Abstract
Recently, a number of magnetic resonance imaging protocols have been reported that seek to exploit the effect of dissolved oxygen (O2, paramagnetic) on the longitudinal 1H relaxation of tissue water, thus providing image contrast related to tissue oxygen content. However, tissue water relaxation is dependent on a number of mechanisms and this raises the issue of how best to model the relaxation data. This problem, the model selection problem, occurs in many branches of science and is optimally addressed by Bayesian probability theory. High signal-to-noise, densely sampled, longitudinal 1H relaxation data were acquired from rat brain in vivo and from a cross-linked bovine serum albumin (xBSA) phantom, a sample that recapitulates the relaxation characteristics of tissue water in vivo. Bayesian-based model selection was applied to a cohort of five competing relaxation models: (1) monoexponential, (2) stretched-exponential, (3) biexponential, (4) Gaussian (normal) R 1-distribution, and (5) gamma R 1-distribution. Bayesian joint analysis of multiple replicate datasets revealed that water relaxation of both the xBSA phantom and in vivo rat brain was best described by a biexponential model, while xBSA relaxation datasets truncated to remove evidence of the fast relaxation component were best modeled as a stretched exponential. In all cases, estimated model parameters were compared to the commonly used monoexponential model. Reducing the sampling density of the relaxation data and adding Gaussian-distributed noise served to simulate cases in which the data are acquisition-time or signal-to-noise restricted, respectively. As expected, reducing either the number of data points or the signal-to-noise increases the uncertainty in estimated parameters and, ultimately, reduces support for more complex relaxation models.
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Acknowledgements
We are pleased to contribute this article in celebration of Professor James S. Hyde on the special occasion of his 85th birthday. Research supported, in part, by the McDonnell Center for Cellular and Molecular Neurobiology (JA) and National Institute of Health Grants: P50 CA094056, R01 HD086323, 5T32EB014855, and the Small Animal Cancer Imaging Shared Resource of the Alvin J. Siteman Cancer Center (P30 CA091842). The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.
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Meinerz, K., Beeman, S.C., Duan, C. et al. Bayesian Modeling of NMR Data: Quantifying Longitudinal Relaxation in Vivo, and in Vitro with a Tissue-Water-Relaxation Mimic (Crosslinked Bovine Serum Albumin). Appl Magn Reson 49, 3–24 (2018). https://doi.org/10.1007/s00723-017-0964-z
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DOI: https://doi.org/10.1007/s00723-017-0964-z