As discussed in Chapters 1 and 2, the amount of data that needs to be interpreted in DCE-MRI is often huge, and is likely to increase in the future. Thus, radiologists can be overwhelmed by the amount of data and the increasing work load. Parametric models of enhancement provide ways to visualise the data more efficiently, decrease the size of the data and permit the development of kinetic features for the automated classification of breast lesions (the subject of Chapter 6).
Existing approaches vary between using the raw data, its derived statistics and a range or empiric kinetic and pharmacokinetic models. This chapter introduces the reader to the motivation and types of parametric models in DCE-MRI. It reviews existing models of enhancement and presents a novel parametric model of enhancement for DCE-MRI of the breast. Also, it presents an empirical evaluation of the goodness-of-fit of four parametric models of contrast enhancement for DCE-MRI of the breast: the Tofts (Tofts and Kermode, 1991), Brix (Brix et al., 1991), and Hayton (Hayton et al., 1997) pharmacokinetic models, and the proposed empiric model. Each of these models has three free parameters. The aim of this work was to analyse the behaviour of each model under different optimization conditions to determine which one had the best performance for each given optimisation system. The core material of this chapter was published in (Gal et al., 2007b).
Parametric models of contrast enhancement reduce the dimensionality of DCE-MRI by transforming a dataset of typically 5-9 time points (i.e. volumes) to two or three parameters. This conversion helps standardise the size of the data (to have a constant size, instead of a varying number of volumes) and makes the data easier to visualise (by using the parameter values from the fitted model) (Mehnert et al., 2005, Vidholm et al., 2007). Also, computer-assisted evaluation often derives information from such models to segment or classify suspicious lesions.�
In most protocols used with DCE breast MRI, the injection is applied as a bolus (i.e. rapidly injected intravenous injection). Variations in injection time, in addition to the lag times between the injection and the imaging need to be considered when analysing the shape of the enhancement curves. Contrast enhancement patterns help to differentiate the benign from the malignant lesions in DCE-MRI of the breast (Furman-Haran and Degani, 2002). These are particularly helpful when the morphometric features of a lesion make the differentiation, and thus the indication if the tissue is benign or malignant, difficult. The behaviour of the contrast agent in the body tissues can be described using a model-based equation that approximates the entry and washout of the agents in the body.
Gd-based contrast agents cannot cross the cell membranes and enter the cells. Therefore, many models assume that the contrast agent is distributed between two main tissue compartments, the intra-vascular plasma volume and the extra-vascular/extra-cellular volume (Error! Reference source not found.). Many models also share several additional assumptions, usually related to the water exchange between the tissue compartments and water interaction with the contrast agent. Those assumptions usually lead to extra parameters that are experimentally tested or are estimated by the model fitting process.
Several pharmacokinetic models for breast DCE-MRI have been developed to date including, Tofts