Magnetic resonance imaging (MRI) has been used clinically for many years. Image interpretation is almost always qualitative — differences in contrast between anatomical structures are used to distinguish between normal and abnormal tissues. But, from the outset, scientists and clinicians understood the potential power of quantitative MRI (qMRI), which can be used to measure a wide range of chemical, physical and physiological properties. qMRI is becoming more and more common, thanks to technological advancements overcoming some of the inherent challenges, but the uncertainty associated with the measurements obtained is rarely discussed.

This course will help MR physicists determine the measurement uncertainty associated with MRI relaxation parameters. We focus on T₂ measurement throughout, but the content can also be applied to T₁ measurement.

Consisting of one module of three lessons, this course will:

• Describe quantitative MRI relaxation parameters and T₁ and T₂ measurements
• Formulate a weighted non-linear least-squares regression problem, comprising measurement data and a model of the data including the relaxation parameters
• Explore possible ways of quantifying the data uncertainties, which are used in both the formulation of the regression problem and the evaluation of the uncertainties of the estimates of the relaxation parameters
• Describe how ‘black box’ software can be harnessed to deliver estimates of the relaxation parameters
• Look at ways of validating the fitted model, which gives us confidence in the estimates of the relaxation parameters
• Examine how the outputs of the ‘black box’ are used to evaluate the uncertainties of the estimates of the relaxation parameters
• Consider an alternative approach to obtaining estimates of the relaxation parameters, which involves transforming the regression problem to a weighted linear least-squares problem

The course was developed for MR physicists who understand the measurement data they obtain. They may have used ‘black box’ software to fit an exponential model to that data, but have little knowledge of:

• What is inside the ‘black box’
• How to evaluate the uncertainties of the parameter estimates defining the fitted model

We strongly recommend you take our ‘Measurement Explained’ and ‘Metrology for MRI’ e-learning courses before this one. We also recommend ‘Uncertainty Propagation for Quantitative MRI’, ‘Introduction to Measurement Uncertainty’ and ‘Understanding Uncertainty Budgets’. Please see our course catalogue for more information about these courses.

The code included in this course has been developed for and is intended for use in a research environment only. No endorsement can be given for other use including, but not limited to, use in a clinical environment.