title: Incorporating relaxivities to more accurately reconstruct MR images.
abstract: OBJECTIVE
  To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step.
  
  
  METHODS
  In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T2(⁎), T1, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted by image warping, blurring, and loss in image intensity. Although T1 on tissue relaxation time provides valuable quantitative information on tissue characteristics, the T1 recovery term is typically neglected by assuming a long repetition time. In this study, the linear framework presented in the work of Rowe et al., 2007, and of Nencka et al., 2009 is extended to develop a Fourier reconstruction operation in terms of a real-valued isomorphism that incorporates the effects of T2(⁎), ∆B, and T1. This framework provides a way to precisely quantify the statistical properties of the corrected image-space data by offering a linear relationship between the observed frequency space measurements and reconstructed corrected image-space measurements. The model is illustrated both on theoretical data generated by considering T2(⁎), T1, and/or ∆B effects, and on experimentally acquired fMRI data by focusing on the incorporation of T1. A comparison is also made between the activation statistics computed from the reconstructed data with and without the incorporation of T1 effects.
  
  
  RESULTS
  Accounting for T1 effects in image reconstruction is shown to recover image contrast that exists prior to T1 equilibrium. The incorporation of T1 is also shown to induce negligible correlation in reconstructed images and preserve functional activations.
  
  
  CONCLUSIONS
  With the use of the proposed method, the effects of T2(⁎) and ∆B can be corrected, and T1 can be incorporated into the time series image-space data during image reconstruction in a single step. Incorporation of T1 provides improved tissue segmentation over the course of time series and therefore can improve the precision of motion correction and image registration.
authors.affiliation: Center for MR Research, University of Illinois at Chicago, Chicago, IL, USA.
authors.forename: Muge
authors.initials: M
authors.lastname: Karaman
authors.affiliation: Duke/UNC Brain Imaging and Analysis Center, Duke University, Durham, NC, USA.
authors.forename: Iain P
authors.initials: IP
authors.lastname: Bruce
authors.affiliation: Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, WI, USA; Department of Biophysics, Medical College of Wisconsin, Milwaukee, WI, USA. Electronic address: daniel.rowe@marquette.edu.
authors.forename: Daniel B
authors.initials: DB
authors.lastname: Rowe
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Correction; Functional MRI (fMRI); Image reconstruction; Longitudinal relaxation time (T(1)); MR relaxivities; Magnetic resonance imaging (MRI)