Models and methods for analyzing DCE-MRI: a review.

Models and methods for analyzing DCE-MRI: A review Fahmi Khalifa, Ahmed Soliman, Ayman El-Baz, Mohamed Abou El-Ghar, Tarek El-Diasty, Georgy Gimel’farb , Rosemary Ouseph, and Amy C. Dwyer Citation: Medical Physics 41, 124301 (2014); doi: 10.1118/1.4898202 View online: http://dx.doi.org/10.1118/1.4898202 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/41/12?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in A new quantitative image analysis method for improving breast cancer diagnosis using DCE-MRI examinations Med. Phys. 42, 103 (2015); 10.1118/1.4903280 Elastic registration of multimodal prostate MRI and histology via multiattribute combined mutual information Med. Phys. 38, 2005 (2011); 10.1118/1.3560879 Breast MRI: Fundamentals and Technical Aspects Med. Phys. 35, 1163 (2008); 10.1118/1.2840347 An objective method for combining multi-parametric MRI datasets to characterize malignant tumors Med. Phys. 34, 1053 (2007); 10.1118/1.2558301 Automatic identification and classification of characteristic kinetic curves of breast lesions on DCE-MRI Med. Phys. 33, 2878 (2006); 10.1118/1.2210568

Models and methods for analyzing DCE-MRI: A review Fahmi Khalifa BioImaging Laboratory, Department of Bioengineering, University of Louisville, Louisville, Kentucky 40292 and Electronics and Communication Engineering Department, Mansoura University, Mansoura 35516, Egypt

Ahmed Soliman and Ayman El-Baza) BioImaging Laboratory, Department of Bioengineering, University of Louisville, Louisville, Kentucky 40292

Mohamed Abou El-Ghar and Tarek El-Diasty Radiology Department, Urology and Nephrology Center, Mansoura University, Mansoura 35516, Egypt

Georgy Gimel’farb Department of Computer Science, University of Auckland, Auckland 1142, New Zealand

Rosemary Ouseph and Amy C. Dwyer Kidney Transplantation–Kidney Disease Center, University of Louisville, Louisville, Kentucky 40202

(Received 29 July 2014; revised 11 September 2014; accepted for publication 1 October 2014; published 17 November 2014) Purpose: To present a review of most commonly used techniques to analyze dynamic contrastenhanced magnetic resonance imaging (DCE-MRI), discusses their strengths and weaknesses, and outlines recent clinical applications of findings from these approaches. Methods: DCE-MRI allows for noninvasive quantitative analysis of contrast agent (CA) transient in soft tissues. Thus, it is an important and well-established tool to reveal microvasculature and perfusion in various clinical applications. In the last three decades, a host of nonparametric and parametric models and methods have been developed in order to quantify the CA’s perfusion into tissue and estimate perfusion-related parameters (indexes) from signal- or concentration–time curves. These indexes are widely used in various clinical applications for the detection, characterization, and therapy monitoring of different diseases. Results: Promising theoretical findings and experimental results for the reviewed models and techniques in a variety of clinical applications suggest that DCE-MRI is a clinically relevant imaging modality, which can be used for early diagnosis of different diseases, such as breast and prostate cancer, renal rejection, and liver tumors. Conclusions: Both nonparametric and parametric approaches for DCE-MRI analysis possess the ability to quantify tissue perfusion. C 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4898202] Key words: DCE-MRI, pharmacokinetic, dynamic perfusion, contrast agent, arterial input function 1. INTRODUCTION Dynamic MRI is widely explored in many clinical studies for noninvasive detection, characterization, and therapy monitoring of different diseases such as heart failure, breast and prostate cancer, renal rejection, and liver tumors. In acquiring dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), a tracer, or contrast agent (CA) is injected into the blood stream before or during the acquisition of a time series of T1-weighted images with fast imaging techniques. MR signal intensities in volume elements (voxels) of a target tissue under the measurement are changing as a result of changing CA concentrations. Thus, DCE-MRI provides superior information about the tissues’ anatomy and function.1–14 Examples of cross-sectional DCE-MRI time series of the heart, kidney, and prostate are shown in Fig. 1. Due to its ability to describe organ functionality in addition to anatomy, DCE-MRI has been widely investigated in perfusion-related studies in many clinical applications, e.g., in evaluation of the kidney, heart, breast, and prostate. Parameters of the CA’s delivery to a tissue of interest can be 124301-1

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derived from DCE-MRI shortly (up to about 2 min) after CA administration.15 Kinetics (spatial and temporal distributions) of the CA transit depend heavily on tissue perfusion, vessel permeability, and volume of the extracellular and extravascular space (EES). Following CA administration, perfusion can be depicted using changes over time in the recorded MR signal intensity, S(t). An example of a time varying signal S(t) shown in Fig. 2 demonstrates that the tissue intensity rises at bolus arrival (wash-in), reaches its maximum, and then decreases slowly afterward (wash-out). Such S(t) allows for deriving or estimating perfusion-related indexes (parameters) of the tissue’s vascularization. Next, the most common approaches for analyzing S(t) are discussed. Traditional DCE-MRI analysis is based on subjective evaluation of signal enhancement curves in voxels or a region-ofinterest (ROI) by an experienced observer to associate each curve with one out of a small number of predefined shape categories (see e.g., Fig. 3). Although this approach is the most intuitive,16 it is prone to errors due to experts’ experience and bias, and provides no quantifiable indexes (like a

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Khalifa et al.: Models and methods for analyzing DCE-MRI

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F. 1. Cross section DCE-MRI images of the heart, kidney, and prostate at different time instants before and after administering the CA into the blood stream.

rate of tracer uptake or wash-out) or measurements of tissue perfusion and permeability. In addition to expert’s experience and bias, qualitative curve pattern analysis can also be affected by data acquisition protocols, such as temporal resolution. Therefore, other quantitative methods have been proposed for the analysis of DCE-MRI. This paper focuses on the two most well-known groups of approaches to quantitatively analyze DCE-MRI, namely, nonparametric (model-free) and parametric (analytical) techniques. The nonparametric approaches derive empirical indexes that characterize the shape and structure of S(t). Typical examples of these parameters are shown in Fig. 2. Straightforward and simple definitions and computations of these

F. 2. An example of a S(t) curve showing the time points that quantify the CA’s dynamics and result in different metrics that qualitatively characterize the agent’s perfusion: onset time (To ), time-to-peak (T P ), peak signal intensity, wash-in slope (initial up-slope), wash-out slope (down-slope), area under the curve (AUC), and initial area under the curve (IAUC). Note that S0 is the intensity before the administration of CA and Tmax is the time period of the MR experiment. Medical Physics, Vol. 41, No. 12, December 2014

empirical parameters are their main advantages. Empirical indexes correlate with the physiology of the organ as evidenced by their changes with diseases (e.g., cancer, renal rejection). However, it is difficult to estimate tissue’s physiological quantities, such as vascular permeability and blood flow, directly from these empirical indexes. Parametric approaches, on the other hand, aim to estimate kinetic parameters directly by fitting one of the several well-known pharmacokinetic (PK) models to the concentration curves. PK models are potentially able to extract a set of kinetic parameters that are physiologically interpretable, e.g., the EES volume and capillary permeability.17 However, the underlying assumptions of each PK model may not be applicable to all tissue types or tumors. Therefore, the choice of a PK model depends on the clinical application.18 Nonparametric approaches are suited more for fast and simple noninvasive image-based diagnostics, whereas parametric ones support studying the CA kinetics in a certain

F. 3. Different enhancement patterns: Type I (persistent)—a progressive signal intensity increase, Type II (plateau)—an initial peak followed by a relatively constant enhancement, and Type III (wash-out)—a sharp uptake followed by an enhancement decrease over time.

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tissue or organ when physiological parameters of the underlying tissue are required. Strengths and weaknesses of common nonparametric and parametric approaches for analyzing dynamic MRI, together with various clinical applications and findings using these methods, are discussed in Secs. 2 and 3. 2. NONPARAMETRIC DCE-MRI ANALYSIS The first category for the analysis of CA perfusion is based on nonparametric or model-free techniques. The established nonparametric dynamic perfusion analysis measures empirical indexes directly from S(t). The perfusion-related measurements, shown in Fig. 2, include the onset (lag or arrival) time, peak signal intensity, wash-in slope (maximum or initial upslope),15 wash-out slope (down-slope),19 maximum intensity time ratio (MITR),20 time-to-peak, signal enhancement ratio (SER),21,22 and others. These perfusion-related measurements are defined as follows: To

Sm

∆S

∆S So

TP

T90 △S TP

△S (T P −To )

Smax−Sfinal (Tmax−T P )

S E −S o (S L −S o )

the onset (lag or bolus arrival) time of an enhancement curve, i.e., the time from the CA injection to the appearance of contrast in the tissues. maxt S(t)—the maximum signal intensity (peak enhancement) of a given time-varying signal S(t). Sm − So —the peak (maximal absolute) enhancement of a given signal S(t), i.e., the difference between Sm and baseline (So ) intensities. the relative signal intensity (RSI) or peak enhancement ratio (PER), i.e., the relative peak enhancement. the time-to-peak, i.e., the time before the CA reaches its highest value in the tissue during the first-pass cycle. the time before the CA in the tissue reaches 90% of the maximal signal intensity. the MITR, i.e., the ratio between the peak enhancement ∆S and the time-to-peak TP . Also, the normalized MITR (nMITR), S o△STP , is used. the wash-in slope (the maximal or initial upslope), i.e., the slope of the line connecting So and Sm points. the wash-out slope (down-slope), i.e., the slope of the line connecting Sm and the last point of the signal curve Sfinal. the SER is the ratio of early to late contrast enhancement; where SE and SL are the early and late contrast signal intensities measured at predefined times of TE and TL , respectively.23,24

However, the CA kinetics change rapidly during the transient phase of the CA transit, so that the limited temporal sampling results in noisy measurements. To overcome this problem, perfusion can be characterized using several data points over the signal intensity time series. This can be achieved by calculating the total AUC and the average signal change Medical Physics, Vol. 41, No. 12, December 2014

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during the more slowly varying phase (plateau or tissue distribution), as shown in Fig. 2 • Average plateau, i.e., average signal change during the T tissue distribution (wash-out) phase = (1/Tmax −Tp ) T pmax S(t)dt, starting approximately at Tp (≈30 s) and extending to approximately Tmax = 2 min for peripheral injections.25 • AUC, i.e., area under S(t) (relative or absolute). Some methods use AUC of S(t) for a time point t (e.g., AUC60 and AUC90, etc.) and the area under the initial uptake portion of S(t), called the IAUC. Obvious advantages of the nonparametric DCE-MRI analysis include (i) less complicated and time-consuming acquisition requirements [e.g., no need for the so-called arterial input function (AIF) measurement], (ii) parameter estimation is performed directly from S(t) without converting them into CA concentrations, and (iii) possibilities to completely describe S(t) curves with a large set of measurements (see Fig. 2). However, since the analysis is based on the signal intensity, MR acquisition parameters and scanner type and settings can influence the measurements. Comparisons of results obtained at different times and/or at different sites are also difficult unless totally identical settings are used.26 Although the nonparametric analysis cannot derive physiological information, e.g., vascular permeability and blood flow, directly from S(t), there exists a correlation between the curve-related measurements and the underlying physiology. For example, increased washin slope, AUC, and peak enhancement and decreased timeto-peak are likely related to an improved organ functionality (e.g., renal transplant), bad response to therapy (e.g., cancerous tissue), or increased vascular density and/or vascular permeability. 2.A. Clinical applications of nonparametric approaches

The promise of DCE-MRI as a new diagnostic modality and the feasibility of the nonparametric analysis of perfusion MRI for developing noninvasive computer-aided diagnostic (CAD) systems was investigated in various clinical studies. These studies try to correlate the DCE-MRI measurements with diseases, as will be discussed below. DCE-MRIbased diagnosis has been explored in different clinical studies, including monitoring the effects of chemotherapy in bone sarcomas or melanoma,27,28 head and neck,29–31 cardiac,5,32–40 pelvic,41 rectal,42–47 pancreatic cancer,48 liver,49 lung,50 colon,51 breast,52–68 uterus,69–80 renal,10,81–92 prostate,11,93–104 and bladder105 applications. Recent applications of the nonparametric DCE-MRI analysis and their findings for the assessment of heart disease, kidney function, and prostate and breast cancers are overviewed below. Ischemic heart disease is the most common cause of heart failure, which affects approximately 6 million US patients annually.106 Therefore, detecting precursors to prevent progression to end-stage disease is of important clinical concern. The nonparametric DCE-MRI analysis has been used for the

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assessment of myocardial perfusion in patients with heart diseases in Refs. 5 and 32–40. Schwitter et al.32 detected and sized the compromised myocardium by using DCE-MRI, comparing with quantitative measures of coronary angiography and positron emission tomography (PET). The up-slope index was used to measure the myocardial perfusion. According to their results, the MRI measurements could reliably detect and quantify perfusion deficits in patients with the coronary artery disease, even when perfusion abnormalities were confined to the subendocardial layer. Ibrahim et al.33 measured in a similar way the coronary flow reserve (CFR) defined as the stress-torest ratio of the maximal up-slope and myocardial peak signal intensity indexes. The MRI-based CFR was underestimated with respect to the PET-based one. A semiautomated approach by Positano et al.34 characterized the myocardial perfusion in patients with suspected coronary artery diseases using the wash-in slope, time-to-peak, and peak signal intensity for a number of user-defined equiangular sectors. Their postprocessing pipeline included image alignment, left ventricle wall segmentation, and extraction of the time/intensity curves and the related perfusion. However, their study did not provide any correlation of the estimated indexes with the disease. Semiautomated evaluation of regional myocardial perfusion by Tarroni et al.5 quantified perfusion regionally with the peak signal intensity, initial up-slope, and the product of the amplitude and the slope. The up-slope index had the highest diagnostic accuracy compared to a coronary angiography reference for the presence of obstructive coronary artery disease. An automated assessment of cardiac perfusion in patients with acute myocardial infarction by Ólafsdóttir et al.35 used parametric maps of three perfusion-related indexes (maximum up-slope, time-to-peak, and peak value) to assess coronary artery diseases. The maximum up-slope confirmed a severe perfusion deficit at the anteroseptal and inferoseptal wall for all slices. A similar approach by Xue et al.36 employed the scale-space theory and the nonmaximal suppression.107 The generated parameter maps were found to be effective in identifying the hypoenhanced regions, which are consistent with the signal attenuation on the original and motion corrected images. A framework for evaluating the perfusion indexes for normal and ischemic myocardium was proposed by Su et al.37 The segment-wise ratio of the maximum up-slope (i.e., the up-slope at stress) to the up-slope at rest using the 17-segment model108 differentiated between ischemic and nonischemic myocardium. In addition to studying ischemic heart diseases, the dynamic MRI was also employed for evaluating the follow-up on therapy. Khalifa et al.38,39 and Beache et al.40 analyzed myocardial first-pass MRI of patients with ischemic damage from heart attacks who were undergoing a stem cell myoregeneration therapy. The perfusion was quantified using pixel-wise perfusionrelated maps of the peak signal intensity, time-to-peak, initial up-slope, and average plateau indexes. The derived perfusion maps demonstrated the ability to show regional perfusion differences and improvements with treatment, including transmural effects. Breast cancer is one of the most common malignancies in women worldwide that accounts in total for more than 20% of new cancer cases and about 15% of cancer deaths.109 Medical Physics, Vol. 41, No. 12, December 2014

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Therefore, its early detection, diagnosis, and treatment are of prime importance. The accuracy of early detection and/or diagnosis using the nonparametric DCE-MRI measurements has been tested and improved in a number of CAD systems.52–67 An approach for the extraction and visualization of perfusion parameters of breast DCE-MRI was proposed by Glaßer et al.52 To reveal the most suspicious region and the heterogeneity of the tumor, their study employed voxel-wise parametric maps of relative enhancement of breast tumors. Karahaliou et al.53 investigated the feasibility of discriminating between the malignant and benign breast tumors by texture analysis. Discriminatory features quantifying the heterogeneity of the lesion enhancement kinetics were obtained from the maps of three indexes [Sm , measured for the first 3 min after the CA injection; (Sm − Sfinal)/Sm ; the signal enhancement ratio, (Sm − S0)/(Sfinal − S0), see Fig. 2]. Discriminating abilities of the texture features were investigated using the minimum least-squares distance classifier. To improve the diagnostic performance of Type II enhancement curves of the breast, Fusco et al.55 used the difference between the percentage enhancement at the last time point and the peak percentage enhancement as a discriminatory feature. In addition to breast cancer detection and diagnosis, nonparametric DCE-MRI based evaluation and follow-up on treatment have also been explored.54,56–59 A study by Abramson et al.54 evaluated the ability of the nonparametric DCE-MRI analysis to predict pathological response after one cycle of neoadjuvant chemotherapy (NAC) for patient with locally advanced breast cancer. Their study concluded that DCEMRI with high temporal resolution possesses the ability to discriminate patients with an eventual pathological complete response. Martincich et al.56 predicted histological responses in patients undergoing primary chemotherapy for breast cancer using the total lesion volume, precontrast uptake (signal intensity over the baseline normalized by the baseline intensity), and the enhancement pattern categorized into Types I, II, and III, shown in Fig. 3. Their study confirmed the ability of DCE-MRI to predict the effect of NAC in breast cancer and the tumor volume reduction after two cycles had the strongest predictive value. A similar study by El Khoury et al.57 for patients with breast cancer under preoperative chemotherapy quantified the tumors using the wash-out variation maps (i.e., the maps of the difference between Sfinal and Sm of the dynamic series in each voxel, see Fig. 2). Nonparametric MRI-based indexes were used by Johansen et al.58 for the early prediction of the response to the NAC and the 5-yr survival for patients with locally advanced breast cancer. In the baseline DCE-MRI study, which was performed prior to the start of therapy, the patients surviving for more than 5 yr had significantly less heterogeneous RSI distribution than the nonsurvivors. The usefulness of the DCE-MRI in analyzing and predicting the survival of the breast cancer patients has been demonstrated also by Tuncbilek et al.59 Renal diseases, including cancer, artery stenosis, and transplant rejection, can also be diagnosed with nonparametric DCE-MRI techniques.10,81–92 A semiautomated framework by Ho et al.81 evaluated renal lesions, which were identified manually by observers, with a percentage of the enhancement ratio

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between the pre- and postcontrast signals in each set of images. A 15% threshold was used to distinguish between cysts and solid renal lesions. All malignancies were accurately diagnosed between 2 and 4 min after administering the CA (100% sensitivity for true tumors and 6% or fewer false-positive (FP) tumor diagnoses). Michaely et al.82 assessed the feasibility of the renal MR perfusion for grading renal artery stenosis effects on parenchymal perfusion. The gamma variate function110 was used to describe the transient (first pass or wash-in) phase of the time varying signal S(t). Then perfusion-related indexes after agent bolus, such as the mean transit time (MTT), maximal up-slope, maximum signal intensity, and time-topeak, were calculated from the fitted S(t). The evaluated perfusion reflected the renal function measured with serum creatinine in a cohort of 73 patients. The peak signal intensity, MTT, initial up-slope, and time-to-peak were also used to analyze the perfusion by Positano et al.83 Other research groups have exploited DCE-MRI for early detection of renal rejection following kidney transplantation.10,84–86,88–92 A DCE-MRI based CAD system for early diagnosis of acute renal transplant rejection proposed by Farag et al.85 and El-Baz et al.86,88 classified the kidney status of each patient using four indexes: peak signal intensity, time-to-peak, wash-in slope, and washout slope, calculated from the MRI signal for the kidney cortex. Similar approaches, but with the perfusion curves for the whole kidney, rather than only the cortex, were proposed in Refs. 89 and 90. The latter CAD system was tested on 100 patients. A nonparametric MRI-based technique for analyzing kidney perfusion by Khalifa et al.10 accounts first for kidney deformations in order to accurately calculate indexes for the classification of the transplanted kidney status and evaluation of acute renal rejection. The kidney status is characterized by both the transient phase indexes (peak signal intensity, initial up-slope, and time-to-peak) and the tissue phase signal change index (the average plateau). This technique was extended in92 by applying a simplified gamma variate fit111 to S(t). Prostate cancer is the most frequently diagnosed male malignancy and the second leading cause (after lung cancer) of cancer-related death in the USA with more than 2 38 000 new cases and a mortality rate of about 30 000 in 2013.112 Early diagnosis improves the effectiveness of the treatment and increases the patient’s chances of survival. Nonparametric DCE-MRI analyses have been widely used to identify and classify prostate cancer.11,93–104 Engelbrecht et al.93 separated cancerous and normal prostate tissues in the peripheral zone (PZ) and central zone (CZ) by combining the T2-relaxation rate with the DCE-MRI indexes, calculated from the concentration curves, rather than S(t). According to receiver operating characteristics (ROC), the relative peak enhancement index was the best for discriminating the prostate carcinoma in the PZ and CZ. Noworolski et al.94 used the DCE-MRI data to classify the prostate tissues into cancerous or normal PZ and stromal benign or glandular hyperplasia. Capabilities of the DCE-MRI indexes in diagnosing benign and malignant prostate tissues were evaluated by Ren et al.,95 who also investigated relationships between characteristics of the S(t)-curves and angiogenesis. Their studies confirmed that DCE-MRI and histological findings are correlated. DCE-MRI based CAD Medical Physics, Vol. 41, No. 12, December 2014

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systems introduced by Puech et al.96,97 and Firjani et al.100,101 classified the prostatic tissue using the wash-in and wash-out slopes derived from S(t). Isebaert et al.102 evaluated the correlation to histopathology of nonparametric DCE-MRI characteristics, such as the time-to-peak, maximal signal enhancement, wash-in slope, and the clearance rate of the CA (the wash-out), for detecting prostate carcinoma and separating malignant and benign prostate tissue regions. According to their study, the wash-in slope is the most accurate separator of the malignant and benign tissues. Niaf et al.103 developed a CAD system using multiple MRI data (namely, T2-weighted MRI, DCE-MRI, and DW-MRI) to diagnose prostate cancer in the PZ. Four supervised classifiers of malignant and benign tissues were compared: a nonlinear support vector machine, the linear discriminant analysis, a K-nearest neighbor (KNN), and a naïve Bayes classifier, combining image intensity, texture, and gradient with functional features (e.g., PK features, the peak intensity, and the wash-in and wash-out slopes). Based on the ROC analysis, the combined nonlinear SVM classifier with a t-test feature selection approach yielded the highest diagnostic performance. In addition to cancer detection and classification, DCE-MRI facilitated prostate cancer therapy evaluations. Haider et al.11 compared the accuracy of DCE-MRI diagnostic with conventional T2-weighted MRI for detecting and localizing recurrent prostate cancer in the PZ for patients with biochemical failures after external beam radiotherapy. A DCE-MRI based voxel-enhancement criterion at 46 s after CA injection outperformed T2-weighted MRI. A similar study was conducted by Casciani et al.98 to detect local cancer recurrence after radical prostatectomy using combined endorectal MRI and DCE-MRI. Their multiparametric MRI analysis showed a higher sensitivity and specificity in detecting local recurrences after radical prostatectomy compared with MRI alone. Multivariate analysis of magnetic resonance spectroscopic imaging (MRSI) and DCE-MRI was used by Valerio et al.99 to differentiate between various prostate diseases, such as chronic inflammation, fibrosis, and adenocarcinoma. Their study showed that the multivariate analysis applied on MRSI/DCE-MRI results allows to differentiate among the various prostatic diseases in a noninvasive way with a 100% accuracy. Capabilities of DCE-MRI, combined with T2-weighted MRI, in staging prostate cancer were investigated by Fütterer et al.104 To separate the stage 2 and stage 3 prostate carcinoma, four perfusionrelated indexes were calculated from the concentration curves of the dynamic MRI data instead of S(t), as shown in Ref. 93. The ROC analysis documented a significant improvement in prostate cancer staging by combining nonparametric DCEMRI features with unenhanced T2-weighted MRI for less experienced observer; with no benefit to the experienced observers.

3. PARAMETRIC DCE-MRI ANALYSIS Parametric approaches fit mathematical PK models to dynamically acquired tissue concentration curves, so that quantitative tissue parameters (e.g., permeability and volume fractions)

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that are related to vascularity can be estimated. The pioneering works by Larsson,113 Brix,114 and Tofts115 for the study of multiple sclerosis113,115 and brain tumors113,114 showed the potential promise of PK models to better understand the CA perfusion kinetics in human tissue. Later on, these initial techniques enabled modeling of CA kinetics with DCE-MRI and were used to estimate perfusion and capillary permeability in several clinical applications.116 Recent PK analyses reveal physiological characteristics by relating perfusion to the tissue vascular functionality, which enables measurement of blood volume and capillary permeability.117 The literature’s PK models proposed for quantitative analysis of the DCE-MRI data are based on different assumptions and simplifications. The choice of a particular model for solving a certain clinical problem depends on many factors, including:118,119 (i) the unique physiology of the tissue of interest (e.g., brain, breast, or prostate) that governs the CA behavior; (ii) dominant conditions affecting the MR signal (e.g., fast or limited water exchange); (iii) whether the depicted anatomy allows for determining an AIF; (iv) the temporal MRI data resolution needed to accurately capture the CA uptake, etc. Dynamic perfusion data analysis involves two main categories of PK models, namely, compartmental and spatially distributed models. The former category includes the Larsson (LM),113 Brix (BM),114 Tofts and Kermode (TK),115 extended TK (ETK),120 two-compartment exchange (2CXM),6 and Patlak (PM)121 models, whereas the latter category comprises the distributed parameter (DP),122 tissue homogeneity (TH)123 model, and the adiabatic approximation of the TH (AATH) model.124 Compartmental PK models describe complex blood–tissue exchanges of an administered CA with a collection of interacting homogeneous components, called compartments. Two assumptions are sufficient to completely define the CA kinetics: (i) compartments are well-mixed, i.e., the CA concentration is spatially uniform at any given time within the volume and (ii) an output CA flux of any compartment is directly proportional to its concentration. Generally, the larger the number of compartments, the higher the accuracy of the PK model, but the higher the analysis complexity.125 Due to simplicity and small numbers of parameters to be estimated, compartmental models have gained considerable attention in many clinical investigations over the past two decades. Spatially distributed kinetic models123,124 are based on more realistic models for flow (e.g., a plug-flow model), carrying an administered CA through a tube by a flow, where all particles travel with the same velocity. In these models, the tissue space is considered as a series of infinitesimal compartments that is allowed to exchange CA with only nearby locations in the capillary bed with no axial CA transportation along the capillary length.117 Unlike compartmental models, spatially distributed models account for both spatial and temporal variations of an administered CA. Therefore, these models correspond more closely to reality, are expected to reflect the underlying physiology more accurately than the compartmental ones, and potentially increase modeling accuracy and provide additional information.7,126,127 However, their higher complexity requires higher data quality to Medical Physics, Vol. 41, No. 12, December 2014

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maintain the accuracy and precision of the estimated model parameters and thus limits their widespread popularity.128 Since measuring or determining the CA concentration in the blood plasma, or the so-called AIF, is a key requirement of most of the PK modeling, most common AIF determination methods are outlined below.

3.A. AIF

The AIF describing the changes of the CA concentration over time in a blood vessel feeding the tissue of interest has to be determined or measured for almost all parametric DCE-MRI models.129 However, it is difficult to accurately determine or estimate the true AIF due to problems including flow artifacts, inflow and nonlinear effects of high CA concentrations, and partial volume effects.130 The AIF kinetics differ from the tissue concentration as it is characterized by a sharp uptake, followed by a short-lived peak value, and subsequently a longer wash-out period. Current techniques to measure or to determine the AIF can be stratified into five groups: the gold standard, population-based, subject-specific, reference tissue-based, and jointly estimated AIFs, which are briefly reviewed below. Gold standard AIF is determined by analyzing blood samples collected during DCE-MRI acquisition from an arterial catheter inserted into the subject.113,131 Larsson et al.113,131 measured the CA amount in a series of blood samples taken at intervals of 15 s after a CA bolus injection. The main advantage of this method for AIF determination is the precise measurement of Cp in each sample over time, i.e., accurate characterization of the AIF as a function of time. However, this invasive approach is inconvenient for patients and its accuracy depends on temporal resolution (the number of samples that can be collected), especially for depicting small lesions. Additionally, it is unsuitable for some clinical applications, such as breast DCE-MRI, due to the lack of big vessels in the field of view. Population-based AIF is determined by measuring blood samples from a small group of subjects and using their average measurement for subsequent studies.132 Tofts and Kermode115 used a population-based AIF and described it by a sum of two decreasing exponentials [see Fig. 4(a)] with parameters estimated by fitting plasma concentration measurements, taken from control subjects, in the earlier work by Weinmann et al.132 Cp (t) = D a1e−m1t + a2e−m2t , (1) where D is the CA dose (mM kg−1 of body mass), a1 = 3.99 kg and a2 = 4.78 kg are amplitudes of the exponentials, and m1 = 0.144 min−1 and m2 = 0.011 min−1 are their rate constants.115 Parker et al.130 proposed another population-based AIF where a mixture of two Gaussian kernels plus an exponential modulated with a sigmoid function [see Fig. 4(b)] fits the average MRI signal measurements from 23 cancer patients Cp (t) =

2  √ 2 Be−m1t ai −((t−µ i )/σ i 2) + e , √ 1 + e−m2(t−t c ) i=1 σi 2π

(2)

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F. 4. The population-based AIFs by (a) Tofts and Kermode (Ref. 115) with D = 0.1mM kg−1 and (b) Parker et al. (Ref. 130). Different time scales are used to better visualize CA uptake and wash-out phases.

where B = 1.050 mM and m1 = 0.1682 min−1 are the amplitude and the decay constant of the exponential; m2 = 38.078 min−1 and t c = 0.1483 min are the sigmoid width and center; a1 = 0.809 mM min, a2 = 0.330 mM min, σ1 = 0.0563 min, σ2 = 0.132 min, µ1 = 0.170 min, and µ2 = 0.365 min are the scales, widths, and centers of the Gaussian kernels, respectively. As demonstrated in Fig. 4, the AIF by Parker et al.130 is closer by kinetics to the true AIF and therefore is more realistic than the AIF proposed by Tofts and Kermode115 The population-based AIFs are widely used in parametric DCE-MRI studies due to their simplicity and the fact that no additional MR measurements in other regions of interest are required.133 However, ignoring variations of the CA injection rates and doses, and presuming small intersubject variabilities are their main limitations, which can result in large errors in both the AIF characterization and subsequent PK analysis. Subject-specific or individual-based AIF is determined from the patient’s DCE-MRI data.134–136 Typically, the MRI signal from a region, which contains a large feeding artery located near the tissue of interest, is monitored and converted to CA concentration (such a conversion is detailed in Sec. 3.B) to directly characterize the AIF.134,137 This approach is a completely noninvasive technique and is expected to closely approximate the true AIF. However, the required large arterial vessel within the depicted field of view may not exist if small lesion areas, e.g., breast cancer, are imaged. Also, the accuracy of the measured AIF depends on the chosen MRI pulse sequence parameters,138 namely, the optimization of temporal resolution for determining the AIF accurately could result in undesirable spatial resolution and signal-to-noise ratio (SNR).133 Additionally, MR signal measurements from a large feeding artery near the tissue of interest can be distorted by other artifacts, such as the partial volume effect,139,140 inflow effect,141,142 and blood flow pulsatility and turbulence effects.143 It is worth mentioning that the AIF obtained from a feeding artery characterizes the whole arterial blood and must be corrected to account for the hematocrit factor in order to represent the plasma concentration. Reference tissue-based AIF144–148 overcomes limitations of the subject-specific AIF and inaccuracies of the populationbased AIF. Instead of measuring the MRI signal in a nearby feeding artery or assuming a particular form of the AIF, the Medical Physics, Vol. 41, No. 12, December 2014

CA concentration in a well-characterized, healthy reference tissue (e.g., a muscle) is measured to calibrate signal intensity changes in the tissue of interest. These techniques are stratified into two groups called the single and multiple reference tissue-based methods, respectively. The former presume the known PK parameter values for a single healthy reference tissue and use its CA uptake curve to inversely derive the AIF.144 However, this assumption does not necessarily hold due to interindividual variability of the kinetic parameters,149 which affects the accuracy and reduces the reproducibility of the results.147 Additionally, the single reference tissue-based AIF is assumed to be the same for both the reference tissue (e.g., a muscle) and the tissue of interest (e.g., a tumor). Moreover, single reference tissue-based AIF is applicable only for simple DCE-MRI modeling, which does not include the fractional volume of plasma per unit volume of tissue, or v p .150 The double150,151 and multiple152–154 reference tissue-based techniques involve no assumptions about the kinetic parameters in the reference tissue. The multiple reference tissue-based AIFs have demonstrated better PK modeling compared with the population-based methods.153 Although the double reference tissue-based AIF methods effectively avoid the need of literature values for reference tissue kinetic parameters, they are used in certain types of tissue that can only be described by a two-compartment PK model.152 Like the single reference tissue methods, the double region-based methods are only applicable for simple DCE-MRI models which do not include vp.153,155 On the other hand, multiple reference tissuebased AIF method can be applied, theoretically, to general DCE-MRI PK models; however, their practical application using Tofts model120 employed predefinition of the ve in the reference tissue regions.156 Jointly estimated AIF is specified as an acceptable function with adjustable parameters of blood plasma concentration, which can be jointly estimated with the PK parameters. No measurements of, or assumptions about, an AIF are involved. Both the PK and AIF parameters are jointly adjusted for fitting the tissue CA concentration curve, while the AIF parameters are tuned for obtaining the best fit.157 The main advantage is that no special DCE-MRI protocol for measuring the AIF is required. As shown in Refs. 158 and 159, the joint estimation of both the AIF and PK model

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parameters decreases biases and uncertainties in the PK estimates compared to a population-based technique. Monoexponential functions160 are the simplest AIF forms; however, these simplifications may give significant errors in the estimated PK parameters.150 More realistic AIF forms with a large number of free parameters [see, e.g., Eqs. (1) and (2)] increase the computational cost of the DCE-MRI analysis. For example, the Tofts model161 and the AIF by Parker et al.130 require in total 12 free parameters (two for the Tofts model and ten for the AIF), which makes the search space for the optimum parameters of the tissue concentration curve in each voxel very big, and therefore the probability of being trapped in local minima is high. This most recent AIF determination technique requires additional investigations, similar to the multiple reference tissue-based approach. Additionally, a crucial aspect for the blind deconvolution methods157–159 to work is that the multiple tissue regions must have different levels of perfusion and an approximately identical arterial input. Therefore, if the tissue time activity curves are the same in all tissue regions, these methods will fail. Since most of the PK models for DCE-MRI analysis require the conversion of the measured MR signal intensity [S(t)] into CA concentration curve, the estimation of the CA concentration from the signal data is briefly described below.

3.B. Estimating contrast agent concentrations

Almost all parametric DCE-MRI analysis calls for determining both the tissue, Ct (t), and blood plasma, Cp (t), CA concentration curves from the signal intensity (strength) time–course curve, or S(t). Determination of CA concentrations may not be necessary as long as the relationship between S(t) and CA concentration is linear and is the same for blood and tissue. In other words, one could change the scale on which CA concentrations are measured and it would not change the results for blood flow, permeability-surface area products, etc. However, in most cases, the relationship between S(t) and CA concentration is nonlinear due to the effects of signal saturation at higher CA concentrations.162 DCE-MRI measures the CA presence effect on proton relaxation times, T1 and T2, rather than the signal change from the CA uptake. But since changes in T1 and T2 affect the recorded MRI signal, a S(t) can be transformed into CA concentration using the Bloch’s equations163 for any MRI sequence. Typical MRI acquisition techniques include saturation recovery, inversion recovery, spin echo, and gradient echo sequences. A spoiled gradient echo (SPGRE) sequence is frequently used in gadolinium chelate acid-based studies of T1-weighted DCE-MRI.133 This sequence provides high temporal sampling, being adequate to characterize the CA transit, while maintaining an acceptable SNR and spatial resolution for visualizing the anatomy. The expected signal intensity using a SPGRE sequence is given by164 S(t) = M0

∗ e−(TE /T2 ) 1 − e−(T R /T1(t)) sin(α) 1 − cos(α)e−(T R /T1(t))

,

Medical Physics, Vol. 41, No. 12, December 2014

(3)

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where M0 is a scaling factor that depends on the scanner gain and proton density; α is the flip angle; TR is the repetition time (msec); TE is the echo time (msec); T1 and T2 are the spin–lattice (longitudinal) and spin–spin (transverse) relaxation times, respectively. In heavily T1-weighted scenarios (TE ≪ T2∗), the T2∗ effect on signal degradation can be ignored and Eq. (3) can be simplified by incorporating the effects of T2, TE , and other scanner parameters into the M0 term, denoted below S0 1 − e−(T R /T1(t)) sin(α) S(t) = S0 . (4) 1 − cos(α)e−(T R /T1(t)) In theory, the tissue CA concentration, Ct , under the assumption of the fast exchange regime relates linearly to the timevariant relaxation rate161,165 1 1 = +r 1Ct , T1(t) T10

(5)

where the longitudinal CA relaxation coefficient r 1 (mM−1s−1) depends on temperature, field strength, and chemical structure of the CA165 and T10 is a so-called native relaxation time, i.e., the value of T1 before injecting any CA. In MR literature, Eq. (5) used for applications in which the exchange of water molecule between tissue compartments is assumed to be infinitely fast throughout the course of the DCE-MRI acquisition, which is generally called the fast exchange limit (FXL) scenarios.166 To determine the CA concentration, both the pre- (T10) and postinjection [T1(t)] relaxation times essentially have to be calculated. Different techniques have been proposed for T1 measurements including the inversion recovery,167–169 LookLocker,170,171 and multiple flip angles172–175 methods. The multiple flip angles in SPGR DCE-MRI acquisition is widely used for T1 measurements due to its superior SNR and time efficiency.176 For the two flip angle scenario, T10 can be obtained analytically, while for the multiple flip angles, scenario nonlinear regression is used to find T10. In the case of two flip angles, α1 and α2, the preinjection signal intensities are calculated from the two SPGRE pulse sequences acquired using these angles. Then, using Eq. (3), the ratio, Rα = Sα1/Sα2, of the two measurements allows for finding the T10 value analytically as177,178    Sα1 cos(α1)sin(α2) − Sα2 sin(α1)cos(α2) −1 . (6) T10 = TR ln Sα1 sin(α2) − Sα2 sin(α1) In other studies, the multiple flip angles method is used to estimate T10,173,175 where three or more SPGRE signal intensities Sα i , α i ; i = 3, 4,... are used to estimate T10. Rearranging Eq. (4) yields a straight line equation Y = mX + S0 (1 − m),

(7)

where Y = Sα i /sin(α i ), X = Sα i /tan(α i ), and m = exp(−(TR/ T1)) represent the slope of the line. Hence, from the Y against-X plot, the T10 = −(TR/ln(m)) value can be calculated. A study by Schabel and Morrell179 has shown that the dual-flip angle approach with the correct angles is often better for T10 calculation than the method that uses more

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flip angles. The T1(t) can be estimated using a postinjection DCE-MRI scan acquired at a single flip angle α in conjunction with a DCE-MRI preinjection scan, with the assumption that proton density does not change due to the CA uptake.180 After all, inaccurate determination of both AIF and T1 can cause significant parameter estimation errors in DCE-MRI.14 Therefore, for a more accurate DCE-MRI analysis and better evaluation of the PK parameters, the estimated T1(t) and T10 values should be compared with the known ones for different tissues (e.g., muscles, gray matter, and white matter) to ensure that these estimates are in the acceptable ranges. Once T10 and AIF are measured or determined, and the S(t) is converted to tissue CA concentration using Eq. (5), the PK model is then used to fit the latter. After fitting, the CA concentration in the tissue, Ct , is described in terms of various rates and volume parameters of the model used. Strengths and weaknesses of the most common compartmental and distributed tracer-kinetic models that are used for analyzing DCE-MRI, are outlined below. 3.C. Compartmental models

For the last two decades, many compartmental models of various complexities and under different assumptions have been proposed for quantifying the CA uptake in the tissue. Well-known compartmental models are based on the original principles of the Kety’s model.181 A two-compartment model, widely used for quantitative analysis of tissue perfusion, is sketched in Fig. 5. Its compartments specify the CA concentrations in the EES [i.e., Ce (t)] and the blood plasma or the intravascular space [i.e., Cp (t)]. An arterial input CA amount, Ca (t), administered to the system yields a dynamic concentration, Cp (t), in the first compartment, whereas the intercompartmental CA exchange results in a dynamic concentration, Ce (t), in the second compartment. Intercompartment exchange rates are governed by forward and backward volume transfer constants, k12 and k21, respectively, and CA losses from the system are described by an excretion rate, kel. Since, the parameters k12 and k21 control the CA transfer from the blood plasma to the tissue, they are related to capillary permeability.161 The total tissue CA concentration is as follows: Ct (t) = vpCp (t) + veCe (t), where vp and ve (0 < vp, ve < 1) are the fractional plasma and EES volumes,

F. 5. Two-compartment model: the function C a (t) quantifies the arterial input into the plasma compartment; the peripheral compartment receives the CA from, and returns the CA to, the plasma compartment at the rates k 12 and k 21, respectively; the rate k el specifies the CA loss from the system. Medical Physics, Vol. 41, No. 12, December 2014

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F. 6. The LM for a capillary–tissue system: blood plasma flows in the capillary at an F p rate and exchanges CA with EES at a k ep rate.

respectively. The most common compartmental models for analyzing CA perfusion in the tissue are detailed below. 3.C.1. LM

LM is one of the earliest kinetic models for analyzing DCEMRI that was developed by Larsson et al.113 In this model, the CA transfer between the blood plasma in the capillary and EES (also called the interstitial water space) is assumed to be controlled by a single transfer constant k ep (min−1) combining three parameters: the capillary blood flow, Fp ; the extraction fraction, E; the fractional EES volume, see Fig. 6. To build the model, the CA concentration in the plasma compartment, Cp (t), is obtained using the gold standard AIF, namely, by measuring the CA amount in a series of blood samples taken in 15 s intervals after a bolus CA injection. The measurements are then fitted with a sum of three exponentials with the amplitudes ai and time constants mi , respectively (i = 1, 2, 3) Cp (t) =

3 

ai e−m i t .

(8)

i=1

The temporal tissue CA concentration uptake change in the EES compartment is described using the transfer equation dCt = kep Cp (t) −Ct (9) dt which can be solved for Ct using Cp (t) in Eq. (8) as follows: 3  ai e−kept − e−m i t Ct (t) = k ep . (10) mi − kep i=1 The LM assumes that the MR signal S(t) relates linearly to the CA concentration:  ′  k (t) S(t) = S0 + Ct , (11) kep  where k ′(t) = S ′(t)/ 3i=1 ai , S0 is the baseline signal intensity before the CA injection, and S ′(t) is the initial signal slope, or equivalently

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3  ai e−kept − e−m i t S(t) = S0 + k (t) . mi − kep i=1 ′

(12)

The LM is applicable under a very limited tissue permeability, i.e., when the permeability is considerably lower than the flow, and is fully described by the single transfer constant, kep. The latter can be estimated via optimization, e.g., by the least-squares techniques. The main limitation of the LM is its assumed negligible contribution of the plasma (intravascular space) tracer. Additionally, the work presented in Ref. 113 provides only a combined estimation of both permeability and the mean extravascular space. However, Larsson and his coworkers provisioned a method that allows for separate estimation of permeability and ve, using in-vitro value of relaxivity and a measurement of T10.182 3.C.2. BM

Proposed by Brix et al.114 is one of the most well-known compartmental models for analyzing DCE-MRI. In the BM, kinetics of the CA exchange between the blood plasma and the peripheral (interstitial) EES compartments are described with several rate and transfer constants, shown in Fig. 7. The CA is administered at a constant rate of kin over a time-span τ, exchanged between the plasma and EES compartments at kpe (forward) and kep (reverse) transfer rates, and eliminated from the plasma at a rate of kel. Unlike the LM, which requires a predetermined AIF, for the BM, a particular AIF is taken to be known from the infusion rate (the flux) entering the body. Relationships between the intravascular and peripheral compartments in the BM are described using the mass conservation principle114 dCp kin (u(t) −u(t − τ)) − k elCp (t), = dt Vp

(13)

Vp dCt = k pe Cp − kepCp (t), dt Ve

(14)

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where u(t) is the Heaviside step function, and Vp and Ve are the intravascular plasma and the EES compartment volumes, respectively. Solving Eqs. (13) and (14) under the initial conditions Cp (t) = 0 and Ct (t) = 0 for t = 0 gives the following CA concentrations in the blood plasma and tissue:12 kin  kelt ′  kelt (15) e −1 e , Vp kel   −k t  kin k pe e el kelt ′  e−kept  kept ′  − 1 , (16) e −1 − e Ct = Vp(kep − k el) kel kep

Cp (t) =

where t ′ = t if 0 ≤ t ≤ τ and t ′ = τ if τ ≤ t. To fit the measured signal S(t), the BM uses three parameters, namely, the CA exchange rate, kep; the elimination rate, kel; an additional parameter, ABrix, being an arbitrary constant that depends on the tissue properties and the MR sequence parameters. The relationship between the signal S(t) and these free model parameters at any time is as follows:114   S(t) ABrix e−kelt  kelt ′  e−kept  kept ′  = 1+ e −1 − e − 1 , (17) S0 kep − k el kel kep where t ′ = t if 0 ≤ t ≤ τ and t ′ = τ if τ ≤ t. After a CA bolus injection, Eq. (17) is reduced to  −k t −kept  S(t) e el − e ≈ 1 + τ ABrix . (18) S0 kep − kel A modified version of the BM proposed by Hoffmann et al.160 reduces the CA infusion length to 1 min. The afterbolus signal S(t) is fitted using  −k t −kept  S(t) e el − e ≈ 1 + kep AH (19) S0 k ep − k el the amplitude parameter, AH approximately corresponds to the EES size if the CA relaxation properties, the native T1, and the CA dose do not vary significantly.161 Although the BM has been widely used due to its simplicity and proved ability to closely fit the tissue DCE-MRI data, its basic assumption of approximating Cp (t) with a single exponential function for up to 20 min after the CA injection is seldom supported by experimental observations.115,132 Additionally, the BM provides no direct measure of capillary permeability and is applicable only under specific permeability-limiting conditions.183 However, the vasculature permeability can be roughly estimated with the product of the amplitude parameter, ABrix, and the rate constant, k ep.114,184,185 3.C.3. TK model

F. 7. Schematic illustration of the Brix model. The CA is administered at a constant rate of k in into the plasma compartment, exchanged between the two compartments at rates of k ep and k pe, respectively, and eliminated (cleared) from the plasma at a rate of k el. Medical Physics, Vol. 41, No. 12, December 2014

The most common PK model proposed by TK115 has unified many previous ones and introduced common characteristic parameters and naming conventions.120 It assumes that the CA diffuses from and returns to the blood plasma at rates governed by the forward transfer constant, Ktrans (min−1), and the reverse constant, kep (min−1), respectively (see Fig. 8). The tissue CA concentration is derived in the TK from the EES components only, while the intravascular (plasma) compartment contribution is ignored, i.e., Ct (t) = veCe (t). The

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3.C.4. ETK model

The original TK depends on two parameters, Ktrans and ve, and assumes that the tissue is weakly vascularized (vp = 0). However, this assumption is invalid for many tissues, especially tumors. The generalized TK,161 known commonly as the extended TK (ETK), includes the intravascular contribution vpCp (t) to the tissue concentration by representing the total tissue concentration as Ct (t) = vpCp (t) +Cp (t) ⊗ HTK(t)  t ′ = vpCp (t) + Ktrans Cp (t ′)e−((Ktrans/ve)(t−t ))dt ′,

(24)

0

F. 8. Schematic illustration of the CA transfer in the TK model between the central (plasma) compartment and the EES space with the Ktrans and k ep rates, respectively.

tissue concentration, Ct (t), is described by the transfer equation   dCt Ct (t) = KtransCp (t) − kepCt (t) = Ktrans Cp (t) − , (20) dt ve where kep = Ktrans/ve. The CA concentration in the plasma, Cp (t), after injection specifies the AIF and is used as the initial condition to estimate Ct (t). Under the initial conditions Cp (t) = Ct (t) = 0 at t = 0, Eq. (20) has the following solution:120  t ′ Ct (t) = Ktrans Cp (t ′)e−(Ktrans/ve)(t−t )dt ′. (21)

where vp is the fractional plasma volume per unit of tissue volume. Free ETK parameters, Ktrans, ve, and vp, can be estimated by fitting an empirical tissue concentration estimated from the MRI data by the curve Ct (t) of Eq. (24) with a measured or determined AIF (as described in Sec. 3.A). For fitting, the signal intensity is converted to the CA concentration using Eq. (5). Both TK (Ref. 115) and ETK (Ref. 161) models are considered the best-established models for analyzing T1weighted DCE-MR images. However, because the volume transfer constant, Ktrans, incorporates both the plasma flow and tissue permeability, these latter parameters cannot be estimated separately. The use of a population-based AIF that was originally introduced by Weinmann et al.132 differs significantly from the true AIF and is an additional disadvantage of both the models. However, individually measured AIF or any other AIF type can be used for TK and ETK models.

0

Alternatively, the TK output, Ct (t), in Eq. (21), can be found by using the convolution theory. Namely, Ct (t) is obtained by the convolution (denoted ⊗) of the input signal, Cp (t), with the tissue impulse response, HTK(t), i.e., Ct (t) = Cp (t) ⊗ HTK(t) where HTK(t) = Ktranse−(Ktrans/ve)t .

(22)

A population-based AIF in the original TK,115 described by a sum of two exponentials [see Eq. (1) and Fig. 4(a)] results in the following output Ct (t) of Eq. (21):  a1  −((Ktrans/ve)t) −m1t  Ct (t) = DKtrans e −e m1 − kep  a2  −((Ktrans/ve)t) −m2t  + e −e , (23) m2 − k ep where D is the CA dose (mM kg−1 of body mass) and Ktrans and ve are the TK model free parameters that determine the shape of the fitted data from which kep = Ktrans/ve is determined. Physiologically, Ktrans is the most important and significant tissuedependent parameter in the TK model. It assesses either plasma flow Fp in flow-limited scenarios or tissue permeability (represented by the tissue permeability–surface area product, PS) in permeability-limited scenarios for the uptake. In mixed scenarios, it indicates a combination of the flow and permeability properties of the tissue and acts as a lump measure of their joint effect. Medical Physics, Vol. 41, No. 12, December 2014

3.C.5. PM

Unlike the above PK models, Patlak et al.121 have proposed a graphical approach, called Patlak plot, for compartmental analysis in order to estimate the CA transfer constant between the blood plasma and the EES space. The PM assumes the reverse vascular transfer constant, kep, from the EES back to the plasma in Fig. 8 and Eq. (20) is negligibly small due to low permeability and short measuring time. This assumption results in the following tissue concentration:  t Ct (t) = vpCp(t) + Ktrans Cp (t ′)dt ′, (25) 0

where vp is the vascular fraction. The Patlak plot linearizes Eq. (25) as Y = Ktrans X + vp,

t

(26)

where Y = Ct (t)/Cp (t) and X = 0 Cp (t ′)dt ′/Cp (t). Estimation of the parameter Ktrans by constructing visual linear graphical plots and simple interpretation are the main advantages of the PM. This linearized graphical analysis has a widespread popularity in certain clinical studies, such as renal applications186–190 where Ktrans is equal to the kidney’s glomerular filtration rate (GFR). However, this model does not take into account the reverse flow (k ep); therefore, its estimates can be highly inaccurate and the analysis results could have some limitations.191 Moreover, if the model assumption is violated,

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the plotted points are not collinear and the estimation of the parameters is no longer correct.192 Chen et al.192 developed an extended graphical PM, which is an intermediate between PM and ETK and yields more stable and unbiased Ktrans estimates within short acquisition durations. It expands the ETK by correcting for reflux while retaining the central PM’s advantages, such as linearity in the parameters estimated, simple graphical interpretation, and stable fitting procedures. Due to accommodating CA efflux, the extended graphical PM became less susceptible to bias.193

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plasma and EES compartments’ volumes. The Ct (t) is specified by convolving the AIF with the tissue impulse response function, multiplied by the blood plasma flow, Fp Ct (t) = Fp H2CXM(t) ⊗ Ca (t),

(30)

where the tissue response, H2CXM(t), is found by solving Eqs. (27) and (28) for the input delta-function Ca (t) = δ(t) under the initial conditions Cp (t) = Ce (t) = 0 for t = 0 and using Eq. (29)194 H2CXM(t) = Be−m1t + (1 − B)e−m2t ,

3.C.6. 2CXM 113–115,161

The earlier PK models allowed, in principle, for estimating the volume transfer constant, Ktrans, that combines both the blood flow and tissue permeability. A recent more general 2CXM (Refs. 6, 127, and 194) allows for separate estimation of the permeability, PS, and the plasma blood flow, Fp . A block diagram of the 2CXM is schematized in Fig. 9, which consists of two compartments: the intravascular plasma and the EES compartments. The intravascular compartment experiences an external flow, Fp , of plasma and the CA exchanges between both compartments at a symmetric rate of PS. Using mass conservation principle, the CA diffusion between capillary plasma and EES is described by the coupled system of differential equations6 Fp dCp PS = Ce (t) −Cp (t) + Ca (t) −Cp (t) , dt vp vp dCe PS = Cp (t) −Ce (t) , dt ve Ct (t) = vpCp (t) + veCe (t),

(27) (28) (29)

where Cp (t), Ce (t), and Ca (t) are the intravascular plasma, EES space, and arterial plasma CA concentrations, respectively. Here, vp and ve are the respective fractional capillary

F. 9. Schematic illustration of the 2CXM. The CA delivered via arteries to the plasma compartment at a rate of FP is exchanged between the compartments at a symmetric rate of PS, and is eliminated subsequently from the plasma compartment. Medical Physics, Vol. 41, No. 12, December 2014

(31)

where B, m1, and m2 relate to the model parameters (Fp , PS, vp, and ve) as follows:    m1 = 12 a + b+ (a + b)2 − 4bc ,  m2 =

1 2





a + b− (a + b) − 4bc , 2

B=

m2 − c , m2 − m1

(32)

where a=

Fp + PS , vp

b=

PS , ve

c=

Fp . vp

(33)

As a generalization of the 2CXM model, multicompartment models with multiple tissue compartments have also been proposed.135,195–199 These models possess the ability to appropriately describe the observed CA dynamics.135 However, the increased complexity of these models, sensitivity to the choice of initial values, and numerical instability have prevented the widespread use of these multicompartment models.197 Generally, most of the well-known PK models can be derived from the 2CXM under specific assumptions. For example, the ETK model is derived from the 2CXM model by assuming that the plasma flow is so high such that the time taken for the CA to pass through the plasma compartment, i.e., the MTT is negligible. Under this assumption, the intravascular plasma concentration cannot be distinguished from the AIF, i.e., Cp (t) Ca (t). However, a study by Donaldson et al.127 in the carcinoma of the cervix suggested that the assumption of negligible plasma MTT is not appropriate and the 2CXM is better suited for the analysis than the TK model. Moreover, a breast cancer study by Li et al.200 suggests that the TK and ETK models can grossly underestimate blood flow, vessel wall permeability, and the EES fraction. As the most general compartmental model, the 2CXM is gradually becoming more common for fitting the MRI data in many clinical applications.2,127,194 Its main advantage is the possibility to estimate both the regional blood flow and capillary permeability as well as the volume fractions of the intravascular (plasma) and the interstitial (EES) space.6 The main limitation of this and other compartmental models is the assumed well-mixed tissue compartments so that spatial variations of the CA diffusion are not taken into account. In addition, all compartmental models assume a FXL regime, i.e., the intercompartmental water exchange is assumed to be infinitely fast throughout DCE-MRI acquisition. However, this assumption is not always valid or true,

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especially for the high CA concentration in the voxel of interest.201 To account for this, other PK models have been developed to allow finite intercompartmental water exchange kinetics.201,202 In these models, the extravascular space is divided into two separate compartments, namely, the EES and the extravascular-intracellular space (EIS), and a special shutter speed model is introduced to account for the water exchange rate between the compartments. Unlike the conventional PK models that assume well-mixed compartments with a fast water exchange between them relative to the MRI time frame, the shutter speed model assumes that the tissue compartments are not well-mixed and the water exchange between the compartments (i.e., between plasma and EES; and between EES and EIS) is not sufficiently fast.203 Therefore, the linear relationship between the relaxation rate of the tissue and CA concentration in the tissue given by Eq. (5) is no longer valid. It was recently shown that relieving the FXL constraint leads to a remarkable performance for breast204–208 and prostate166,209 cancer diagnoses using DCE-MRI and the shutter speed model. It is worth mentioning that the water exchange sensitivity can be minimized by changing the MRI data acquisition parameters as was shown by Li et al.209,210 More details about these models can be found in Refs. 200, 201, 203–207, and 211–214. 3.D. Spatially distributed models

Compartmental models have been widely employed in many clinical studies due to their simplicity. However, these models do not possess sufficient realism due to the inherent assumptions that the CA gradients within compartments are assumed to be zero at all times. Also, these models assume a fast CA movement and an even distribution throughout the compartment instantaneously on CA arrival in each compartment.126 This makes the CA concentration a function of time only, but not space. Advanced spatially distributed kinetic models, detailed below, that account for both temporal and spatial CA concentration distributions123,124,126,215–217 have been introduced for a more complete analysis of the perfusion data. 3.D.1. DP model

The DP model122 is the first type of the spatially distributed kinetic models. The DP model is based on a plug-flow model, an alternative to a compartmental model, which assumes that the administered CA is carried through a tube by a flow where all particles are traveling with the same velocity.117,218 In contrast to compartmental models, the DP does not assume homogeneous (well-mixed) compartments, but accounts instead for a CA concentration gradient within the plasma and EES compartments making their CA concentrations functions of both the time and distance along the capillary length (see Fig. 10). The DP is based on three basic assumptions:117 (i) there is no radial (direction perpendicular to the capillary bed) change in CA concentration, such that the CA distribution is described by a 1D variation Cp (x,t), Medical Physics, Vol. 41, No. 12, December 2014

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F. 10. Schematic illustration of the DP model. The CA concentration within the capillary decreases with position (x) along the capillary length (L), producing concentration gradients between the arterial (x=0) and venous (x=L) capillary ends. During the CA passage, a portion of the CA molecules diffuses between the plasma and EES at a controlled PS rate, so that the plasma, C p (x, t), and EES, C e (x, t), concentrations show both the spatial and temporal dependence.

(ii) the EES is modeled as a series of infinitesimal compartments exchanging the CA with only nearby locations in the capillary bed, and (iii) no axial CA transportation (along the x-direction in Fig. 10) is allowed in the EES. From the mass conservation, the DP can be represented with a system of differential equations for an elementary volume dx along the axial length L of a capillary tube122 ∂Cp (x,t) ∂Cp (x,t) = −LFp − PS Cp (x,t) −Ce (x,t) , (34) ∂t ∂x ∂Ce (x,t) ve = PS Cp (x,t) −Ce (x,t) . (35) ∂t Similar to the 2CXM, the analytical DP solution is obtained by the convolution of Ca (t) (the AIF) with the tissue impulse response function, multiplied by Fp . The latter function is found again by solving Eqs. (34) and (35) for the delta-function input of CA (Refs. 117 and 118) as   PS HDP(t) = u(t) −u(t −Tc)exp − Fp   0.5  t−Tc  1 ′ × 1 + PS e−((PS/ve)t ) ′ t Fpve 0  ′  0.5  t ′ * + ×I1 2PS dt , (36) Fpve , where Tc = vp/Fp is the MTT of the capillary, I1(.) is the modified Bessel function,219 and u(t) is the Heaviside unit step function. Compared to compartmental models, the DP is more realistic and makes fewer assumptions about microcirculation. However, like all distributed kinetic models in general, the DP is computationally more intensive and requires data with higher temporal resolution in order to derive meaningful results.128 vp

3.D.2. TH model

Another spatially distributed kinetic model is the TH model that was first described by Johnson and Wilson123 and applied in nuclear medicine by Sawada et al.215 The TH model is a special case of the DP assuming the homogeneous

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(well-mixed) spatial distribution of the CA concentration within the EES, and therefore, only the time-dependent EES concentration. The TH and DP equations are identical apart from the x-position-independent EES concentration123,220 ∂Cp (x,t) ∂Cp (x,t) = −LFp − PS Cp (x,t) −Ce (t) , ∂t ∂x ∂Ce (x,t) = PS Cp (t) −Ce (t) , ve ∂t vp

(37) (38)

where Cp (t) and Cp (x,t) denote the average CA concentration in plasma and the local CA concentration at x, respectively.117 Unlike the DP, the TH has no analytical solution in the time domain, hindering its widespread applicability for DCE-MRI analysis.124 The closed-form model solution exists only in the Laplace space.220 According to Garpebring et al.,221 the TH solution could be found with the fast Fourier transform. This approach removes many practical obstacles to using the TH in DCE-MRI analysis.117 St. Lawrence and Lee124 found a time-domain TH solution by assuming adiabatic (slow) changes in the EES compartment with respect to the change rate in the capillaries. Unlike the TH, their model is based on two basic assumptions: the capillary walls are impermeable to the CA and the EES receives influx with clearance EFp from the venous capillary end; where the extraction fraction E = 1 − exp −PS/Fp is the intravascular-to-EES CA fraction extracted in the first CA pass through the capillary bed. The assumptions lead to the following coupled transfer equations117: ∂Cp (x,t) ∂Cp (x,t) = −LFp , ∂t ∂x ∂Ce (x,t) ve = EFp Cp (L,t) −Ce (t) , ∂t vp

(39) (40)

where Cp (L,t) is the CA concentration at the venous capillary end. The resulting compact closed-form solution, called the AATH, determines Ct (t) by convolving the AIF with the tissue impulse response function HAATH(t)124 Ct (t) = Fp HAATH(t) ⊗ Ca (t),

(41)

where HAATH(t) = u(t) + Eu(t −Tc)e−((E F p /ve)(t−Tc)).

(42)

The AATH has four free parameters: Fp , E, ve, and Tc. In addition, other physiological parameters can also be calculated,120 e.g., Ktrans = EFp , k ep = EFp /ve, vp = FpTc, and PS = −Fp /ln(1 − E). The main advantage of the AATH is a closed time-domain solution, which allows for estimating the TH parameters from DCE-MRI data. However, the TH estimation is somewhat difficult and slow even with the AATH, due to a large number of initial guesses in order to avoid too large parameter values.222 The computational cost increases if voxel-wise parametric maps needed also hinder the wider use of the model.221 Medical Physics, Vol. 41, No. 12, December 2014

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3.E. Clinical applications of parametric models

Over the past two decades, several PK models have been developed to capture the dynamics of CA perfusing into the tissue. These models are able to extract microvascular characteristics and physiological parameters, such as the fractional blood volume and permeability, that describe the blood flow (perfusion) in a biological tissue. The PK analyses provide radiologists with additional functional information about the tissue perfusion, which can facilitate diagnosis, prognosis, treatment choice, or follow-up on treatment. The dynamic perfusion data analysis can be performed by using two common types of the kinetic models, namely, compartmental and spatially distributed ones. The choice of a particular PK type influences notably the accuracy and precision of the estimated PK parameters18 and depends on many factors including the underlying application, as well as data quality and structure, e.g., an injection protocol, temporal resolution, acquisition, time, and noise level. Compartment models (LM, BM, TK, ETK, PM, and 2CXM) have gained a widespread popularity due to their simplicity and a small number of parameters to be estimated. While being introduced initially to study blood-brain barrier, they have been used to analyze DCE-MRI in a wide range of clinical applications. In particular, the LM has been applied to study multiple sclerosis,113 assess heart diseases,4,134,223–227 quantify regional myocardial perfusion in healthy humans,228,229 and diagnose breast cancer.230,231 The BM, which is particularly attractive since the AIF need not be known a priori,232 has been used to study the brain114,160,233 and breast tumors,7,135,160,233–238 as well as to analyze contrast uptake patterns in other applications, including intracranial meningiomas,239 malignant pleural mesothelioma,240 cervical cancer241–243 and its chemoradiotherapy outcome,232,244 colorectal245 and liver tumors,246 prostate diseases,12,247,248 and bone perfusion.185 The most straightforward PK models to interpret are the TK and ETK models, which have been extensively applied to characterize the brain,3,115,175,249–255 lung,256,257 breast,200,258–269 prostate,13,149,270–282 liver,246 and colorectal283–289 tumors. These models have also shown promise in a variety of other clinical applications, such as renal carcinoma,290 rheumatoid arthritis,291,292 quantification of myocardial blood flow (MBF),293,294 nasopharyngeal carcinoma,295 arterial occlusive disease296 and carotid atherosclerotic plaque,193,297 hepatocellular carcinomas,298 and tumor heterogeneity analysis.284,299,300 New fields, such as assessment of preoperative oral cancer therapy,301 pancreatic302 and cervical cancer,127,154,232,303–306 head and neck cancers,307–312 and cardiac diseases313–315 are also regularly explored. The Patlak plot is the simplest PK technique having been widely used in the dynamic MRI data analysis. The slope of the Patlak plot is a useful quantitative index for characterizing the CA kinetic properties in certain applications, such as quantifying the MBF,294,316,317 assessing the kidney function,9,187–189 predicting the blood-brain barrier disruption after an embolic stroke in rats,318 measuring the blood-brain barrier permeability,175 and studying the abdominal aortic aneurysm319 and carotid stenosis.193

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The 2CXM model6,127,194 and the more general multicompartment models135,195,197–199 resolve the ambiguity in interpreting the Ktrans-estimates from the TK and ETK models. This is a well-known model in classical pharmacokinetics320 and has been applied to analyze nuclear medicine data by Larson et al.126 and adopted for the perfusion analysis by Brix et al.321,322 and Cheong et al.323 Classification of breast tumors by Brix et al.6 was its first DCE-MRI application. Recently, the 2CXM is gradually becoming common in various applications, such as brain1,2,194 and lung cancer,324 myometrium,325 cervix127 and bladder cancer,326 head and neck tumors,327 and carotid atherosclerotic plaques.193 Compared to compartmental models, the spatially distributed kinetic models (DP, TH, and AATH) account much more accurately for the underlying physiology. The DP has been first described by Sangren and Sheppard122 and applied to DCE-MRI by Bisdas et al.328 for studying head and neck cancer and more recently by Koh et al.329 for studying hepatic metastases. In contrast to the DP, the TH has not been widely used for DCE-MRI analysis due to the lack of a closed-form solution in the time domain. Because the closed-form solution exists only in the Laplace space,220 the fast Fourier transform was used by Garpebring et al.221 to apply the TH for studying brain tumors. The AATH has been first applied to characterize animal brain tumors using DCE-MRI by Henderson et al.330 Among all current models measuring Fp and PS separately, the AATH has been most widely used in a number of DCE-MRI studies, such as detecting viable myocardium331 and lung nodules,257 exploring breast tumors7,332 and prostate cancer,222,333–335 cerebral perfusion mapping,1 and investigating hepatocellular carcinomas in animals.298 In summary, the PK modeling capabilities to noninvasively characterize microvascular physiology have been explored and taken advantage in a wide range of clinical applications. This section covered the clinical applications of the reviewed PK models. There is no uniform consensus for the choice of an appropriate PK model for specific oncologic application. Identification of objective criteria for PK model selection to fit a given application is a promising trend.191,257,336–338 Due to their simplicity, the TK and the ETK models have been widely used in many brain, breast, and prostate applications, even by using data with limited temporal resolution and without accurate AIF information.18 Based on the reviewed studies (see Table I), the TK and ETK models’ parameters have been successfully able to evaluate the perfusion and permeability of brain tumors,339 discriminate between different brain tumors,175,340 detect breast tumors,261,266 and evaluate response to treatment.263,300 In cardiac applications, Ktrans is related to the MBF which gives valuable information about the severity and progression of cardiac disease, and response to therapy and prognosis. Usually, cardiac applications employ LM and PM models for Ktrans estimation. The utility of the Ktrans and ve parameters has been found relevant to describe tumor vasculature Medical Physics, Vol. 41, No. 12, December 2014

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perfusion and permeability in several prostate DCE-MRI reports. These parameters are known to be elevated in cancer and therefore are relevant for cancer detection and prognosis270,271,273,276,280,299 as well as assessing cancer aggressiveness.13,278 For renal application, various compartmental models have been proposed for the analysis of kidney DCEMRI. The GFR measurement is usually obtained using the PM,188 Rutland–Patlak,189 and more advanced models in which the kidney is modeled as a combination of a vascular and one187 or more tubular compartments.190,341 Table I summarizes a number of important findings in a wide range of nontumor and tumor studies, including tumor detection, characterization, and staging, as well as therapy monitoring.

4. SUMMARY AND DISCUSSION In this paper, we have presented an overview of the explored DCE-MRI analysis and modeling techniques as well as their applications in a wide range of clinical studies in the last two decades. Promising theoretical findings and experimental results for the reviewed models and techniques in a variety of clinical applications suggest that DCE-MRI is a clinically relevant imaging modality. For example, the classical mammography has a significantly lower sensitivity (33%–59%) in early detection of breast cancer than DCE-MRI analysis (71%– 96%).60,65,259,261,263,265,266 Among all MRI modalities, DCEMRI also offers the highest diagnostic accuracy of small (less than 1 cm) breast lesions20,264,342 and the most accurate localization and staging of prostate cancer.13,93,100,101,104,247,270,280 Additionally, DCE-MRI has been shown as an effective tool for evaluating changes in tumor vascular support after therapies.343,344 Furthermore, DCE-MRI allows for differentiating very accurately between various brain tumors, such as glioma, meningioma, acoustic neuroma, or metastases3,249,340,345 and is a promising noninvasive tool for detecting acute renal rejection at its earliest stage.10,87–92 As discussed in this paper, both nonparametric and parametric approaches for DCE-MRI analysis possess the ability to quantify tissue perfusion. The main advantage of these analysis methods is that they reduce the original DCE-MRI data dimensionality to a small set of parameters that describe the tissue perfusion. The straightforward nonparametric techniques characterize shapes and structures of signal enhancement curves by computing descriptive indexes (e.g., the maximum enhancement, time-to-peak, and up-slope) directly from these curves. The advantages of these techniques are twofold: (i) no need to convert the recorded MR signals into CA concentrations and (ii) the complete analysis of the whole enhancement curve cycle by computing perfusion-related indexes from both wash-in and wash-out phases. However, the relation of the indexes to the underlying physiology is often unclear, although some correlation with quantitative or at least qualitative physiological measurements can be established. For example, increased wash-in slope, AUC, and peak enhancement and decreased time-to-peak are likely related to an improved organ functionality (e.g., renal transplant), bad response to therapy (e.g., cancerous tissue), or increased

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T I. Recent clinical applications of parametric DCE-MRI analysis. Study

PK model

Tissue of interest

Objectives (o) and conclusions (c)

Harrer et al. (Ref. 339)

TK, ETK, and the first-pass leakage profile (Ref. 74)

Brain; 18 patients

(o) Characterizing human gliomas with three PK models. (c) Highly correlated ETK- and the first-pass leakage profile-based estimates of Ktrans and vp validate the use of these models for the evaluation of perfusion and permeability in tumors.

Haris et al. (Ref. 340)

TK

Brain; 103 patients

(o) Assessing capabilities of various perfusion indexes to separate infective from neoplastic brain lesions. (c) Ktrans and ve are useful indexes for discriminating between infective brain lesions and gliomas.

Bergamino et al. (Ref. 175)

ETK and PM

Brain; 25 patients

(o) Investigating blood-brain-barrier permeability associated with different brain tumors using DCE-MRI. (c) Different permeability measurements based on Ktrans for different tumor grades: the higher the histological grades, the higher the permeability values. (c) Significantly different ETK- and PM-related Ktrans-values for the high grade tumors.

Chih-Feng et al. (Ref. 369)

ETK

Brain; 10 patients

(o) Correlating Ktrans-values and the IAUC of the concentration–time curve for parametric and nonparametric PK modeling, respectively, in clinical patients with brain tumors. (c) High correlation coefficient (0.913) between the IAUC and Ktrans suggests the IAUC as an alternative for evaluating physiological condition in DCE-MRI.

Bisdas et al. (Ref. 3)

TK

Brain; 18 patients

(o) Investigating the feasibility of PK modeling to distinguish recurrent high-grade gliomas from radiation injury. (c) Significantly higher Ktrans-values in recurrent gliomas in comparison to radiation-induced necrosis sites. (c) 100% sensitivity and 83% specificity of detecting recurrent gliomas on the basis of a cutoff Ktrans-value, compared to 71% sensitivity and 71% specificity of the like diagnostics with nonparametric AUC.

Lee et al. (Ref. 312)

ETK

Head and neck; 63 patients

(o) Examining DCE-MRI capabilities in differential diagnostics of various head and neck cancers. (c) Significantly different Ktrans-values obtained by PK analysis between the undifferentiated carcinomas (UDC) and squamous cell carcinoma (SCC), as well as between the UDC and lymphoma. (c) The obtained Ktrans-values correlate with the vascular endothelial growth factor (VEGF) expression.

Donaldson et al. (Ref. 327)

2CXM


(o) Analyzing DCE-MRI data and correlating the obtained PK parameters with measurements of hypoxia and VEGF expression in patients with squamous cell carcinoma. (c) Negative correlation between the perfusion and both the VEGF expression and hypoxia.

Lee et al. (Ref. 310)

ETK


(o) Investigating the radiation exposure effect on the DCE-MRI parameters and correlating the radiation dose and the degree of parotid gland atrophy. (c) The correlation between the greater glandular atrophy and a lower baseline ve and vp, as well as a higher post-treatment increase in ve showed sound potentialities of the DCE-MRI for predicting and assessing the radiation injury in the parotid glands.

Adluru et al. (Ref. 293)

TK

Heart; 10 patients

(o) Assessing the accuracy of a PK-based registration of myocardial DCE-MRI for quantifying the MBF. (c) Improved estimation of the regional perfusion flow indexes for 77% out of all data sets.

Pärkkä et al. (Ref. 228)

LM

Heart; 18 patients

(o) Assessing myocardial perfusion reserve (MPR) in healthy humans using DCE-MRI in comparison with PET. (c) Significant correlation between MRI- and PET-based estimation of MPR. (c) Myocardial perfusion can be quantified by PK modeling of the DCE-MRI.


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T I. (Continued). Study

PK model

Tissue of interest


Fritz-Hansen et al. (Ref. 229)

LM

Heart; 10 patients

(o) Evaluating the MPR in humans by using DCE-MRI and 13N-ammonia PET as a reference. (c) High correlation coefficient (0.96) between the mean perfusion values at rest and hyperemia derived from both DCE-MRI and PET data.

Pack and DiBella (Ref. 294)

TK and PM

Heart; 20 subjects

(o) Comparing different quantitative techniques for regional myocardial perfusion quantification. (c) No significant differences between the aggregate Ktrans-values for both the TK and the Patlak plot analysis.

Kerwin et al. (Ref. 315)

ETK

Heart; 45 patients

(o) Characterizing vasa vasorum in the carotid artery in patients with carotid atherosclerosis disease. (c) Ktrans-values estimated for the adventitial carotid region are significantly correlated with serum inflammation markers, such as C-reactive protein levels (r = 0.57; p = 0.01). (c) The adventitial Ktrans-value may be a risk marker.

Kurita et al. (Ref. 316)

PM

Heart; 20 patients

(o) Comparing the regional MPR with the CFR found, respectively, by DCE-MRI-based estimation of myocardial perfusion and with the intracoronary Doppler flow wire. (c) Significant direct correlations between DCE-MRI-based MPR assessments and Doppler-based CFR assessments (correlation coefficients of 0.87 and 0.86 for culprit and nonculprit arteries, respectively).

Ichihara et al. (Ref. 317)

PM

Heart; 10 patients

(o) Quantifying DCE-MRI based MBF estimation and comparing it with that obtained from coronary sinus blood flow. (c) The means of 86 ± 25 and 89 ± 30 ml/min 100 g−1, for MBFs from DCE-MRI-related perfusion estimates and coronary sinus blood flow, respectively.

Radjenovic et al. (Ref. 372)

BM

Breast; 52 patients

(o) Studying the effectiveness of quantitative DCE-MRI parameters for monitoring NAC. (c) The parameters Ktrans and k ep exhibit the highest correlation with the high-grade breast carcinomas, whereas differ significantly in the low-grade ones.

Schmid et al. (Ref. 332)

AATH

Breast; 12 patients

(o) Evaluating the accuracy of a Bayesian P-spline-based semiparametric quantification of CA concentration curves obtained from DCE-MRI. (c) The P-spline model demonstrates a superior fit to the observed concentration curves and captures accurately the time series up-slope.

Furman-Haran et al. (Ref. 261)

TK

Breast; 121 patients

(o) Quantifying microvascular perfusion parameters in various breast lesions and determining whether the parameters vary between benign and malignant lesions. (c) High specificity (96%) and sensitivity (93%) of the Ktrans-values for breast cancer detection. (c) Significant improvements of breast cancer diagnosis using PK models.

Padhani et al. (Ref. 300)

TK

Breast; 25 patients

(o) Correlating early changes in the PK parameters’ distribution with treatment response assessments. (c) Changes in vascular heterogeneity quantified by Ktrans at the end of the second cycle of systemic chemotherapy can predict both clinical and histopathological responses after three to six cycles of the therapy.

Vincensini et al. (Ref. 263)

TK

Breast; 92 patients

(o) Studying the effectiveness of quantitative DCE-MRI parameters to characterize malignant breast lesions. (c) Excellent classification sensitivity and specificity of the k ep-parameter. (c) Monitoring the k ep-value may be used to discriminate between lesions that respond well or poorly to therapy at the early treatment stage.

El Khouli et al. (Ref. 267)

ETK

Breast; 95 patients

(o) Comparing the ETK model performance with conventional morphology plus kinetic curve type analysis. (c) The kinetic curve type assessment or PK modeling improve similarly the diagnostic performance.


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PK model

Tissue of interest


Schabel et al. (Ref. 266)

ETK

Breast; 74 patients

(o) Prospective investigation of whether PK parameters could provide diagnostically useful information to distinguish between benign and malignant breast lesions. (c) Higher AUC of 0.915, sensitivity (91%), and specificity (85%) of the Ktrans and k ep based classification with respect to mammography (the sensitivity of 88% and specificity of 68%).

Ah-See et al. (Ref. 265)

TK

Breast; 28 patients

(o) Investigating whether the PK modeling parameters for pre- and post-NAC could predict final clinical and pathological response. (c) According to the ROC analysis, the parameter Ktrans is the best pathological nonresponse predictor (the AUC of 0.93, sensitivity of 94%, and specificity of 82%). (c) Correctly identified 94% of nonresponders and 73% of responders, being comparable to the change of the MRI-derived tumor size that failed to predict the pathological response.

Fusco et al. (Ref. 7)

ETK, BM, and AATH

Breast; 4 patients

(o) Analyzing the performance of different DP and compartmental PK models. (o) Comparing TK and BM on real breast DCE-MRI data. (c) The AATH achieved better fit than TK and BM with respect to three goodness-of-fit metrics: the residual sum of squares, the Bayesian information criterion, and Akaike information criterion (AIC).

Naish et al. (Ref. 257)

TK, ETK, and AATH

Lung; 6 patients

(o) Comparing the performance of the three PK models and a model-free analysis in distinguishing between malignant and nonmalignant lung tissues. (c) The AATH gives the best description of the lung tumor data with respect to the AIC.

de Senneville et al. (Ref. 9)

PM

Kidney; 20 patients

(o) Evaluating the effect of DCE-MRI motion correction on the estimated GFR. (c) Significant uncertainty reduction on the computed GFR for native, but not the transplanted kidneys.

Sourbron et al. (Ref. 190)

Sourbron model (Ref. 190)

Kidney; 15 volunteers

(o) Measuring GFR with the gadobenate dimeglumine (Gd-BOPTA) CA using a Sourbron mode—the two-compartment PK model with bolus dispersion and tubular outflow. (c) About 40%-underestimation of GFR (arguably, due to low albumin binding of the Gd-BOPTA , which leads to reduced relaxivity in the tubular system and incomplete glomerular filtration).

Anderlik et al. (Ref. 373)

Sourbron model (Ref. 190)

Kidney; 11 volunteers

(o) Quantitative assessment of kidney function using DCE-MRI. (c) Promising estimates of the GFR.

Hahn et al. (Ref. 290)

ETK

Kidney; 56 patients

(o) Investigating DCE-MRI as a pharmacodynamic biomarker of a Sorafenib antiangiogenic agent with renal cancer activity. (c) The derived Ktrans and IAUC90 are pharmacodynamic biomarkers of Sorafenib in metastatic renal cancer. (c) The high baseline Ktrans and vp may act as a prognostic or predictive biomarker, which is beneficial to Sorafenib.

Buckley et al. (Ref. 334)

AATH

Prostate; 22 patients

(o) Prospective evaluation of vascular characteristics of prostate cancer using DCE-MRI and the DP model. (c) Increased plasma flow and EES-space fraction within prostate cancer tissue, when compared to its PZ. (c) Similar permeability and plasma volume fraction estimates in both regions of interest.

Kiessling et al. (Ref. 247)

BM


(o) Evaluating the accuracy of discrimination of prostate cancers from the peripheral gland with descriptive and PK parameters. (c) Potentialities of the PK parameters (ABrix and k ep) in discriminating the prostate cancers from the peripheral prostate tissue. (c) The nonparametric indexes of early signal enhancement after CA injection, such as the AUC and up-slopes at 26, 39, 52, and 65 s, have higher sensitivity and specificity, although at the start of the signal intensity increase, To, these indexes do not discriminate the carcinomas from the glandular tissue.


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PK model

Tissue of interest


Kelm et al. (Ref. 12)

BM


(o) Assessing the efficacy of spatial prior knowledge for estimating PK parameter maps from DCE-MRI. (c) The spatial prior knowledge reduces both the bias and variance of the estimated k ep-parameter maps.

van Dorsten et al. (Ref. 374)

LM


(o) Differentiating prostate carcinoma from healthy PZ and CZ using DCE-MRI and 2D 1H MRSI. (c) Excellent potentialities of the combined high-resolution spatio-vascular information from the dynamic MRI and metabolic information from the MRSI for improving the localization and characterization of the prostate cancer in a clinical setting.

Jackson et al. (Ref. 271)

TK


(o) Assessing the efficacy of spatial prior knowledge for estimating PK parameter maps from DCE-MRI. (c) Pixel-wise parametric maps for Ktrans, ve, and k ep parameters reveal significant differences between benign and malignant tumors in the PZ, while the ROC analysis shows that the PK parameters are only “fair discriminators” between cancer and benign gland. (c) The radiologist interpretation shows similar specificity (85% vs 81%; p = 0.593) and higher sensitivity (50% vs 21%; p = 0.006) of DCE-MRI with respect to T2-weighted MRI for cancer localization. (c) Guiding the radiotherapy beam with DCE-MRI and PK modeling can improve the outcome of radiotherapy.

Ocak et al. (Ref. 270)

TK


(o) Determining PK parameters, being useful for prostate cancer diagnostics in patients with biopsy-proven lesions. (c) Four PK parameters: Ktrans, k ep, ve, and the AUC of the gadolinium concentration curve were determined and compared for cancer, inflammation, and healthy peripheral. (c) Improved prostate cancer specificity of the conventional T2-weighted MRI for the Ktrans and k ep parameters.

Langer et al. (Refs. 273 and 276)

TK

Prostate; 25 in Ref. 273 (o) Investigating relationships between the multimodal MRI [diffusion tensor imaging and 24 in Ref. 276 (DTI), T2-weighted, DCE-MRI] measurements and the underlying composition of patients normal and malignant prostate tissues. (c) Significant differences between cancer and normal PZ tissues for the MRI-derived apparent diffusion coefficient (ADC), T2, Ktrans, and ve parameters and the percentage areas of all tissue components except stroma.

Vos et al. (Ref. 275)

TK


(o) Developing a multimodality (T2-weighted MRI and DCE-MRI) CAD system with a SVM classifier to diagnose prostate cancer in the PZ. (c) Using T2-weighted sequence significantly improves the diagnosis performance obtained with only DCE-MRI PK parameters, namely, the ROC’s AUC increases from 0.83 (0.75–0.92) to 0.89 (0.81–0.95).

Kershaw et al. (Ref. 333)

AATH


(o) Evaluating microvascular and relaxation parameters of prostate and nearby muscle in patients with benign prostatic hyperplasia and examining measurement reproducibility. (c) Significantly different bootstrap analysis of the PK parameters (F p , Tc, Ktrans, and PS) in the prostate’s CZ, comparing with the PZ.


TK


(o) Investigating the feasibility of an automated CAD system with a linear discriminant analysis (LDA) classifier to detect prostate’s cancer-suspicious regions. (c) The CAD system detects 74% of all tumors at a FP level of 5. (c) The system’s sensitivity of 88% for the high-grade tumors at the FP level of 5.

Li et al. (Ref. 281)

TK


(o) Investigating and comparing the diagnostic performance of DTI, DCE-MRI, or their combination in detecting prostate’s cancerous areas in the PZ. (c) The combination of DTI and DCE-MRI has better diagnosis in detecting prostate cancer than either technique alone.


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PK model

Tissue of interest



TK


Chikui et al. (Ref. 301)

TK

Oral cancer; 29 patients (o) Evaluating usefulness of a PK analysis to monitor the oral cancer response to chemoradiotherapy (CRT). (c) Statistical analysis reveals that the ve-increase strongly suggests a good tumor response to the CRT. (c) Significantly larger Ktrans-changes for responders, than for nonresponders.

de Lussanet et al. (Ref. 284)

ETK

Rectal cancer; 17 patients

de Lussanet et al. (Ref. 296)

TK

Thigh; 15 male rabbits (o) Assessing the use of MRI (DCE-MRI and MRA) to evaluate the muscle perfusion recovery and the growth of collateral arteries in a rabbit femoral artery ligation model. (c) Combined DCE-MRI and MRA data allow for noninvasive serial monitoring of changes in the muscle blood flow and growth of submillimeter sized collateral arteries.

Donaldson et al. (Ref. 127)

2CXM and TK

Cervix; 30 patients

Zahra et al. (Ref. 304)

TK

Cervix; 13 patients (o) Evaluate DCE-MRI-based prediction of the response to cervix cancer (each with three scans) radiotherapy. (c) In spite of statistically significant correlation between the percentage tumor regression and both the nonparametric indexes (the peak time, slope, maximum slope, and contrast enhancement ratio) and PK parameters, such as Ktrans (p = 0.043) and k ep (p = 0.022), for the pretreatment DCE-MRI, the same characteristics for the second and third scans show no correlation.

Andersen et al. (Ref. 232)

BM and TK

Cervix; 81 patients

(o) Assessing the prognostic value of the PK parameters derived from prechemoradiotherapy DCE-MRI of cervical cancer patients. (c) According to the prognostic significance of the PK parameters [International Federation of Gynecology and Obstetrics (FIGO) stage and tumor volume], being assessed with the multivariate analysis, the estimated imaging parameters prior to chemoradiotherapy may be used to identify patients at risk of treatment failure.

Akisik et al. (Ref. 302)

TK

Pancreas; 11 patients

(o) Evaluating capabilities of PK modeling of DCE-MRI to predict a pancreatic cancer response to combined chemo and antiangiogenic therapy. (c) Significant reduction of all parameters, such as Ktrans, ve, the peak concentration, up-slope, and AUC at 60 s, after combined therapy. (c) The pretreatment Ktrans-measurement in pancreatic tumors can predict response to antiangiogenic therapy.

Ma et al. (Ref. 185)

BM

Bone perfusion; 165 subjects

(o) Investigating PK modeling of bone perfusion in subjects with varying bone mineral density. (c) Notable reduction of the PK parameter ABrix in osteoporotic subjects compared to the normal ones. (c) Less pronounced reductions in the permeability constant, ABrixk ep, and the elimination one, k el.


(o) Assessing cancer aggressiveness in the PZ with a combination of kinetic parameters, Ktrans and k ep, and model-free parameters wash-in and wash-out slopes. (c) According to the ROC analysis, the 75-percentile of wash-in, Ktrans, and k ep discriminate the best between low-grade and intermediate/high-grade prostate cancer cases.

(o) Evaluating radiation therapy-related microvascular changes in locally advanced rectal cancer using DCE-MRI and histology. (c) Lower intratumoral heterogeneity in Ktrans and vp for primary rectal cancer patients receiving the radiation therapy than for those without the radiation therapy.

(o) Comparisons of 2CXM and TK models on reporting microvascular parameters in patients with cervical cancer. (c) The 2CXM model demonstrated better fit to the data for all patients. (c) Inaccurate PK parameter estimates for TK due to its inherent assumption of negligible plasma MTT.

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vascular density and/or vascular permeability. Nevertheless, the indexes can be reproducible at different sites only if an identical data acquisition protocol is used.346 The parametric techniques fit one of the well-known mathematical PK models to the concentration curves in order to estimate physiologically meaningful parameters, e.g., the EES volume and capillary permeability of a tissue of interest. The parametric PK modeling has the following advantages: (i) estimation of a set of kinetic parameters that have physiological interpretations, (ii) they provide a way for better understanding of the interaction between drugs (i.e., contrast agent) and human tissue, and (iii) the lesser sensitivity of parameter estimates to noise, image settings, and data acquisition protocols.17 However, both the data acquisition and analysis become more complicated in comparison with the nonparametric techniques. The complexity arises from the required conversion of MR signal intensities into CA concentrations involving the measurements of tissue relaxation time (T1), native relaxation time (T10), and the tissue AIF. Based on their mathematical foundations and hypothesis for describing the kinetics of blood flow and capillary-tissue CA exchange, spatially distributed PK models account much more accurately for the underlying physiology and often result in a better fit to the data.127 However, these techniques require more investigations and evaluations as other studies showed that compartment and distributed models result in the same tissue curve331 or distributed models even produce results that are different than expected.1 The PK models are typically refined to more closely reflect physiological processes by including additional parameters, e.g., water exchange and CA diffusion. However, the refinement mostly complicates DCE-MRI analysis, and its usefulness requires additional investigation.200,326,347–349 It is worth mentioning that the blood flow can also be determined using another approach that is based on the Kenneth L Zierler’s central volume principle.350 Zierler’s technique avoids the use of kinetic models and is based on the deconvolution theory. Namely, the mean blood perfusion is estimated from a residue function that is derived from the deconvolution of the tissue response with a measured AIF. Deconvolution analysis has been used in many perfusion studies, such as brain351,352 and cardiac applications.353–355 However, it can only determine the blood flow, but not other perfusion parameters, such as the vascular volume or the capillary permeability-surface area product.356 Accurate DCE-MRI analysis is faced with multiple challenges. One of the challenges in gadolinium-based DCE-MRI analysis is the risk of nephrogenic systemic fibrosis, which is increased in patients with renal dysfunction.357 Also, the choice of an appropriate CA dose for the quantitative DCEMRI analysis is a challenging problem: the high dose increases the signal enhancement in the tissue, but may cause overestimation of the PK parameters due to saturation or nonlinearity of the MRI signal190 or their underestimation due to transendothelial water exchange effects.358 Investigations of alternative CA types, such as superparamagnetic iron oxide (SPIO) and ultra SPIO (USPIO) particles remain an open research area. However, it should be pointed out that Medical Physics, Vol. 41, No. 12, December 2014

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those CA agents are mostly intravascular agents and their use probably will not enable measurement of vessel permeability. Temporal resolution is another challenge for accurate DCEMRI data analysis. Compartmental models (other than the 2CXM model) are usually used to analyze data sets with long imaging intervals (i.e., low temporal resolution), where the CA movement appears instantaneous and the capillary-tissue components could be approximated as well-mixed compartments. On the other hand, spatially distributed PK models are relevant for DCE-MRI data with short imaging intervals (i.e., higher temporal resolution) as they do not assume instantaneous CA movement in the capillary, but rather employ the effect of the capillary transit time Tc .330 A simulation study by Henderson et al.359 showed that a temporal resolution of 16 s or less is required to ensure that the estimation error in Ktrans and kep be less than 10% of their true values. A similar study by Schabel158 found that stable estimates of Ktrans and k ep parameters can be obtained using sampling rates of 12 s. Recently, Larsson et al.360 investigated the effect of variations in temporal resolution (between 2.1 and 68 s) on the estimations of DCE-MRI-derived PK parameters in patients with high-grade gliomas. Their study concluded that for temporal resolution greater than 20 s, there is a significant overestimation of Ktrans and under estimation of ve. On the other hand, a study by Kershaw and Cheng128 concluded that a temporal resolution of 1.5 s is required if all parameters of the AATH model are to be measured with minimal bias. Therefore, higher temporal resolution is desirable, even for compartmental models, to allow for more accurate modeling and thus more accurate DCE-MRI parameter estimation, particularly for PK models with large numbers of parameters.128 However, increasing temporal resolution greatly affects the spatial resolution and may not be obtainable due to hardware limitations. Due to recent technological progress in rapid MR acquisition, it is expected that DCEMRI data with sufficient spatial and temporal resolutions will be obtainable in the near future. Comparison of different published results is another challenging problem, in part, due to the lack of standardized DCEMRI acquisition protocols; difficulties of achieving adequate spatial and temporal DCE-MRI resolutions simultaneously; various analytical postprocessing, which sometimes may not describe adequately the relevant physiology; different types of diseases, subjects’ numbers, and treatment scenarios. Recent trends to increase the reliability and accuracy of DCE-MRI-derived perfusion parameters include (i) objective criteria for choosing a suitable PK model among the existing ones to fit a given application; (ii) a standard consensus for a DCE-MRI data acquisition protocol in each specific application; (iii) better data normalization techniques that account for different physiological and scanning factors, e.g., patient weight/size and scanner type/acquisition parameters, respectively; (iv) since the analysis techniques describe a direct relation between the MRI signal and the underlying model, a new trend is to apply motion correction techniques before analyzing DCE-MRI data10 to remove noise and motion effects in order to assure that the change in the signal is related to the CA transit in the tissue; (v) including spatial information into voxel-wise estimation of PK parameters is another trend in DCE-MRI data

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analysis,12,198,199,361,362 which has shown to be very informative in some applications, such as the assessment of tumors’ heterogeneity;53,348,363–365 (vi) since nonparametric approaches are simple and fast, a new trend is to develop complete noninvasive image-based diagnostic systems for early diagnosis of different diseases, e.g., lung and prostate cancer; (vii) fusion of parametric and nonparametric approaches is one more new trend toward more robust diagnostic decisions in each application.3,92,103,248,254,268,278,282,295,304,366–369 The high correlation between the estimated physiological (parametric) and nonparametric indexes92,254,268,282,367–369 suggests the nonparametric DCE-MRI analysis can help in avoiding the complexity and limitations of the parametric methods for evaluation of physiological conditions; (viii) distributed-parameter models are more realistic and make fewer assumptions about microcirculation, therefore they are the main focus of research in recent years and their usefulness requires additional investigation; (ix) in order to account for scanner hardware drift and physiological fluctuations, another trend to increase the reliability of DCE-MRI is to perform reproducibility and repeatability test, especially for longitudinal studies.145,147,193,366,370,371

a)Author

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