Sources of Error

As mentioned in Sect. 6.4 of this chapter, major sources of error may include the common assumption of a straightforward signal change - contrast agent concentration relationship and of a standard arterial input function. Other factors that can significantly affect both the accuracy and the precision of kinetic modelling results include the blood haematocrit, contrast agent relaxivity, errors in T1 measurement, image artefact, in particular those caused by motion, model over-simplification and spatial undersampling of data. Leaving aside errors introduced during to data acquisition, the major remaining modelling-related sources of error are therefore the haematocrit, model over-simplification, and spatial undersampling.

The blood haematocrit (Hct) plays a significant role in the measurement of kinetic parameters, as MRI contrast agents occupy only the plasma compartment of the blood. It is therefore the concentration of contrast agent in the blood plasma (Cp), rather than the whole blood, that drives diffusive transport across endothelial walls (Eq. 7). Any arterial input function measurement therefore needs to convert the measured blood concentration Cb to a measure of Cp via the relationship Cp = Cb/(1-Hct). Most DCE-MRI studies have not included an explicit measurement of Hct, and a value of approximately 0.4 is generally assumed, or Hct is ignored entirely. This lack of Hct measurement will undoubtedly lead to errors, as Hct may vary in patients with advanced cancer. An additional frequently-overlooked consideration is the likely difference in Hct between large vessels (where the AIF measurement is performed) and the microvasculature (where the modelling of contrast agent transfer is performed). The packing of red blood cells in the capillary bed is less dense, leading to a smaller value of Hct. In normal capillary beds Hct is approximately 0.7 of that in large vessels; however, in the poorly-formed and variably perfused vessels within a tumour there is scope for this factor to vary considerably.

As discussed in Sect. 6.4.2, Hct is factored into the definition of a number of key modelling parameters. Ktrans is equal to EFp(1-Hct) (TofTs et al. 1999), and it also occurs in a number of other modelling steps (see for example Eqs. 8, 13, 14). Errors in Hct will consequently also affect the modelling process at this stage.

All modelling of a complex biological system requires significant simplification of reality to gen erate an analysis method that is robust but that provides useful summary functional parameters. Modelling methods therefore provide an approximation of true tissue status, and the simpler the model the greater the degree of approximation, which can lead to systematic errors in the physiological parameters being assessed and a weakened relationship between the true physiological parameter and its modelling analogue. This is due to the simplified model 'compensating' for parameters that have been omitted by distorting the fitted parameters to include effects that are caused by an omitted factor. Examples of this are the lack of a blood pool component and the lack of a measured AIF in modelling analysis, which has been shown to lead to artefactually high estimated Ktrans values and an incorrect assignment of high Xtrans in blood vessels (Fig. 6.6) (Parker 1997; Parker et al. 1996) . These findings are in agreement with simulation studies that also suggest that more complex models also reduce bias in parameter estimates of ve and Vp (Buckley 2002). However, typically the loss of accuracy caused by the use of simpler models is accompanied by an increase in precision as fitting processes become more stable (as fewer fitted parameters are being extracted from the data) and noise levels are reduced (as acquisition times often become longer). It is therefore not to be presupposed that precisely measured, but dif-ficult-to-interpret parameters are of more or less use in understanding, assessing, and following disease process than the more comprehensive (but noisier) complex model parameters.

DCE-MRI analysis should ideally take into account the heterogeneity of tumour vascular characteristics. As may be appreciated in Figs. 6.1 and 6.6, tumours in all regions of the body may exhibit large internal variation in their microvascular characteristics, reflecting variation in microvessel density, VEGF expression, and areas of avascular-ity or necrosis. Many DCE-MRI studies utilize user-defined regions of interest (ROIs), yielding graphical outputs with good signal-to-noise ratio (Figs. 6.4 and 6.5), but which lack spatial resolution and are prone to partial volume averaging errors. Additionally, the placement of ROIs can have profound effects on the outcome of analysis (Liney et al. 1999), and tell you nothing of the heterogeneity of tumour characteristics, which may in itself be a useful diagnostic/prognostic feature. Another approach to the analysis problem is to utilise parametric mapping (Figs. 6.1 and 6.6). This type of display has a number of advantages including the appreciation of heterogeneity of enhancement and the removal of the need for selective placement of user-defined regions of interest. An important advantage is being able to spatially match tumour vascular characteristics such as blood volume, blood flow, Ktrans, and ve. The risk of missing important diagnostic information and of creating ROIs that contain more than one tissue type is reduced. However, voxel mapping

Fig. 6.6. a,b K*rans maps in an axial brain slice incorporating a high-grade glioma. a Result of fitting Eq. 9 without a blood pool contribution and with an assumed AIF. b Result of fitting Eq. 9 with a blood pool contribution and an AIF measured in the middle cerebral artery. Note the assignment of high Ktrans in sulcal vessels when using the simpler model (a), which should show theoretically zero K*rans. The more complex model (b) shows much lower values in these vessels. c Vp Map generated during the more complex model fitting for (b). Note that many areas of apparently high vessel Ktrans in (a) are now correctly identified as high blood volume areas

Fig. 6.6. a,b K*rans maps in an axial brain slice incorporating a high-grade glioma. a Result of fitting Eq. 9 without a blood pool contribution and with an assumed AIF. b Result of fitting Eq. 9 with a blood pool contribution and an AIF measured in the middle cerebral artery. Note the assignment of high Ktrans in sulcal vessels when using the simpler model (a), which should show theoretically zero K*rans. The more complex model (b) shows much lower values in these vessels. c Vp Map generated during the more complex model fitting for (b). Note that many areas of apparently high vessel Ktrans in (a) are now correctly identified as high blood volume areas has a poorer signal-to-noise ratio than ROI analysis and it can be difficult to compare model outputs between two tumours or during a programme of treatment in a meaningful way (see Chap. 16). Recently, histogram analysis has been used to quantify the heterogeneity of tumours for comparative and longitudinal studies, for monitoring the effects of treatment, and to show the regression or development of angiogenic hot spots (Mayr et al. 2000; Hayes et al. 2002). Simple frequency distributions can be plotted and descriptive statistics can be used to quantify the variability therein.

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