Drew Mitchell^{1}, David Fuentes^{1}, Jason Stafford^{1}, James Bankson^{1}, and Ken-Pin Hwang^{1}

A mutual information-based mathematical
framework is developed to quantify the information content of various
acquisition parameters and subsampling approaches. A recursive conditional
formulation quantifies information content given previous acquisitions. This
framework is applied to 3D QALAS. Mutual information between reconstructed M0,
T1, and T2 uncertainty and measurement noise is calculated for an *in silico*
phantom and the results applied to measurements on a System Standard Model 130
phantom. Reconstructions from these measurements demonstrate the potential use
of information theory in guiding pulse sequence design to maximize reconstruction
quality.

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2. Odrobina, E. E., Lam, T. Y. J., Pun, T., Midha, R., & Stanisz, G. J. (2005). MR properties of excised neural tissue following experimentally induced demyelination. NMR in Biomedicine, 18(5), 277–284. https://doi.org/10.1002/nbm.951

3. Zhang, T., Pauly, J. M., & Levesque, I. R. (2015). Accelerating parameter mapping with a locally low rank constraint. Magnetic Resonance in Medicine, 73(2), 655–661. http://doi.org/10.1002/mrm.25161

Figure 1. 3D QALAS pulse sequence diagram. Longitudinal magnetization
is shown as a function of time. The T2 sensitization pulse encodes the T2
relaxation time on the longitudinal axis. One acquisition takes place during
this phase. Four additional acquisitions take place after the T1 sensitization pulse.

Figure 2. Tissue
label map used for the generation of realistic synthetic data. Label 1
corresponds to gray matter, 2 corresponds to white matter, and 3 corresponds to
cerebrospinal fluid. To generate synthetic data, normally distributed values centered
about literature M0, T1, and T2 values are assigned to each respective
tissue type. With these values and the selected acquisition parameter values as
input, the signal model is used to create synthetic measurements, which are
then corrupted by normally distributed noise to simulate measurement data.

Figure 3. Acquisition parameters for the two scans
performed.

Figure 4. Standard
deviations of reconstructed parametric map values (M0, T1, and T2 from left to
right) as a function of mutual information. Each plotted circle represents the
standard deviation of voxel values within one of the phantom’s 14 M0, T1, or T2
elements for the first set of acquisition parameters. Each plotted x represents
the same for the second set of acquisition parameters.

Figure 5. Reconstructed
parametric maps for fully sampled, mutual information-guided subsampled, and empirically
subsampled cases.