1. Iterative Optimization Method for Accelerated Acquisition and Parameter Estimation in Quantitative Magnetization Transfer Imaging
#3336 70
Computer
Henrik Marschner, André Pampel, & Harald E. Möller
Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
M0b/M0a
M0b/M0a
MT data
MT data
12 h
2 sec
Reference parameter estimation by non-linear least-squares fitting using 19 samples.
Artificial Neural Networks based parameter estimation using 8 optimal samples and no T1obs map.

2. Background: Quantitative Magnetization Transfer
Information about macromolecules can be obtained from magnetization-transfer (MT) experiments [1,2].
Quantitative MT techniques (qMT) are preferable.
Limitations:
Time-consuming scanning protocol.
Multiple images at various MT saturation frequencies/powers.
𝐵1 and 𝐵0 field maps needed for corrections.
𝑇 1 𝑜𝑏𝑠 map to obtain pool sizes.
Time-consuming parameter fitting.
[1] S.D. Wolff & R.S. Balaban. Magn. Reson. Med. 10: 135 (1989). [2] C. Morrison et al. J. Magn. Reson. B 108:103 (1995).

3. Purpose of this Work
Further investigation of artificial neural networks (ANNs) for accelerated parameter estimation[3].
Examination of input variable selection (IVS) as a method to iteratively optimize the design of qMTI experiments.
[3] H. Marschner, D.K. Müller, A. Pampel, J. Neumann, H.E. Möller. Proc. ISMRM 21: 4239 (2013).

4. Experiments: Pulsed MT Imaging
Experiments in 7 healthy 3T (Magnetom TIM Trio, Siemens, Erlangen, Germany); 32-channel head coil.[4]
Single-slice MT-prepared GRE acquisitions (19 off-resonance frequencies; 2 MT pulse flip angles 180o and 540o; NA=8);
𝐵0 map to correct off-resonance frequencies in the MT parameter estimation.
𝐵1 map to correct flip angles in the MT parameter estimation.
𝑇 1 𝑜𝑏𝑠 map.
[4] D.K. Müller, A. Pampel, H.E. Möller. J. Magn. Reson. 230: 88 (2013).

5. Conventional MT Parameter Fitting I
Binary spin-bath model:[5]
Liquid pool “a” and semi-solid pool “b”.
Fitting of 6 model parameters ( 𝑇 1 𝑏 1s):
𝜎 𝑀 0 𝑎 (size of pool “a” with weighting factor);
𝑀 0 𝑏 / 𝑀 0 𝑎 (relative size of pool “b”);
𝑅 𝑀 0 𝑎 (exchange rate constant);
𝑇 1 𝑎 =1/ 𝑅 1 𝑎 (longitudinal relaxation time of pool “a”);
𝑇 2 𝑎 =1/ 𝑅 2 𝑎 (transverse relaxation time of pool “a”);
𝑇 2 𝑏 =1/ 𝑅 2 𝑏 (transverse relaxation time of pool “b”).
[5] R.M. Henkelman et al. Magn. Reson. Med. 29: 759 (1993).

6. Conventional MT Parameter Fitting II
No analytical fitting function available.
Parameter fitting by numerical simulation of entire pulse sequence.
Fitting performed using a Levenberg-Marquardt algorithm.
Optimized calculation and fitting routines from Ref. [4].
[4] D.K. Müller, A. Pampel, H.E. Möller. J. Magn. Reson. 230: 88 (2013).

7. qMT Parameter Estimation with Artificial Neural Networks
General ANN Training
Input:
Z-spectra from 4 healthy volunteers (excluding voxels exceeding an error bound during fitting).
𝐵0, 𝐵1, 𝑇 1 𝑜𝑏𝑠 maps.
Target:
MT parameters obtained by conventional fitting.
𝑆/𝑆0
100
1000
10000
𝑓𝑠𝑎𝑡 / Hz
Acquired data point

8. Implementation Details: ANN Training
MatLab version (R2013b); Neural Network Toolbox version 8.1 (R2013b).
Multilayer feed-forward neural networks.
4-5 hidden layers with ~100 total neurons.
Tan-sigmoid transfer function between hidden layers.
Linear transfer function in output layer.
Learning algorithms: Scaled Conjugate Gradient and Levenberg- Marquardt; generalization via Early Stopping.
Ratio of training, testing, and validation datasets: 0.7:0.15:0.15.
Interleaved Data Division.

9. Iterative Optimization of Z-Spectrum Sampling
ANNs process Z-spectrum samples as part of their input variables.
Application of input variable selection (IVS) methods.[6]
100
1000
10000
𝑓𝑠𝑎𝑡 / Hz
𝑆/𝑆0
Data point selected by iterative optimization
[6] R. May, G. Dandy, H. Maier. In: K. Suzuki (Ed.); Artificial Neural Networks - Methodological Advances and Biomedical Applications; pp , InTech, Rijeka (2011).

10. Input Variable Selection for ANNs
Backward elimination of input variables.
Initial conditions:
Input:
Acquired Z-spectra (multiple qMT experiments with different saturation powers, off-resonance frequencies, and repetition times).
Maps of 𝐵0, 𝐵1, 𝑇 1 𝑜𝑏𝑠 .
𝑆/𝑆0
100
1000
10000
𝑓𝑠𝑎𝑡 / Hz
Acquired data point

11. Input Variable Selection for ANNs
Backward elimination of input variables.
Constant conditions:
Target:
Selection of MT parameters obtained by conventional fitting of recorded data.

12. Input Variable Selection for ANNs
Backward elimination of input variables.
Steps per optimization iteration:
Input:
Temporarily eliminate one out of all available input variables.
Train networks on reduced set of input variables.

13. Input Variable Selection for ANNs
Permutations
Backward elimination of input variables.
Steps per optimization iteration:
Input:
Temporarily eliminate one out of all available input variables.
Train networks on reduced set of input variables.
Repeat training for each permutation of “eliminating one”.
Permanently eliminate the input variable of permutation with least estimation error. 1 2 3

14. Input Variable Selection for ANNs
Backward elimination of input variables.
Course over all optimization iterations:
Input:
Consecutively eliminate all but one final input variable.

15. Input Variable Selection for ANNs
Backward elimination of input variables.
Course over all optimization iterations:
Optimization procedure:
Use weights to favor certain qMT parameters in the estimation.
Apply different error measures to modulate the optimization outcome.

16. Input Variable Selection for ANNs
Backward elimination of input variables (IVs)
Course over all optimization iterations:
Example:
Estimating only M0b/M0a.
Mean squared error (MSE) of ANN training as error measure.
Optional: no T1obs in IVs.

17. Input Variable Selection for ANNs
Backward elimination of input variables (IVs)
Course over all optimization iterations:
Example:
Estimating only M0b/M0a.
Mean squared error (MSE) of ANN training as error measure.
Optional: no T1obs in IVs.
Reference
18 IVs
8 IVs
6 IVs
4 IVs

18. Input Variable Selection for ANNs
Backward elimination of input variables (IVs)
Course over all optimization iterations:
Example:
Estimating only M0b/M0a.
Mean squared error (MSE) of ANN training as error measure.
Optional: no T1obs in IVs.
Reference
18 IVs R=0.88
8 IVs R=0.75
6 IVs R=0.85
4 IVs R=0.69
Correlation plots of reference vs. estimated values of M0b/M0a.

19. Input Variable Selection for ANNs
Backward elimination of input variables (IVs)
Course over all optimization iterations:
Example:
Estimating only M0b/M0a.
Mean squared error (MSE) of ANN training as error measure.
Optional: no T1obs in IVs.
Reference
18 IVs
8 IVs
6 IVs
4 IVs
Course of IV elimination.

20. Evaluation of qMT Parameter Maps
Example experiment
Optimization settings:
19 recorded Z-spectrum samples.
Maps of B0, B1 and T1obs.
Data from 4 subjects for training, from 3 subjects for evaluation.
Equal weights for each qMT parameter map.
MSE of ANN training as error measure.

21. Evaluation of qMT Parameter Maps
Example experiment
ANN settings:
6 independent ANNs, one per qMT parameter.
4 hidden layers with 20, 40, 30, and 10 neurons.
Levenberg-Marquardt training algorithm.
Training samples collected from 4 subjects.

22. Results: qMT Parameter Maps
𝑀 0 𝑏 / 𝑀 0 𝑎 (pool-size ratio)
0.35
0.22
0.10
ANN
FIT
𝑀 0 𝑏 / 𝑀 0 𝑎
Map obtained from sparsely sampled Z-spectrum (6 IVs) agrees well with reference.
Parameter map reproduces fine details even without averaging effect from denser sampling.
Parameter estimation is much faster (factor of ~20,000) compared to conventional fitting once the ANNs are trained.

23. Results: qMT Parameter Maps
𝑇 2 𝑏 (semi-solid pool) 15 11 8
𝑇 2 𝑏 / µs
ANN
FIT
Parameter maps agree well.

24. Results: qMT Parameter Maps
𝑅 1 𝑎 (liquid pool) 2
𝑅 1 𝑎 / s−1
1.25
ANN
FIT
0.5
Small deviations in areas of larger errors in the conventional fits.

25. Results: qMT Parameter Maps
𝑅 𝑀 0 𝑏 (forward exchange rate constant) 5
2.5
𝑅 𝑀 0 𝑏 / s−1
ANN
FIT
Small deviations in areas with substantial inhomogeneity in B0 or B1.

26. Results: qMT Parameter Maps
𝑅 𝑀 0 𝑎 (backward exchange rate constant) 20 10
𝑅 𝑀 0 𝑎 / s−1
ANN
FIT
Small deviations in areas with substantial inhomogeneity in B0 or B1.

27. Discussion I
ANNs, if sufficiently trained by a few densely sampled data sets, enable parameter estimation from sparsely sampled MT data. A complete training on a single slice takes less than 1 hour.
Parameter estimation is much faster with relative computation times per slice of less than 2 s compared to ~12 hours required for conventional fitting without simplifying assumptions.

28. Discussion I
ANNs, if sufficiently trained by a few densely sampled data sets, enable parameter estimation from sparsely sampled MT data. A complete training on a single slice takes less than 1 hour.
Parameter estimation is much faster with relative computation times per slice of less than 2 s compared to ~12 hours required for conventional fitting without simplifying assumptions.
Option to save scan time due to reduction of required number of Z- spectrum samples.

29. Discussion II
Variable settings in the optimization process allow for the search for individually optimized sampling patterns, minimizing the total acquisition time while maximizing qMT estimation quality.
Observations show that the minimum number of required Z- spectrum samples varies between 4 and 8, depending on the parameter(s) of interest.
More steps in the variation of the saturation power helps to minimize the number of required Z-spectrum samples.

30. Thank you for your interest!
Acknowledgements:
Funded by the Helmholtz Alliance ICEMED—Imaging and Curing Environmental Metabolic Diseases.
Thanks to Dirk K. Müller for providing the MRI data.