Signal modeling for quantitative magnetic resonance imaging

Andreas Petrovic

Research output: ThesisDoctoral Thesis


Quantitative magnetic resonance imaging (qMRI) attempts to determine physical and physiological parameters intrinsic to the body. This methodical approach allows for more objective medical analysis and diagnosis compared to the individual interpretation
of conventional MR scans with a contrast that can substantially vary depending on the sequence and measurement parameters used. Furthermore, technical shortcomings, such as field inhomogeneity, can impair image contrast and obfuscate relevant details. Those limitations are alleviated using quantitative MRI but only inasmuch as the applied measurement and analysis techniques are accurate and precise. Since the sought physical parameters are mostly estimated from data using nonlinear models, the accuracy of those results is strongly dependent on the validity of the underlying model and its assumptions.
This thesis is dedicated to calculating, testing, and applying newly derived models for multi-echo spin-echo sequences for the quantification of the transverse relaxation time parameter T2 using the Generating Functions formalism (z-transform). To that end, existing formulas were extended and refined to incorporate RF field inhomogeneities and effects of non-ideal slice profiles into the parameter estimation process. Beyond that, a closed form time domain solution for the decay of transverse magnetization in
multi-echo spin-echo sequences was derived. Furthermore, a closed form solution also for the longitudinal magnetization was found that can be applied in the simultaneous estimation of T1 and T2 with a modified multi-echo spin-echo sequence.
The presented models and their impact on the parameter estimation accuracy were tested using simulations and experiments on MR phantoms. In vivo measurements were conducted and the results were compared to gold standard and other methods, as well as literature values.
In conclusion, the newly developed signal models could in all cases outperform the established methods. Simulations proved a high accuracy and precision and data from measurements showed excellent agreement with the model computations.
Original languageEnglish
  • Stollberger, Rudolf, Supervisor
  • Bammer, R., Supervisor, External person
Publication statusPublished - 2020


  • T2 mapping
  • quantitative MRI
  • z-transform
  • Generating functions
  • multi-echo spin-echo

Cite this