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Fitting Simulated Data

Two-point search (Triay Bagur et al. 2019)

Reminder:

Frequencies in 1000 runs with same signal different noise.

Fitting model:

Initial: ρw = 1, ρf = 0

Initial: ρw = 0, ρf = 1

Fat fraction:

R2* = 0

True FF = 0.7

R2* = 300

True FF = 0.7

Chemical Shift/Dixon MRI

The generated signal will have S(0) = 1.

However, the real data will have varing S(0) values.

The signals behave the same way after scalling.

Simulating the noisy data with SNR of 70[1].

Fitting a single signal

Signals for TE = every 0.1ms between 0 and 10ms.

Signals for TE = [1.15, 2.3, 3.45, 4.6, 5.75, 6.9] ms

SSD objective:

References

Initial ρw = 1, ρf = 0

Initial ρw = 0, ρf = 1

Local miminum:

simulated noisy signal

Magnitude

fitted signal

Questions?

Magnitude

Constants chosen for the simulated data:

ρw = 0.3, ρf = 0.7, r = [0.087, 0.694, 0.128, 0.004, 0.039, 0.048], freq = [-0.498, -0.447, -0.345, -0.261, -0.063, 0.064] kHz

  • Bray, Timothy J. P., Alan Bainbridge, Emma Lim, Margaret A. Hall-Craggs, and Hui Zhang. 2023. ‘MAGORINO: Magnitude-Only Fat Fraction and R*2 Estimation with Rician Noise Modeling’. Magnetic Resonance in Medicine 89 (3): 1173–92. https://doi.org/10.1002/mrm.29493.

  • Bray, Timothy JP, Manil D Chouhan, Shonit Punwani, Alan Bainbridge, and Margaret A Hall-Craggs. 2018. ‘Fat Fraction Mapping Using Magnetic Resonance Imaging: Insight into Pathophysiology’. The British Journal of Radiology 91 (1089): 20170344. https://doi.org/10.1259/bjr.20170344.

  • Dixon, W T. 1984. ‘Simple Proton Spectroscopic Imaging.’ Radiology 153 (1): 189–94. https://doi.org/10.1148/radiology.153.1.6089263.

  • Horng, Debra E., Diego Hernando, Catherine D. G. Hines, and Scott B. Reeder. 2013. ‘Comparison of R2* Correction Methods for Accurate Fat Quantification in Fatty Liver’. Journal of Magnetic Resonance Imaging : JMRI 37 (2): 414. https://doi.org/10.1002/jmri.23835.

  • Li, Jianqi, Huimin Lin, Tian Liu, Zhuwei Zhang, Martin R. Prince, Kelly Gillen, Xu Yan, et al. 2018. ‘Quantitative Susceptibility Mapping (QSM) Minimizes Interference from Cellular Pathology in R2* Estimation of Liver Iron Concentration’. Journal of Magnetic Resonance Imaging 48 (4): 1069–79. https://doi.org/10.1002/jmri.26019.

  • Triay Bagur, Alexandre, Chloe Hutton, Benjamin Irving, Michael L. Gyngell, Matthew D. Robson, and Michael Brady. 2019. ‘Magnitude‐intrinsic Water–Fat Ambiguity Can Be Resolved with Multipeak Fat Modeling and a Multipoint Search Method’. Magnetic Resonance in Medicine 82 (1): 460–75. https://doi.org/10.1002/mrm.27728.

Phantom Data

Doing two point search for the phantom data:

Why does ambiguity occur?

256x256x20x6

Single Peak Model

(from the single peak model)

FF map

R2* map

(by Euler's Formula)

Fat/Water Ambiguity

The signal for voxel (80, 145) at layer 12

Cross section of the phantom data at layer 12,

across different TEs

(Single Peak Model)

(because )

This representation of |S|^2 makes it clear that the signal magnitude function|S| is symmetric in the fat/ water density parameters.

Multipeak Simulated Data

Ambiguity Doesn't always occur when there are multiple peaks.

Fitting subject data (320, 320, 40, 6)

Subject data at layer 20

Fat fraction map

R2* map

Multi-Peak Model

(no attenuation)

Background

(attenuation)

Further tasks:

Models

We model S as a function of .

  • Single Peak Model

Known Parameters

  • Multi-Peak Model
  • no attenuation
  • with attenuation

The SSD for different R2* and Fat fraction pairs with ground truth R2* = 300, FF=0.7

Alternative Visualisation

  • DIXON method (Dixon 1984)
  • Applications in the liver, pancreas, muscle and bone marow (Bray et al. 2023)
  • Measures fat fraction (FF)
  • Almost all signals in MRI comes from fat and water

  • The advantage
  • Confounder correction, R2* and FF measured at the same time

  • Why is R2* important?
  • A confounder (Li et al. 2018), may bias FF measurements (Bray et al. 2018)

3d plot here

Background

Distribution of the magnitude of noise

Bray et al. (2018)

  • Existing work
  • Complex fitting: unrealistic
  • Magnitude fitting: simple

  • Challenge
  • Fat-water ambiguity (Bray et al. 2018)

  • Solution
  • Two-point search (Triay Bagur et al. 2019)
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