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1 Division of Imaging Science and Biomedical Engineering, Stopford Medical School, University of Manchester, Manchester M13 9PT and 2 AstraZeneca, Alderley Park, Macclesfield, Cheshire SK10 4TG, UK
Correspondence: Professor A Jackson, Imaging Science and Biomedical Engineering, The Stopford Medical School, University of Manchester, Manchester M13 9PT, UK
| Abstract |
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), and endothelial permeability (kfp) maps. The technique was assessed in patients with cerebral glioma (n=5) by examining the reproducibility of endothelial permeability and
between two separate examinations conducted with a 2-day interval. The technique produces maps of endothelial permeability that appear to be free of any contribution from intravascular contrast agent. Maps of
show close correlation with maps of blood volume calculated from independently acquired dynamic susceptibility weighted MRI examinations, with no evidence of residual permeability effects. The results were highly reproducible with strong intra-class correlation between the two examinations for mean values and for 97.5 percentiles of endothelial permeability and
. The excellent reproducibility of this technique and the ability to calculate endothelial permeability and
values from rapidly acquired data sets offer considerable advantages over conventional approaches and support the use of this methodology for therapeutic monitoring or trials of novel therapeutic agents. | Introduction |
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The requirement for imaging strategies that allow repeated measurements during therapy, and the ionizing radiation involved in CT studies have led workers in this field to concentrate on the use of dynamic contrast enhanced MRI [7, 8]. However, the temporal changes in MRI signal intensity that occur following injection of contrast agent (CA) are affected by a number of factors, including the innate T1 and T2 relaxation times of the tissue, scanner dependent scaling factors, variations in injection technique and the patient's cardiovascular status. In order to develop biologically appropriate measures that are not confounded by these effects, several workers have attempted to apply pharmacokinetic models of CA distribution to MRI data. These models can be used to calculate transfer coefficients, typically the endothelial permeability surface area product (Ktrans), that characterize the leakage of CA into tissues [911]. Such metrics are expected to be comparable across patient groups, despite physiological variations between patients and variations in scanning hardware and sequences. In general terms, these models use signal intensity time course data to calculate the time course of variations in CA concentration (C(t)). These CA concentration images are used to derive the plasma contrast concentration function (PCCF) and tissue residue function (TRF) in tissue voxels. These can then be used to calculate the intercompartmental transfer function for the model [9, 10, 12]. Unfortunately, accurate mapping of pre-contrast relaxation rate (R10) values and measurement of the PCCF are technically complex and have restricted the clinical application of these techniques [13]. These technical restrictions have proven sufficiently problematic that many studies have been forced to employ the same idealized values for PCCF in all cases [9, 12, 14]. Most techniques for the measurement of endothelial permeability assume that the contribution of intravascular CA is negligible, giving rise to artificially elevated values for transfer constants. A further problem with many available techniques is that movement of CA across leaky endothelia into the interstitial space prevents assessment of vascular volume, causing artificial elevation of calculated rBV values.
Several workers have described T1 weighted (T1W) and T2* weighted (T2*W) dynamic MRI techniques to allow simultaneous measure of vascular volume, or flow, and Ktrans [7, 1518]. We have taken an alternative approach by decomposing tissue residue functions measured during the first passage of a CA bolus on T1W images into intravascular and extravascular components. The objective of this study is to develop an analysis technique for the decomposition of the tissue residue function that is sufficiently robust and reproducible for use in therapeutic trials. A detailed description of this technique is provided. Results from a group of five patients with pathologically proven high grade gliomas (IIIIV) are presented. These patients were studied on two occasions with an interval of 2 days between examinations, to allow assessment of the reproducibility of the technique.
| Materials and methods |
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Image Processing
variate model for calculation of rBV
T2*W dynamic data were used to derive parametric maps of relative cerebral blood volume (rCBVT2) by estimation of the area under a fitted
variate function, as previously described [20]. These maps were later compared with relative cerebral blood volume (rCBV) maps from T1W data to assess how effectively the new technique compensates for errors owing to CA leakage.
First-pass pharmacokinetic model
This model describes the distribution of CA between the intravascular and extravascular compartments during the first passage of a CA bolus. The model is used to analyse the T1W dynamic imaging sequence.
Intravoxel C(t)s are composed of interstitial and intravascular components, Ce(t) and Cv(t), respectively:
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le;ve
le;100%), Cp(t) is the mean plasma CA concentration time course curve (equal to the PCCF), and Ktrans is the volume transfer constant between blood plasma and the leakage space, which is equivalent to the endothelial permeability surface area product where CA delivery is not limited by flow [9, 21]. On the assumption that backflow during the first pass of the CA bolus is negligible (Ce(t)<<Cp(t)) [22], we integrate |
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Cv(t) can be derived by subtraction of Ce(t) from C(t) as indicated by Equation 3
. The technique presented here uses an iterative approach to improve estimates of the separation of the bulk tissue concentration, C(t), into its interstitial and intravascular components, Ce(t) and Cv(t), respectively. This technique represents a new approach to the decomposition of C(t), which we have designed to improve the reproducibility of the signal decomposition.
Application of the pharmacokinetic model to T1W data
The analysis technique for T1W data sets is graphically represented by the flowchart in Figure 1
. The symbols, definitions and abbreviations employed in the flowchart are described in Table 2
. The individual steps in the analysis are described in detail below.
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le;t
le;TrR. TrR is the time of the beginning of the recirculation phase identified from the PCCF. Examples of Cp(t) measured from the SSS in a patient with a glioma on day 0 and day 2 are shown in Figure 2a
variate density function [24] concatenated with a steady state concentration [25]. The extended first pass LP was then calculated using a five point NewtonCotes numerical integration method. Figure 2b
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Step 2. An initial estimate of the intravascular component of C(t), Cv(t)i=0, can be obtained simply by subtracting the initial estimate of the interstitial component derived in step 1 from the C(t): Equation 1
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Step 3. The volume transfer constant kfp was estimated by subtracting the contribution of recirculation of CA through the intravascular compartment, calculated in step 2, from C(t) and refitting the resulting curve (C(t)d). This fitting was also weighted to allow the steady state part of C(t), after the onset of recirculation of CA bolus, to dominate the fit:
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Step 4. Steps 2 and 3 were repeated in an iterative fashion to optimize the separation of intravascular and extravascular CA effects. The criterion for convergence was that the interval of two successive estimations of kfp was smaller than a predefined threshold value,
, (equal to 10-4 min-1 in the current study).
Step 5. Voxel by voxel relative cerebral blood volume (rCBV) maps, corrected for the effects of CA leakage into the interstitial space (
), which also represent the "true" relative tumour blood volume, were then calculated by
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Assessment of reproducibility
Subjective visual comparison was made between 3D maps of kfp and
on day 0 and day 2, 3D maps of
and multislice 2D maps of rCBVT2. A volume of interest for each tumour was manually drawn using maps of 3D kfp and 3D
. Frequency distributions of kfp and
(histograms) of the entire tumour volume measured on day 0 and day 2 were plotted in pairs for visual comparison. A single tailed WaldWolfowitz runs test [26] was used to test for differences in the distributions (histograms) of kfp and
values measured on day 0 and day 2. Mean and 97.5 percentiles of kfp and
for the whole tumour volume were calculated for each patient and for each observation, and were used as an indicator of the spread of measurements [8].
The coefficient of variation (CoV) of repeated kfp and
values was calculated using the formula CoV=(standard deviation/mean) x100%. Intra-class correlation coefficients (rI) of the repeated measurements of kfp and
for both mean and 97.5 percentiles were also calculated:
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| Results |
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and rCBVT2 showed a high level of correspondence with identical demonstration of major vascular structures and a close correlation between the distributions of tumoural cerebral blood volume (CBV) values on two maps (Figure 3
also demonstrated differences in CBV between normal grey and white matter, similar to those seen on rCBVT2. 3D maps of kfp demonstrated high values only in enhancing tumour and in the choroid plexus. There was no evidence of elevated kfp in major vessels (Figure 3
and kfp maps acquired on days 0 and 2 demonstrated no discernible differences in any patient.
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in tumour voxels (Figure 4
were dominated by voxels with low values. However, the conformance of histograms between day 0 and day 2 was excellent in all patients. The WaldWoffowitz runs tests demonstrated no significant differences in histogram distributions between days 0 and 2 for either kfp of
(p>0.05).
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for each subject expressed as the CoV of both the mean values and 97.5 percentile values of the data range. The CoV of mean values ranged from 0.026.34% for kfp and from 0.75.34% for
. The CoV of 97.5 percentile values ranged from 0.076.54% for kfp and 2.064.79% for
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and 97.5 percentiles of
. There are strong intra class correlations between mean values and 97.5 percentiles of kfp measured on day 0 and day 2 with intra-class correlation coefficients rI>0.997 and rI>0.984, respectively. There are also strong intra-class correlations between mean values and 97.5 percentiles of
measured on day 0 and day 2, with intra-class correlation coefficients rI>0.981 and rI>0.979, respectively.
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| Discussion |
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A major advantage of the first-pass model is the ability to decompose the C(t) data to produce separate curves for intravascular and extravascular CA. The existence of tumour voxels containing mixtures of permeable capillary beds and large blood vessels causes problems in the estimation of both endothelial permeability and blood volume. Because Gd compounds increase both T2 and T1 relaxation rates, the signal drop in T2*W dynamic series will be reduced by competing increases in signal in regions where T1 effects are significant, such as tumour tissues with high CA leakage. This will result in consequent underestimation of rCBV. In contrast, where T1W dynamic sequences are used, the presence of transendothelial CA leakage will act synergistically on signal intensity, causing artefactual increases in apparent rCBV [5, 29]. In addition, attempts to measure endothelial permeability in voxels where a significant proportion of CA is in the intravascular compartment will result in artificially high K values of Ktrans, which have been called pseudopermeability effects [4, 22]. The first attempt to separate effect of CA leakage from the presence of extravascular CA was made by Weisskoff et al [15]. These authors modelled the combined T1 and T2 relaxivity effects of Gd compounds on MR signals to allow simultaneous measurement of blood volume and permeability. Ostergaard et al [17] have successfully applied this technique to simultaneously measure blood flow, blood volume and blood-brain barrier permeability in a group of patients with brain tumours. The accuracy of decomposition of intravascular and extravascular CA contributions from T2*W dynamic data are related to extraction rate of CA into the tumour tissue. In the presence of large extraction fractions, the authors expect the model to be less appropriate [15]. The presence of significant T1 shine-through represents the worst case [20], where parts of a tumour with highly permeable capillary beds shows significant T1 related enhancement during the first passage of the CA bolus.
Weisskoff et al [15] suggested that, in such cases, the use of other techniques to minimize relaxivity enhancement would be required in order to more aggressively correct for CA leakage. Possible approaches might include the use of a larger dose of CA pre-load or macromolecular intravascular agents to reduce first-pass extraction [7, 15].
The iterative technique, which we have developed, is based on the use of T1W dynamic data, where conKtrans and
are therefore more resilient to variations in CA extraction fraction than methods based on T2*W dynamic studies, where very poor signal-to-noise ratio will be encountered if the contribution from both intravascular and extravascular compartments are of a similar magnitude. Theoretical modelling of the first pass technique (unpublished observations) shows that errors in the estimation of Ktrans associated with values of blood flow, interstitial volume fraction and extraction fractions, typically seen in the glioma data presented here, will be small (<20%). However, these errors will potentially become significant when the distribution fraction is small or where Ktrans is particularly high, such as in the liver or kidney where blood flow and extraction are both high. In areas where contrast extraction is negligible, such as normal brain tissue, the model is much more accurate than the Tofts and Kermode model [9], which fails under these circumstances [30].
The iterative approach also makes full use of previous knowledge of PCCF, which in this study was measured from a large vessel (sagittal sinus). The automatic decomposition scheme uses the ratio between peak CA concentration and CA concentration at the beginning of the recirculation phase in the vascular compartment to drive the iterative process. This value is used, together with Pv, to estimate a theoretical value for the CA concentration during the recirculation phase (rR). Comparison of measured and predicted values of rR forms the driving function for the iterative process. In most cases, the algorithm reaches convergence after two to four iterations for most voxels in the tumour volume. Using this approach, the decomposition of the C(t) data is no longer arbitrary but data driven. Since the driving function chosen is estimated from the plasma C(t) data for each patient, the technique can be predicted to have greater computational stability and reproducibility.
The hypothesized improvements of the iterative approach depend on accurately reproducible identification of the time point that marks the end of the first-pass curve and the beginning of the rR. In order to obtain high signal-to-noise ratio in the PCCF, an image sequence with very short repetition and echo times was used. PCCF was always measured from sagittal sinus, where blood flow is relatively slow (mean linear velocity <5 cm s-1) with respect to the very short repetition time (=0.004 s), and a thick imaging slab (15 cm) was used. This approach minimizes the signal loss resulting from heterogeneous phase evolution of laminar flow within the imaging volume. The radio-frequency pulse sequence employed has a broad bandwidth and heavy duty cycle. The in-flow effect of blood flow in the sagittal sinus, from which the PCCF is measured, is also fully suppressed. The combination of these factors has produced a PCCF with clearly identified recirculation peaks, allowing confident identification of the beginning of the recirculation phase (Figure 2
). We did not add flow compensation gradients into the pulse sequence. Signal loss due to velocity induced spin dephasing in the transverse plane was negligible, since a very short echo time (0.0011 s) was used in this study. In addition, the benefit of phase correction by the first moment nulling is largely compromised by the considerable increases of minimum repetition time that this requires. In this study, the 3D T1W-GRE dynamic sequence, combining a large imaging volume, very short repetition time and selective saturation of spins in the upstream portion of sagittal sinus, yielded much higher index of signal-to-noise ratio in the time cause data (
SImax(SS)/
) (equal to 485, where
is the root mean square noise) than is seen with 2D T1W-GRE (slice thickness 3 mm,
SImax(SS)/
=81) or T2*W echo planar imaging (
SImax(SS)/
=18). The effects of vascular proton (water) exchange on MR signal intensities were also minimized by the use of very short repetition times in the T1W-GRE sequence [31].
Using the LP, which is the integral of the C(t) curve, has several advantages. First, it is less susceptible to noise related errors [32], including those owing to motion related phase shift artefacts [33]. Second, fine adjustment can be made by scaling individually measured LP with an averaged value of the height of the LP from the whole patient group. This allows correction for small variations in the individual measured peak values of PCCF, which result from averaging effects owing to the relatively low temporal resolution of the sampling strategy compared with the length of the first-pass bolus [34, 35]. This averaging process is appropriate since the value of LP at the end of the passage of the bolus is unaffected by either the length of the bolus or cardiac function, if the dose of CA per unit body weight is constant.
The exact clinical application of parametric mapping techniques of this type is still being defined. Maps of blood volume may provide indices of malignancy, tumour grade, tumour heterogeneity and prognosis [4, 5, 36] in a variety of tumour types.
Measurements of Ktrans have less clearly defined clinical implications. The definition of Ktrans is the mathematical product of the endothelial surface area and the endothelial permeability. In practice it must also be appreciated that Ktrans will be dependent on tissue perfusion. In areas with high blood flow, the measured values of Ktrans will depend principally on endothelial permeability and surface area. However, in areas of poor perfusion and high Ktrans, the leakage of contrast will be limited by the contrast delivery rate (flow). This affects all methods for the measurement of Ktrans so that measured values represent a parameter weighted by contributions from permeability, vascular surface area and flow in unknown proportions.
The recognition that cytokines, such as VEGF, act both as promoters of angiogenesis and as potent stimuli of endothelial permeability suggests a role for such measurements in the identification and quantification of angiogenic effects in a variety of malignant and inflammatory disease processes. The use of such quantitative measurements has major implications for therapeutic monitoring and for the development and testing of novel therapeutic agents, which target the angiogenic process. For these applications the techniques used to derive vascular parameters must be computationally stable and reproducible. Ideally, the measurements produced should uniquely reflect individual physiological parameters, such as permeability, and be free of other confounding effects.
The measurement of reproducibility in this context is not straightforward and the method used depends on the analysis to which parametric data will be subjected. In most cases, interest is centred on the frequency and location of areas where endothelial permeability and blood volume are raised [37]. The distribution of parametric values is therefore of prime importance, and it seems probable that tumour grading, prognostic judgements and measurements of therapeutic agent effect will all strongly depend on the accurate measurement of these raised values [4, 36]. Histograms of kfp and
show that the distribution of these values is highly skewed and that, even in aggressive gliomas, the proportion of pixels with high values is small. In view of this it is essential that studies of reproducibility specifically assess the shape of the distribution curve and the reproducibility of measurements in pixels that lie in the tail of the distribution.
Several indices of reproducibility have been used to assess the new analysis technique. Subjective comparison of images and pixel distribution histograms shows excellent reproducibility. This is confirmed by the WaldWolfowitz runs test, which identified no significant differences between the examinations performed on days 0 and 2.
Use of the approach described here is associated with a number of potential disadvantages. First, the use of an analysis based entirely on the collection of dynamic data during passage of the contrast bolus makes significant demands on the temporal resolution of the imaging sequence. Temporal resolution of 5.1 s, which mathematical modeling suggests represents the lowest acceptable temporal sampling rate (unpublished observation) was used. Where blood flow is greater, an increase in temporal resolution will be required that will limit the coverage achievable with conventional sequences. One potential solution to this is the use of parallel imaging systems that will allow an increase in temporal resolution without sacrificing spatial coverage. A specific disadvantage is the lack of any allowance in the model for backflow from the interstitial tissue into the vascular compartment. As stated above, errors in the estimation of Ktrans associated with values of blood flow, interstitial volume fraction and extraction fractions, typically seen in the glioma data presented here, will be small (<20%). However, these errors will potentially become significant when the distribution fraction is small or where Ktrans is particularly high, such as in the liver or kidney, where blood flow and extraction are both high. In contrast, the technique also has a number of specific advantages. First, the decomposition of intravascular and extravascular contrast contributions to the time course signal allows calculation not only of Ktrans but also of rBV. This in turn abolishes pseudopermeability effects with very beneficial effects on reproducibility, particularly at higher values of Ktrans. Another obvious advantage of using a first-pass model is that the time needed for image acquisition is much shorter than those required by multicompartmental models. An image acquisition lasting only 70 s can provide adequate dynamic data for the entire study (Figure 1
). In addition 16 s of imaging time is needed to acquire the three sets of images for calculation of R10 maps. In comparison, traditional multicompartmental methods using either infusion or bolus injection rely heavily on the characteristics of the later part of the C(t) curve and therefore typically require data collection over 68 min [8, 12, 14]. As a result of the rapid image acquisition, the new technique is extremely resistant to movement artefact and can be easily adapted for use in areas of the body where respiratory motion is problematic.
In conclusion, we have described a novel analytic approach that uses T1W first-pass data to produce independent estimates of endothelial permeability and blood volume. The technique uses patient specific data acquired from the vascular compartment to drive an automatic decomposition of intravascular and extravascular CA effects. The technique has proven highly reproducible and is free from pseudopermeability effects that are seen with other models and that can produce erroneous estimates of the frequency of areas of elevated endothelial permeability. High precision (small CoV) and strong intra class correlation between the results from short-term repeated studies indicate its potential for serial studies, such as treatment monitoring and therapeutic trials.
| Footnotes |
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Received for publication July 13, 2001. Revision received June 27, 2002. Accepted for publication July 4, 2002.
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