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British Journal of Radiology (2003) 76, S159-S173
© 2003 British Institute of Radiology
doi: 10.1259/bjr/22322389
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2003 Sir Godfrey Hounsfield Lecture

Imaging microvascular structure with contrast enhanced MRI

A Jackson, PhD, FRCR, FRCP

Imaging Science and Biomedical Engineering, Department of Medicine, Stopford Building, University of Manchester, Oxford Road, Manchester M13 9PT, UK

Introduction

Over the past 10 years there has been increasing interest in the development of novel MRI techniques that enable researchers and clinicians to study the development and structure of vasculature in pathological tissues. Although the majority of this work has been performed in studies of human tumours the techniques are potentially widely applicable in other pathological states [1–4].

All tissues depend on their vasculature for an adequate supply of nutrients and removal of waste metabolic materials. As tissues develop, an adequate and appropriately structured vascular supply must develop at the same time. This process, known as angiogenesis, is also an essential component of the behaviour of many pathological tissues including tumours and inflammatory disease [1, 5]. More importantly, the angiogenic process appears to be largely independent of the developing tissue. This has given rise to the concept of antiangiogenic therapies which could be effective in a wide range of tumours independent of the tissue type.

The angiogenic process is complex and can be stimulated by any one of several mechanisms. Typically, growth of tissue which has outstripped its local blood supply results in regional hypoxia and hypoglycaemia which stimulates the release of local chemical messengers from the cells of the tissue itself. The best known of these messengers is the cytokine, vascular endothelial growth factor (VEGF) [6–9]. VEGF is a common and potent angiogenic stimulator, which is found in many pathological tissues. It is released in response to local hypoglycaemia and/or hypoxia and has several effects each of which will improve metabolic supply. In the short term VEGF will act directly on local capillaries to increase endothelial permeability resulting in an immediate increase in the supply of nutrients [10]. This increase in permeability is also believed to form an important part of the metastatic mechanism allowing passage of tumour cells into the circulation. In the medium to long term, VEGF will stimulate mitosis in endothelial cells from local blood vessels so that they divide and develop a new vascular infrastructure to supply the tumour. The angiogenic mechanism also is responsible for breakdown of local connective tissues, which allows in-growth of new blood vessels.

Where the angiogenic process fails tissue development cannot occur and novel antiangiogenic therapies are currently being developed which use this mechanism for the treatment of a wide range of cancers and other pathologies [11, 12]. The increasing understanding of the role of the angiogenic process in disease progression has led to interest in methods for documenting the presence and activity of angiogenesis [12–14]. In particular there has been considerable interest in the development of reliable quantitative methods which can provide independent indicators of the status of, and changes in, microvascular structure [13, 14].

In pathological tissues the angiogenic process is often abnormal, leading to the development of distorted vascular beds characterized by an excessive proportion of blood vessels and blood vessels with abnormal morphology and flow characteristics [15].

Central areas of a rapidly growing tumour will commonly exhibit inadequate blood flow due to reduce local perfusion pressure resulting from a combination of inadequate vascularization and increased interstitial tumour pressure. Finally, the angiogenic neovasculature will exhibit increase endothelial permeability to medium and large sized molecules [16, 17].

Initial studies of microvascular structure in tumours were undertaken using histological techniques, however these are essentially unsatisfactory for a number of reasons [18, 19]. Pathological assessment relies on the acquisition of tissue samples which is clearly invasive and which can be repeated only infrequently. Furthermore, many tumours and other pathological tissues demonstrate considerable heterogeneity in microvascular structure so that isolated regional biopsies may give misleading information. These limitations have led to the development of imaging based methods for quantification of microvascular structure. These methods are commonly based on dynamic contrast enhanced imaging techniques using MRI or CT data collection combined with analytic algorithms to calculate descriptive parameters related to microvascular structure. The availability of quantitative imaging based methods to describe the microvasculature in biological tissues is potentially of considerable importance. Such methods can provide important surrogate markers of therapeutic response in trials of novel antiangiogenic therapy and the majority of applications to date have been in this area. However, these techniques can also be seen to have directly clinical relevance providing information about diagnosis, tumour grade, therapeutic response, tumour recurrence and prognosis. At the present time the majority of technical development of these techniques has been centred around the use of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). This article will describe the development and range of DCE-MRI techniques and the range of image analysis approaches available. The article aims to provide insight into the benefits and disadvantages of specific approaches rather than to detail the actual analysis mechanisms in detail.

Microvascular features of pathological tissues

It is important to consider the structural features of the microvasculature which will affect the behaviour of injected contrast media. Following an injection of contrast medium the contrast bolus will pass through the vascular bed entering through arterial vessels, passing through the capillary bed and draining into the venous system. The amount of contrast that passes into the vascular system will depend on the contrast dose injected and on the blood flow rate through the vessels which will in turn be related to factors governing local perfusion pressure such as tissue interstitial pressure. Within any given voxel the amount of intravascular contrast present at any time will depend on the proportion of the voxel formed by blood vessels. As contrast passes through the capillary bed it will leak into the extravascular extracellular space (EES) (Figure 1Go). The rate at which this leakage occurs will reflect the difference in contrast concentration between the blood plasma and the EES. For any given concentration ratio the amount of contrast that leaks will also be restricted by the permeability and surface area of the endothelial membrane. As contrast leaks into the EES it will diffuse through the space so that the concentration of contrast within each voxel will also depend on the size of the EES. Eventually as the contrast concentration within the vascular space decreases, due to leakage into other tissues and renal excretion, contrast will begin to pass back from the EES into the vessels.



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  		Figure 1. Diagramatic representation of the distribution of contrast media within a voxel. Contrast molecules (black dots) will enter within the plasma and their delivery will be controlled by the plasma concentration (Cp) and by the flow of blood through the voxel (F). Leakage will occur into the extravascular extracellular space whose fractional value is expressed as the variable ve. Current models assume that contrast leakage does not occur into the intracellular space (vi). The leakage of contrast will be governed by the concentration difference between the plasma and the extracellular extravascular space and by the permeability and surface area of the capillary endothelia which is expressed as permeability–surface area product (PS).

 
It can be seen that the behaviour of contrast material within any given voxel will be related to the concentration time course of contrast entering the arterial vessels, the regional blood flow, the local proportional blood volume, the endothelial permeability, the surface area of the endothelium and the size of the EES. Analysis schemes for DCE-MRI are designed to identify surrogate markers which represent one of, or combinations of these biological features [4].

Dynamic contrast imaging

T2 and T2* based techniques
In order to quantify features of the microvasculature it is essential to record high quality dynamic image data. Image acquisition can be performed using either T2, T2*or T1 weighted images. The use of T2 and T2* dynamic imaging acquisitions is commonly performed for the calculation of perfusion and local blood volume in brain tissue. The presence of an intact blood–brain barrier means that no contrast leakage into the EES will be seen and the data can be treated as a purely intravascular or blood pool marker. For perfusion calculations this is beneficial since T2* weighted sequences display changes due to the effect of contrast on both blood vessels and the surrounding tissues [20]. In capillary beds where the cerebral blood volume (CBV) is low the signal change on T2* weighted images will be proportionally larger than that which results from contrast in large vessels (Figures 2 and 3GoGo). This is helpful in techniques that are designed to quantify the characteristics of normal cerebral capillary beds [21–23]. Where leakage of contrast occurs as in pathological tissues the signal changes due to intravascular and extravascular contrast will occur in opposite directions. The T2* effect of intravascular contrast will cause signal loss whereas the predominant T1 effect of extravascular contrast will cause signal increase. This effect, known as "T1 shine-through" can be eliminated by a number of techniques so that the signal time course data reflects principally intravascular contrast [15] (Figure 4Go). These data sets allow accurate measurement of blood volume which relates to both tumour grade and prognosis. Using T2 or T2* weighted imaging to quantify contrast leakage is more difficult for a number of reasons [24]. Although techniques have been described they suffer from problems related to the non-linearity of the signal changes observed and are seldom used.



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  		Figure 2. (a) Dynamic time course series through the brain using a T2* weighted acquisition during passage of bolus of contrast agent. Note the decrease in signal intensity within the brain during the passage of the contrast bolus. (b) Signal intensity changes in a large blood vessel (A), grey matter (B) and white matter (C). (c) Calculated changes in contrast concentration derived from the vascular and grey matter curves. Open circles and crosses represent the original data measurements. The solid lines show the result of a gamma variate curve fit to each of the data sets. Note that the curve fitting procedure eliminates the effects of contrast re-circulation in the later phases of the images. (Courtesy of Dr F Calamante.)

 


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  		Figure 3. Calculated parametric images of cerebral blood volume (CBV), cerebral blood flow and mean transit time (MTT) from a normal healthy volunteer. The images were acquired using T2* weighted dynamic imaging techniques. Data were analysed using a gamma variate curve fit analysis to allow calculation of each parameter. Note the clear distinction between grey matter, white matter and blood vessels in both the CBV and flow maps. In the MTT map slight prolongation of the MTT can be seen in the watershed areas.

 


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  		Figure 4. (a) Time course data from a region of interest in an enhancing meningioma following injection of contrast agent. Images were acquired using a T2* weighted acquisition protocol. Note the initial dip in signal intensity as a contrast agent enters blood vessels within the voxel followed by a rapid enhancement effect as contrast leaks into surrounding tissues. The preliminary drop is due largely to T2* (susceptibility) effects in the image whereas the rise is due to residual T1 weighted (relaxivity) effect. (b) Signal change from the same region of interest from a second contrast injection performed several minutes after the first. The pre-enhancement with the initial dose of contrast has saturated the T1 sensitivity of the tissues and only the susceptibility effects are now seen. Note the significant signal drop due to intravascular contrast and the failure of the signal to return to the baseline during the re-circulation phase. (c) A calculated regional relative cerebral blood volume (rCBV) map of a large glioma. Note the high CBV in the large feeding vessels and draining veins. Central areas of poor perfusion are seen as negative values. (d) The relationship between median rCBV and tumour grade in a series of gliomas. Note the clear grade specific relationship of CBV calculated in this way.

 
Analysis of data from T2 and T2* based techniques
The signal changes observed during the passage of a contrast bolus through the vessels can be transformed to contrast concentration maps and these can subsequently be used to derive quantitative images of physiological parameters. A number of analysis techniques have been described and a common feature of many is the use of a gamma variate curve fitting procedure to define the shape and timing of the bolus of contrast media during its first passage through the tissue [21, 25] (Figure 2Go). The need for this step arises from the signal changes which occur later as contrast re-circulates on subsequent passes through the peripheral and pulmonary circulations. As a result of this re-circulation the plasma contrast concentration fails to return to pre-enhancement levels. The use of a curve fitting technique allows us to estimate what the first pass bolus would have looked like if no re-circulation had occurred. Parametric images of regional cerebral blood volume (rCBV) can be derived from the area under the contrast concentration time course curve and can be normalized to the measurements in large vessels to provide absolute measurements of CBV. Measurements of CBV are of particular interest in the study of tumours where they can be considered as an imaging based surrogate marker of microvascular density (MVD). MVD is a well described quantitative parameter derived from histological studies which has shown close links with tumour grade and prognosis in a wide range of tumour types. In actual fact these two parameters do not always correlate particularly well where direct comparisons have been performed since imaging based techniques can only measure contributions due to vessels which have active flow [18, 19]. None the less, both MVD and CBV have been shown to have similar correlations with tumour grade and behaviour [26–28]. A number of other parameters such as those which indicate bolus arrival time can also be accurately derived from the data. However, these have little value in neoangiogenic tissue although they are widely used in studies of cerebrovascular disease. Measurements of absolute blood flow are more complicated and subject to errors due to effects such as bolus dispersion and arrival time delays [29]. Another interesting parameter provides an estimate of abnormality during the re-circulation phase of the contrast passage. This "relative re-circulation" (rR) parameter quantifies any abnormal elevation of the contrast concentration in the period immediately after the passage of the contrast bolus [15, 27, 30] (Figure 5Go). In theory the rR will be increased by local vascular factors such as absolute flow rate, flow rate heterogeneity and therefore by local perfusion pressure. Studies of rR in glioma have shown a close relationship with tumour grade and spatial distribution of abnormal values in areas of tumour where slow flow and the decreased perfusion pressure would be anticipated (Figures 6 and 7GoGo). Despite the range of parameters that can be extracted from T2 and T2* weighted data, their use has been largely limited to cerebral tumours due to the considerable problems of T1 shine-through effects which are experienced in peripheral tissues when normal leakage of contrast agent may be considerable.



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  		Figure 5. Demonstrates the concept of the relative re-circulation parameter. The dotted line shows the expected changes in contrast concentration within a voxel which contains no contrast leakage. The initial peak is due to the passage of the contrast agent bolus and the second peak represents the second passage and subsequent re-circulation. The black line shows typical data observed from enhancing tumours. The elevation of the re-circulation phase data reflects slow perfusion and/or irregular flow through areas of low perfusion pressure and is equivalent to the tumour blush seen on conventional angiography. Since the expected shape of the first pass curve can be estimated by gamma variate fitting the difference between this and the actual measured value can be estimated (hatched area). This measure can then be used as an indicator of flow irregularity.

 


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  		Figure 6. Calculated images from dynamic T2* weighted perfusion data in (a) a large meningioma and (b) a glioblastoma. The black and white scales illustrate the relative cerebral blood volume (rCBV) which can be seen to be elevated throughout the meningioma and also in the peripheral component of the glioma. Red areas illustrate abnormally high values of relative recirculation. None are seen in the meningioma, which is classically characterized by well-organized and well-developed vascular structures. In the glioblastoma a number of areas are seen in the deep part of the enhancing portion of the tumour adjacent to the non-enhancing components. This corresponds to areas where tumour staining would be seen on angiography and where flow can be anticipated to be irregular and slow.

 


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  		Figure 7. (a) The distribution of pixel values of relative re-circulation (rR) in a patient with a grade 3 glioma. Note that the distribution of the values fits normal distribution with a skewness value of 0.45. (b) A similar distribution graph from a patient with a glioblastoma multiforme. Note the marked skew of the data to the right side due to an increase of pixels with high values. This gives rise to a skewed distribution with a skewness of 1.22. (c) The distribution of rR values within a group of gliomas of varying grades. A clear relationship between grade can be identified with far higher values of skewness in grade 4 tumours than in grade 2 and 3. (d) A scattergram showing the distribution of mean values of relative cerebral blood volume (rCBV) on the x-axis and skewness of rR on the y-axis. The points represent grade 2 (triangles), grade 3 (diamonds) and grade 4 (circles) gliomas.

 
T1 based techniques
The choice of imaging sequence for T1 weighted DCE-MRI is driven by a number of considerations. Since we are interested in the changes in contrast concentration over time the temporal resolution of the imaging sequence will be constrained by the analysis technique to be employed (vide infra). The main consideration when choosing an appropriate temporal resolution is the shape of contrast concentration curve in plasma, which is commonly called the arterial input function (AIF). If a bolus injection of contrast is employed accurate quantification of the initial passage of contrast bolus will require a high temporal resolution usually of 5 s or less. This time constraint will limit the spatial resolution of the imaging sequence and the amount of tissue that can be encompassed in any given imaging volume. Most centres use a simple multislice gradient echo sequence, which on current conventional clinical scanners can provide an imaging matrix in the region of 256 x 256 x 25 within the 5 s period. The imaging sequences currently used as our centre are shown in Table 1Go. In order to provide adequate data to allow clear separation of the effects of contrast diffusion through the EES the dynamic data collection will typically need to continue in excess of 5 min.


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  		Table 1. Typical imaging protocol for dynamic contrast-enhanced MRI

 
Two other constraints on the imaging sequences must also be considered if pharmacokinetic analysis of the data is to be performed. The pharmacokinetic analysis will require contrast concentration data rather than signal change data. The relationship between signal change and contrast concentration is non-linear and will depend on the baseline T1 value of the voxel. It is therefore necessary to produce quantitative T1 images of the imaging volume prior to contrast injection. This can be time-consuming and complex and most centres have developed quantification methods using multiple T1 weighted images acquired with varying flip angles to allow T1 calculations [12, 31]. Pharmacokinetic analyses also require measurement of the contrast concentration changes with time in the vessels supplying the tissue (the AIF). Identification of an appropriate AIF can be difficult and is further complicated by the additional signal changes produced by inflow effects on most imaging sequences [12, 32–34]. Using a multislice gradient echo acquisition inflow effects are usually negligible in all slices except for those at the edges of the volume so that an AIF can be acquired from an appropriate vessel.

Data analysis

The extraction of appropriate parameters to describe the microvasculature from DCE-MRI data is extremely complex and many analysis approaches are available. The choice of analysis approach will depend on the expected changes in the tissue and the features of the microvasculature that are of particular interest. The simplest approach relies on quantification of the signal changes observed, which avoids the complexity of calculating contrast concentrations from the baseline data (Figure 8Go). A number of such metrics have been described and most characterize the shape of the signal time course curve based on the maximal amplitude of the signal and the time taken to reach this value. Other metrics compare the signal intensity achieved in any given period of time. Typical metrics include T90 [35], which is the time taken to reach 90% of the maximal enhancement value and the maximal intensity change per time interval ratio (MITR) [36] which measures the maximal rate of enhancement. These simple metrics suffer from problems, which have limited their application and led many authors to adopt the more complex pharmacokinetic analysis techniques. First, metrics based entirely on signal change characteristics will reflect both intravascular and extravascular contrast concentrations and separation of signal change effects due to blood flow and contrast leakage is difficult. More worryingly these measurements will be unpredictably affected by variations in scanning protocol, including those that may change from scan to scan such as receiver gain. Despite these limitations, simple measurements based on signal change alone can be diagnostically useful and have found application in a number of clinical applications [17].



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  		Figure 8. T1 weighted MRI of the distal femur osteosarcoma after injection of contrast medium. The study was performed following initial chemotherapy and prior to tumour resection. Regions of representative tissue types are shown with corresponding dynamic signals for the four areas of the tumour (A) and necrotic central core, (B) viable soft tissue component with increased extracellular space, (C) viable marrow with stable microcirculation and (D) rapidly proliferating tumour. Image courtesy of Professor June Taylor, University of Utah.

 
Pharmacokinetic analyses of T1 weighted DCE-MRI data have a number of theoretical advantages [13, 14, 37]. 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 [1, 4]. Table 2Go shows a synopsis of the terms commonly used to describe specific features of microvasculature in pharmacokinetic analyses [14]. 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 characterize the AIF and the tissue contrast concentration curve. These two functions are then used to derive the parameters which control the relationship between AIF and tissue contrast content. The simplest of the pharmacokinetic models, such as that described by Tofts and Kermode [13], 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 (Figure 9Go). 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 incorrect 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 intravascular contrast where measured values of Ktrans will be artificially elevated. Despite these shortcomings the model described by Tofts and Kermode [13] is widely used [38, 39]. None the less, many workers have attempted to refine the pharmacokinetic analysis to provide more accurate estimates of individual microvascular parameters, particularly permeability–surface area product and blood flow. 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 antiangiogenic therapies [4]. 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. The basic pharmacokinetic model described by Tofts and Kermode can be modified to specifically model the signal contribution produced by contrast medium within the plasma (vb) [14, 39]. This reduces errors due to the so-called "pseudopermeability" effect where intravascular contrast gives rise to falsely elevated values of Ktrans (Figure 6Go). 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 Laurence and Lee [40] allow direct estimation of local tissue blood flow (F) in addition to ve, vb and Ktrans (Figure 10Go). In this model the Ktrans will effectively represent the permeability–surface area product. 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 higher temporal resolution, more accurate and reliable curve fitting and is associated with increased variability and susceptibility to noise. 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.


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  		Table 2. List of abbreviations and standard terms used in pharmacokinetic analyses

 


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  		Figure 9. Scattergram showing the distribution of the values of ve and Ktrans for a group of gliomas (squares), meningiomas (diamonds) and vestibular schwannomas (triangles). Note that vestibular schwannomas can be distinguished by increase in extravascular extracellular space fraction and that more aggressive forms of meningioma and glioma are characterized by higher values of Ktrans. This analysis was performed using a standard 2-compartment pharmacokinetic model.

 


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  		Figure 10. Example curve fits from data in (a) a grade 3 and (b) a grade 4 glioma. The fitting has been performed using the adiabatic model described by St Lawrence and Lee [40] and therefore gives individual estimates of flow (F), permeability–surface area product (PS), fractional vascular volume (v(b)) and fractional extravascular extracellular space volume (v(e)). (Cartesy of Dr D Buckley, University of Manchester.)

 
The choice of image acquisition and analysis techniques is also governed by local features relating to the anatomy and physiology of the tissue being studied. In some cases high blood flow may require higher temporal resolution imaging; this is typically seen in the prostate and soft tissue sarcomas [41]. More important are problems associated with physiological movement since all analysis techniques assume that data across the time course is collected from the same tissue voxel. In practice respiratory movement will strongly affect spatial sampling accuracy particularly in the lung, liver, spleen and kidneys. Cardiac movement may also be a significant confound when imaging lesions adjacent to or in the mediastinum. One approach to problems of respiratory motion is to use some form of image co-registration which relies on local features around the tissue of interest to provide adequate reduction in movement artefact. This is not entirely satisfactory, particularly in deformable organs where rigid co-registration techniques cannot be reliably applied. An alternative approach is to modify the data collection and analysis to allow breath hold acquisitions. This necessitates modification of the pharmacokinetic models to deal with data collected purely during the initial passage of the contrast bolus. One such model described by our group uses high temporal resolution data during a breath hold acquisition [42]. The data is analysed using a two-step process. Contrast time course data is initially decomposed into two separate contrast time course data sets representing intravascular and extravascular contrast, respectively. The intravascular contrast time course data are used to estimate the local blood volume. The extravascular contrast time course data is analysed using a modified pharmacokinetic model to calculate Ktrans (Figures 11 and 12GoGo). This model is unable to estimate ve and is subject to errors in the estimation of Ktrans when endothelial permeability values are high. Nonetheless, the removal of respiratory artefact leads to excellent reproducibility of parametric values (Figure 13Go).



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  		Figure 11. Maps of (a) Ktrans and (b) kfp on a patient with a glioblastoma multiforme. Note the standard conventional 2-compartment model (a) shows apparent areas of extremely high permeability in the region of feeding and draining blood vessels. Small blood vessels throughout the brain also appear as areas of high permeability. In the modified model (b), contributions from intravascular contrast are explicity modelled. This image of kfp is therefore free of these pseudopermeability effects. Elevated areas of kfp can be seen within the tumour and in the choroid plexus and peripineal organs where the blood–brian barrier is not intact.

 


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  		Figure 12. Maps of (a) kfp and (b) relative blood volume in a patient with a hypervascular hepatic metastasis. The lower images were acquired 24 h after administration of vascular endothelial growth factor (VEGF) antagonist and show significant decreases in both Ktrans and cerebral blood volume within the tumour.

 


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  		Figure 13. Data using the first pass pharmacokinetic model described by Li et al [43] showing reproducibility of mean values of (a) kfp and (b) the 97.5th centile value of the same data. These data were taken from five patients scanned on two occasions on subsequent days without intervention or treatment. Note the excellent reproducibility not only of mean values but of the percentile values.

 
Accuracy and reproducibility
A clinician or researcher faced with the use of such complex measurement techniques must remain constructively sceptical about their application. It is important to understand how accurate and precise these techniques are. We should ask: do these techniques give me the same answer every time and if so is it the right answer? The reproducibility of the techniques can be directly studied by repeated examinations in individual patients (Figure 11Go). A number of groups have published such studies and shown variable reproducibilities depending on individual technique and the application [27, 43–46]. In most cases the techniques are capable of detecting changes in the order of 20% with confidence. However this can vary if for instance there is poor signal-to-noise ratio, poor maintenance of bolus shape, or if blood flow is particularly low. In longitudinal studies of therapeutic effects it is therefore becoming common to perform baseline reproducibility scans for each patient in order to ensure that the reproducibility and confidence intervals for each measurement are known. In clinical practice this is impractical; however, it is important that the baseline reproducibility of techniques be known and in most cases I would suggest a local test of reproducibility to examine potential problems with acquisition sequences and analysis software. Another potential anxiety is the use of measurements derived from curve fitting analyses. In principle a series of measurements over time are used to confine a known mathematical function or shape to its best fit. It is essential to realise that in most cases once this fit has been performed the original data is effectively discarded. This raises significant problems since curve fitting algorithms will produce an optimized estimate in almost all cases. Unfortunately this is true even when data are dominated by noise rather than signal. These techniques will therefore produce measurements of parameters such as CBV, which may have large degrees of error. This is particularly problematic in imaging data where many thousands of pixels will be represented by individual time resolved data sets. Statistically it is likely that some of these pixels will show poor conformance to the predicted curve shapes and a parameters estimated in them will have large degrees on accuracy. Many research groups now estimate parametric images of fitting error which show the confidence limits which can be attached to individual pixels [12, 42] (Figure 14Go). This allows principled selection techniques to be applied to images in order to exclude unreliable measurements. Unfortunately the majority of commercially available software for clinical use does not offer this facility and relies on the clinician examining the accuracy of the curve fits in selected individual pixels.



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  		Figure 14. Three-dimensional plots of 40 histograms of (a) Monte Carlo estimated relative cerebral blood volume (rCBV) and (b) mean transit time (MTT) values, normalized to have median values of 0. Values were obtained with signal-to-noise ratio (SNR) ranging from 8.8–8.3. Each histogram contains 104 samples. The widths of the histograms are measures of the variation of rCBV and MTT values which represent the uncertainties in the calculation of rCBV and MTT.

 
It is much harder to answer the question "is the technique giving the right answer?" In some cases it is reasonable to argue that if measurements are reproducible and can be shown to represent the physiological variable of interest then the ability to measure changes in parameters is adequate. Testing the accuracy of absolute measurements is more difficult although several groups have attempted to do this using mathematical modelling techniques [42, 43, 47] (Figure 15Go). These studies have been able to confirm expected sources of inaccuracy related to the design of individual pharmacokinetic models but have overall shown relatively good agreement between true and measured values for many of the techniques.



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  		Figure 15. Results from a Monte Carlo modelling experiment to assess the accuracy of pharmacokinetic models in estimating Ktrans. Graphs on the left show data with a very high signal-to-noise ratio (SNR) central graphs show data using a lower SNR and data on the right shows the results where the SNR is low. The upper series of graphs show the accuracy and standard deviations associated with fitting synthetic data using the standard Tofts and Kermode model. It can be seen that at low SNR this technique becomes highly inaccurate and imprecise. The middle row shows the effect of using the first pass pharmacokinetic model described by Li et al [43]. This model systematically underestimates high values of kfp but shows good reproducibility even at relatively low SNRs. The lower series of graphs shows a more complex model which combines the two analysis techniques [43]. This hybrid method shows good accuracy and precision across a wide range of SNR values.

 
Representing quantitative imaging data
Finally, it is important to realise that these techniques generate incredibly complex data sets. The calculation of multiple physiological parameters from many thousands of pixels is routine. Furthermore, images represent a complex mixture of tissues including normal and pathological components. In most tumours and pathological components will also be markedly heterogeneous. It is therefore difficult to decide exactly what summary variables should be used to describe the behaviour of individual parameters and the published literature shows a wide spread in parameters that have been selected. Most groups will define regions of interest (ROIs) on which to undertake subsequent analyses. The definition of ROIs varies widely. Some groups include entire tumours, others will select only visibly enhancing part of a tumour and others only the most prominently enhancing components. Within these ROIs some groups will measure mean and standard deviation whilst others recognising that the parameters seldom conform to a normal distribution will present median and quartile values or ranges (Figures 15 and 16GoGo). Other groups identifying that many of these distributions are skewed will present other appropriate summary variables such as the geometric mean, the mean of logarithmically normalized data or even direct measurements of skewness (Figure 7Go). This variability in the literature is extremely confusing for the reader and also makes direct comparison between studies practically impossible in many cases. The reasons behind this variability should be carefully considered since they are important. Some microvascular quantitative parameters may well show a normal distribution particularly if ROI data are extracted only from homogeneous samples of tissue. In these circumstances simple mean and standard deviation variables will adequately describe the distribution although efforts must be made to ensure conformance to a normal distribution in all cases. Where the distribution is not normal the use of ranges of data is generally misleading. The use of multi-parametric curve fitting techniques combined with the statistical probability of poor quality data in some individual pixels means that the range of pixels is unlikely to be informative. Normalization of data before extraction of mean values is an appropriate technique and will in most cases also adequately describe the data. However, some parameters such as rR might be anticipated to be abnormal only in a small number of the pixels within a tumour. The use of gross summary variables is likely to miss these effects since shifts of small numbers of pixels might significantly change the shape of the distribution but not its mean or median value. These problems become more complex where the ROI might include more than one tissue type. At the present time there is no generally agreed method for the interrogation of pixels based data derived from DCE-MRI. However, it seems likely that the increasing use of more complex summary descriptive variables that is seen in the literature is appropriate and that the choice of summary variables where individual studies should be made carefully only after preliminary exploration of the properties of the data.



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  		Figure 16. Changes in kfp occurring as a result of administration of a vascular endothelial growth factor (VEGF) antagonist in groups of patients with advanced epithelial cancers. Note the immediate drop in kfp as a result of the drug administration and the gradual recovery over the following months. Also note the dose effect with minimal effects seen at the lowest dose (0.3 mg kg–1) and more marked effects at the higher dose regimens.

 
Conclusions

Quantitative characterization of microvascular structure using DCE-MRI is a powerful tool capable of providing valuable information for clinical purposes and for therapeutic trials. The data acquisition and image analysis protocols must be independently selected for individual studies following consideration of which parameters are of interest, the tissue characteristics and the spatial and temporal resolution required in the imaging sequence. Although pharmacokinetic analyses are complex they yield biological parameters of direct relevance to tissue characterization in a way that is reproducible and independent of scan related variables. Continued improvements in the design of scanning equipment and analysis algorithms are progressively improving the specificity of biological parameters which can be calculated allowing detailed quantitative characterization of microvascular structure in a large range of pathological tissues.

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