Bi-exponential proton transverse relaxation rate (R2) image analysis using RF field intensity-weighted spin density projection: potential for R2 measurement of iron-loaded liver
Introduction
Magnetic resonance imaging methods for the non-invasive measurement of liver iron concentration have focused primarily on quantifying the proton transverse relaxation enhancement caused by biogenic iron oxide deposits within the liver. The intent behind these studies is to determine a calibration curve that relates the reduction in hydrogen proton signal intensity within the liver with the liver iron concentration, either through the liver signal intensity from a single image [1], [2], or from the liver transverse relaxation rate (R2) calculated from multiple spin-echo images [3], [4], [5]. Of these two approaches, signal intensity ratio (SIR) methods are inherently less sensitive than relaxation rate methods, as the SIR is effectively calculated for a single point in time on the transverse magnetisation decay curve.
The factors affecting the accuracy, sensitivity, and dynamic range of transverse relaxation rate measurements are the spin-echo measurement times at which the images are acquired, the volume of the liver over which the relaxation rates are calculated, the measured signal intensity, and the image processing scheme used to model the signal decay. Where the spin-echo times are too long to enable the measurement of sufficient signal intensity for the accurate calculation of transverse relaxation times, no correlation with liver iron concentration has been found [6], [7]. However, for shortened image acquisition times, a significant correlation between R2 (1/T2) and liver biopsy iron concentration has been observed [3], [4], [5]. The dynamic range for the quantification of liver iron levels is further improved by magnetic resonance spectroscopy (MRS) techniques [8], [9]. However, MRS techniques sacrifice imaging capability for the improved signal-to-noise ratio (SNR) of measuring a single enlarged volume element at shorter echo times. Consequently, localized volume spectroscopy provides only a single value for the liver iron concentration throughout the measurement volume. R2 imaging of the liver, on the other hand, yields information on the variation in iron concentration throughout the liver, enabling both the average iron concentration to be calculated and the variation in iron concentration to be imaged [10], [11].
A limitation of the former transverse relaxation rate measurement techniques [3], [4], [5], [8], [9], [10] is that they all employ mono-exponential analysis for determination of the transverse relaxation processes within the liver. However, given the anatomic and chemical compartmentalisation of the body’s hydrogen protons [12], [13], multi-exponential transverse relaxation is expected of the various organs and tissues of the body. For hereditary hemochromatosis patients, MRS measurements [14] have shown that transverse relaxation processes within iron loaded liver are at least bi-exponential in nature.
To improve the diagnostic capability of R2 measurements of the liver, particularly in relation to the measurement of liver iron overload, the move to bi-exponential analysis of transverse relaxation processes is warranted. Further, to enable accurate bi-exponential transverse relaxation rate analysis across multiple MR platforms, the analysis technique must accommodate both instrument and patient dependencies. The key factors to be taken into account are:
- i)
The change or drift in imaging gain between successive spin-echo measurements.
- ii)
The effects of thermal and structured noise originating from both the instrument and patient on the non-zero baseline noise distribution of the magnitude image data.
- iii)
The noise filtering necessary for accurate determination of the relaxation parameters.
- iv)
The curve fitting procedure for calculation of the relaxation parameters where a small data set is available for analysis; N ≈ 2M, where M is the number of unknown parameters and N is the number of spin-echo images available. A small number of spin-echo images will typically be available for analysis where a single spin-echo imaging methodology is used [3], [4], [10].
In this paper, an R2 image analysis technique is presented which enables the discrimination of bi-exponential transverse relaxation processes in systems with rapid transverse relaxation enhancement, where the transverse relaxation times may be shorter than the minimum echo time that can be measured. The R2 image analysis is facilitated by incorporating an estimate of the initial proton spin density signal within the subject weighted by the spatial variation in RF field intensity. The RF intensity at each point within the region of interest is computed by the solution of a boundary value problem presented by a high spin density, long T2 material encompassing the region for analysis. To evaluate the precision and accuracy of the R2 imaging technique on both mono-exponential and bi-exponential transverse relaxation systems, a series of aqueous manganese chloride (MnCl2) phantoms were studied, from which the bi-exponential system was digitally simulated. The relaxation rates and relative population densities of the two compartments in the bi-exponential system were chosen according to the bi-exponential relaxation properties reported for normal and iron-loaded animal liver [15], [16].
Section snippets
Phantom system preparation
The mono-exponential R2 phantom system consisted of a series of aqueous MnCl2 solutions prepared to concentrations of 0.100, 0.200, 0.300, 0.400, 0.500, 0.600, 0.700, 0.800, 1.000, 1.200, 1.400, 1.600, 1.800, 2.000, 2.400, 2.800 and 3.200 mM. The solutions were imaged in test tubes of 25 mm internal diameter and 25 mL in volume, arranged in alternating high and low concentrations in a cardboard box padded with plastic bags filled with lard. The lard was obtained from commercially extracted pig
Noise distribution modeling
An example of the underlying noise profile in the spin-echo image data is illustrated in Fig. 1 for a region of the background in the 6 ms spin-echo image that was free of image artifacts. The histogram is fitted with both a Rician and generalized Poisson distribution, for which the respective Pearson correlation coefficients are 0.987 and 0.994. The F -test on the reduced χ-squares ratio of the Rician fit to the noise data relative to the GPD is 2.1, which indicates that the GPD is a better
Discussion
The accurate quantification of proton transverse relaxation processes in systems where there is compartmentalisation of the transverse relaxation requires multi-exponential analysis of the transverse magnetisation decay. For example, bi-exponential modeling of transverse relaxation in tissues has been shown to distinguish between the chemical compartmentalisation of hydrogen protons, such as that between water and fat [27], [28], [29], as well as that of different anatomic compartments, such as
Conclusion
The bi-exponential proton transverse relaxation rate image analysis technique presented in this study is particularly well suited to the discrimination of dual compartment transverse relaxation behavior where a limited number of spin-echo images are available for analysis. Further, the method of RF field intensity-weighted spin density projection enables the accurate determination of bi-exponential components in instances of rapid transverse relaxation enhancement, where the transverse
Acknowledgements
We are grateful to the NH&MRC for funding (Project Grant 211947). We would like to thank Dr. Jay Ives for making imaging time available at SKG Radiology’s MRI facilities at the St. John of God Hospital, Subiaco, Western Australia. Erin Robins kindly performed the radiography.
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