Pharmacokinetic Analysis

As discussed in Chaps. 1 and 6 pharmacokinetic analyses of T1-weighted DRCE-MRI data have a number of theoretical advantages (Tofts et al. 1999). The use of pharmacokinetic models leads to the derivation of parameters which are independent of the scanning acquisition protocol or any features associated with it. In theory, such parameters should reflect only tissue characteristics supporting the use of these measurements in multicentre studies employing varying image acquisition protocols and equipment (Padhani and Husband 2001) (see also Chap. 16). In practice pharmacokinetic analysis is complex and the choice of pharmacokinetic model controls the range of parameters that can be extracted. Each of the pharmacokinetic analysis approaches uses curve fitting techniques to characterise the arterial input function (AIF) and the tissue contrast concentration curve. These two functions are then used to derive the parameters which control the relation ship between AIF and tissue contrast content. The simplest of the pharmacokinetic models, such as that described by Tofts and Kermode (1991), use a single arterial input function and time course data describing contrast concentration from individual voxels to calculate the size of the EES (ve) and the bulk transfer coefficient Ktrans (Fig. 9.5). The transfer constant Ktrans is simply a mathematical function which describes the relationship between the AIF and contrast concentration changes occurring in the voxel. The measurements of Ktrans will be affected by blood flow, blood volume, endothelial permeability and endothelial surface area. Changes in any of these variables can produce observable changes in Ktrans and the specific contribution of the individual components cannot be identified. This simple model is also based on an invalid assumption that the signal changes within the measurement voxels will result entirely from extravasated contrast medium within the EES. This gives rise to significant errors in voxels which contain intra vascular contrast where measured values of Ktrans will be artificially elevated. Despite these shortcomings the model described by Tofts and Kermode (1991) is widely used (Parker et al. 1997). Nonetheless, many workers have attempted to refine the pharmacoki-netic analysis to provide more accurate estimates of individual microvascular parameters, particularly permeability surface area product and fractional plasma volume (vp). One reason for the refinement of analysis techniques is that these techniques are widely used in drug development and discovery and, particularly, for the study of new anti antiangiogenic therapies (see Chap. 16). As we have described the angiogenic cytokine VEGF has a specific action in promoting endothelial permeability so that measurements of endothelial permeability, uncontaminated by other factors, are highly desirable (Gossmann et al. 2000; van der Sanden et al. 2000; WeissledeR and Mahmood 2001). The basic pharmacokinetic model described by the Tofts and Kermode can be modified to specifically model the signal contribution produced by contrast medium within the plasma (Tofts et al. 1999). This reduces errors due to the so-called pseudo permeability effect where intravascular contrast gives rise to falsely elevated values of Ktrans. The Ktrans values from this modified model will differ significantly from those obtained with the classic model and will more accurately reflect changes in permeability surface area product although they will still be dependent on adequate blood flow to the tissue to support contrast leakage. It is important to realise that the exact meaning of the Ktrans variable depends on the method of analysis used. More complex pharmacokinetic models such as those described by St. Lawrence and Lee (1998) allow direct estimation of local tissue blood flow (F) in addition to ve, vb and permeability surface area product (P.S). It seems clear that models such as these are more desirable than simpler approaches to the analysis; however, separate identification of extra fitting parameters requires more accurate and reliable curve fitting and is associated with increased variability and susceptibility to noise (Fig. 9.6). The choice of analysis techniques is therefore not straightforward and must be made based on the likely quality of the data to be obtained and the specific biological question to be answered.

Fig. 9.5. Parametric images of Ktrans and ve in a patient with a left-sided high-grade glioma generated using a simple pharmacokinetic model. Note the elevated values of Ktrans within the enhancing rim of the glioma and also in the region of large blood vessels. These areas of pseudo-permeability reflect an error in the model which fails to account for the presence of large amounts of intravascular contrast

Fig. 9.5. Parametric images of Ktrans and ve in a patient with a left-sided high-grade glioma generated using a simple pharmacokinetic model. Note the elevated values of Ktrans within the enhancing rim of the glioma and also in the region of large blood vessels. These areas of pseudo-permeability reflect an error in the model which fails to account for the presence of large amounts of intravascular contrast

Fig. 9.6. Curve fitting analysis using the model described by St. Lawrence and Lee (1998) to produce estimates of flow (F), endothelial permeability surface area product (PS), vascular distribution volume (V(b)) and extra-cellular extra-vascular space (V(e)). The curve fits are performed on data from regions of interest in order to improve signal-to-noise ratio. The underlying data points are indicated by circles. The arterial input function used in the analysis is shown in grey. The results showed clear differences in all parameters between a low-grade glioma (left) and a high-grade glioma (right).

Fig. 9.6. Curve fitting analysis using the model described by St. Lawrence and Lee (1998) to produce estimates of flow (F), endothelial permeability surface area product (PS), vascular distribution volume (V(b)) and extra-cellular extra-vascular space (V(e)). The curve fits are performed on data from regions of interest in order to improve signal-to-noise ratio. The underlying data points are indicated by circles. The arterial input function used in the analysis is shown in grey. The results showed clear differences in all parameters between a low-grade glioma (left) and a high-grade glioma (right).

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