-built alternatives. The design of effective phantoms requires precise knowledge of material relaxation times ( $T_1$ , $T_2$ ) and complex permittivities (dielectric strength and electrical conductivity) at clinical Larmor frequencies. However, existing literature often predates the widespread adoption of 1.5 T and 3 T clinical systems, or lacks data for emerging field strengths such as 0.35 T (used in MRI-guided radiation therapy) and 7 T (high field). Furthermore, assumptions regarding the behavior of relaxation times with increasing field strength (e.g., that $T_1$ always rises) may not hold true for all phantom constituents. This study addresses the gap in comprehensive, multi-field strength data for common phantom materials.

Methodology
The authors measured $T_1$ , $T_2$ , and complex permittivities for three categories of materials: hydrogels, paramagnetic electrolytes, and oils. Measurements were conducted at 21°C across three magnetic field strengths: 0.35 T (ViewRay MRIdian), 1.5 T (Philips Ingenia), and 3 T (Siemens mMR).

Relaxation Measurements: $T_1$ was determined using an inversion recovery (IR) echo planar imaging (EPI) sequence with variable inversion times. $T_2$ was measured using a Carr–Purcell–Meiboom–Gill (CPMG) multiple spin-echo sequence. Data were fitted to three-parameter nonlinear models to extract relaxation rates ( $R_1$ , $R_2$ ) and relaxivities ( $r_1$ , $r_2$ ).
Permittivity Measurements: Complex permittivity was measured using a coaxial dielectric probe connected to an impedance analyzer (14 MHz to 1 GHz). Static dielectric constants ( $\varepsilon_s$ ) and static electrical conductivities ( $\sigma_s$ ) were derived by fitting data to the Cole-Cole relaxation model. DC conductivity was also measured independently.
Materials Tested:
- Hydrogels: Miller's LB agar, gelatin, polyethylene glycol (PEG), polyvinyl alcohol (PVA), polyvinylpyrrolidone (PVP), sodium alginate, sodium polyacrylate, and xanthan gum.
- Paramagnetic Electrolytes: Aqueous solutions of Copper Sulfate ( $CuSO_4$ ), Nickel Chloride ( $NiCl_2$ ), and Manganese Nitrate ( $Mn(NO_3)_2$ ).
- Oils: Canola, castor, and grapeseed oils.
Data Processing: $T_1$ values were interpolated for 0.55 T and extrapolated for 7 T using a power-law model ( $T_1(B_0) = A \cdot B_0^C$ ). Linear fits were generated for relaxivities and permittivities versus concentration.

Key Results
The study generated extensive datasets (Tables 3–15) detailing relaxation times, relaxivities, and permittivities across varying concentrations and field strengths.

Field Strength Dependence: Contrary to the general assumption that $T_1$ increases with field strength, the study observed that $T_1$ for $NiCl_2$ did not rise with increasing field strength. Additionally, $T_2$ decreased with increasing field strength for PEG, PVA, sodium polyacrylate, and $Mn(NO_3)_2$ , whereas $T_2$ increased for $CuSO_4$ .
Relaxivities:
- $T_1$ relaxivity ( $r_1$ ) remained constant for PEG and PVP but rose for $NiCl_2$ .
- $T_2$ relaxivity ( $r_2$ ) typically remained constant or rose with field strength, but dropped for $CuSO_4$ .
- $Mn(NO_3)_2$ exhibited the highest relaxivities among all tested paramagnetic samples.
Hydrogel Performance:
- Challenging Materials: Sodium polyacrylate, PVP, and PEG hydrogels were found difficult to prepare homogeneously, leading to high variance in relaxation rates. PEG and PVP conductivities did not rise with concentration.
- Viable Candidates: Sodium alginate, Miller's LB agar, and xanthan gum demonstrated good properties for phantom generation, though they are susceptible to biological growth.
- Dielectric Properties: Most hydrogels and paramagnetic solutions maintained high static dielectric constants ( $\varepsilon_s \approx 70$ ), similar to water. PVP was an exception, capable of reducing $\varepsilon_s$ to below 40.
Oils: All three tested oils (canola, castor, grapeseed) exhibited low static dielectric constants ( $\varepsilon_s < 10$ ) and low conductivities, making them suitable for high-field applications where dielectric artifacts are a concern.
Conductivity: Static electrical conductivities generally rose with concentration for Miller's LB agar, gelatin, PVA, sodium alginate, sodium polyacrylate, xanthan gum, and the paramagnetic salts.

Significance and Claims
The authors position this work as a unique resource covering variations of phantom materials against both concentration and field strength (0.35 T to 7 T). The study challenges established assumptions, specifically noting that $T_1$ does not universally rise with field strength and that relaxivity behavior is material-dependent.

The paper concludes with practical recommendations for phantom construction:

Material Selection: Sodium alginate, Miller's LB agar, and xanthan gum are recommended for hydrogel-based phantoms, while oils are recommended for low-dielectric, high-field applications.
Safety and Stability: While paramagnetic electrolytes offer high relaxivities and antimicrobial properties, the authors caution regarding their toxicity (neurotoxicity of $Mn^{2+}$ , carcinogenicity of $Cu^{2+}$ and $Ni^{2+}$ ) and corrosiveness. Synthetic polymers are preferred over organic ones for longevity, though hydrogels generally have shorter lifespans (<3 months) compared to oils or electrolytes.
Limitations: The study is limited to single-component (oils) or duplex (water + gel/electrolyte) materials. The authors note that the heterogeneity of some hydrogels remains a challenge for generating consistent phantoms.

Overall, the paper provides a foundational dataset for researchers designing MRI phantoms for quality assurance across a broad spectrum of clinical and research field strengths.

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