Iterative Progressive Length Conjugate Gradient Reconstruction in MR-PARSE
Charles G Cantrell1, Parmede Vakil1,2, Donald R Cantrell3, Yong Jeong1, Sameer A Ansari3, and Timothy J Carroll1,3

1Biomedical Engineering, Northwestern, Chicago, IL, United States, 2College of Medicine, University of Illinois, Chicago, IL, United States, 3Radiology, Northwestern, Chicago, IL, United States

Synopsis

We have found that performing iterative PLCG dramatically (on average 55% better) improves reconstruction quality of an MR-PARSE acquisition. Moreover, iterative PLCG has shown to be capable of reconstruction in regions with large susceptibility artifact. Consistent frequency measurements allow us to remove static offsets caused by air interfaces near the earholes and sinuses leaving dynamic frequency offsets which transpose linearly to OEF. Furthermore, our approach to prevent local minima solutions, through the use of an iterative PLCG, represents a new approach that may improve upon many other complex reconstruction methods.

Introduction

Parameter Assessment by Retrieval from Signal Encoding (PARSE) is a multi-parameter imaging technique [1]. PARSE simultaneously extracts relaxation rate (R2*), local frequency offsets (δω), and proton density (M0) maps from a single FID by utilizing a longer acquisition window to exacerbate R2* decay and ω shifts in the signal received by the scanner. The speed of PARSE (65ms per image) and its ability to measure phase shifts make it ideal for measuring temporal BOLD fluctuations (used in reactive Oxygen Extraction Fraction (OEF) calculations). Here we develop an improved PARSE reconstruction algorithm that prevents local minima solutions and provides higher quality images.

Sequence and Recon

For measurement, we use a rosette trajectory--characterized by fast oscillating frequency (ω1 = 3874.8 Hz) and a slow rotating frequency (ω2 = 1610.8 Hz). PARSE provides us with the ability to measure high Signal-to-Noise (SNR) phase accrual because of the frequent re-sampling of the low frequency/center of k-space. An iterative Progressive Length Conjugate Gradient (PLCG) algorithm is used to solve a discretized form of Equation 1. $$ S(t) = \int\int{M_0(x,y)e^{-(R_2^*(x,y)-i\omega(x,y))t}e^{-2\pi i(k_xx+k_yy)}dxdy} $$ Between every iteration of PLCG the result is perturbed and the solution is again allowed to relax using conjugate gradient. At each iteration the least squares estimate is obtained by minimizing the residual between the observed signal and model estimate. The estimate is determined to be adequate when the same minimal square error is reached on 3 separate PLCG iterations. This occurred within (10.4 ± 4.3) iterations.

Methods

Utilizing the sequence described above, ten hemodynamically compromised subjects (M/F 5/5, <age> = 58.2 ± 9.9 years) and 3 healthy volunteers (M/F, 2/1, <age> = 31.3 ± 2.5) were tested. For each subject we acquired a single slice 2D image (5.0 mm thick, 220 mm x 220 mm FOV, 96x96 matrix, resolution = 2.3 x 2.3 x 5.0 mm3). In one healthy volunteer we acquired five slices separated by 15 mm from the ventricles up. FID data were exported and reconstructed offline. The iterative PLCG reconstruction sum squared signal error was compared against that of the more standard PLCG algorithm. To examine the reconstruction effect on OEF reactivity, estimated local frequency offsets were transposed to OEF using a linear relationship (assuming constant Hematocrit of 18 p.p.m.) [2].

Results

Student’s t-test analysis shows a statistically significant reduction of sum squared error in the iterative PLCG reconstruction vs the more standard PLCG (p< 0.001, Figure 1a) with an average error reduction of 55%. The more accurate fitting results in better anatomical images (shown in Figure 1b). Iterative PLCG yielded improved measured mean OEF in non-affected normal brain parenchyma to 36.87 ± 6.6% and showed affected regions in symptomatic patients reaching 84.05 ± 4.54%--both of which correlate well with literature. Reconstruction has shown to be quite robust even in regions with large susceptibility artifact (Figure 2).

Discussion/Conclusion

We have found that performing iterative PLCG dramatically improves reconstruction quality of an MR-PARSE acquisition. Moreover, iterative PLCG has shown to be capable of reconstruction in regions with large susceptibility artifact (near earholes and sinus, Figure 2). For the purpose of OEF measurements, our primary goal, stable and accurate measurements of frequency shifts are vital. Consistent frequency measurements allow us to remove static offsets caused by air interfaces near the earholes and sinuses leaving dynamic frequency offsets which transpose linearly to OEF. Furthermore, our approach to prevent local minima solutions, through the use of an iterative PLCG, represents a new approach that may improve upon other complex reconstruction methods.

Acknowledgements

AHA 14PRE20380810, NIH/NHLBI R01 HL088437

References

[1] Twieg, MRM 2002, [2] Menon, JCBFM 2014

Figures

Figure 1: (A) Table of patient data, sum square error of both reconstruction techniques and percent error improvements. (B) A sample reconstruction showing the improvement of dw, R2* and M0 maps under the iterative PLCG method.

Figure 2: Iterative PLCG PARSE reconstructed images of a healthy volunteer. Higher rows represent higher slices. Notice how the ear holes and sinuses cause frequency offsets.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
1772