Application of Partial Least Squares regression for Fast and Robust Dictionary Matching for Magnetic Resonance Fingerprinting
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 MRF1. PLS consists of Principle Component Analysis (PCA) and regression analysis2, 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 T1 and T2 ranging from 100-5000ms and 20-2000ms. The steps size selected for dictionary matching for T1 was 100 to 2000 in steps of 20 , 2000 to 5000 in steps of 300. The steps size selected for T2 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 T1/T2 were the response variables. The response variables were computed based on 109 TR/alpha combinations. Different combinations of T1/T2 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 T1 and T2 maps obtained through PnP-DP [6] matching is as shown in the first column of figure 1. The second column shows the T1 and T2 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 T1 &T2 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 T1& T2of 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

1.Dan 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

3. Gaston Sanchez “PLS path modeling with R” Trowchez Editions, Berkeley, 2013.

4. Hanicke W et al “An Analytical Solution to SSFP signal in MRI ”Magnetic Resonance in Medicine 2002

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

Figures

Figure 1: First row and second row shows the T1 map and T2 map obtained through PnP-DP and PnP-PLS respectively.

Figure 2: (a) shows the T1/T2 maps for different noise levels ( 8, 11, 15db SNR) introduced at different places during the signal evolution using PnP-PLS, (b) shows the T1/T2 maps for different noise levels (8, 11, 15db SNR) introduced at different places during the signal evolution using PnP-DP

Table 1: Shows the previously reported T1/T2 values for different tissue types of the brain and T1/T2 values obtained through PnP-PLS

Table 2: Shows the T1 values from (PnP-DP) for different tissue types at different SNR levels and also from PnP-PLS

Table 3: Shows the T2 values from (PnP-DP) for different tissue types at different SNR levels and also from PnP-PLS



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
4332