Shivaprasad Ashok Chikop1, Vimal Chandran2, Imam Shaik1, Rashmi Rao1, Mauricio Antonio Reyes Aguirre2, and Sairam Geethanath1
1Medical Imaging Research Center, Dayananda Sagar Institutions, Bangalore, India, 2Institute of Surgical Technology and Biomechanics, University of Bern, Bern, Switzerland
Synopsis
The
step size of the parameters used for simulation of dictionary determines the
parameters being determined. Partial Least squares (PLS) can be used as a
general frame work for fast and robust dictionary matching. Regression co-efficient
matrix obtained from PLS can be used for localizing the different brain tissue
types thus avoiding iterative searching.
The increase in contrast between the grey matter and white matter can be
attributed to the intermediate values generated by PLS based matching. PLS
matches comparatively better at low SNR images compared to the straight forward
dot product method.Purpose
Dictionary
building is a key component of Magnetic Resonance Fingerprinting (MRF) and the
step sizes of the parameters simulated typically determines the quanta of the
parameters being determined. Current work involves demonstration of Partial
Least Squares (PLS) regression as a general framework for rapid and noise
tolerant dictionary matching for MRF
1. PLS consists of Principle Component
Analysis (PCA) and regression analysis
2, 3. PLS provides the
intermediate values not defined as part of the dictionary steps as it involves
a linear summation of regression coefficients. In addition, it also performs
denoising (PCA part of PLS) of the maps in the presence of low SNR relevant to
acquisitions like MRF. PLS provides the regression coefficient matrix and hence
iterative search is not necessary. This provides for fast dictionary matching.
Methods
PSIF
is a Steady State Free Precession (SSFP) based sequence. The echo intensity of
PSIF sequence can be obtained using the analytical equation using equation (17)
from ref.
4. The dictionary
was generated using the analytical equation with TR/alpha ranging from
0-100ms/0-900 and T
1 and T
2 ranging from 100-5000ms
and 20-2000ms. The steps size selected for dictionary matching for T
1
was 100 to 2000 in steps of 20 , 2000 to
5000 in steps of 300. The steps size selected for T
2 was 20 to 100
in steps of 10, 100 to 200 in steps of 50 and 200 to 3000 in steps of 200. Three
data sets with 109 brain images were acquired from Siemens Avanto 1.5T scanner
with TR/alpha ranging from 15-66ms/170-350 respectively
with minimum echo time (TE). TR/alpha combinations were considered as predictor
and T
1/T
2 were the response variables. The response
variables were computed based on 109 TR/alpha combinations. Different
combinations of T
1/T
2 based on the step size employed to
build the dictionary. Regression co-efficient matrix (β) was obtained through
training on this dictionary. Each signal evolution obtained from the scanner
was multiplied with the regression co-efficient matrix for localizing different
brain tissues. PLS was tested for its ability of matching by considering
different Signal-to-Noise Ratio (SNR) images as compared to traditional dot
product matching for in vivo data. Gaussian
noise was simulated for required SNR values of 8, 11 and 15db as in ref 5.
The noise generated for required SNR was introduced at different time intervals
in the data. Noise was introduced to the data at three different intervals
i.e., the first 10 images, time points 51 - 60 and last 10 images. The noise-corrupted data was then used for
map generation using both PLS and dot product methods.
Results
The
T
1 and T
2 maps obtained through PnP-DP [6] matching is as
shown in the first column of figure 1. The second column shows the T
1
and T
2 maps obtained through PnP-PLS method. It can also be noticed
that the relaxation time values lie in the physiological ranges for these
tissues. The values of T
1 &T
2 obtained for different
tissue types of the brain through PnP-PLS is as shown in the table 1. It can be
observed that these values are similar to previously published values for these
parameters.
The
results for Gaussian noise simulated for PnP-PLS and PnP-DP is as shown in
figure 2. The qualitative results show that at lower
SNR levels PnP-PLS can match better compared to PnP-DP. It can also be observed
that PnP-PLS can match better in the presence of noise at the intermediate and end
of the signal evolution as compared to the beginning of the signal evolution. This
might be attributed to the relatively low TR combinations employed in PnP-DP during the first 10 acquisitions and hence inherently low SNR data. Table 2 and
table 3 shows the values T
1& T
2of different brain
tissue types at various noise levels
Discussion and conclusion
Higher contrast
between grey and white matter in PnP-PLS can be attributed to the intermediate
values provided by regression coefficients through PLS matching. This enables
determination of parametric values lying between the discrete steps of the
dictionary. PCA component of PLS has the ability to denoise the data and
perform linear regression significantly better than the straight forward dot
product. Performance of PLS on retrospective noisy data is validated by the
results shown in figure 2. Current and future work involves application of this
method to derive partial volume of gray matter, white matter and CSF within a
given voxel and generate probability maps of these quantities.
Acknowledgements
1. This work was supported by Vision Group on Science and Technology (VGST), Govt. of Karnataka
2. Department of Science and Technology (DST), Govt. of India under the program Technology Systems Development (TSD) for the project “Novel acquisition and reconstruction strategies to accelerate magnetic resonance imaging using compressed sensing”, No: DST/TSG/NTS/2013/100-G.
References
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Ma et al. “Magnetic Resonance Fingerprinting” Nature 2013; 495 (7440): 187-92
2.
Randall D. Tobias “An Introduction to Partial Least Squares”. SUGI
Proceedings, 1995
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Gaston Sanchez “PLS path
modeling with R” Trowchez
Editions, Berkeley, 2013.
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5. Geethanath et al “Retrospective analysis
of application of compressive sensing to 1H MR metabolic imaging of the human
brain” SPIE 2010
6. Chikop et al “Plug-n-Play Magnetic
Resonance Fingerprinting” ISMRM- 2015