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Reproducibility of quantitative dynamic contrast-enhanced MRI in newly presenting glioma

¹ Division of Imaging Science and Biomedical Engineering, Stopford Medical School, University of Manchester, Manchester M13 9PT, ² Cancer Research Campaign Department Medical Oncology, Christie Hospital, Wilmslow Road, Withington, Manchester M20 4BX and ³ AstraZeneca, Alderley Park, Macclesfield, Cheshire SK10 4TG, UK

Correspondence: Professor Alan Jackson, Imaging Science and Biomedical Engineering, Stopford Medical School, Oxford Road, Manchester M13 9PT, UK

	Abstract

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We have investigated the reproducibility of dynamic contrast enhanced imaging techniques in nine patients with cerebral glioma. Patients were imaged twice with a 2 day interval between scans. Maps were produced of the time taken to achieve 90% enhancement (T90), the maximal intensity change per time interval ratio (MITR), the volume transfer coefficient between plasma and the extravascular extracellular space (K^trans) and the extravascular extracellular contrast distribution volume, v_e. Measurements of K^trans greater than 1.2 min^-1 were used to exclude pixels where first pass perfusion effects dominated the measurement. Measures of the test–retest coefficient of variation (CoV) and intraclass correlation coefficients were used to assess reproducibility for measurements from a volume of interest containing enhancing tissue from the whole tumour. MITR showed poor reproducibility (mean CoV 17.9%, 95% confidence limits for group comparisons 20.2%). T90 showed good reproducibility (mean CoV 7.1%, 95% confidence limits for group comparisons 5.2%). Calculated values of K^trans and v_e also showed good reproducibility (mean CoV 7.7% and 6.2% respectively, 95% confidence limits for group comparisons 6.2% and 4.8%, respectively). We conclude that the measurements of K^trans and v_e derived from pharmacokinetic analysis are sufficiently reproducible to support their use as a biological markers in therapeutic trials.

	Introduction

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Inhibition of angiogenesis presents new therapeutic opportunities for cancer therapy by targeting of the newly formed vessels or by inhibition of the angiogenic process itself [1]. Consequently there is a need for indicators of biological activity that can be used in trials of novel anti-angiogenic therapies. Imaging based parameters that relate to the status of the tumour microvasculature, particularly those based on MRI, present an ideal potential solution. These techniques are non-invasive and incur no radiation dose so that they can be repeated as necessary to examine the effects of a potential therapy or to monitor tumour progression. Furthermore, they produce images of the distribution of variations in microvascular features which allow accurate localization to the tumour or even to a specific component of the tumour. Dynamic contrast enhanced techniques have been particularly popular for the quantification of the angiogenic process since contrast agent administration will produce signal changes due to intravascular contrast, which will reflect variations in regional blood volume and blood flow [1–6], and due to contrast leakage, which will reflect endothelial surface area, endothelial permeability and the size of the extravascular extracellular space [7–12].

Since promotion of endothelial permeability is a prime effect of vascular endothelial growth factor (VEGF) and other angiogenic cytokines [13], changes in the capillary leakage of contrast agents is a predictable response to some classes of anti-angiogenic therapies [7, 14–17]. Quantification of the enhancement effect is therefore a prime candidate as a potential surrogate marker of drug activity. In addition, such measurements can also provide valuable clinical information concerning tumour stage and behaviour [9, 18–21]. Quantification of enhancement characteristics can be performed using a range of techniques, which range from simple measures of the rate of enhancement to complex algorithmic analyses that apply pharmacokinetic models to the imaging data with the intention of measuring the transfer constant of contrast between the plasma and the extravascular extracellular space (K^trans) [22, 23]. Measured values of K^trans will be affected by the rate of contrast delivery (blood flow), the surface area of the permeable endothelium and the endothelial permeability. In tissues where flow is high enough to deliver an excess of contrast agent to the endothelium, measurements of K^trans will reflect the endothelial permeability surface area product, whereas in cases where the extraction ratio of contrast is high compared with flow, K^trans will reflect principally local blood flow. Despite this potential shortcoming, measurements of K^trans are increasingly popular as a method for the quantification of contrast enhancement since they are designed to describe the distribution of contrast agent free from scanning and machine dependant variables, which allows comparison of results from different studies and imaging centres [1, 24]. If dynamic enhanced MRI is to provide surrogate markers of therapeutic response and reliable clinical information, it is essential to establish and optimize the reproducibility of the techniques [24–26].

The aims of this study are (1) to compare three techniques for quantifying the enhancement characteristics of tumours, and (2) to determine the reproducibility of these techniques by repeating the dynamic study, without therapeutic intervention, on two occasions several days apart. Three quite different, but commonly used, methods for the quantification of enhancement were chosen for comparison. The simplest of these is a measurement of the time taken for tumour tissue to attain 90% of its subsequent maximal enhancement (T90) [27]. The second measures the maximum rate of change of enhancement (maximal intensity change per time interval ratio (MITR) [28]). The third method, described by Tofts and Kermode [11] uses a three compartment pharmacokinetic model to measure K^trans.

	Materials and methods

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Patients
11 patients with suspected cerebral glioma were included in the study. Glioma patients were recruited at diagnosis from the neurosurgical clinic at the Central Manchester Healthcare Trust. All patients had initial clinical imaging consisting of contrast enhanced CT (three patients) or MRI (eight patients). All patients gave informed consent and the Central Manchester Healthcare Trust Medical Ethics Committee approved the study. Patients underwent MR scanning on two occasions; firstly within 48 h of initial diagnosis and on a second occasion 36–56 h after the first scan. Histological confirmation of the diagnosis was sought after the imaging studies in all cases and the diagnosis of glioma was confirmed in all cases. All patients received steroid therapy from diagnosis (Dexamethasone 4 mg four times a day (qds), by mouth (od), no other treatment was given prior to or during the study. Two patients were excluded from the analysis. One of these was diagnosed as a metastasis on histology whilst the other had a low grade glioma that failed to enhance. The remaining nine patients were included in the study group. Table 1 shows the demographic and histological data for each patient.

The imaging protocol for dynamic contrast enhanced studies consisted of three consecutive three-dimensional (3D) radiofrequency (rf) spoiled (T₁ weighted) field echo acquisitions with an array of flip angles (=2°, 10° and 35°) to allow calculation of T₁ maps (see Appendix A). The third sequence was then repeated (n=120) to produce a T₁ weighted dynamic data set (T₁dy) with a time resolution of 5.18.7 s and a duration of 10.617.4 min. Contrast (0.1 mmol kg^-1 of gadodiamide, (5,8-Bis(carboxymethyl)-11-(2-(methylamino)-2-oxoethyl)-3-oxo-2,5,8,11-tetraazatridecan-13-oato(3-))gadolinium (Gd-DTPA-BMA; Nycomed, Oslo, Norway) was given as a manual intravenous bolus injection over a period of 3–4 s following the seventh dynamic scan. The contrast bolus was flushed with an equal volume of normal saline administered at the same rate in order to improve bolus coherence. Injection rate was controlled using a metronome. Detailed scanning parameters are given in Table 2.

Tumour segmentation
Pre-contrast images were subtracted from images acquired 3 min after contrast administration to generate maps of contrast enhancement. 3D volumes of interest (VOI) were then manually identified from the subtraction images by a radiologist (XPZ). The same operator defined all regions of interest from all studies. VOIs from the repeat studies in the same individual were defined at separate sittings and VOIs were defined in random order to avoid bias due to prior knowledge.

Calculation of enhancement rate parameters
Two simple, previously described, enhancement rate parameters were calculated for each examination. These were the time taken to achieve 90% of maximal cumulative enhancement (T90) [27] and the maximal intensity change per time interval ratio (MITR) [28]. Both measurements were slightly modified from the original descriptions, as described below, in order to compensate for the use of high temporal resolution data and to allow the generation of parametric images. In all other ways the methods were implemented as originally described.

Calculation of the T90 was performed on a pixel-by-pixel basis rather than for the large regions of interest used in the original description [27]. Maximal enhancement was measured as the average signal intensity between 2 min and 3 min, as maximal enhancement had occurred in all tumours at these intervals. Data were smoothed by temporal averaging to remove high frequency noise in the dynamic data using an averaging length of 2 samples for data with a temporal resolution of 8.7 s and 4 samples for data with a temporal resolution of 5.1 s. The T90 value was calculated by identifying the measurement points around the 90% value and assuming a linear signal change with time between these points.

The MITR was also calculated on a pixel-by-pixel basis. Due to the high temporal resolution of some of the data the first maximum intensity point in our data was commonly the peak of the first pass of the contrast bolus. In order to avoid artefactual values of MITR due to this, any maxima occurring within the first pass period (20 s) were excluded and the first subsequent maximum value employed. The MITR was then calculated as the ratio of the maximum intensity change from baseline divided by the time interval over which it occurred [28].

Calculation of parametric maps of K^trans and v_e
Pharmacokinetic modelling was performed using the model described by Tofts and Kermode [11]. Several modifications were made to the method in order to improve reproducibility and to compensate for the use of high temporal resolution data, which were not available when the model was first described. These modifications were (1) modification of the technique used to calculate contrast concentration maps to reduce computation instability resulting from fluctuation in small values of native signal intensity, (2) use of a patient specific vascular input function (VIF) and (3) modification of the VIF fitting procedure to remove errors due to variations in contrast concentration during the first passage of the contrast bolus. The calculation of parametric maps was performed in three stages:

1. Calculation of maps of contrast agent concentration. Four dimensional (4D; x, y, z, t) maps of Gd tissue concentration were calculated for each case [11]. The modifications made for calculating maps of longitudinal relaxation rate (R₁) and tissue Gd concentrations based on field echo image data sets are described in Appendix A. The multiple flip angle technique is described in detail by Zhu et al [29]. The method used to determine the T1 relaxivity of Gd-DTPA-BMA is described in Appendix B.
   
2. Derivation of the vascular input function. The estimate of the VIF used in the analysis is a potential major source of error [30]. Measurement of VIF is complicated by the co-existing inflow effects that are exacerbated by contrast induced T₁ shortening to produce non-linear errors. In order to remove inflow errors we used a combination of a large volume selection gradient and hard radiofrequency pulses to provide pre-saturation of in-flowing spins, positioning the volume in such way that the proximal superior sagittal sinus ran through the volume parallel to the slab selection gradient. The time course of intravascular contrast concentration was then measured from the distal superior sagittal sinus and used to calculate VIF. The VIF was calculated by fitting the plasma contrast concentration time course data C_p(t) from the superior sagittal sinus to a bi-exponential decay curve [11]:
   

where D is the dose of Gd-DTPA-BMA, a₁, m₁ are amplitude and rate constants of the fast exponential decay (leakage of contrast into peripheral tissues), and a₂, m₂ are amplitude and rate constants of the slow decay due to renal excretion.

The bi-exponential model of vascular input function originally used by Tofts and Kermode [11] assumes instantaneous mixing and uniform distribution of contrast agent throughout the entire plasma volume. In practice, of course, this is untrue for either bolus injections or infusions of contrast agent. When rapid injection techniques are employed the bolus of contrast remains coherent producing unpredictable peaks in concentration during the early part of the acquisition. These errors are particularly marked in high temporal resolution data and will affect derived values of K^trans in an unpredictable manner from case to case [31]. In order to reduce errors due to this cause we modified the technique for estimation of the vascular input function. Assuming perfect mixing throughout the plasma volume a contrast agent dose of 0.1 mmol kg^-1 would producea concentration of approximately 2.6 mmol l^-1 of plasma. In our analysis the sum of a₁ and a₂ was therefore fixed at 26 kg l^-1 [10]. The bi-exponential function was then fitted using a Levenberg–Marquart non-linear least squares fitting.

The reproducibility of the resulting technique was tested by calculation of test–retest coefficients of variation (CoV) for each of the descriptive parameters (a₁, a₂, m₁ and m₂) from Equation 1. This revealed CoV of a₁=8.8%, a₂=8.7%, m₁=4.0% and m₂=27.1%. The large CoV of m₂ reflects the importance of data points late in the collection period on this value. Reproducibility of m₂ could be improved only by extending the data collection period beyond that used in the study (10.6–17.4 min). In view of these variations the VIF for each individual was calculated as the average of the VIF functions measured on the two examinations [10]. This approach allows the use of a customized VIF function to compensate for patient to patient variations whilst minimizing the effect of random errors introduced by the fitting procedure.

(3) Calculation of parametric maps. Values of K^trans, v_e (Figure 1) and scaled fitting errors of whole tumour volumes were calculated using the individually measured VIF and 4D C(t) maps using the tri-exponential model described by Tofts and Kermode [11]. Details of the technique are presented in Appendix C.

View larger version (60K): [in this window] [in a new window]   Figure 1. Transaxial section through map volumes from a patient with a glioblastoma multiforme (arrow head), acquired on day 0 (top and day 2 (bottom): (a) Time taken to achieve 90% enhancement (T90); (b) Maximal intensity change per time interval (MITR); (c) Volume transfer coefficient between plasma and the extravascular space (Ktrans); and (d) the extravascular extracellular contrast distribution volume (ve) maps. All parametric maps are colour rendered. Yellow represents high values, i.e. long T90, high MITR, high Ktrans and large ve. Dark-blue represents low values, i.e. short T90, low MITR, low Ktrans and small ve.

Statistical analysis of the data
Mean values of each calculated parameter (tumour volume, MITR, T90, R₁₀, number of pixels where K^trans>1.2 min^-1, K^trans and v_e) were used to test the hypothesis that there is no difference between the measures from scan 1 and scan 2 using a t-test. The test–retest CoV was calculated for each parameter. For each subject, i, the CoV is the standard deviation, _i, for the two measurements on that subject, divided by the mean measurement, µ_i, for the subject. The overall test–retest CoV for a group of N subjects is then equal to:

In addition, intraclass correlation coefficients for mean values were calculated for tumour volume, MITR, T90, K^trans and v_e using both a two-way mixed effect model to provide a measure of consistency within cases and using a one-way random effect model. The correlation coefficients were used to calculate the asymmetric 95% confidence limits for detection of difference for both intraclass and single measurements. Since there was a significant change in R₁₀ values between scans, which was believed to reflect steroid therapy, intraclass correlation coefficients were not calculated for this value.

	Results

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Review of the dynamic imaging data showed no evidence of significant motion in any case. Figure 2 shows the changes in the measured parameters; tumour volume, T90, MITR, R10, K^trans and v_e over the study period and Table 3 summarizes the data and shows the estimated CoV. Over the 2 day interval the glioma tumour volumes did not change and reproducibility of tumour volume (test–retest CoV) was 4.0%. Over the same interval the mean longitudinal relaxation rate R₁₀ within the gliomas increased by 10.3% (p=0.008).

View larger version (33K): [in this window] [in a new window]   Figure 2. Changes in measured parameters over the 2 day study period. (a) Tumour volume (vol). (b) Maximal intensity change per time interval (MITR). (c) Time taken to achieve 90% enhancement (T90). (d) R10. (e) Volume transfer coefficient beween plasma and the extravascular space (Ktrans). (f) The Extravascular extracellular contrast distribution volume (ve). Symbols represent individual patients.

Application of the pharmacokinetic model produced significant numbers of tumour voxels that failed to conform to the inclusion criteria described above (range 13.0–74.0%, mean 39.0±16.2). The number of pixels above the 1.2 min^-1 threshold was also highly reproducible with a CoV of 5.9%. The highest value was seen in patient 3, who had a highly vascular tumour.

Mean values of K^trans ranged from 0.12 min^-1 to 0.63 min^-1 and mean values for v_e from 7.5% to 30.5%. Test–retest CoV was 7.7% for K^trans and 6.2% for v_e and no significant change in either parameter was observed in any patient.

Measurements of K^trans did not correlate with measures of either T90 or MITR. T90 demonstrated a negative correlation with the number of excluded pixels in the pharmacokinetic model (Spearman's Correlation coefficient, -0.714, p<0.01).

The intraclass correlation coefficients for tumour volume (Vol), MITR, T90, K^trans and v_e together with associated 95% confidence limits are shown in Table 4 and Table 5. Table 4 shows the correlation coefficient for intraclass differences using both a two-way mixed effect model and a one-way random effect model. The use of a two-way model illustrates the expected reliability of repeated measures derived from groups of cases where the expected direction of change is unknown. The use of a one-way random effect model assumes that the expected direction of change is known and illustrates the expected reliability of repeated measures derived from groups of cases where this is the case. Table 4 shows the correlation coefficient for single measures using both a two-way mixed effect and a one-way random effect model.

	Discussion

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One tempting approach to these problems is to develop metrics that are extracted from the image intensity data directly without calculation of true contrast agent concentration or pharmacokinetic modelling. These offer the benefits of simplicity but must be designed to minimize variation between patients due to scanning and scaling parameters. We have examined two examples of such metrics that have been previously employed by other groups. The simplest is the T90, which is a measure of the time taken to achieve 90% of the maximal enhancement; defined as the increase in signal intensity over a pre-determined time period. This measure is computationally trivial. The T90 is expected to be relatively free from variations due to changes in contrast dose, imaging sequence or scanner gain which should favourably affect reproducibility. Reproducibility studies confirmed this with a mean test–retest CoV of 7.1% and 95% confidence limits on intraclass correlation coefficients of only 5.2% for group comparisons and 9.77% for single values (Table 4 and Table 5) . Unfortunately this measure fails to distinguish between contrast changes resulting from intravascular contrast and those resulting from true contrast leakage. In pixels containing large blood vessels, 90% of the maximal value will be attained very quickly during the first passage of the contrast bolus. In these circumstances the measurement will reflect regional vascularity and will not be affected by endothelial permeability. This effect can be seen in the results of this study where T90 correlated inversely with the number of pixels excluded from the pharmacokinetic analysis by the threshold used to identify voxels dominated by intravascular contrast.

The second simple metric that we employed was the MITR. This measure reflects the maximal rate of change of signal intensity and will therefore be sensitive to variations in receiver gain, scanning sequence and contrast dosage. More importantly the measurement is affected by the temporal resolution of the data acquisition. This was a clear problem with our data sets where the high temporal resolution generated spurious high values of MITR in voxels with a prominent first pass curve. In order to avoid this error we modified the MITR so that it will discount any maximal value observed during the first pass period. Despite this, the reproducibility of the MITR was disappointing with a mean test–retest CoV of 17.9% and 95% confidence limits on intraclass correlation coefficients of 20.2% for group comparisons and 32.3% for single values (Tables 4 and Table 5). This variability could result from many causes including variations in receiver gain or coil loading, errors in detection of the signal intensity maxima or physiological variations such as changes in cardiac output.

Although the T90 value is highly reproducible, the presence of large vessels in voxels adversely affects both these measures producing data that reflects regional blood volume rather than permeability. This is a particular problem if the measures are applied to large regions of interest, as in the original descriptions [6], since the contributions from vascular and tissue voxels cannot be determined. In principle it is possible to make an attempt to minimize the impact of this effect if data is analyzed on a pixel by pixel basis by setting exclusion thresholds intended to identify pixels where first pass effects dominate the calculated parameter. An alternative approach is to remove first pass effects by the use of contrast infusions [33]. This will avoid spurious identification of an intra-vascular bolus as the time of peak enhancement but does not avoid the inappropriate calculation of permeability related variables from voxels dominated by blood vessels. In our patients the number of these voxels (K^trans>1.2 min^-1) was highly variable ranging from 13% to 47%. Such measures must therefore reflect an unknown mixture of permeability and perfusion effects.

The use of a pharmacokinetic model such as the one employed in this study offers significant theoretical advantages since it attempts to compensate for many of the variables related to machine performance and variation in contrast bolus, contrast dose and patient physiology. However, in order to achieve this a number of additional processing steps are required, each of which can potentially introduce additional errors. We have implemented a number of modifications to the original technique, which are intended to improve the reproducibility of the final measured values of K^trans and v_e. The first step in these calculations is to transform the observed signal changes into changes in contrast agent concentration for use in the model. This requires accurate measurement of the native T1 value (T₁₀) of each pixel. In the original description of this technique [11] T1 maps were obtained using traditional inversion recovery images, however this is very slow and suffers from artefacts due to errors in slice profile prescription. Recently, several groups have suggested the use of fast gradient imaging with different flip angles for the calculation of T₁₀ maps [12, 32, 34]. Current advances in shielded gradient techniques enable us to do this with echo times as short as 1.1 s, allowing the collection of 3D field echo (FE) data sets with different flip angles for T₁₀ map calculation in very short and clinically acceptable times. In this study, we have acquired three sets of 3D FE images with a matrix of 128 x 128 x 25 in 15 s. We have previously established the accuracy of maps of native relaxivity (R₁₀=1/T₁₀) values obtained with this technique by comparison with an established reference sequence [29]. The use of these fast techniques for the calculation of initial R₁₀ represent a significant contribution to the reproducibility of the subsequent measures since the alternative would be to assume standard R₁₀ values for all pixels leading to unavoidable and unpredictable errors in the calculated concentration of contrast agent. The ability to measure R₁₀ in individual cases is important since variations can occur due to a wide range of causes. In our patients with glioma an increase in R₁₀ was noted over the study period. This can be attributed to the use of steroid therapy, which is routinely used from the time of diagnosis in these patients. This change makes calculation of intraclass correlation coefficients inappropriate and, therefore, we cannot assign reproducibility values to the R₁₀ parameter since there is evidence of a significant change between examinations.

The second modification into the original Tofts and Kermode technique is that in order to convert the T1W dynamic data into high quality 4D maps of R₁(t) we have used the difference between S(t) and S(0) (see Equation A2, Appendix A) rather than dividing S(t) by S(0) [34–36]. This approach reduces computation instability resulting from fluctuation in small values of S(0) and improves the reproducibility of derived values of R₁(t) and derived C(t) [6].

The third modification to the original Tofts and Kermode technique is the use of a measured VIF. This can be extremely difficult since the calculation of contrast agent concentration in major vessels is complicated by in-flow effects and by the restricted dynamic range of gradient echo sequences [36]. Many workers have resorted to the use of literature values of VIFs as the contrast driving function in subsequent calculations [1, 24, 32, 34]. However, the assumed normal plasma contrast concentration function derived from measurements of low temporal resolution will cause errors in the determination of the volume transfer constant, K^trans [35, 37]. In-flow effects can be eliminated by the use of regional saturation bands (REST slabs) placed upstream from the measurement point. However, this increases the required repetition time (TR) consequently reducing the size of the data volume that can be acquired in any given time. In this study the very short and relatively hard radiofrequency (rf) pulses employed for 3D fast gradient echo imaging have been taken advantage of. The slab selection gradient in these patients covers the upstream path of the sagittal sinus so that residual in-flow effects are negligible. Robust measures of VIF parameters have been obtained using this method in both volunteers and patients [30].

The final modification to the original Tofts and Kermode technique addresses problems with the use of a measured VIF. The model uses a bi-exponential model to fit the VIF data (Equation 1) [11]. This assumes instantaneous mixing of contrast throughout the plasma volume and ignores the impact of the first passage of the contrast bolus. With the improvement of MRI technology, the temporal resolution of data sets can be sufficiently high that the first measured point is dominated by the peak concentration of the contrast bolus and not the concentration achieved after even contrast mixing as the model assumes. We have approached this error in the basic assumptions by fixing the first data point of the VIF at a value of 26 kg l^-1 for a unit dose. This value represents the expected contrast concentration after complete mixing, assuming a normal relationship between the circulating blood volume and body weight [10]. Despite this it is still possible for the first pass data to affect the fitted VIF by its effect on subsequent data points. In order to reduce this effect we have used the mean value of the VIF on the two occasions for the calculation of K^trans, which will optimize reproducibility whilst still compensating for patient-to-patient variation in the distribution and mixing of contrast. Alternative approaches to dealing with the unpredictable high concentrations of gadolinium observed in the first pass period after the bolus injection are to model this mathematically or to reduce the first pass effect by slow injections. Several groups have used slow injections or infusion techniques [33]. Unfortunately, the use of an infusion makes separation of intravascular and extravascular components much more difficult. This is a theoretical limitation if one wishes to calculate K^trans free from the effects of intravascular contrast. Modelling of the first passage of contrast following a bolus injection is a more attractive approach, which we have also described [2]. However, this approach is extremely demanding of high temporal resolution imaging and is not suitable for routine implementation in many clinical sites at the present time.

The modifications of the Tofts and Kermode technique, which have been described, were designed to improve the reproducibility of the measured K^trans and v_e on repeated examinations. A pragmatic approach to these modifications has been taken, implementing changes that might be expected to improve algorithmic stability in order to achieve the best reproducibility using this model. It should be appreciated that the major changes made, namely using an individualized VIF and constraining the fitting parameters of the observed VIF, are necessary to address the increased temporal resolution of modern datasets and are not due to problems with the model itself. Values of K^trans obtained with and without the modifications have not been directly compared since each of the technical modifications will clearly improve the accuracy of K^trans estimations. Similarly, data have not been analyzed using standard literature values for VIF since the results of reproducibility studies using this approach have already been published [25]. The technique, as modified, results in a mean test–retest CoV in K^trans of 7.7% and 95% confidence limits on intraclass correlation coefficients of 6.2% for K^trans and 4.8% for v_e for group comparisons and 11.5% and 8.8%, respectively, for single values (Table 4 and Table 5). These results compare with a reduction of K^trans of 97% in grafted human breast carcinoma in animals, 24 h after administration of anti-VEGF [7]. The results compare well with the study of Galbraith et al [25] who found 95% confidence limits for within patient repeatability of K^trans and v_e of 32% and 7.6% compared with 11.5% and 8.8%, respectively, in the current study. The improvement in the reproducibility of the K^trans measure may reflect the use of individualized VIF in the current study compared with scaled literature values, which were employed by Galbraith et al in addition to the other methodological changes outlined above.

The results presented here indicate that both the T90 parameter and the K^trans and v_e values derived from pharmacokinetic studies have excellent reproducibility, which is more than adequate for longitudinal studies. Previous studies also have acceptable levels of reproducibility for other measured parameters, including the integrated area under the contrast concentration time course curve (AUC) [25] and the regional blood volume derived from T₂* weighted dynamic contrast studies [26]. However, the choice of parameters for use in individual studies is not dependant only on reproducibility. The chosen parameter should ideally reflect the features of the microvasculature which are expected to change, with little sensitivity to other confounding effects. In studies of dynamic contrast enhancement the observed signal changes will result from intravascular contrast, which will reflect variations in regional blood volume and blood flow [1–6], and from contrast leakage, which will reflect endothelial surface area, endothelial permeability and the size of the extravascular extracellular space [7–12]. Ideally we would like to be able to measure each of these physiological parameters independently. In practice the dynamic enhancement parameters available to us are invariably affected by more than one, and usually many, physiological parameters. The T90 parameter is unable to distinguish changes due to intravascular and extravascular contrast with the result that it is dominated by pixels containing large vessels with high flow. This is demonstrated by the lack of correlation with measured values of K^trans and the close correlation with the number of pixels where measured K^trans exceeds 1.2 min^-1. This arbitrary cut-off value was originally described to exclude pixels where the signal changes result primarily from variations in intravascular contrast concentration. Measurements of K^trans are popular because they should offer consistency between different scanning centers and different studies. As described above K^trans can be related principally to either blood flow or to the product of endothelial permeability and endothelial surface area. The relative balance between these effects reflects the balance between blood flow and contrast leakage in the voxel. Since this is unknown the physiological effect underlying, changes in K^trans remains uncertain if the classical analysis approaches are used. The Tofts and Kermode model also uses an arbitrary threshold to exclude pixels where the change in signal results principally from intravascular contrast. This has the effect of excluding purely vascular pixels and concentrating on those where signal changes principally reflect contrast leakage. The v_e measurement appears to be very reproducible although its value in angiogenesis studies is uncertain. Since it represents the size of the extravascular extracellular space it does not specifically relate to either vascular structure or function.

In conclusion, we have shown that dynamic contrast enhanced MRI studies of tumour enhancement can be used for repeated studies with reasonable reproducibility. Simple measurements such as the T90 and MITR, whilst attractive are strongly affected by the vascularity of the tissue and the MITR is susceptible to a wide range of other measurement errors that significantly affect reproducibility. We have proved that the application of a pharmacokinetic model such as that described by Tofts and Kermode [11] can remove the effects of non-physiological variables in the scan process sufficiently to allow highly reproducible measures of K^trans and v_e. Nonetheless, it is clear that the use of high temporal resolution data reveals significant problems with this and other models that are commonly applied to these data. Future developments must address the impact of the passage of the bolus of contrast agent around the blood stream and the identification of voxels where the dynamic contrast characteristics are dominated by this effect.

	Appendix A. Calculation of r1(T) and C(t) maps

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Maps of proton density (M0) and intrinsic longitudinal relaxation rate (R₁₀1/T₁₀) maps were calculated by fitting the steady state T1-FE signals S() with the Ernst formula (assuming TE<<T2*):

where has three discrete values (=2°, 10°, 35°) and E1₀=exp(-TR·R₁₀).

Four dimensional (4D; x, y, z, t) longitudinal relaxation rate (R₁(t)) maps were calculated for each dynamic phase using signal intensity data from pre- and post-contrast T₁-FE images [S(t)-S(0)]:

where =35°, TR=4.37.0 ms, A=[S(t)-S(0)]/(M0·sin), B=(1-E1₀)/(1-cos· E1₀).

4D Gd-DTPA-BMA concentration maps were then calculated for each dynamic phase:

where r₁ is the relaxivity of Gd-DTPA-BMA determined experimentally, r₁=4.39 s^-1 mM^-1 (at 37°C) (see Appendix B).

	Appendix B. Determination of relaxivity of Gd-DTPA-BMA

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A phantom was constructed containing one distilled water sample and 17 samples of Gd-DTPA-BMA solutions with concentrations ranging between 0 and 1.2 mmol l^-1. The samples were taped around the thighs of a volunteer to maintain their temperature at approximately 37°C and then scanned with the 1.5 T scanner. A commercial sequence for the calculation of T1 and T2, which uses a combination of invasion recovery spin echo (IR-SE), was applied for calibration purpose. Scan parameters of the IR-SE mix sequence were SE2000/13,100, IR4000/13, 100/160. Relaxivity of Gd-DTPA-BMA (R₁) was calculated by fitting the paired Gd-DTPA-BMA concentration and R₁ data using a linear least-square algorithm:

T1 relaxivity was found to be 4.39 s^-1 mM^-1 at 37°C and 1.5 tesla. It should be noted that in vitro measurements of this type will only approximate the effective relaxivity of contrast media in vivo.

	Appendix C. Calculation of Ktrans maps

Top Abstract Introduction Materials and methods Results Discussion Appendix A. Calculation of... Appendix B. Determination of... Appendix C. Calculation of... References

 
Maps of R₁₀, C(t) and the VIF were used to calculate the K^trans and v_e on a pixel by pixel basis using the tri-exponential model described by Tofts and Kermode [11]:

where b₁=K^trans·a₁/(K^trans/v_e-m₁) and b₂=K^trans·a₂/(K^trans/v_e-m₂), and where m₁ and m₂ are the rate constants of the fast and slow components of the plasma contrast concentration decay curve. The simplex minimization procedure was employed in the curve fitting.

Received for publication April 9, 2001. Revision received August 10, 2002. Accepted for publication November 19, 2002.

	References

Top Abstract Introduction Materials and methods Results Discussion Appendix A. Calculation of... Appendix B. Determination of... Appendix C. Calculation of... References

 

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