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FRESH-MRI: Turning Magnetic Susceptibility Artefacts into Quantitative Volume Fraction Measurements in Multiphase Flows

This paper introduces FRESH-MRI, a novel method that transforms magnetic susceptibility-induced frequency shifts into quantitative local volume fraction measurements for multiphase flows using standard MRI scanners without the need for calibration, tracers, or specialized hardware.

Original authors: Alberto Biagini, M. Raquel Serial, Christian Poelma, Willian Hogendoorn

Published 2026-07-09

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CC BY 4.0

Original authors: Alberto Biagini, M. Raquel Serial, Christian Poelma, Willian Hogendoorn

Original paper licensed under CC BY 4.0 (https://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 trying to take a photo of a crowded room where some people are wearing bright red shirts and others are wearing blue. In a normal photo, if the red shirts are too bright, the camera might get "blinded" by the glare, and you can't see how many people are actually wearing them. You might just see a white blob.

For a long time, scientists studying multiphase flows (mixtures like bubbles in water, oil droplets in vinegar, or sand in a river) faced a similar problem with a powerful imaging tool called MRI.

Usually, MRI is great at seeing soft tissues, but when different materials (like air and water) are mixed, they mess up the magnetic field. This creates "static" or "glare" in the image, making it impossible to count how much of each material is present. Scientists usually tried to fix this by adding chemicals to make the materials look the same to the MRI, but that changed how the mixture actually behaved.

Enter FRESH-MRI.

The researchers at TU Delft came up with a clever twist: Instead of trying to fix the "glare," they decided to use it as a flashlight.

Here is how it works, using a few simple analogies:

1. The "Magnetic Tug-of-War"

Think of the MRI machine as a giant, invisible magnet holding a crowd of tiny spinning tops (water molecules) in perfect alignment.

When you introduce a bubble (air) or a plastic bead into the water, it's like a bully pushing on the spinning tops. Because air and plastic react to magnets differently than water does, they push the tops slightly out of line.
In old MRI methods, this push caused the signal to disappear (the "glare").
In FRESH-MRI, the scientists realized that the amount the tops get pushed depends exactly on how many bubbles or beads are there. The more bubbles, the bigger the push.

2. Turning Noise into a Ruler

The researchers developed a new way to listen to the "hum" of these spinning tops.

The Old Way: They looked at how bright the image was. If the "bully" (the bubble) pushed too hard, the image went dark, and they couldn't count the bubbles.
The FRESH-MRI Way: They looked at the pitch of the hum (the frequency). The "bully" changes the pitch of the spin. By measuring exactly how much the pitch changes, they can calculate the volume fraction—essentially, "what percentage of this space is air, and what percentage is water?"

It's like listening to a choir. If one singer is slightly off-key, you can hear it. If many singers are off-key in the same way, the whole choir's pitch shifts. By measuring that shift, you can count how many singers are in the room without even seeing them.

3. What They Tested

The team proved this "glare-to-ruler" trick works on three very different types of mixtures:

Bubbles in Water (High Contrast): Like a fizzy drink. The air pushes the magnetic field hard. Here, FRESH-MRI is a superhero, seeing clearly where traditional MRI goes blind.
Plastic Particles in Water (Low Contrast): Like sand in a jar. The push is weak, so the "pitch shift" is subtle. It's harder to hear, but the method still worked, matching up with traditional cameras.
Oil Droplets in Water (Low Contrast): Like a salad dressing. Again, the difference is small, but the method successfully tracked how the oil droplets floated to the top (creaming) over time.

4. The Best Part: No Extra Stuff Needed

Usually, to measure these things, you need to:

Add special "tracer" particles (like glitter) to the mix.
Do complex math to reconstruct the image from scratch.
Calibrate the machine for every single new experiment.

FRESH-MRI needs none of that.

It uses standard MRI scanners found in hospitals and labs.
It needs no glitter or tracers.
It doesn't need to be calibrated because it relies on the known magnetic "personality" of the materials (you just need to know that air is different from water).
It can measure speed and concentration at the same time. It's like a camera that tells you not only where the bubbles are, but also how fast the water is flowing around them.

Summary

The paper claims that FRESH-MRI turns a known problem (magnetic interference) into a solution. It allows scientists to see inside opaque, messy mixtures (like bubbles, particles, and droplets) and measure exactly how much of each ingredient is present and how fast it's moving, all without changing the mixture or using special equipment. It works best when the materials are very different from each other (like air and water), but it still works for similar materials too.

Technical Summary: FRESH-MRI

Problem Statement
Multiphase flows are fundamental to natural phenomena (e.g., oceanic gas exchange, blood circulation) and industrial processes (e.g., food emulsions, green hydrogen production). However, understanding the governing mechanisms of these flows is hindered by a lack of experimental data regarding local volume fraction distributions ( $\phi$ ). Existing measurement techniques face significant limitations: invasive methods (e.g., impedance probes) disturb the flow and offer only discrete data points; optical and acoustic methods fail in opaque or dense systems due to scattering; and radiation-based methods (e.g., X-ray) involve ionizing radiation and often require computationally intensive tomographic reconstruction. While Magnetic Resonance Imaging (MRI) offers non-invasive, three-dimensional capabilities, its application to multiphase flows has been limited by magnetic susceptibility differences between phases. These differences traditionally induce local magnetic field distortions, leading to signal loss and imaging artifacts that obscure quantitative analysis. Current strategies to mitigate these effects, such as susceptibility matching with additives, often alter key flow properties (e.g., surface tension) or require complex system-specific tuning.

Methodology: FRESH-MRI
The authors introduce FRESH-MRI (Frequency Shift MRI), a quantitative framework that transforms magnetic susceptibility artifacts into useful measurements of local volume fraction. Instead of compensating for susceptibility mismatches, the method exploits the frequency shift ( $\delta f$ ) induced by the contrast in magnetic susceptibility ( $\Delta\chi$ ) between the dispersed and continuous phases.

The core of the methodology relies on an effective medium formulation inspired by Maxwell–Garnett theory. This model extends single-inclusion susceptibility theory to multi-inclusion systems, treating the multiphase flow as a homogeneous medium with an effective magnetic susceptibility ( $\chi_{eff}$ ). For spherical inclusions, the relationship between the measurable frequency shift and the local volume fraction is derived as:

$\delta f = \frac{\chi_m \Delta\chi \phi}{3\chi_m + \Delta\chi(1 - \phi)}$

where $\chi_m$ is the susceptibility of the continuous phase and $\Delta\chi = \chi_i - \chi_m$ .

Experimental Implementation:

Acquisition: The method utilizes standard clinical and preclinical MRI scanners with standard flow-compensated phase-contrast (PC-MRI) sequences.
Measurement: A reference acquisition (pure water, no flow) is used to isolate background field inhomogeneities. The phase difference between the reference and the flow case encodes the local susceptibility-induced frequency shift.
Simultaneity: By combining flow-encoding gradients, the technique simultaneously measures the liquid velocity field and the volume fraction distribution without requiring tracer particles, calibration, or tomographic reconstruction.
Applicability: The method requires only the known magnetic properties of the two phases and is independent of inclusion size.

Key Results
The authors validated FRESH-MRI across three representative liquid-phase systems:

High Susceptibility Contrast (Air Bubbles in Water):
- In a bubble column, air bubbles induce strong frequency shifts that cause severe signal attenuation in traditional amplitude-based MRI.
- FRESH-MRI successfully generated quantitative, spatially resolved volume fraction maps where conventional imaging failed.
- The technique simultaneously captured liquid velocity fields, revealing entrainment effects and mass conservation patterns (e.g., negative velocities near walls).
- A limiting volume fraction ( $\phi_{lim} \approx 30\%$ ) was identified where phase wrapping occurs, a limit that can be extended via parameter adjustment or phase-unwrapping algorithms.
Low Susceptibility Contrast (Polystyrene Particles in Water-Glycerol):
- In solid-liquid sedimentation experiments, the susceptibility contrast was weak, resulting in a lower signal-to-noise ratio for phase-based measurements compared to amplitude-based ones.
- Despite this, FRESH-MRI measurements of mean volume fraction showed strong agreement with reference amplitude-based measurements and Free Induction Decay (FID) data.
- The method successfully resolved the spatial segregation of particles, including the formation of concentric rings near the vessel walls consistent with wall-induced ordering effects.
Low Susceptibility Contrast (Sunflower Oil Droplets in Water):
- In liquid-liquid emulsion creaming experiments, FRESH-MRI tracked the evolution of volume fraction over time.
- The results demonstrated the formation of a dense cream layer at the top of the vial, with volume fractions approaching the random loose packing limit ( $\phi_{rlp} \approx 55\%$ ).
- Minor discrepancies between phase and amplitude results were attributed to imperfect fat saturation in the scanner, but the overall spatial distribution and temporal trends were consistent.

Significance and Claims
The paper claims that FRESH-MRI provides a general, non-invasive method for obtaining quantitative, three-dimensional, and multi-parametric measurements of multiphase flows. Its primary significance lies in:

Turning Artifacts into Data: It converts a traditionally adverse phenomenon (susceptibility-induced artifacts) into a robust measurement principle.
Calibration-Free Operation: The method requires no calibration, tracer particles, or susceptibility matching, relying solely on known magnetic properties.
Versatility: It is applicable across diverse systems (gas-liquid, solid-liquid, liquid-liquid) and can be implemented on standard MRI hardware without specialized sequences or post-processing tomographic reconstruction.
Model Validation: By providing direct access to both concentration and velocity fields, FRESH-MRI offers essential data for validating mathematical models, informing closure relations, and understanding microscale interactions in dense multiphase flows.

The authors position FRESH-MRI as a complementary tool, particularly powerful in high-susceptibility contrast systems (like bubbles) but also effective in low-contrast regimes when combined with amplitude-based analysis. Potential applications highlighted include lithium-ion battery recycling (sedimentation of materials), green hydrogen production (bubbly flows), and biomedical detection of magnetic nanoparticle-labeled cells.

1. The "Magnetic Tug-of-War"

2. Turning Noise into a Ruler

3. What They Tested

4. The Best Part: No Extra Stuff Needed

Summary

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