The neovasculature formed as a lesion outgrows the local blood supply is incompletely formed.  This makes these vessels prone to leak macromolecular contrast agents, and it is this property of soft tissue lesions which allows the accumulation of a contrast agent within a lesion and hence alters the magnetic resonance (MR) signal. Since it is thought that the amount, and rate, of signal enhancement due to the accumulation of a contrast agent is an important aid in diagnosis, the accuracy and reliability of the quantitative phase of the image analysis are important issues in need of evaluation.  This work has investigated several methodological issues. As the quantitation of signal enhancement on a T1 weighted image due to the accumulation of a contrast agent is dependent upon the pre-contrast T1 of the tissue that is imaged, T1 measurements are made before the dynamic phase of an imaging protocol. A commonly used method of T1 measurement makes use of 2 images acquired at different flip angles.  Two novel methods of T1 measurement were investigated: the first based upon the 2 point method relies upon a linear regression; the second method uses an non linear least squares fit (NLLS).  The NLLS method is recommended. Fitting a mathematical model to a set of real data points involves minimising the sum of the squares of the differences between the real points and the points predicted by the model.  Two models commonly used in DCE-MRI were investigated with respect to their ability to find the true minimum in the presence of noise.  Furthermore, we show that the use of a single start point for all minimisations leads to unexpected fitting failures, and as such we propose a solution to this. Contrast media are cleared from the body by the kidneys.  Hence the effects of renal function on measurements made with the same tow models were investigated.  We show that  this significantly affects results.