This paper describes a quantitative approach to understanding the signal, contrast and weighting of magnetic resonance (MR) images. It uses the concept of pulse sequences as tissue property (TP) filters and models the signal, contrast and weighting of sequences using either a single TP-filter (univariate model) or several TP-filters (the multivariate model). For the spin echo (SE) sequence using the Bloch equations, voxel signal intensity is plotted against the logarithm of the value of the TPs contributing to the sequence signal to produce three TP-filters, an exponential ρm-filter, a low pass T1-filter and a high pass T2-filter. Using the univariate model which considers signal changes in only one of ρm, T1, or T2 at a time, the first partial derivative of signal with respect to the natural logarithm of ρm, T1 or T2 is the sequence weighting for each filter (for small changes in each TP). Absolute contrast is then the sequence weighting multiplied by the fractional change in TP for each filter. For large changes in TPs, the same approach is followed, but using the mean slope of the filter as the sequence weighting. These approaches can also be used for fractional contrast. The univariate TP-filter model provides a mathematical framework for converting conventional qualitative univariate weighting as used in everyday clinical practice into quantitative univariate weighting. Using the multivariate model which considers several TP-filters together, the relative contributions of each TP to overall sequence and image weighting are expressed as sequence and imaging weighting ratios respectively. This is not possible with conventional qualitative weighting which is univariate. The same approaches are used for inversion recovery (IR), pulsed gradient SE, spoiled gradient echo (SGE), balanced steady state free precession, ultrashort echo time and other pulse sequences. Other TPs such as susceptibility, chemical shift and flow can be included with phase along the Y axis of the TP-filter. Contrast agent effects are also included. In the text TP-filters are distinguished from k-space filters, signal filters (S-filters) which are used in imaging processing as well as to describe windowing the signal width and level of images, and spatial filters. The TP-filters approach resolves many of the ambiguities and inconsistencies associated with conventional qualitative weighting and provides a variety of new insights into the signal, contrast and weighting of MR images which are not apparent using qualitative weighting. The TP-filter approach relates the preparation component of pulse sequences to voxel signal, and contrast between two voxels. This is complementary to k-space which relates the acquisition component of pulse sequences to the spatial properties of MR images and their global contrast.
Keywords: Magnetic resonance (MR) imaging; contrast; filters; phase; pulse sequences; quantitation; signal; tissue properties (TPs); weighting.
2020 Quantitative Imaging in Medicine and Surgery. All rights reserved.