development of novel antiangiogenic agents has posed a new challenge to medical imaging technologies . unlike the systemic cytocidal effect of traditional cytotoxic drugs , these new agents are selectively targeted to the endothelial cells of tumor neovasculature , inducing a rapid shutdown of tumor blood supply without substantially affecting any morphologic metric . their cytostatic nature makes the conventional method of tumor size measurement inadequate for response evaluation . several molecular and functional imaging techniques , namely , dynamic contrast - enhanced magnetic resonance imaging ( dce - mri ) [ 2 , 3 ] , positron emission tomography ( pet ) [ 2 , 4 ] , and dynamic contrast enhanced computed tomography ( dce - ct ) [ 2 , 5 ] , have been developed in response to this challenge by monitoring pathophysiologic changes in various aspects of tumor vascular structure and functionality .   among these imaging techniques , consequently , its repeated use in response assessment is not limited by patient dose considerations [ 2 , 6 ] . in fact , daily or weekly repeats of dce - mri examinations are common in preclinical and clinical studies , allowing researchers to capture rapid change in tumor vasculature during the short  normalization window moreover , the wide availability of mr scanners makes this technique easily accessible to both clinicians and patients . as of september , 2010 , american college of radiology ( acr ) has accredited 5498 mr facilities in the united states , compared to only 963 acr - accredited pet facilities . all these advantages make dce - mri a convenient yet flexible modality for noninvasive evaluation of tumor microvasculature and angiogenesis . it has been applied to many preclinical studies and early phase clinical trials of various antiangiogenic and antivascular agents , as well as in nontrial settings for tumor grading and clinical outcome prediction [ 8 , 9 ] . quantitative imaging biomarkers derived from pharmacokinetic modeling of dce - mri data have been demonstrated to be correlated with various physiologic and pathophysiologic parameters in human and animal models , and found to be predictive of response rate and progression in patients accepting ptk / zk treatment [ 10 , 11 ] . although preclinical and clinical results have shown that dce - mri is a powerful technique for the detection of subtle changes in tumor vascular function , many improvements are still needed for this technique to reach its maximum potential . heterogeneous distribution of neovasculature has been reported in almost all types of solid tumor [ 1214 ] . this phenomenon reflects the more fundamental heterogeneity in the clones of different tumor cell genomic subtypes and the expression of various pro- and antiangiogenic genes [ 1517 ] . recent studies suggest that cancer relapse and metastasis are likely to be governed by a small population of cancer stem cells in aberrant vascular niches [ 1921 ] . this new understanding strongly implies tumor vascular heterogeneity may have key importance for the understanding of disease mechanism and the discovery of novel treatment strategies . however , so far this critical information was simply ignored or only briefly mentioned as qualitative description in most preclinical and clinical studies . even in the limited number of cases where quantification efforts have been made , this lack of consensus has greatly hindered the investigation of tumor vascular heterogeneity and its influence on treatment response with dce - mri . in this paper , we critically review different quantification methods for heterogeneity currently available in the literature , and discuss several methodological and technological issues that are important in assessment of tumor vascular heterogeneity . although these methods can be applied to any dce - mri image or parametric map , we emphasize their application on pharmacokinetic parametric maps as pharmacokinetic modeling is the most advanced dce - mri data analysis approach that provides pathophysiologically meaningful quantitative interpretation of dce - mri data . in most solid tumors , the neovasculature developed through angiogenesis has an abnormal structure , with defects on walls that make them more permeable than normal vessels . as blood carrying a low molecular weight contrast agent ( such as gadopentetate dimeglumine ) flows through tumor vasculature , the contrast agent molecule leaks into the interstitial space and accumulates there . interaction between the paramagnetic gd ion and adjacent water protons enhances tissue longitudinal ( t1 ) relaxation   rate , generating a brighter signal in t1-weighted images . the magnitude and rate of signal enhancement are determined by tissue vascular fraction , perfusion , microvascular permeability , and relative volume of the extracellular extravascular space ( ees ) . the brightness information can be converted to contrast agent concentration with the linear relationship between gadolinium concentration and t1 relaxation rate . the dynamic change of contrast agent concentration can be described by various model - free parameters or fitted to a pharmacokinetic model ( figure 1 ) [ 2226 ] , yielding parametric maps that give an intuitive and quantifiable illustration of tumor vascular heterogeneity . the most commonly used pharmacokinetic and model - free parameters are summarized in tables 1 and 2 , using the standard nomenclature proposed in the consensus paper by tofts et al . . details about the use and interpretation of these parameters are beyond the scope of this paper . interested readers are referred to the in - depth reviews written by tofts et al .   and evelhoch . heterogeneity in tumor vasculature is subject to change over time . during tumor growth , proliferation of tumor cells is faster than angiogenesis , leading to the formation of poorly perfused hypoxic zones near the tumor center . rim enhancement is frequently observed in dce - mri images of various types of primary cancers , metastases , and xenografts . in the breast , it is a strong indicator of cancer in small lesions and malignancy in larger masses . in general , fast progressing diseases and malignancies are associated with highly heterogeneous enhancement patterns in dce - mri images . this feature can be used to facilitate cancer diagnosis and staging . in human gliomas , rose et al . found that low- and high - grade tumors are significantly different in several spatial heterogeneity statistics of dce - mri pharmacokinetic parameters [ 35 , 36 ] . in breast imaging , different internal enhancement patterns have been identified as an important diagnostic characteristic by the acr breast imaging - reporting and data system ( bi - rads ) mri lexicon .   in cancer treatment , tumor heterogeneity is usually associated with poor response , a higher chance of developing metastasis , and substantially shorter progression - free and overall survival [ 37 , 38 ] . the mechanism is probably through the selection of more aggressive tumor cells that can better tolerate the hostile acidic , hypoxic environment in poorly perfused low - enhancing regions [ 19 , 39 ] . treatment - induced changes in tumor vascular heterogeneity have been reported in several preclinical and clinical settings . observed that in human pc-3 prostate adenocarcinoma xenografts receiving zd6474 treatment , the core region in the xenograft tumor revealed a larger reduction in the pharmacokinetic parameter k than the enhancing rims , suggesting a change in the distribution patterns of perfusion and permeability . found that primary rectal cancer patients receiving radiation therapy have lower intratumoral heterogeneity in the pharmacokinetic parameters k and vp than patients without radiation therapy . several groups also explored the possibility of predicting treatment efficacy with tumor vascular heterogeneity and its early change . investigated the relationship between the   distributions of dce - mri model - free parameters and patient 5-year survival in a small cohort of 24 breast cancer patients receiving neoadjuvant chemotherapy . they found that patients   surviving for more than 5 years have significantly less heterogeneous relative signal intensity ( rsi ) distribution than nonsurvivors in the baseline dce - mri study performed prior to the start of therapy . in a similar study , padhani et al . correlated early changes in the distribution of dce - mri pharmacokinetic parameters with treatment response assessment . changes in vascular heterogeneity quantified by the range of k distribution at the end of cycle two were found to be predictive of both clinical and histopathologic responses after three to six cycles of therapy . analyzed serial dce - mri studies of 101 patients during early treatment of cervical cancer . part of their data has low temporal resolution so a complete pharmacokinetic analysis was not possible . tumor vascular heterogeneity was thus quantified by the lower percentiles of voxel signal intensities in the plateau phase of the dynamic curves . low values of the 5th to 20th percentiles were found to be correlated with poor primary tumor control and short disease - free survival . the 5th percentile measured at 22.5 weeks of therapy provided the best prediction for 8-year primary tumor control . for a long time , radiologists identify intratumoral heterogeneity solely by their visual perception of the image . even though some level of consensus can be achieved with stringent training of readers and standardization of descriptive vocabularies , this approach is still subjective . many factors , like the imaging hardware , personal bias , or even the physical condition of the reader , can affect the readers ' judgement and lead to intra- and interobserver variations in assessment . this problem is now becoming even more meaningful with the development of novel quantitative imaging techniques like dce - mri and perfusion ct . these techniques introduce a new dimension of spatially resolved functional information into the data space , which is usually displayed as pseudocolor overlays on the conventional morphologic images . human color perception , however , is both nonlinear to luminance and nonuniform for different colors . as demonstrated by giesel et al . , reader 's perception of intratumoral homogeneity / heterogeneity can easily be exaggerated or understated by simply choosing a different display range or color scheme ( figure 2 ) [ 45 , 46 ] . in order to tackle this problem , all these methods are quantitative , seeking to extract a set of well - defined quantities rather than ambiguous verbal descriptions to summarize some key features of tumor vascular heterogeneity .   in this section , technological issues and methodological considerations that we deem important in study design and data acquisition and analysis will be discussed in the next section . a simple , straightforward strategy for dealing with intratumoral heterogeneity is to subdivide the tumor into regions with less spatial variability . in the breast , many researchers prefer to analyze a small region with the highest enhancement ( i.e. , the  hot - spot  ) instead of the whole tumor . if the hot - spot roi is small enough and correctly placed , the hot - spot average is equivalent to the maximum of the whole tumor histogram . the hot - spot analysis can be performed semiautomatically , thus reducing the observer - related variability in roi placement [ 34 , 47 ] . in an early study , mussurakis et al . were unable to detect a statistically significant difference in peak enhancement ratio ( per ) between 71 malignant and 37 benign lesions , and concluded that hotspot analysis may not provide any diagnostic advantage over the whole - tumor method . however , their result is probably undermined by an inappropriate selection of parameter : it is now known that in dce - mri , the most profound difference between malignant and benign breast lesions is not the maximum signal enhancement , but the shape of the entire dynamic enhancement curve . their dynamic curves are characterized by a fast increase to the peak followed by a slow washout or a stable  plateau  . benign lesions usually have a persistently increasing dynamic curve in which the maximum signal intensity is achieved by the   end of the observation window . liney et al . took this factor into consideration by introducing a new model - free parameter , the maximum - intensity - time - ratio ( mitr ) , that corrects per with the time to peak enhancement ( tmax ) . their results from a study of similar size ( 81 malignant and 36 benign lesions ) agreed with mussurakis et al . conclusion about per , but also showed that the lesion differentiation ability of the   hot - spot analysis is significantly improved over the whole - tumor method when mitr is used . other parameters that have been demonstrated to be effective in hot - spot analysis include signal enhancement ratio obtained at a fixed time point 6090 seconds postinjection   and the pharmacokinetic parameter k . inspired by the commonly seen  rim enhancement  pattern in solid tumors , some researchers also segment a tumor into a poorly enhancing  core  and a strongly enhancing  periphery  or  rim  [ 40 , 51 ] . benjaminsen et al . developed this rough segmentation methodology into a quantitative approach to describe radial heterogeneity in tumor perfusion . in this method , a tumor parametric map is divided into several concentric bands with approximately the same width . median or mean parameter values are calculated for each band and plotted against band number or radius . the rofstad group in norway used this method to study the radial distribution of tumor perfusion and ees fraction in a series of preclinical studies with human melanoma xenografts a-07 and r-18 between 2004 and 2008 [ 5257 ] . at about the same time , jia et al . applied a similar method to the model - free parameter washout slope in colorectal cancer liver metastasis , and gave this approach an intuitive name  onion - peeling  . a major advantage of this method is that the radial distribution curve can be normalized and compared between parameters obtained with different assessment techniques . used this method to compare the radial distributions of the dce - mri pharmacokinetic parameter ef and tumor blood supply measured with a freely diffusible radioactive tracer natco4 . the close match of radial distribution curves partially validated the authors ' hypothesis that ef measures tumor perfusion in these preclinical models . their results also showed that a-07 and r-18 xenografts are characterized by different radial distributions of ef   and  ( a dce - mri pharmacokinetic parameter proportional to ve , ) , suggesting a potential application in tumor characterization . it should be noted that the success of the  onion - peeling  method in rofstad 's studies is partly due to their relatively simple preclinical model . growth of in vivo tumors may be restricted or slowed down on certain directions by the existing anatomical structures , leading to an irregular or diffused tumor shape in which a  center  can hardly be defined . nonradial heterogeneity patterns are also frequently seen in many human tumors ( figure 3 ) . therefore , this method is probably working best in small scale preclinical studies with well - controlled tumor growth conditions . in large scale clinical studies , other quantification methods that are less specific about the heterogeneity pattern , such as the texture analysis methods , might be more appropriate . tumors are typically characterized by a skewed distribution with a long tail towards strong enhancement or high k values . multiple peaks may be observed if the tumor contains a significant fraction of poorly perfused hypoxic mass . disease progression is usually accompanied by an expansion of the histogram to the right , with the peak broadening its width but decreasing its height . a successful treatment , on the contrary ,  suppresses  the histogram leftwards , making the peak narrower and more normal [ 30 , 42 ] . functional principal component analysis also revealed that antiangiogenic treatment with zd6474 causes the disappearance of a second peak with high k values in mice bearing pc-3 human prostate adenocarcinoma xenografts . a number of studies have demonstrated that incorporating summary statistics describing histogram width or asymmetry leads to substantial improvement in disease diagnosis and response assessment . in primary breast tumors , both the sensitivity and specificity of malignant / benign lesion differentiation can be improved by adding the k standard deviation information to the conventional analysis approach using k mean alone . in another study , median k was demonstrated to be less sensitive than the range of the k histogram in predicting treatment response in breast cancer patients receiving systemic chemotherapy . similar results were also reported in cervical cancer patients receiving radiation therapy , where mayr et al . found that the 10th percentile of rsi is a better predictor for tumor recurrence than the mean or median values . although the rationale for this approach is straightforward to understand , it is in general an inefficient technique : a certain number of bins are needed for the histogram to accurately reflect the shape of the underlying distribution . in clinical research , this number is typically between 10 and 30 . when all these bins are simultaneously compared , the need for multicomparison correction makes the whole test very insensitive . for example , if an overall significance level of 0.05 is assigned to a comparison between two normalized histograms with 20 bins each , the individual significance level for every single bin will be only 0.05/20 = 0.0025 with the basic bonferroni correction . with such a low individual significance level , subtle changes in the histogram are very likely to be masked . a better strategy for histogram analysis is to summarize only the most relevant information into a few descriptive quantities . almost all summary statistics have been used in the literature to describe the distribution histogram . a partial list includes the range , mean , median , standard deviation , skewness , kurtosis , entropy , and various percentiles [ 30 , 41 , 43 , 60 , 64 ] . however , the percentiles are probably more robust than the range and moment statistics on pharmacokinetic parametric maps . an  allowed range  is usually set for each pharmacokinetic parameter by the iterative fitting algorithm to accelerate convergence . if the true range of the actual distribution is wider than this  allowed range  , the long tails outside the allowed range will be truncated and replaced by artificial  peaks  on the maximum or minimum allowed values . unlike the range and moment statistics , the percentiles are insensitive to this artificial distortion of histogram shape because they are not affected by changes in a few extreme values . the histogram analysis only looks at the distribution of individual voxels within a tumor roi . theoretically , a tumor with an enhancing rim could have an identical histogram with a tumor having many enhancing foci scattered over the entire mass . spatial distribution information is needed to better differentiate lesions with similar histogram but distinctive enhancement patterns . a number of studies have been conducted along this direction using image texture analysis techniques [ 31 , 6570 ] . in dce - mri data analysis , the most frequently used texture analysis technique is the cooccurrence matrix method first described by haralick et al . . briefly speaking , the cooccurrence matrix element pd,(i , j ) measures the probability of starting from any voxel with value i in an image , moving d voxels along direction  , and arriving at another voxel with value j. therefore , the cooccurrence matrix is a two dimensional histogram describing a joint distribution of all possible moves with step size d and direction  on the image . textural features , such as contrast and correlation , can be exacted from this 2d histogram . they are then averaged over four directions (  = 0 , 45 , 90 , and 135 ) to remove angular dependency . in medical imaging studies , sinha et al . used this technique to obtain eight textural features that made a reasonably good discrimination ( specificity 70% , sensitivity 75% ) between 20 malignant and 23 benign breast lesions . 2d technique to 3d , and achieved a significant improvement in classification performance using features obtained from a volumetric texture analysis in a cohort of 77 malignant and 44 benign lesions . positive results were also reported with various model - free   and pharmacokinetic parametric maps   as well as on four dimensional dynamic series . further associated the textural features ( gray level entropy and sum average ) with the visual descriptors in bi - rads lexicon ( enhancement intensity and internal enhancement patterns ) , thus giving the highly mathematical approach an intuitive interpretation . currently , the major problem associated with dce - mri texture analysis is the high dimensionality of the feature space . researchers are encouraged to adopt a concise study design and dimensionality reduction techniques to improve the reliability of their conclusions . an interesting approach of heterogeneity quantification was described in the exploratory works of rose et al . [ 35 , 36 ] . in their approach , dce - mri pharmacokinetic parameters were not treated in the conventional way as voxel values in a 3d imaging volume . instead , they were interpreted as the height on a fourth dimension in an  extruded geometric features like ( hyper-)surface area , ( hyper-)volume , ( hyper-)surface to ( hyper-)volume ratio , and box - count fractal dimension can be calculated for this spatial - parametric hypervolume , and used as quantitative descriptors of tumor vascular heterogeneity . in a recent study , although the small sample sizes prevented any decisive conclusion about its value to be made at this moment , initial results in glioma grading and liver metastasis treatment response seem to be promising . this method is conceptually interesting in that spatial and parametric information are treated equally as dimensions in the 4d hypervolume . geometric features of the hypervolume thereby describe variations in both spatial and parametric domains by nature . bi - rads lexicon suggests that both morphologic and heterogeneity information are critical in diagnosis of breast cancer . therefore , geometric features of the spatial - parametric hypervolume compose a pool of potential biomarkers that can simultaneously quantify tumor morphology and heterogeneity . such a biomarker , if identified , may have important uses in tumor diagnosis and response prediction because it can improve the robustness of the classifier / predictor through reduction of input space dimensionality . many descriptive and textural features of imaging data can be extracted from the analysis of tumor heterogeneity . some researchers tend to use a large number of features in their studies . in an extreme example we found more than 600 features were investigated in only 23 patients . while the researchers ' desire of getting the maximum yield from their data is understandable , this practice is fundamentally problematic because as the number of features increases , the problem of data sparsity arises due to bellman 's  curse of dimensionality  . a sparsely - distributed sample set can not provide adequate information to fully represent the complex behaviors in a large population . consequently , any prediction made from such a sample set is highly unstable and thus practically useless . this problem is probably responsible for our finding that some complex discriminators are claimed to have ( artificially ) excellent performance in a relatively small patient population but never develop into real clinical application . there is no real remedy for the sparse data problem except for thorough consideration and careful planning in the designing stage of a study . the number of features used for classification or prediction must be strictly controlled from the very beginning . a rule of thumb is to keep the ratio between the number of patients in each class and the number of features above 10 , that is , for a typical study of about 100 patients divided into two groups , the number of features that can be investigated should not exceed five . this stringent restriction requires the investigators to include only the most promising features into their analysis rather than use all the parameters they can get unselectively . of course , information about the other less promising features is also interesting and may lead to important discoveries . no effort should be made to get any statistical inference from these data . in this way , these data can be preserved without harming the statistical power of the whole study . they may serve as part of the raw data set for future metaanalyses which may provide statistically meaningful information that can never be derived from any single study . some researchers chose to classify individual voxels instead of the whole tumor or subject [ 67 , 68 , 75 ] . while this method does help to greatly reduce the stringent restriction on feature set size , caution is needed in the interpretation of the results . simply stating that a voxel has a  responder - like  curve or it is more preferable to characterize voxels with imaging features that have well - recognized association with tumor biology on cellular or tissue levels . dimensionality reduction techniques are also powerful tools that may help the investigators to fight the  curse of dimensionality  . it should be noted that dimensionality reduction techniques are only supplements to , but not replacement for , careful study design and successful dimensionality control . they should only be applied to a small feature set carefully selected according to the rule of thumb mentioned above . applying a dimensionality reduction technique to a poorly designed study some of them use a t1-weighted fast low - angle shot ( flash ) sequence , while the others use saturation recovery or inversion recovery techniques . the measured signal intensities may be converted to gadolinium concentration through the use of a calibration phantom , calculation of relative signal enhancement , or precontrast t1   or proton density measurements . many model - free and pharmacokinetic parameters have been described in the literature ( tables 1 and 2 ) . most model - free parameters do not have a clear definition that is strictly followed within the dce - mri community . for example , many investigators reported the model - free parameter area - under - the - curve ( auc ) in their studies , but the way they measured it can be quite different : in some studies it was measured from the relative signal enhancement dynamic curve , while in the others the gadolinium concentration dynamic curve was used . even though pharmacokinetic parameters are generally better defined than model - free parameters , considerable variability still exists in the choice of the pharmacokinetic models [ 2226 ] and deconvolution techniques [ 82 , 83 ] . it is known that many factors in data acquisition and analysis can substantially affect the reliability of results in dce - mri studies . the accuracy and precision of the pharmacokinetic parameter estimates , for example , are largely determined by the signal - to - noise ratio ( snr ) and temporal resolution of the mr sequence . systematic errors can be introduced from various sources , such as voluntary or involuntary patient motion , inappropriate use of postprocessing filters , inhomogeneity in b1 excitation field and receiver coil sensitivity , breakdown of linearity in the gadolinium concentration calibration curve , and unequal definitions of the same pharmacokinetic parameter ( such as k ) in different models [ 22 , 23 ] . therefore , the methodological variability described above actually contains a large number of potential error sources . their complex yet poorly understood interaction makes it extremely difficult to compare dce - mri data from different sources . as we have mentioned in the discussions above , an individual study can only investigate a very small fraction of all parameters that characterize intratumoral heterogeneity . the only way to accelerate the investigation process is through meta - analysis that combines results from different studies . obviously , this can only be achieved with high quality data acquired and analyzed following an optimized standard procedure . a standardization effort is currently underway driven by the dce - mri subcommittee of the radiological society of north american ( rsna ) quantitative imaging biomarkers alliance ( qiba ) initiative . the most recent progress of their collaborative effort is a comprehensive technical profile that specifies basic standards in dce - mri data acquisition , analysis , and quality control on 1.5  tesla systems . it is recommended that dce - mri should be performed on a clinical scanner qualified with a standard phantom , using a 3d flash or equivalent sequence without any magnetization preparation or postprocessing filter . the image intensity should be converted to gadolinium concentration through the use of a variable flip angle precontrast t1 map   after necessary corrections for patient motion and inhomogeneity in b1 field or coil sensitivity . the pharmacokinetic parameter k ( estimated with the standard tofts ' model ) and model - free parameter iaugc ( auc measured from the gadolinium concentration curve up to 90 seconds postinjection ) are recommended as standard quantitative endpoints that should be employed in clinical trials and practice . guidelines on the minimally acceptable and ideal ranges of various scan parameters ( like temporal resolution and slice thickness ) are also provided . investigators in this area are encouraged to follow the progress of the qiba initiative through journal publications and online updates ( http://qibawiki.rsna.org/index.php?title=dce-mri_subctte ) , and adopt the most up - to - date consensus to their own studies to ensure their data have the highest quality standard and the maximum level of comparability . an important issue that is not addressed in the present version of qiba dce - mri profile is the lack of quality control in the vascular parameter fitting stage . it also raises a philosophical question whether it is appropriate to treat reliable and unreliable parameter estimates equally in the assessment of tumor heterogeneity . hence , we suggest that dce - mri researchers should always report the asymptotic confidence intervals with the  best fit estimates for pharmacokinetic parameters , and adopt an exclusion criterion or weighting scheme that controls the influence of unreliable estimates from noisy data . we also expect that as the awareness of this issue is raised , a consensus will be developed through the collective effort of the whole dce - mri community , and will be included in future standards . it is difficult to validate dce - mri parameters because they measure a mixed effect of blood flow , microvascular permeability , and ees volume . a number of studies have demonstrated broad correlations between various dce - mri parameters and tissue perfusion , microvascular density ( mvd ) [ 45 , 89 ] , or angiogenic factor expression . one reason for this controversy might be tumor heterogeneity at the subvoxel level . in a human cervical carcinoma xenograft study , matched dce - mri images and histological sections showed substantial intravoxel heterogeneity in morphology and tissue composition , even though the voxel size ( 0.23  0.47  2.0  mm ) is already ten times smaller than those used in human studies . therefore , dce - mri parameters may be better validated against immunohistochemical measurements averaged over several fields randomly picked from the region of interest . beside the roi - averaged parameter values , the distribution of dce - mri parameters also needs to be validated in studies of tumor vascular heterogeneity . this task is relatively simple if the  gold standard  is another imaging modality with similar spatial resolution , for which direct comparison can be made between summary statistics , histogram shapes , or certain heterogeneity patterns [ 52 , 55 ] . mvd values or angiogenic factor expression levels need to be compared with dce - mri parameters within multiple subregional rois or along a line profile . special techniques , like mri - guided biopsy , may be used to help reduce sampling error caused by mismatch between dce - mri images and histological slides . initial studies in patients and animal models have shown promising results in disease diagnosis , tumor grading , and response assessment . these results give us additional understanding of tumor biology and justify the necessity of continuous development along this direction . however , the quality of a dce - mri heterogeneity study can easily be undermined by various methodological and technological issues , such as poor study design or lack of standardization . this paper may serve as a guideline to help investigators understand and also avoid these possible pitfalls in study design , data acquisition , and analysis in future studies of tumor vascular heterogeneity .
tumor microvasculature possesses a high degree of heterogeneity in its structure and function . 
 these features have been demonstrated to be important for disease diagnosis , response assessment , and treatment planning . 
 the exploratory efforts of quantifying tumor vascular heterogeneity with dce - mri have led to promising results in a number of studies . 
 however , the methodological implementation in those studies has been highly variable , leading to multiple challenges in data quality and comparability . 
 this paper reviews several heterogeneity quantification methods , with an emphasis on their applications on dce - mri pharmacokinetic parametric maps . 
 important methodological and technological issues in experimental design , data acquisition , and analysis are also discussed , with the current opportunities and efforts for standardization highlighted .