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1.  Feasibility of Using Limited-Population-Based Arterial Input Function for Pharmacokinetic Modeling of Osteosarcoma Dynamic Contrast-Enhanced MRI Data 
For clinical dynamic contrast-enhanced (DCE) MRI studies, it is often not possible to obtain reliable arterial input function (AIF) in each measurement. Thus, it is important to find a representative AIF for pharmacokinetic modeling of DCE-MRI data when individual AIF (Ind-AIF) measurements are not available. A total of 16 patients with osteosarcomas in the lower extremity (knee region) underwent multislice DCE-MRI. Reliable Ind-AIFs were obtained in five patients with a contrast injection rate of 2 cc/s and another five patients with a 1 cc/s injection rate. Average AIF (Avg-AIF) for each injection rate was constructed from the corresponding five Ind-AIFs. For each injection rate there are no statistically significant differences between pharmacokinetic parameters of the five patients derived with Ind-AIFs and Avg-AIF. There are no statistically significant changes in pharmacokinetic parameters of the 16 patients when the two Avg-AIFs were applied in kinetic modeling. The results suggest that it is feasible, as well as practical, to use a limited-population-based Avg-AIF for pharmacokinetic modeling of osteosarcoma DCE-MRI data. Further validation with a larger population and multiple regions is desirable.
doi:10.1002/mrm.21432
PMCID: PMC2782487  PMID: 18429032
dynamic contrast-enhanced MRI; arterial input function; osteosarcoma; Ktrans; pharmakinetic modeling
2.  The Impact of Arterial Input Function Determination Variations on Prostate Dynamic Contrast-Enhanced Magnetic Resonance Imaging Pharmacokinetic Modeling: A Multicenter Data Analysis Challenge 
Dynamic contrast-enhanced MRI (DCE-MRI) has been widely used in tumor detection and therapy response evaluation. Pharmacokinetic analysis of DCE-MRI time-course data allows estimation of quantitative imaging biomarkers such as Ktrans(rate constant for plasma/interstitium contrast reagent (CR) transfer) and ve (extravascular and extracellular volume fraction). However, the use of quantitative DCE-MRI in clinical prostate imaging islimited, with uncertainty in arterial input function (AIF, i.e., the time rate of change of the concentration of CR in the blood plasma) determination being one of the primary reasons. In this multicenter data analysis challenge to assess the effects of variations in AIF quantification on estimation of DCE-MRI parameters, prostate DCE-MRI data acquired at one center from 11 prostate cancer patients were shared among nine centers. Each center used its site-specific method to determine the individual AIF from each data set and submitted the results to the managing center. Along with a literature population averaged AIF, these AIFs and their reference-tissue-adjusted variants were used by the managing center to perform pharmacokinetic analysis of the DCE-MRI data sets using the Tofts model (TM). All other variables including tumor region of interest (ROI) definition and pre-contrast T1 were kept the same to evaluate parameter variations caused by AIF variations only. Considerable pharmacokinetic parameter variations were observed with the within-subject coefficient of variation (wCV) of Ktrans obtained with unadjusted AIFs as high as 0.74. AIF-caused variations were larger in Ktrans than ve and both were reduced when reference-tissue-adjusted AIFs were used. The parameter variations were largely systematic, resulting in nearly unchanged parametric map patterns. The CR intravasation rate constant, kep (= Ktrans/ve), was less sensitive to AIF variation than Ktrans (wCV for unadjusted AIFs: 0.45 for kep vs. 0.74 for Ktrans), suggesting that it might be a more robust imaging biomarker of prostate microvasculature than Ktrans.
doi:10.18383/j.tom.2015.00184
PMCID: PMC4869732  PMID: 27200418
3.  Assessment of repeatability and treatment response in early phase clinical trials using DCE-MRI: comparison of parametric analysis using MR- and CT-derived arterial input functions 
European Radiology  2015;26:1991-1998.
Objectives
Pharmacokinetic (PK) modelling of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data requires a reliable measure of the arterial input function (AIF) to robustly characterise tumour vascular properties. This study compared repeatability and treatment-response effects of DCE-MRI-derived PK parameters using a population-averaged AIF and three patient-specific AIFs derived from pre-bolus MRI, DCE-MRI and dynamic contrast computed tomography (DC-CT) data.
Methods
The four approaches were compared in 13 patients with abdominal metastases. Baseline repeatability [Bland-Altman statistics; coefficient of variation (CoV)], cohort percentage change and p value (paired t test) and number of patients with significant DCE-MRI parameter change post-treatment (limits of agreement) were assessed.
Results
Individual AIFs were obtained for all 13 patients with pre-bolus MRI and DC-CT-derived AIFs, but only 10/13 patients had AIFs measurable from DCE-MRI data. The best CoV (7.5 %) of the transfer coefficient between blood plasma and extravascular extracellular space (Ktrans) was obtained using a population-averaged AIF. All four AIF methods detected significant treatment changes: the most significant was the DC-CT-derived AIF. The population-based AIF was similar to or better than the pre-bolus and DCE-MRI-derived AIFs.
Conclusions
A population-based AIF is the recommended approach for measuring cohort and individual effects since it has the best repeatability and none of the PK parameters derived using measured AIFs demonstrated an improvement in treatment sensitivity.
Key Points
• Pharmacokinetic modelling of DCE-MRI data requires a reliable measure of AIF.
• Individual MRI-DCE-derived AIFs cannot reliably be extracted from patients.
• All four AIF methods detected significant Ktranschanges after treatment.
• A population-based AIF can be recommended for measuring cohort treatment responses in trials.
doi:10.1007/s00330-015-4012-9
PMCID: PMC4902841  PMID: 26385804
Magnetic resonance imaging; Computed tomography; Drug evaluation; Clinical trials, phase 1; Comparative study
4.  A Comparison of Two Methods for Estimating DCE-MRI Parameters via Individual and Cohort Based AIFs in Prostate Cancer: A Step Towards Practical Implementation 
Magnetic resonance imaging  2014;32(4):321-329.
Multi-parametric Magnetic Resonance Imaging, and specifically Dynamic Contrast Enhanced (DCE) MRI, play increasingly important roles in detection and staging of prostate cancer (PCa). One of the actively investigated approaches to DCE MRI analysis involves pharmacokinetic (PK) modeling to extract quantitative parameters that may be related to microvascular properties of the tissue. It is well-known that the prescribed arterial blood plasma concentration (or Arterial Input Function, AIF) input can have significant effects on the parameters estimated by PK modeling. The purpose of our study was to investigate such effects in DCE MRI data acquired in a typical clinical PCa setting. First, we investigated how the choice of a semi-automated or fully automated image-based individualized AIF (iAIF) estimation method affects the PK parameter values; and second, we examined the use of method-specific averaged AIF (cohort-based, or cAIF) as a means to attenuate the differences between the two AIF estimation methods.
Two methods for automated image-based estimation of individualized (patient-specific) AIFs, one of which was previously validated for brain and the other for breast MRI, were compared. cAIFs were constructed by averaging the iAIF curves over the individual patients for each of the two methods. Pharmacokinetic analysis using the Generalized kinetic model and each of the four AIF choices (iAIF and cAIF for each of the two image-based AIF estimation approaches) was applied to derive the volume transfer rate (Ktrans) and extravascular extracellular volume fraction (ve) in the areas of prostate tumor. Differences between the parameters obtained using iAIF and cAIF for a given method (intra-method comparison) as well as inter-method differences were quantified.
The study utilized DCE MRI data collected in 17 patients with histologically confirmed PCa. Comparison at the level of the tumor region of interest (ROI) showed that the two automated methods resulted in significantly different (p<0.05) mean estimates of ve, but not of Ktrans. Comparing cAIF, different estimates for both ve, and Ktrans were obtained. Intra-method comparison between the iAIF- and cAIF-driven analyses showed the lack of effect on ve, while Ktrans values were significantly different for one of the methods.
Our results indicate that the choice of the algorithm used for automated image-based AIF determination can lead to significant differences in the values of the estimated PK parameters. Ktrans estimates are more sensitive to the choice between cAIF/iAIF as compared to ve, leading to potentially significant differences depending on the AIF method. These observations may have practical consequences in evaluating the PK analysis results obtained in a multi-site setting.
doi:10.1016/j.mri.2014.01.004
PMCID: PMC3965600  PMID: 24560287
prostate cancer; DCE-MRI; Arterial Input Function; pharmacokinetic modeling; quantitative imaging
5.  A Model-Constrained Monte Carlo Method for Blind Arterial Input Function Estimation in Dynamic Contrast-Enhanced MRI: II) In Vivo Results 
Physics in medicine and biology  2010;55(16):4807-4823.
Accurate quantification of pharmacokinetic model parameters in tracer kinetic imaging experiments requires correspondingly accurate determination of the arterial input function (AIF). Despite significant effort expended on methods of directly measuring patient-specific AIFs in modalities as diverse as dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), dynamic positron emission tomography (PET), and perfusion computed tomography (CT), fundamental and technical difficulties have made consistent and reliable achievement of that goal elusive. Here, we validate a new algorithm for AIF determination, the Monte Carlo Blind Estimation (MCBE) method (which is described in detail and characterized by extensive simulations in a companion paper), by comparing AIFs measured in DCE-MRI studies of eight brain tumor patients with results of blind estimation. Blind AIFs calculated with the MCBE method using a pool of concentration-time curves from a region of normal brain tissue were found to be quite similar to the measured AIFs, with statistically significant decreases in fit residuals observed in six of eight patients. Biases between the blind and measured pharmacokinetic parameters were the dominant source of error. Averaged over all eight patients, the mean biases were +7% in Ktrans, 0% in kep, −11% in vp, and +10% in ve. Corresponding uncertainties (median absolute deviation from best fit line) were 0.0043 min−1 in Ktrans, 0.0491 min−1 in kep, 0.29% in vp, and 0.45% in ve. Use of a published population-averaged AIF resulted in larger mean biases in three of the four parameters (−23% in Ktrans, −22% in kep, −63% in vp), with the bias in ve unchanged, and led to larger uncertainties in all four parameters (0.0083 min−1 in Ktrans, 0.1038 min−1 in kep, 0.31% in vp, and 0.95% in ve). When blind AIFs were calculated from a region of tumor tissue, statistically significant decreases in fit residuals were observed in all eight patients despite larger deviations of these blind AIFs from the measured AIFs. The observed decrease in root-mean-square fit residuals between the normal brain and tumor tissue blind AIFs suggests that the local blood supply in tumors is measurably different from that in normal brain tissue and that the proposed method is able to discriminate between the two. We have shown the feasibility of applying the MCBE algorithm to DCE-MRI data acquired in brain, finding generally good agreement with measured AIFs and decreased biases and uncertainties relative to use of a population-averaged AIF. These results demonstrate that the MCBE algorithm is a useful alternative to direct AIF measurement in cases where acquisition of high-quality arterial input function data is difficult or impossible.
doi:10.1088/0031-9155/55/16/012
PMCID: PMC3533373  PMID: 20679695
Magnetic resonance imaging; dynamic contrast-enhanced; DCE-MRI; arterial input function
6.  A Model-Constrained Monte Carlo Method for Blind Arterial Input Function Estimation in Dynamic Contrast-Enhanced MRI: I) Simulations 
Physics in medicine and biology  2010;55(16):4783-4806.
Widespread adoption of quantitative pharmacokinetic modeling methods in conjunction with dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has led to increased recognition of the importance of obtaining accurate patient-specific arterial input function (AIF) measurements. Ideally, DCE-MRI studies use an AIF directly measured in an artery local to the tissue of interest, along with measured tissue concentration curves, to quantitatively determine pharmacokinetic parameters. However, the numerous technical and practical difficulties associated with AIF measurement have made the use of population-averaged AIF data a popular, if suboptimal, alternative to AIF measurement. In this work, we present and characterize a new algorithm for determining the AIF solely from the measured tissue concentration curves. This Monte Carlo Blind Estimation (MCBE) algorithm estimates the AIF from subsets of D concentration-time curves drawn from a larger pool of M candidate curves via nonlinear optimization, doing so for multiple (Q) subsets and statistically averaging these repeated estimates. The MCBE algorithm can be viewed as a generalization of previously published methods that employ clustering of concentration-time curves and only estimate the AIF once. Extensive computer simulations were performed over physiologically- and experimentally-realistic ranges of imaging and tissue parameters, and the impact of choosing different values of D and Q was investigated. We found the algorithm to be robust, computationally-efficient, and capable of accurately estimating the AIF even for relatively high noise levels, long sampling intervals, and low diversity of tissue curves. With the incorporation of boostrapping initialization, we further demonstrated the ability to blindly estimate AIFs that deviate substantially in shape from the population-averaged initial guess. Pharmacokinetic parameter estimates for Ktrans, kep, vp, and ve all showed relative biases and uncertainties of less than 10% for measurements having a temporal sampling rate of 4 seconds and a concentration measurement noise level of σ = 0.04 mM. A companion paper discusses the application of the MCBE algorithm to DCE-MRI data acquired in eight patients with malignant brain tumors.
doi:10.1088/0031-9155/55/16/011
PMCID: PMC3533367  PMID: 20679691
Magnetic resonance imaging; dynamic contrast-enhanced; DCE-MRI; arterial input function
7.  A Novel AIF Tracking Method and a Comparison of DCE-MRI Parameters Using Individual and Population Based AIFs in Human Breast Cancer 
Physics in medicine and biology  2011;56(17):5753-5769.
Quantitative analysis of dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) data requires the accurate determination of the arterial input function (AIF). A novel method for obtaining the AIF is presented here and pharmacokinetic parameters derived from individual and population based AIFs are then compared. A Philips 3.0 T Achieva MR scanner was used to obtain 20 DCE-MRI data sets from ten breast cancer patients prior to and after one cycle of chemotherapy. Using a semi-automated method to estimate the AIF from the axillary artery, we obtain the AIF for each patient, AIFind, and compute a population averaged AIF, AIFpop. The extended standard model is used to estimate the physiological parameters using the two types of AIFs. The mean concordance correlation coefficient (CCC) for the AIFs segmented manually and by the proposed AIF tracking approach is 0.96, indicating accurate and automatic tracking of an AIF in DCE-MRI data of the breast is possible. Regarding the kinetic parameters, the CCC values for Ktrans, vp, and ve as estimated by AIFind and AIFpop are 0.65, 0.74, and 0.31, respectively, based on region of interest analysis. The average CCC values for the voxel-by-voxel analysis are 0.76, 0.84, and 0.68 for Ktrans, vp, and ve, respectively. This work indicates that Ktrans and vp show a good agreement between AIFpop and AIFind while there is a weak agreement on ve.
doi:10.1088/0031-9155/56/17/018
PMCID: PMC3176673  PMID: 21841212
dynamic contrast enhanced MRI; arterial input function; pharmacokinetic modeling; breast cancer
8.  Comparison between population average and experimentally measured Arterial Input Function in predicting biopsy results in prostate cancer 
Academic radiology  2010;17(4):520-525.
Rationale and objective
To test whether individually measured Arterial Input Function (AIF) provides more accurate prostate cancer diagnosis then population average AIF when DCE MRI data are acquired with limited temporal resolution.
Material and methods
26 patients with a high clinical suspicion for prostate caner and no prior treatment underwent Dynamic Contrast Enhanced (DCE) MRI examination at 3.0 T prior to biopsy. DCE MRI data were fitted to a pharmacokinetic model using three forms of AIF: an individually measured, a local population average, and a literature double exponential population average. Receiver Operating Characteristic (ROC) analysis was used to correlate MRI with the biopsy results. Goodness of fit (χ2) for the three AIFs was compared using non-parametric Mann-Whitney test.
Results
Average Ktrans values were significantly higher in tumour than in normal peripheral zone for all three AIFs. The individually measured and the local population average AIFs had the highest sensitivity (76%), while the double exponential AIF had the highest specificity (82%). The areas under the ROC curves were not significantly different between any of the AIFs (0.81, 0.76, and 0.81 for the individually measured, local population average and double exponential AIFs respectively). χ2 was not significantly different for the 3 AIFs, however, it was significantly higher in enhancing than in non-enhancing regions for all 3 AIFs.
Conclusions
These results suggest that, when DCE MRI data are acquired with limited temporal resolution, experimentally measured individual AIF is not significantly better than population average AIF in predicting the biopsy results in prostate cancer.
doi:10.1016/j.acra.2009.11.006
PMCID: PMC2891013  PMID: 20074982 CAMSID: cams1175
dynamic contrast-enhanced MRI; prostate cancer; arterial input function; biopsy
9.  Effect of T2* correction on contrast kinetic model analysis using a reference tissue arterial input function at 7T 
Magma (New York, N.Y.)  2015;28(6):555-563.
Object
To investigate the effect of T2* correction on estimation of kinetic parameters from T1-weighted dynamic contrast enhanced (DCE) MRI data when a reference-tissue arterial input function (AIF) is used.
Materials and Methods
DCE-MRI data were acquired from 7 mice with 4T1 mouse mammary tumors using a double gradient echo sequence at 7T. The AIF was estimated from a region of interest in the muscle. The extended Tofts model was used to estimate pharmacokinetic parameters in the enhancing part of the tumor, with and without T2* correction of the lesion and AIF. The parameters estimated with T2* correction of both the AIF and lesion time-intensity curve were assumed to be the reference standard.
Results
For the whole population, there was significant difference (p<0.05) in transfer constant (Ktrans) between T2* corrected and not corrected methods, but not in interstitial volume fraction (ve). Individually, no significant differences were found in Ktrans and ve of four and six tumors, respectively, between the T2* corrected and not corrected methods. In contrast, Ktrans was significantly underestimated, if the T2* correction was not used, in other tumors of which median Ktrans was larger than 0.4 min−1.
Conclusion
T2* effect on tumors with high Ktrans may not be negligible in kinetic model analysis, even if AIF is estimated from reference tissue where the concentration of contrast agent is relatively low.
doi:10.1007/s10334-015-0496-1
PMCID: PMC4657861  PMID: 26239630
DCE-MRI; contrast kinetic model; T2* effect; reference tissue; arterial input function
10.  Demonstration of the reproducibility of free-breathing diffusion-weighted MRI and dynamic contrast enhanced MRI in children with solid tumours: a pilot study 
European Radiology  2015;25(9):2641-2650.
Objectives
The objectives are to examine the reproducibility of functional MR imaging in children with solid tumours using quantitative parameters derived from diffusion-weighted (DW-) and dynamic contrast enhanced (DCE-) MRI.
Methods
Patients under 16-years-of age with confirmed diagnosis of solid tumours (n = 17) underwent free-breathing DW-MRI and DCE-MRI on a 1.5 T system, repeated 24 hours later. DW-MRI (6 b-values, 0-1000 sec/mm2) enabled monoexponential apparent diffusion coefficient estimation using all (ADC0-1000) and only ≥100 sec/mm2 (ADC100-1000) b-values. DCE-MRI was used to derive the transfer constant (Ktrans), the efflux constant (kep), the extracellular extravascular volume (ve), and the plasma fraction (vp), using a study cohort arterial input function (AIF) and the extended Tofts model. Initial area under the gadolinium enhancement curve and pre-contrast T1 were also calculated. Percentage coefficients of variation (CV) of all parameters were calculated.
Results
The most reproducible cohort parameters were ADC100-1000 (CV = 3.26 %), pre-contrast T1 (CV = 6.21 %), and Ktrans (CV = 15.23 %). The ADC100-1000 was more reproducible than ADC0-1000, especially extracranially (CV = 2.40 % vs. 2.78 %). The AIF (n = 9) derived from this paediatric population exhibited sharper and earlier first-pass and recirculation peaks compared with the literature’s adult population average.
Conclusions
Free-breathing functional imaging protocols including DW-MRI and DCE-MRI are well-tolerated in children aged 6 - 15 with good to moderate measurement reproducibility.
Key Points
• Diffusion MRI protocol is feasible and well-tolerated in a paediatric oncology population.
• DCE-MRI for pharmacokinetic evaluation is feasible and well tolerated in a paediatric oncology population.
• Paediatric arterial input function (AIF) shows systematic differences from the adult population-average AIF.
• Variation of quantitative parameters from paired functional MRI measurements were within 20 %.
doi:10.1007/s00330-015-3666-7
PMCID: PMC4529450  PMID: 25773937
Reproducibility of results; Diffusion magnetic resonance imaging; Paediatrics; Medical oncology; Functional magnetic resonance imaging
11.  Quantitative pharmacokinetic analysis of prostate cancer DCE-MRI at 3T: Comparison of two arterial input functions on cancer detection with digitized whole mount histopathological validation 
Magnetic resonance imaging  2015;33(7):886-894.
Accurate pharmacokinetic (PK) modeling of Dynamic Contrast Enhanced MRI (DCE-MRI) in prostate cancer requires knowledge of the concentration time course of the contrast agent in the feeding vasculature, the so-called arterial input function (AIF). The purpose of this study was to compare AIF choice in differentiating peripheral zone prostate cancer (PCa) from non-neoplastic prostatic tissue (NNPT), using PK analysis of high temporal resolution prostate DCE-MRI data and whole-mount pathology (WMP) validation.
This prospective study was performed in 30 patients who underwent multiparametric endorectal prostate MRI at 3.0T and WMP validation. PCa foci were annotated on WMP slides and MR images using 3D Slicer. Foci ≥0.5cm3 were contoured as tumor regions of interest (TROIs) on subtraction DCE (early-arterial - pre-contrast) images. PK analyses of TROI and NNPT data were performed using automatic AIF (aAIF) and model AIF (mAIF) methods. A paired t-test compared mean and 90th percentile (p90) PK parameters obtained with the two AIF approaches. ROC analysis determined diagnostic accuracy (DA) of PK parameters. Logistic regression determined correlation between PK parameters and histopathology.
Mean TROI and NNPT PK parameters were higher using aAIF vs. mAIF (p<0.05). There was no significant difference in DA between AIF methods: highest for p90 Ktrans (aAIF differences in the area under the ROC curve (Az) =0.827; mAIF Az=0.93). Tumor cell density correlated with aAIF Ktrans (p=0.03).
Our results indicate that DCE-MRI using both AIF methods is excellent in discriminating PCa from NNPT. If quantitative DCE-MRI is to be used as a biomarker in PCa, the same AIF method should be used consistently throughout the study.
doi:10.1016/j.mri.2015.02.008
PMCID: PMC4465997  PMID: 25683515
prostate cancer; dynamic contrast enhancement; arterial input function; pharmacokinetic analysis
12.  Reproducibility Assessment of a Multiple Reference Tissue Method for Quantitative DCE-MRI Analysis 
Bone metastases of 16 prostate cancer patients were scanned twice one week apart by DCE-MRI at 2 seconds resolution using a 2D gradient-echo pulse sequence. With a multiple reference tissue method (MRTM), the local tissue Arterial Input Function (AIF) was estimated using the contrast agent enhancement data from tumor sub-regions and muscle. The 32 individual AIFs estimated by the MRTM, which had considerable intra-patient and inter-patient variability, were similar to directly measured AIFs in the literature and using the MRTM AIFs in a pharmacokinetic model to derive estimated individual cardiac outputs provided physiologically reasonable results. The MRTM individual AIFs gave better fits with smaller sum of squared errors and equally reproducible estimate of kinetic parameters compared to a previous reported population AIF measured from remote arteries. The individual MRTM AIFs were also used to obtain a mean local tissue AIF for the unique population of this study which further improved the reproducibility of the estimated kinetic parameters. The MRTM can be applied to DCE-MRI studies of bone metastases from prostate cancers to provide an AIF from which reproducible quantitative DCE-MRI parameters can be derived, thus help standardize DCE-MRI studies in cancer patients.
doi:10.1002/mrm.21912
PMCID: PMC2758034  PMID: 19185002
dynamic contrast enhanced (DCE)-MRI; arterial input function; reference tissue; tracer kinetic modeling; reproducibility
13.  A Reference Agent Model for DCE MRI can be used to quantify the relative vascular permeability of two MRI contrast agents 
Magnetic resonance imaging  2013;31(6):900-910.
Dynamic Contrast Enhancement (DCE) MRI has been used to measure the kinetic transport constant, Ktrans, which is used to assess tumor angiogenesis and the effects of anti-angiogenic therapies. Standard DCE MRI methods must measure the pharmacokinetics of a contrast agent in the blood stream, known as the Arterial Input Function (AIF), which is then used as a reference for the pharmacokinetics of the agent in tumor tissue. However, the AIF is difficult to measure in pre-clinical tumor models and in patients. Moreover the AIF is dependent on the Fahraeus effect that causes a highly variable hematocrit (Hct) in tumor microvasculature, leading to erroneous estimates of Ktrans. To overcome these problems, we have developed the Reference Agent Model (RAM) for DCE MRI analyses, which determines the ratio of Ktrans values of two contrast agents that are simultaneously co-injected and detected during a single DCE-MRI scan session. The RAM obviates the need to monitor the AIF because one contrast agent effectively serves as an internal reference in the tumor tissue for the other agent, and it also eliminates the systematic errors in the estimated Ktrans caused by assuming an erroneous Hct. Simulations demonstrated that the RAM can accurately and precisely estimate the relative Ktrans (RKtrans) of two agents. To experimentally evaluate the utility of RAM for analyzing DCE MRI results, we optimized a previously reported multiecho 19F MRI method to detect two perfluorocarbon contrast agents that were co-injected during a single in vivo study and selectively detected in the same tumor location. The results demonstrated that RAM determined RKtrans with excellent accuracy and precision.
doi:10.1016/j.mri.2012.12.002
PMCID: PMC3721191  PMID: 23583323
Dynamic Contrast Enhanced MRI; Permeability; Reference Agent Model; Pharmacokinetics; 19F MRI; Perfluorocarbons; Linear Models
14.  The use of error-category mapping in pharmacokinetic model analysis of dynamic contrast-enhanced MRI data 
Magnetic Resonance Imaging  2015;33(2):246-251.
This study introduces the use of ‘error-category mapping’ in the interpretation of pharmacokinetic (PK) model parameter results derived from dynamic contrast-enhanced (DCE-) MRI data.
Eleven patients with metastatic renal cell carcinoma were enrolled in a multiparametric study of the treatment effects of bevacizumab. For the purposes of the present analysis, DCE-MRI data from two identical pre-treatment examinations were analysed by application of the extended Tofts model (eTM), using in turn a model arterial input function (AIF), an individually-measured AIF and a sample-average AIF. PK model parameter maps were calculated. Errors in the signal-to-gadolinium concentration ([Gd]) conversion process and the model-fitting process itself were assigned to category codes on a voxel-by-voxel basis, thereby forming a colour-coded ‘error-category map’ for each imaged slice.
These maps were found to be repeatable between patient visits and showed that the eTM converged adequately in the majority of voxels in all the tumours studied. However, the maps also clearly indicated sub-regions of low Gd uptake and of non-convergence of the model in nearly all tumours. The non-physical condition ve ≥ 1 was the most frequently indicated error category and appeared sensitive to the form of AIF used.
This simple method for visualisation of errors in DCE-MRI could be used as a routine quality-control technique and also has the potential to reveal otherwise hidden patterns of failure in PK model applications.
doi:10.1016/j.mri.2014.10.010
PMCID: PMC4728188  PMID: 25460333
PK, pharmacokinetic; DCE-MRI, dynamic contrast-enhanced magnetic resonance imaging; eTM, extended Tofts model; AIF, arterial input function; AIC, Akaike information criterion; mRCC, metastatic renal cell carcinoma; MFA, multiple flip angles; ROI, region of interest; DCE-MRI; pharamacokinetic modeling; error analysis; metastatic renal cell carcinoma; repeatability
15.  The MRI-measured arterial input function resulting from a bolus injection of Gd-DTPA in a rat model of stroke slightly underestimates that of Gd-[14C]DTPA and marginally overestimates the blood-to-brain influx rate constant determined by Patlak plots 
The hypothesis that the arterial input function (AIF) of gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) injected by intravenous (iv) bolus and measured by the change in the T1-relaxation rate (ΔR1; R1=1/T1) of superior sagittal sinus blood (AIF-I) approximates the AIF of 14C-labeled Gd-DTPA measured in arterial blood (AIF*) was tested in a rat stroke model (n=13). Contrary to the hypothesis, the initial part of the ΔR1-time curve was underestimated, and the area under the normalized curve for AIF-I was about 15% lower than that for AIF*, the reference AIF. Hypothetical AIF’s for Gd-DTPA (AIF-II) were derived from the AIF* values and averaged to obtain AIF-III. Influx rate constants (Ki) and proton distribution volumes at zero time (Vp+Vo) were estimated with Patlak plots of AIF-I, -II and -III and tissue ΔR1 data. For the regions of interest, the Ki’s estimated with AIF-I were slightly but not significantly higher than those obtained with AIF-II and AIF-III. In contrast, Vp+Vo was significantly higher when calculated with AIF-I. Similar estimates of Ki and Vp+Vo were obtained with AIF-II and AIF-III. In summary, AIF-I underestimated the reference AIF (AIF*); this shortcoming had little effect on the Ki calculated by Patlak plot but produced a significant overestimation of Vp+Vo.
doi:10.1002/mrm.22339
PMCID: PMC2879714  PMID: 20512853
blood-brain barrier; cerebral ischemia; magnetic resonance contrast agents; reference tissue model
16.  High Temporal Resolution Dynamic MRI and Arterial Input Function for Assessment of GFR in Pediatric Subjects 
Magnetic resonance in medicine  2015;75(3):1301-1311.
Purpose
To introduce a respiratory-gated high-spatiotemporal-resolution dynamic-contrast-enhanced MRI technique and a high-temporal-resolution aortic input function (HTR-AIF) estimation method for glomerular filtration rate (GFR) assessment in children.
Methods
A high-spatiotemporal-resolution DCE-MRI method with view-shared reconstruction was modified to incorporate respiratory-gating, and an AIF estimation method that uses a fraction of the k-space data from each respiratory period was developed (HTR-AIF). The method was validated using realistic digital phantom simulations and demonstrated on clinical subjects. The GFR estimates using HTR-AIF were compared to estimates obtained by using an AIF derived directly from the view-shared images.
Results
Digital phantom simulations showed that using the HTR-AIF technique gives more accurate AIF estimates (RMSE = 0.0932) compared to the existing estimation method (RMSE = 0.2059) that used view-sharing (VS). For simulated GFR > 27 ml/min, GFR estimation error was between 32% and 17% using view-shared AIF, whereas estimation error was less than 10% using HTR-AIF. In all clinical subjects, the HTR-AIF method resulted in higher GFR estimations than the view-shared method.
Conclusion
The HTR-AIF method improves the accuracy of both the AIF and GFR estimates derived from the respiratory-gated acquisitions, and makes GFR estimation feasible in free-breathing pediatric subjects.
doi:10.1002/mrm.25731
PMCID: PMC4636486  PMID: 25946307
glomerular filtration rate estimation; high spatio-temporal resolution dynamic imaging; arterial input function estimation; urography; dynamic contrast enhancement
17.  Model-based Blind Estimation of Kinetic Parameters in DCE-MRI 
A method to simultaneously estimate the arterial input function (AIF) and pharmacokinetic model parameters from dynamic contrast-enhanced MRI data was developed. This algorithm uses a parameterized functional form to model the AIF and k-means clustering to classify tissue time-concentration measurements into a set of characteristic curves. An iterative blind estimation algorithm alternately estimated parameters for the input function and the pharmacokinetic model. Computer simulations were used to investigate the algorithm's sensitivity to noise and initial estimates. In 12 patients with sarcomas, pharmacokinetic parameter estimates were compared with “truth” obtained from model regression using a measured AIF. When arterial voxels were included in the blind estimation algorithm, the resulting AIF was similar to the measured input function. The “true” Ktrans values in tumor regions were not significantly different than the estimated values, .99±.41 and .86±.40 min−1 respectively, p=0.27. “True” kep values also matched closely, .70±.24 and .65±.25 min−1, p=0.08. When only tissue curves free of significant vascular contribution are used (vp<0.05), the resulting AIF showed substantial delay and dispersion consistent with a more local AIF such as has been observed in dynamic susceptibility contrast imaging in the brain.
doi:10.1002/mrm.22101
PMCID: PMC2884174  PMID: 19859949
Pharmacokinetic modeling; Tofts-Kety model; Blind Estimation; DCE-MRI; Perfusion Imaging; arterial input function
18.  Arterial input function and gray matter cerebral blood volume measurements in children 
Purpose
To investigate how arterial input functions (AIFs) vary with age in children and compare the use of individual and population AIFs for calculating gray matter CBV values. Quantitative measures of cerebral blood volume (CBV) using dynamic susceptibility contrast (DSC) magnetic resonance imaging (MRI) require measurement of an AIF. AIFs are affected by numerous factors including patient age. Few data presenting AIFs in the pediatric population exists.
Materials and Methods
Twenty‐two previously treated pediatric brain tumor patients (mean age, 6.3 years; range, 2.0–15.3 years) underwent DSC‐MRI scans on a 3T MRI scanner over 36 visits. AIFs were measured in the middle cerebral artery. A functional form of an adult population AIF was fitted to each AIF to obtain parameters reflecting AIF shape. The relationship between parameters and age was assessed. Correlations between gray matter CBV values calculated using the resulting population and individual patient AIFs were explored.
Results
There was a large variation in individual patient AIFs but correlations between AIF shape and age were observed. The center (r = 0.596, P < 0.001) and width of the first‐pass peak (r = 0.441, P = 0.007) were found to correlate significantly with age. Intrapatient coefficients of variation were significantly lower than interpatient values for all parameters (P < 0.001). Differences in CBV values calculated with an overall population and age‐specific population AIF compared to those calculated with individual AIFs were 31.3% and 31.0%, respectively.
Conclusion
Parameters describing AIF shape correlate with patient age in line with expected changes in cardiac output. In pediatric DSC‐MRI studies individual patient AIFs are recommended. J. Magn. Reson. Imaging 2016;43:981–989
doi:10.1002/jmri.25060
PMCID: PMC4864447  PMID: 26514288
arterial input function (AIF); cerebral blood volume (CBV); dynamic susceptibility contrast (DSC) MRI; pediatric; perfusion
19.  Correlation of Volume Transfer Coefficient Ktrans with Histopathologic Grades of Gliomas 
Purpose
To evaluate the roles of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) and optimum tracer kinetic parameters in the noninvasive grading of the glial brain tumors with histopathological grades (I–IV).
Materials and Methods
Twenty eight patients with histopathologically graded gliomas were imaged. Images with five flip angles were acquired before injection of gadolinium-DTPA and were processed to calculate the T1 value of each regions of interest (ROI). All the DCE-MRI data acquired during the injection were processed based on the MRI signal and pharmacokinetic models to establish concentration-time curves in the ROIs drawn within the tumors, counterlateral normal areas, and area of the individual artery input functions (iAIF) of each patient. A nonlinear least square fitting method was used to obtain tracer kinetic parameters. Kruskal-Wallis H-test and Mann-Whitney U-test were applied to these parameters in different histopathological grade groups for statistical differences (P<0.05).
Results
Volume transfer coefficient (Ktrans) and extravascular extracellular space volume fraction (Ve) calculated by using iAIFs can be used not only to distinguish the low (i.e., I and II) from the high (i.e., III and IV) grade gliomas (P(Ktrans) <0.001 and PVe<0.001), but also grade II from III (P(Ktrans) =0.016 and PVe=0.033).
Conclusion
Ktrans is the most sensitive and specific parameter in the noninvasive grading, distinguishing the high (III and IV) from the low (I and II) grade and high grade III from low grade II gliomas.
doi:10.1002/jmri.23675
PMCID: PMC3399966  PMID: 22581762
MR perfusion imaging; gliomas; microvascular permeability; pharmacokinetics; grades of glioma
20.  Automatic Determination of Arterial Input Function for Dynamic Contrast Enhanced MRI in Tumor Assessment 
Dynamic Contrast Enhanced MRI (DCE-MRI) is today one of the most popular methods for tumor assessment. Several pharmacokinetic models have been proposed to analyze DCE-MRI. Most of them depend on an accurate arterial input function (AIF). We propose an automatic and versatile method to determine the AIF. The method has two stages, detection and segmentation, incorporating knowledge about artery structure, fluid kinetics, and the dynamic temporal property of DCE-MRI. We have applied our method in DCE-MRIs of four different body parts: breast, brain, liver and prostate. The results show that we achieve average 89.5% success rate for 40 cases. The pharmacokinetic parameters computed from the automatic AIF are highly agreeable with those from a manually derived AIF (R2=0.89, P(T<=t)=0.19) and a semiautomatic AIF (R2=0.98, P(T<=t)=0.01).
PMCID: PMC2587281  PMID: 18979795
DCE-MRI; AIF; tumor imaging
21.  Arterial input functions (AIFs) measured directly from arteries with low and standard doses of contrast agent, and AIFs derived from reference tissues 
Magnetic resonance imaging  2015;34(2):197-203.
Measurements of arterial input function (AIF) can have large systematic errors at standard contrast agent doses in dynamic contrast enhanced MRI (DCE-MRI). We compared measured AIFs from low dose (AIFLD) and standard dose (AIFSD) contrast agent injections, as well as the AIF derived from a muscle reference tissue and artery (AIFref). Twenty-two prostate cancer patients underwent DCE-MRI. Data were acquired on a 3 T scanner using an mDixon sequence. Gadobenate dimeglumine was injected twice, at doses of 0.015 and 0.085 mmol/kg. Directly measured AIFs were fitted with empirical mathematical models (EMMs) and compared to the AIF derived from a muscle reference tissue (AIFref). EMMs accurately fitted the AIFs. The 1st and 2nd pass peaks were visualized in AIFLD, but not in AIFSD, thus the peak and shape of AIFSD could not be accurately measured directly. The average scaling factor between AIFSD and AIFLD in the washout phase was only 56% of the contrast dose ratio (~6:1). The shape and magnitude of AIFref closely approximated that of AIFLD after empirically determined dose-dependent normalization. This suggests that AIFref may be a good approximation of the local AIF.
doi:10.1016/j.mri.2015.10.025
PMCID: PMC5006387  PMID: 26523650
Dynamic contrast enhanced MRI (DCE-MRI) of prostate cancer; Empirical mathematical model (EMM); Arterial input function (AIF); Contrast agent dose; First pass peak; Reference tissue method
22.  Correction of Arterial Input Function in Dynamic Contrast-Enhanced MRI of the Liver 
Purpose
To develop a post-processing method to correct saturation of arterial input function (AIF) in T1-weighted DCE-MRI for quantification of hepatic perfusion.
Materials and Methods
The saturated AIF is corrected by parameterizing the first pass of the AIF as a smooth function with a single peak and minimizing a least squares error in fitting the liver DCE-MRI data to a dual-input single-compartment model. Sensitivities of the method to the degree of saturation in the AIF first-pass peak and the image contrast-to-noise ratio were assessed. The method was also evaluated by correlating portal venous perfusion with an independent overall liver function measurement.
Results
The proposed method corrects the distorted AIF with a saturation ratio up to 0.45. The corrected AIF improves hepatic arterial perfusion by −23.4% and portal venous perfusion by 26.9% in a study of 12 patients with liver cancers. The correlation between the mean voxelwise portal venous perfusion and overall liver function measurement was improved by using the corrected AIFs (R2=0.67) compared with the saturated AIFs (R2=0.39).
Conclusion
The method is robust for correcting AIF distortion, and has the potential to improve quantification of hepatic perfusion for assessment of liver tissue response to treatment in patients with hepatic cancers.
doi:10.1002/jmri.23636
PMCID: PMC3371299  PMID: 22392876
DCE MRI; AIF saturation; correction; liver; dual-input single compartment model
23.  Kinetic Quantitation of Cerebral PET-FDG Studies Without Concurrent Blood Sampling: Statistical Recovery of the Arterial Input Function 
Kinetic quantitation of dynamic positron emission tomography (PET) studies via compartmental modeling usually requires the time-course of the radio-tracer concentration in the arterial blood as an arterial input function (AIF). For human and animal imaging applications, significant practical difficulties are associated with direct arterial sampling and as a result there is substantial interest in alternative methods that require no blood sampling at the time of the study. A fixed population template input function derived from prior experience with directly sampled arterial curves is one possibility. Image-based extraction, including requisite adjustment for spillover and recovery, is another approach. The present work considers a hybrid statistical approach based on a penalty formulation in which the information derived from a priori studies is combined in a Bayesian manner with information contained in the sampled image data in order to obtain an input function estimate. The absolute scaling of the input is achieved by an empirical calibration equation involving the injected dose together with the subject’s weight, height and gender. The technique is illustrated in the context of 18F-Flu-orodeoxyglucose (FDG) PET studies in humans. A collection of 79 arterially sampled FDG blood curves are used as a basis for a priori characterization of input function variability, including scaling characteristics. Data from a series of 12 dynamic cerebral FDG PET studies in normal subjects are used to evaluate the performance of the penalty-based AIF estimation technique. The focus of evaluations is on quantitation of FDG kinetics over a set of 10 regional brain structures. As well as the new method, a fixed population template AIF and a direct AIF estimate based on segmentation are also considered. Kinetics analyses resulting from these three AIFs are compared with those resulting from radially sampled AIFs. The proposed penalty-based AIF extraction method is found to achieve significant improvements over the fixed template and the segmentation methods. As well as achieving acceptable kinetic parameter accuracy, the quality of fit of the region of interest (ROI) time-course data based on the extracted AIF, matches results based on arterially sampled AIFs. In comparison, significant deviation in the estimation of FDG flux and degradation in ROI data fit are found with the template and segmentation methods. The proposed AIF extraction method is recommended for practical use.
doi:10.1109/TMI.2009.2029096
PMCID: PMC4154632  PMID: 19709971
Blood curve representation; image segmentation; kinetics; mixture modeling; no blood sampling; penalty method
24.  Sensitivity Analysis of an Image-Based Solid Tumor Computational Model with Heterogeneous Vasculature and Porosity 
Annals of Biomedical Engineering  2011;39(9):2360-2373.
An MR image-based computational model of a murine KHT sarcoma is presented that allows the calculation of plasma fluid and solute transport within tissue. Such image-based models of solid tumors may be used to optimize patient-specific therapies. This model incorporates heterogeneous vasculature and tissue porosity to account for non-uniform perfusion of an MR-visible tracer, Gd-DTPA. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) was conducted following intravenous infusion of Gd-DTPA to provide 1 h of tracer-concentration distribution data within tissue. Early time points (19 min) were used to construct 3D Ktrans and porosity maps using a two-compartment model; tracer transport was predicted at later time points using a 3D porous media model. Model development involved selecting an arterial input function (AIF) and conducting a sensitivity analysis of model parameters (tissue, vascular, and initial estimation of solute concentration in plasma) to investigate the effects on transport for a specific tumor. The developed model was then used to predict transport in two additional tumors. The sensitivity analysis suggests that plasma fluid transport is more sensitive to parameter changes than solute transport due to the dominance of transvascular exchange. Gd-DTPA distribution was similar to experimental patterns, but differences in Gd-DTPA magnitude at later time points may result from inaccurate selection of AIF. Thus, accurate AIF estimation is important for later time point prediction of low molecular weight tracer or drug transport in smaller tumors.
doi:10.1007/s10439-011-0349-7
PMCID: PMC3373181  PMID: 21751070
DCE-MRI; drug transport model; extracellular transport; arterial input function; two-compartment model; contrast agent extravasation
25.  Dynamic Contrast-Enhanced Magnetic Resonance Imaging as a Predictor of Outcome in Head and Neck Squamous Cell Carcinoma Patients with Nodal Metastases 
Purpose
Dynamic contrast-enhanced-MRI (DCE-MRI) can provide information regarding tumor perfusion and permeability and has shown prognostic value in certain tumors types. The goal of the present study was to assess the prognostic value of pretreatment DCE-MRI in head and neck squamous cell carcinoma (HNSCC) patients with nodal disease undergoing chemoradiation therapy or surgery.
Methods and Materials
Seventy-four patients with histologically proven squamous cell carcinoma and neck nodal metastases were eligible for the study. Pretreatment DCE-MRI was performed on a 1.5T MRI. Clinical follow-up was a minimum of 12 months. DCE-MRI data were analyzed using Tofts model. DCE-MRI parameters were related to treatment outcome (progression free survival [PFS] and overall survival [OS]). Patients were grouped as no evidence of disease (NED), alive with disease (AWD), dead with disease (DOD) or dead of other causes (DOC). Prognostic significance was assessed using the log rank test for single variables and Cox proportional hazards regression for combinations of variables.
Results
At last clinical follow-up, for stage III, all 12 pts were NED, for stage IV, 43 patients were NED, 4 were AWD, 11 were DOD, and 4 were DOC. Ktrans is volume transfer constant. In a stepwise Cox regression skewness of Ktrans was the strongest predictor for stage IV patients (PFS and OS: p<0.001).
Conclusion
Our study shows that skewness of Ktrans was the strongest predictor of PFS and OS in stage IV HNSCC patients with nodal disease. This study suggests an important role for pretreatment DCE-MRI parameter Ktrans as a predictor of outcome in these patients.
doi:10.1016/j.ijrobp.2011.03.006
PMCID: PMC3177034  PMID: 21601373
Dynamic Contrast Enhanced-MRI (DCE-MRI); head and neck squamous cell carcinoma (HNSCC); volume transfer constant (Ktrans)

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