Research article Received: 8 July 2014,
Revised: 19 February 2015,
Accepted: 5 March 2015,
Published online in Wiley Online Library: 16 April 2015
(wileyonlinelibrary.com) DOI: 10.1002/nbm.3297
Assessment of vessel permeability by combining dynamic contrast-enhanced and arterial spin labeling MRI† Ho-Ling Liua,b, Ting-Ting Changa, Feng-Xian Yana,c, Cheng-He Lia, Yu-Shi Lina and Alex M. Wongd,e* The forward volumetric transfer constant (Ktrans), a physiological parameter extracted from dynamic contrast-enhanced (DCE) MRI, is weighted by vessel permeability and tissue blood flow. The permeability × surface area product per unit mass of tissue (PS) in brain tumors was estimated in this study by combining the blood flow obtained through pseudo-continuous arterial spin labeling (PCASL) and Ktrans obtained through DCE MRI. An analytical analysis and a numerical simulation were conducted to understand how errors in the flow and Ktrans estimates would propagate to the resulting PS. Fourteen pediatric patients with brain tumors were scanned on a clinical 3-T MRI scanner. PCASL perfusion imaging was performed using a three-dimensional (3D) fast-spin-echo readout module to determine blood flow. DCE imaging was performed using a 3D spoiled gradient-echo sequence, and the Ktrans map was obtained with the extended Tofts model. The numerical analysis demonstrated that the uncertainty of PS was predominantly dependent on that of Ktrans and was relatively insensitive to the flow. The average PS values of the whole tumors ranged from 0.006 to 0.217 min1, with a mean of 0.050 min1 among the patients. The mean Ktrans value was 18% lower than the PS value, with a maximum discrepancy of 25%. When the parametric maps were compared on a voxel-by-voxel basis, the discrepancies between PS and Ktrans appeared to be heterogeneous within the tumors. The PS values could be more than two-fold higher than the Ktrans values for voxels with high Ktrans levels. This study proposes a method that is easy to implement in clinical practice and has the potential to improve the quantification of the microvascular properties of brain tumors. Copyright © 2015 John Wiley & Sons, Ltd. Additional supporting information may be found in the online version of this article at the publisher’s web site. Keywords: MRI; permeability; forward volumetric transfer constant (Ktrans); dynamic contrast enhanced (DCE); arterial spin labeling (ASL)
INTRODUCTION MRI using the T1-weighted dynamic contrast-enhanced (DCE) method is useful for the characterization of brain tumors (1–3). Physiological parameters, including the forward volumetric transfer constant (Ktrans), volume fraction of extravascular extracellular space (EES) (ve) and volume fraction of blood * Correspondence to: A. M. Wong, Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital, 5 Fu-Hsing Street, Kwei-shan, Taoyuan, 333 Taiwan. E-mail: [email protected] a H.-L. Liu, T.-T. Chang, F.-X. Yan, C.-H. Li, Y.-S. Lin Department of Medical Imaging and Radiological Sciences, College of Medicine, Chang Gung University, Taoyuan, Taiwan b H.-L. Liu Department of Imaging Physics, University of Texas M. D. Anderson Cancer Center, Houston, TX, USA c F.-X. Yan Department of Radiology, Taipei Medical University/Shuang-Ho Hospital, New Taipei City, Taiwan
642
d A. M. Wong Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital at Keelong, Linkou Medical Center, Taiwan
NMR Biomed. 2015; 28: 642–649
plasma (vp), can be extracted from DCE MRI using pharmacokinetic modeling, such as the extended Tofts model (ETM) (4). In particular, the Ktrans parameter is commonly used as an indicator of vessel permeability, which links to the angiogenesis of tumor progression (5). However, Ktrans is also known to be weighted by tissue blood flow (6). In theory, Ktrans approximates the permeability × surface area product per unit mass of tissue (PS) in a PS-limited scenario and the tissue blood flow in a flowlimited scenario (6). A recent study has confirmed that Ktrans generally has a mixed flow–permeability weighting, which constrains the physiological interpretation of DCE MRI results (7).
e A. M. Wong College of Medicine, Chang Gung University, Taoyuan, Taiwan †
Parts of this work were presented at the 21st Annual Meeting of the International Society of Magnetic Resonance in Medicine, Salt Lake City, UT, USA, 2013. Abbreviations used: 3D, three-dimensional; AATH, adiabatic approximation to the tissue homogeneity; AIF, arterial input function; ASL, arterial spin labeling; CBF, cerebral blood flow; DCE, dynamic contrast enhanced; EES, trans , forward extravascular extracellular space; ETM, extended Tofts model; K volumetric transfer constant; PCASL, pseudo-continuous arterial spin labeling; PS, permeability × surface area product per unit mass of tissue; ROI, region of interest; SNR, signal-to-noise ratio; SPGR, spoiled gradient-echo; ve, volume fraction of extravascular extracellular space.
Copyright © 2015 John Wiley & Sons, Ltd.
MR PERMEABILITY IMAGING By using more complex models, such as the adiabatic approximation to the tissue homogeneity (AATH) (8) and the twocompartment exchange model (9), it is possible to obtain the PS and blood flow as two independent parameters. However, these four-parameter fitting models require imaging data with a high temporal resolution and high signal-to-noise ratio (SNR), which makes voxel-based analysis difficult in clinical practice. Arterial spin labeling (ASL) is a noninvasive MR method that involves the use of arterial water as an endogenous tracer for perfusion imaging (10). ASL MRI has been proven to be reliable and reproducible in the assessment of cerebral blood flow (CBF) in a wide spectrum of pathological conditions (11–13). The recent development of pseudo-continuous ASL (PCASL), combined with a three-dimensional (3D) acquisition, enables whole-brain CBF evaluation with a reasonable SNR (14). This technique has been applied to patients with brain tumors and has been compared with the clinically more established dynamic susceptibility contrast MRI method with strong correlations (15,16). This study proposes to combine the blood flow, measured using PCASL, and Ktrans, obtained using DCE MRI, to estimate PS in brain tumors. A mathematical analysis and numerical simulation were performed to evaluate how errors propagate from the flow and Ktrans estimates to the PS estimates. The feasibility of this method was demonstrated in a small cohort of pediatric patients with brain tumors.
MATERIALS AND METHODS Theory and error propagation ETM is a commonly applied pharmacokinetic model for the fitting of DCE MRI data (4): t
C t ðt Þ ¼ v p C p ðtÞ þ K trans ∫0 C p ðτ Þe
K trans v e ðtτ Þ
dτ
[1]
where Ct(t) and Cp(t) are concentration–time curves of the tissue and blood plasma, respectively. The Ktrans parameter is defined as follows: K trans ¼ EF p
[2]
where E is the extraction ratio and Fp is the blood plasma flow per volume of tissue, i.e. Fp = Fρ(1 Hct), where F is the blood flow per unit mass of tissue, ρ is the tissue density and Hct is the hematocrit (6). Assuming that the capillary bed is a plug-flow system, Equation [2] can be written as follows (6,17): PS K trans ¼ F p 1 e Fp
[3]
If Ktrans and Fp are obtained by measurements, then PS can be calculated as follows: K trans PS ¼ F p ln 1 Fp
[4]
Based on Equation [4], the uncertainty of the PS estimate (σ PS) can be approximated by propagating uncertainties in the Ktrans and Fp measurements (σ K trans and σ F p , respectively):
∂PS ∂K trans
2
NMR Biomed. 2015; 28: 642–649
σ 2K trans þ
∂PS 2 2 σ F p ∂F p
[5]
σ 2 PS
PS
2 2 σ trans 2 E σ Fp 1 K 1E þ 1 2 2 K trans 1 lnð1 E Þ Fp E 1 ½lnð1 E Þ
¼
[6] When σ F p ¼ 0, Equation [6] can be simplified as follows: σ PS 1 σ trans Ktrans ¼ 1 PS K 1 ln ð 1 E Þ j j E
[7]
When σ K trans ¼ 0, Equation [6] can be simplified as follows: E σF σ PS 1E [8] ¼ 1 p PS lnð1 E Þ Fp It should be noted that the fractional error of PS is proportional to the fractional errors of Ktrans and Fp in Equations [7] and [8], respectively, and the proportional constants are dependent on E. Numerical simulation Numerical simulations were performed to evaluate the influence of systematic errors and uncertainty of the measured parameters (Ktrans and Fp) on the derived parameter (PS). This evaluation is essential because the error associated with the proposed method is directly related to the errors arising from the two measured parameters. Two sets of simulations were conducted using MATLAB Version 7.0 (MathWorks, Natick, MA, USA). The first simulation evaluated the relationships between PS and the measured parameters according to Equation [4], and how the relationships changed with ±10%, ±20% and ±30% errors in the measured parameters. This simulation facilitates an understanding of how systematic errors (associated with bias) are transferred. Three true Ktrans values (0.01, 0.1 and 0.15 min1) were simulated, each for a range of Fp values (corresponding to E = 0.1–0.5). Likewise, three true Fp values (0.2, 0.6 and 1.0 min1) were simulated, each for a range of Ktrans values (corresponding to E = 0.1–0.5). The second simulation evaluated the fractional error of PS that would have resulted from a range of –30% to +30% errors in Ktrans and Fp according to Equations [7] and [8], respectively. This simulation facilitates an understanding of how random-like errors (associated with variance) are transferred. E values were set from 0.1 to 0.9, with an interval of 0.1. Although all E values of our clinical brain tumor data were below 0.2, using a wider range in the simulation could provide useful information for other clinical populations. MRI acquisition Fourteen pediatric patients (aged 5 months to 14 years; seven females) with brain tumors, including glioneural tumor, sellar germ-cell tumor, germinoma, brain-stem glioma, medulloblastoma, atypical teratoid/rhabdoid tumor, choroid plexus papilloma, pilocytic astrocytoma and anaplastic ependymoma, participated in this study. The patients had no previous surgical resection, biopsy or other treatment of the tumors. Informed consent for the MRI examination was obtained from the parents or legal guardians of the patients after the nature of the study had been comprehensively explained. The study protocol was
Copyright © 2015 John Wiley & Sons, Ltd.
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σ 2PS ¼
Combining Equations [2]–[5], we obtain the following:
H.-L. LIU ET AL. approved by the local Human Experiments and Ethics Committee. Two of the 14 patients were sedated throughout the intravenous administration of midazolam, and no patient underwent anesthesia. No steroids were given to the patients within 7 days before the MRI examination. All patients were scanned using an eight-channel brain array coil on a clinical 3-T MRI scanner (Discovery MR750, GE Healthcare, Milwaukee, WI, USA). The PCASL perfusion imaging was performed using a 3D backgroundsuppressed fast-spin-echo stack-of-spiral readout module with eight in-plane spiral interleaves (TR/TE = 4463 ms/10.2 ms; labeling duration, 1500 ms; post-labeling delay, 1525 ms; no flow-crushing gradients; in-plane matrix, 128 × 128; number of averages (NEX) = 3; field of view, 240 mm × 240 mm; slice thickness, 5 mm) and an echo train length of 23 to obtain 23 consecutive axial slices (14). The labeling plane was 10 mm thick, placed 20 mm inferior to the lower edge of the cerebellum. The PCASL scan also included the acquisition of a reference image after saturation recovery with a saturation time of 2 s. The total scan time was 259 s. A 3D spoiled gradient-echo (SPGR) sequence with varied flip angles was applied to obtain the T1 maps before contrast injection (T10 maps). The imaging parameters were as follows: TR/TE = 4.9/1.3 ms; flip angle, 2°, 5°, 10° and 20°; acceleration factor, 2; matrix size, 256 × 128. Eight slices centered on the tumor areas were acquired with the same slice thickness and field of view as those for the PCASL scan. The slice locations were matched with eight of the slices acquired with the 3D PCASL. The same sequence and parameters, except for a fixed flip angle of 30°, were used for T1-weighted DCE MRI. Sixty dynamic measurements were acquired during a total acquisition time of 234 s, with a sampling interval of 3.9 s. A bolus injection of 0.1 mmol/kg body weight of Gd-diethylenetriaminepentaacetic acid (DTPA) contrast agent (Magnevist, Schering, Berlin, Germany) and then saline (15 mL), at a rate of 2–4 mL/s, was administered using an MR-compatible power injector (OptiStar LE, Covidien, Mansfield, MA, USA). The contrast medium was given manually if the calculated contrast volume was less than 5 mL. The injection of the contrast agent began at the 10th measurement after the start of the dynamic scan. The post-contrast T1-weighted images were acquired using a conventional spin-echo sequence (TR/ TE = 400/12 ms) with the slice thickness and locations matched to those of the PCASL scan. Data analysis The ASL perfusion data were analyzed on an Advantage Windows workstation using Functool software (Version 9.4, GE Medical Systems, Milwaukee/WI/USA). The blood flow per volume, Fρ (mL/100 mL/min), was calculated using the following equation: PLD ST 1 eT 1t e T 1b PW Fρ ¼ 6000 λ LT 2T 1b 1 e T 1b ε PD
[9]
644
where PW is the perfusion-weighted or raw difference image and PD is the partial saturation of the reference image. Other parameters, which included T1 of blood (T1b) = 1.6 s, T1 of tissue (T1t) = 1.2 s, partition coefficient (λ) = 0.9 and the labeling efficiency (ε) = 0.6, were assumed to be constant. The Fp map was then calculated by assuming Hct = 0.45. The DCE MRI data were processed using nICE software (Nordic ICE, NordicNeuroLab, Bergen, Norway). The baseline longitudinal relaxation rate (R10) was first estimated by fitting the images
wileyonlinelibrary.com/journal/nbm
obtained from varied flip angles using the steady-state SPGR signal equation. The time curve of the change in the longitudinal relaxation rate, ΔR1(t), was then calculated as follows: ΔR1 ðtÞ ¼
K SSð0tÞ 1 1 ln TR K SSð0tÞ cos α 1
! R10
[10]
TRR
10 where K ¼ 1e1e TRR10 cos α , S0 is the baseline signal, S(t) is the signal–time curve and α is the flip angle. By assuming that Ct(t) and Cp(t) were proportional to the corresponding ΔR1(t), the Ktrans map was obtained for each patient using ETM [Equation [1]] (4). The arterial input function (AIF), Cp(t), was obtained for each patient from the internal carotid artery, with T10 assumed to be 1.6 s and Hct = 0.45. AIF was obtained from five voxels that were automatically detected within a manually determined region of interest (ROI) covering the internal carotid artery in each patient. The automatic AIF detection was based on a cluster analysis for selection of the time courses that most closely resembled the excepted AIF properties (large area under the curve, low first moment and high peak enhancement). To minimize the effect of possible patient motion between the PCASL and DCE MRI scans, the Fp map was co-registered to the Ktrans map using SPM8 (http://www.fil.ion.ucl.ac.uk/spm/; Department of Imaging Neuroscience, University College London, London, UK). The PS map was then calculated for each patient based on Equation [4]. The gross tumor ROIs were manually delineated by an experienced neuroradiologist for each patient by referencing post-contrast T1-weighted images using Mango software (Research Imaging Institute, University of Texas Health Science Center, San Antonio, TX, USA). The ROI was drawn on the T1-weighted images and then transferred to the same locations on the corresponding physiological parametric maps to retrieve the mean tumor Fρ, Ktrans and PS values for each patient.
RESULTS The relationships between PS and Fp at three Ktrans levels (0.01, 0.1 and 0.15 min1) are illustrated in (Fig. 1). As expected, the PS values were higher than the Ktrans values at lower Fp and approached the Ktrans values as Fp increased. Under- and overestimation of Ktrans values caused errors in the derived PS in the same directions, with the amounts relatively insensitive to Fp values. Figure 2 shows the relationships between PS and Ktrans at three Fp levels (0.1, 0.3 and 0.8 min1). At low Ktrans, the derived PS values were not affected by errors in Fp values. At higher Ktrans, under- and over-estimation of Fp values caused errors in the derived PS values in the opposite directions. The proportional constants between the fractional errors of PS values and those of Ktrans and Fp values are shown in (Fig. 3), as the results of Equations [7] and [8]. They increased dramatically with E and were approximately one order of magnitude higher for Ktrans than for Fp. Table 1 lists the mean tumor Ktrans, PS and Fρ values of each patient. The mean Ktrans values were found to be significantly lower than the PS values using a paired t-test (p < 0.05). The values averaged across patients (Ktrans = 0.041 min1, PS = 0.050 min1) exhibited an 18% difference, and the greatest discrepancy of 25% was found for the patient with the highest Ktrans (0.162 min1) and PS (0.217 min1) values. (Additional statistical data from ROI analysis of Ktrans and PS values are listed in Tables S1 and S2, respectively.)
Copyright © 2015 John Wiley & Sons, Ltd.
NMR Biomed. 2015; 28: 642–649
MR PERMEABILITY IMAGING
Figure 1. Relationships between permeability × surface area product per unit mass of tissue (PS) and blood plasma flow per volume of tissue trans (Fp) at three forward volumetric transfer constant (K ) values: (a) 1 1 1 0.01 min ; (b) 0.1 min ; (c) 0.15 min . The gray curves show the trans changes in the relationships when K is under- and over-estimated trans . by 10%, 20% and 30%. The broken lines represent PS = K
NMR Biomed. 2015; 28: 642–649
Figure 3. The proportional constants between fractional errors of permeability × surface area product per unit mass of tissue (PS) and of trans ) and blood plasma flow per forward volumetric transfer constant (K volume of tissue (Fp) as a function of the extraction ratio (E).
Copyright © 2015 John Wiley & Sons, Ltd.
wileyonlinelibrary.com/journal/nbm
645
Figure 4 shows post-contrast T1-weighted images and Ktrans, Fρ and PS maps obtained from two patients: one had a sellar germ-cell tumor (top row) and the other had a medulloblastoma (bottom row). The top row images show prominently elevated values in most parts of the tumor on the PS map compared with that on the Ktrans map. The bottom row images show elevated values in only the left portions of the tumor on the PS map compared with that on the Ktrans map. In general, the PS values were higher than the Ktrans values in the tumors. This trend was more apparent in the patient shown in the top row, who had a tumor with low blood flow. Figure 5a illustrates a scatter plot of the estimated PS and measured Ktrans values obtained by averaging across the tumor ROIs of the 14 patients. The results showed that the PS values were increasingly higher than the Ktrans values for tumors with higher Ktrans values. However, for most of the tumors, such as those with Ktrans values of less than 0.04 min1, the Ktrans values appeared approximately equal to the PS values. Figure 5b shows the scatter plot of the intratumoral voxel-by-voxel PS and Ktrans values of two patients (patients 1 and 2 in Table 1). The discrepancies between PS and Ktrans appeared heterogeneous within
Figure 2. Relationships between permeability × surface area product per unit mass of tissue (PS) and forward volumetric transfer constant trans (K ) at three blood plasma flow per volume of tissue (Fp) values: (a) 1 1 1 0.1 min ; (b) 0.3 min ; (c) 0.8 min . The gray curves show the changes in the relationships when Fp is under- and over-estimated by 10%, 20% and 30%.
H.-L. LIU ET AL. Table 1. Physiological parameters [forward volumetric transfer constant (Ktrans), permeability × surface area product per unit mass of tissue (PS) and blood flow per volume (Fρ)] obtained from tumor regions of interest in patients Patient 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mean
Tumor diagnosis
Ktrans (min1)
PS (min1)
Fρ (mL/100 mL/min)
Glioneural tumor Germinoma Germinoma Medulloblastoma Brain-stem glioma Medulloblastoma Atypical teratoid/rhabdoid tumor Brain-stem glioma Anaplastic ependymoma Pilocytic astrocytoma Medulloblastoma Atypical teratoid/rhabdoid tumor Choroid plexus papilloma Germinoma
0.031 0.084 0.018 0.006 0.008 0.011 0.162 0.020 0.101 0.015 0.024 0.023 0.069 0.006 0.041
0.033 0.102 0.019 0.006 0.008 0.011 0.217 0.021 0.130 0.016 0.026 0.025 0.080 0.006 0.050
47.3 47.8 39.6 70.2 46.5 72.0 64.2 65.5 45.1 72.7 36.9 32.7 48.7 27.8 51.2
trans
Figure 4. Post-contrast T1-weighted (T1w) images and forward volumetric transfer constant (K ), permeability × surface area product per unit mass of tissue (PS) and cerebral blood flow (CBF) maps obtained from an 11-year-old girl with pineal gland germ-cell tumor (top row) and a 9-year-old boy with medulloblastoma (bottom row).
the tumors. Some PS values were more than two-fold higher than the Ktrans values for voxels with high K trans levels (see Fig. S1 for time curves from the two voxels with the largest K trans values in Fig. 5b).
DISCUSSION
646
This study proposes the use of the PCASL technique for the separation of flow weighting from the Ktrans measurement by DCE MRI in brain tumors. It is well understood that Ktrans, the forward volumetric transfer constant of a tracer between the blood plasma and EES, depends on both blood flow and vessel permeability, two crucial but independent parameters that can be used to characterize tumor neovasculature (18). In the PS-limited condition, i.e. PS 20) were required to ensure minimal bias (
Revised: 19 February 2015,
Accepted: 5 March 2015,
Published online in Wiley Online Library: 16 April 2015
(wileyonlinelibrary.com) DOI: 10.1002/nbm.3297
Assessment of vessel permeability by combining dynamic contrast-enhanced and arterial spin labeling MRI† Ho-Ling Liua,b, Ting-Ting Changa, Feng-Xian Yana,c, Cheng-He Lia, Yu-Shi Lina and Alex M. Wongd,e* The forward volumetric transfer constant (Ktrans), a physiological parameter extracted from dynamic contrast-enhanced (DCE) MRI, is weighted by vessel permeability and tissue blood flow. The permeability × surface area product per unit mass of tissue (PS) in brain tumors was estimated in this study by combining the blood flow obtained through pseudo-continuous arterial spin labeling (PCASL) and Ktrans obtained through DCE MRI. An analytical analysis and a numerical simulation were conducted to understand how errors in the flow and Ktrans estimates would propagate to the resulting PS. Fourteen pediatric patients with brain tumors were scanned on a clinical 3-T MRI scanner. PCASL perfusion imaging was performed using a three-dimensional (3D) fast-spin-echo readout module to determine blood flow. DCE imaging was performed using a 3D spoiled gradient-echo sequence, and the Ktrans map was obtained with the extended Tofts model. The numerical analysis demonstrated that the uncertainty of PS was predominantly dependent on that of Ktrans and was relatively insensitive to the flow. The average PS values of the whole tumors ranged from 0.006 to 0.217 min1, with a mean of 0.050 min1 among the patients. The mean Ktrans value was 18% lower than the PS value, with a maximum discrepancy of 25%. When the parametric maps were compared on a voxel-by-voxel basis, the discrepancies between PS and Ktrans appeared to be heterogeneous within the tumors. The PS values could be more than two-fold higher than the Ktrans values for voxels with high Ktrans levels. This study proposes a method that is easy to implement in clinical practice and has the potential to improve the quantification of the microvascular properties of brain tumors. Copyright © 2015 John Wiley & Sons, Ltd. Additional supporting information may be found in the online version of this article at the publisher’s web site. Keywords: MRI; permeability; forward volumetric transfer constant (Ktrans); dynamic contrast enhanced (DCE); arterial spin labeling (ASL)
INTRODUCTION MRI using the T1-weighted dynamic contrast-enhanced (DCE) method is useful for the characterization of brain tumors (1–3). Physiological parameters, including the forward volumetric transfer constant (Ktrans), volume fraction of extravascular extracellular space (EES) (ve) and volume fraction of blood * Correspondence to: A. M. Wong, Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital, 5 Fu-Hsing Street, Kwei-shan, Taoyuan, 333 Taiwan. E-mail: [email protected] a H.-L. Liu, T.-T. Chang, F.-X. Yan, C.-H. Li, Y.-S. Lin Department of Medical Imaging and Radiological Sciences, College of Medicine, Chang Gung University, Taoyuan, Taiwan b H.-L. Liu Department of Imaging Physics, University of Texas M. D. Anderson Cancer Center, Houston, TX, USA c F.-X. Yan Department of Radiology, Taipei Medical University/Shuang-Ho Hospital, New Taipei City, Taiwan
642
d A. M. Wong Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital at Keelong, Linkou Medical Center, Taiwan
NMR Biomed. 2015; 28: 642–649
plasma (vp), can be extracted from DCE MRI using pharmacokinetic modeling, such as the extended Tofts model (ETM) (4). In particular, the Ktrans parameter is commonly used as an indicator of vessel permeability, which links to the angiogenesis of tumor progression (5). However, Ktrans is also known to be weighted by tissue blood flow (6). In theory, Ktrans approximates the permeability × surface area product per unit mass of tissue (PS) in a PS-limited scenario and the tissue blood flow in a flowlimited scenario (6). A recent study has confirmed that Ktrans generally has a mixed flow–permeability weighting, which constrains the physiological interpretation of DCE MRI results (7).
e A. M. Wong College of Medicine, Chang Gung University, Taoyuan, Taiwan †
Parts of this work were presented at the 21st Annual Meeting of the International Society of Magnetic Resonance in Medicine, Salt Lake City, UT, USA, 2013. Abbreviations used: 3D, three-dimensional; AATH, adiabatic approximation to the tissue homogeneity; AIF, arterial input function; ASL, arterial spin labeling; CBF, cerebral blood flow; DCE, dynamic contrast enhanced; EES, trans , forward extravascular extracellular space; ETM, extended Tofts model; K volumetric transfer constant; PCASL, pseudo-continuous arterial spin labeling; PS, permeability × surface area product per unit mass of tissue; ROI, region of interest; SNR, signal-to-noise ratio; SPGR, spoiled gradient-echo; ve, volume fraction of extravascular extracellular space.
Copyright © 2015 John Wiley & Sons, Ltd.
MR PERMEABILITY IMAGING By using more complex models, such as the adiabatic approximation to the tissue homogeneity (AATH) (8) and the twocompartment exchange model (9), it is possible to obtain the PS and blood flow as two independent parameters. However, these four-parameter fitting models require imaging data with a high temporal resolution and high signal-to-noise ratio (SNR), which makes voxel-based analysis difficult in clinical practice. Arterial spin labeling (ASL) is a noninvasive MR method that involves the use of arterial water as an endogenous tracer for perfusion imaging (10). ASL MRI has been proven to be reliable and reproducible in the assessment of cerebral blood flow (CBF) in a wide spectrum of pathological conditions (11–13). The recent development of pseudo-continuous ASL (PCASL), combined with a three-dimensional (3D) acquisition, enables whole-brain CBF evaluation with a reasonable SNR (14). This technique has been applied to patients with brain tumors and has been compared with the clinically more established dynamic susceptibility contrast MRI method with strong correlations (15,16). This study proposes to combine the blood flow, measured using PCASL, and Ktrans, obtained using DCE MRI, to estimate PS in brain tumors. A mathematical analysis and numerical simulation were performed to evaluate how errors propagate from the flow and Ktrans estimates to the PS estimates. The feasibility of this method was demonstrated in a small cohort of pediatric patients with brain tumors.
MATERIALS AND METHODS Theory and error propagation ETM is a commonly applied pharmacokinetic model for the fitting of DCE MRI data (4): t
C t ðt Þ ¼ v p C p ðtÞ þ K trans ∫0 C p ðτ Þe
K trans v e ðtτ Þ
dτ
[1]
where Ct(t) and Cp(t) are concentration–time curves of the tissue and blood plasma, respectively. The Ktrans parameter is defined as follows: K trans ¼ EF p
[2]
where E is the extraction ratio and Fp is the blood plasma flow per volume of tissue, i.e. Fp = Fρ(1 Hct), where F is the blood flow per unit mass of tissue, ρ is the tissue density and Hct is the hematocrit (6). Assuming that the capillary bed is a plug-flow system, Equation [2] can be written as follows (6,17): PS K trans ¼ F p 1 e Fp
[3]
If Ktrans and Fp are obtained by measurements, then PS can be calculated as follows: K trans PS ¼ F p ln 1 Fp
[4]
Based on Equation [4], the uncertainty of the PS estimate (σ PS) can be approximated by propagating uncertainties in the Ktrans and Fp measurements (σ K trans and σ F p , respectively):
∂PS ∂K trans
2
NMR Biomed. 2015; 28: 642–649
σ 2K trans þ
∂PS 2 2 σ F p ∂F p
[5]
σ 2 PS
PS
2 2 σ trans 2 E σ Fp 1 K 1E þ 1 2 2 K trans 1 lnð1 E Þ Fp E 1 ½lnð1 E Þ
¼
[6] When σ F p ¼ 0, Equation [6] can be simplified as follows: σ PS 1 σ trans Ktrans ¼ 1 PS K 1 ln ð 1 E Þ j j E
[7]
When σ K trans ¼ 0, Equation [6] can be simplified as follows: E σF σ PS 1E [8] ¼ 1 p PS lnð1 E Þ Fp It should be noted that the fractional error of PS is proportional to the fractional errors of Ktrans and Fp in Equations [7] and [8], respectively, and the proportional constants are dependent on E. Numerical simulation Numerical simulations were performed to evaluate the influence of systematic errors and uncertainty of the measured parameters (Ktrans and Fp) on the derived parameter (PS). This evaluation is essential because the error associated with the proposed method is directly related to the errors arising from the two measured parameters. Two sets of simulations were conducted using MATLAB Version 7.0 (MathWorks, Natick, MA, USA). The first simulation evaluated the relationships between PS and the measured parameters according to Equation [4], and how the relationships changed with ±10%, ±20% and ±30% errors in the measured parameters. This simulation facilitates an understanding of how systematic errors (associated with bias) are transferred. Three true Ktrans values (0.01, 0.1 and 0.15 min1) were simulated, each for a range of Fp values (corresponding to E = 0.1–0.5). Likewise, three true Fp values (0.2, 0.6 and 1.0 min1) were simulated, each for a range of Ktrans values (corresponding to E = 0.1–0.5). The second simulation evaluated the fractional error of PS that would have resulted from a range of –30% to +30% errors in Ktrans and Fp according to Equations [7] and [8], respectively. This simulation facilitates an understanding of how random-like errors (associated with variance) are transferred. E values were set from 0.1 to 0.9, with an interval of 0.1. Although all E values of our clinical brain tumor data were below 0.2, using a wider range in the simulation could provide useful information for other clinical populations. MRI acquisition Fourteen pediatric patients (aged 5 months to 14 years; seven females) with brain tumors, including glioneural tumor, sellar germ-cell tumor, germinoma, brain-stem glioma, medulloblastoma, atypical teratoid/rhabdoid tumor, choroid plexus papilloma, pilocytic astrocytoma and anaplastic ependymoma, participated in this study. The patients had no previous surgical resection, biopsy or other treatment of the tumors. Informed consent for the MRI examination was obtained from the parents or legal guardians of the patients after the nature of the study had been comprehensively explained. The study protocol was
Copyright © 2015 John Wiley & Sons, Ltd.
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σ 2PS ¼
Combining Equations [2]–[5], we obtain the following:
H.-L. LIU ET AL. approved by the local Human Experiments and Ethics Committee. Two of the 14 patients were sedated throughout the intravenous administration of midazolam, and no patient underwent anesthesia. No steroids were given to the patients within 7 days before the MRI examination. All patients were scanned using an eight-channel brain array coil on a clinical 3-T MRI scanner (Discovery MR750, GE Healthcare, Milwaukee, WI, USA). The PCASL perfusion imaging was performed using a 3D backgroundsuppressed fast-spin-echo stack-of-spiral readout module with eight in-plane spiral interleaves (TR/TE = 4463 ms/10.2 ms; labeling duration, 1500 ms; post-labeling delay, 1525 ms; no flow-crushing gradients; in-plane matrix, 128 × 128; number of averages (NEX) = 3; field of view, 240 mm × 240 mm; slice thickness, 5 mm) and an echo train length of 23 to obtain 23 consecutive axial slices (14). The labeling plane was 10 mm thick, placed 20 mm inferior to the lower edge of the cerebellum. The PCASL scan also included the acquisition of a reference image after saturation recovery with a saturation time of 2 s. The total scan time was 259 s. A 3D spoiled gradient-echo (SPGR) sequence with varied flip angles was applied to obtain the T1 maps before contrast injection (T10 maps). The imaging parameters were as follows: TR/TE = 4.9/1.3 ms; flip angle, 2°, 5°, 10° and 20°; acceleration factor, 2; matrix size, 256 × 128. Eight slices centered on the tumor areas were acquired with the same slice thickness and field of view as those for the PCASL scan. The slice locations were matched with eight of the slices acquired with the 3D PCASL. The same sequence and parameters, except for a fixed flip angle of 30°, were used for T1-weighted DCE MRI. Sixty dynamic measurements were acquired during a total acquisition time of 234 s, with a sampling interval of 3.9 s. A bolus injection of 0.1 mmol/kg body weight of Gd-diethylenetriaminepentaacetic acid (DTPA) contrast agent (Magnevist, Schering, Berlin, Germany) and then saline (15 mL), at a rate of 2–4 mL/s, was administered using an MR-compatible power injector (OptiStar LE, Covidien, Mansfield, MA, USA). The contrast medium was given manually if the calculated contrast volume was less than 5 mL. The injection of the contrast agent began at the 10th measurement after the start of the dynamic scan. The post-contrast T1-weighted images were acquired using a conventional spin-echo sequence (TR/ TE = 400/12 ms) with the slice thickness and locations matched to those of the PCASL scan. Data analysis The ASL perfusion data were analyzed on an Advantage Windows workstation using Functool software (Version 9.4, GE Medical Systems, Milwaukee/WI/USA). The blood flow per volume, Fρ (mL/100 mL/min), was calculated using the following equation: PLD ST 1 eT 1t e T 1b PW Fρ ¼ 6000 λ LT 2T 1b 1 e T 1b ε PD
[9]
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where PW is the perfusion-weighted or raw difference image and PD is the partial saturation of the reference image. Other parameters, which included T1 of blood (T1b) = 1.6 s, T1 of tissue (T1t) = 1.2 s, partition coefficient (λ) = 0.9 and the labeling efficiency (ε) = 0.6, were assumed to be constant. The Fp map was then calculated by assuming Hct = 0.45. The DCE MRI data were processed using nICE software (Nordic ICE, NordicNeuroLab, Bergen, Norway). The baseline longitudinal relaxation rate (R10) was first estimated by fitting the images
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obtained from varied flip angles using the steady-state SPGR signal equation. The time curve of the change in the longitudinal relaxation rate, ΔR1(t), was then calculated as follows: ΔR1 ðtÞ ¼
K SSð0tÞ 1 1 ln TR K SSð0tÞ cos α 1
! R10
[10]
TRR
10 where K ¼ 1e1e TRR10 cos α , S0 is the baseline signal, S(t) is the signal–time curve and α is the flip angle. By assuming that Ct(t) and Cp(t) were proportional to the corresponding ΔR1(t), the Ktrans map was obtained for each patient using ETM [Equation [1]] (4). The arterial input function (AIF), Cp(t), was obtained for each patient from the internal carotid artery, with T10 assumed to be 1.6 s and Hct = 0.45. AIF was obtained from five voxels that were automatically detected within a manually determined region of interest (ROI) covering the internal carotid artery in each patient. The automatic AIF detection was based on a cluster analysis for selection of the time courses that most closely resembled the excepted AIF properties (large area under the curve, low first moment and high peak enhancement). To minimize the effect of possible patient motion between the PCASL and DCE MRI scans, the Fp map was co-registered to the Ktrans map using SPM8 (http://www.fil.ion.ucl.ac.uk/spm/; Department of Imaging Neuroscience, University College London, London, UK). The PS map was then calculated for each patient based on Equation [4]. The gross tumor ROIs were manually delineated by an experienced neuroradiologist for each patient by referencing post-contrast T1-weighted images using Mango software (Research Imaging Institute, University of Texas Health Science Center, San Antonio, TX, USA). The ROI was drawn on the T1-weighted images and then transferred to the same locations on the corresponding physiological parametric maps to retrieve the mean tumor Fρ, Ktrans and PS values for each patient.
RESULTS The relationships between PS and Fp at three Ktrans levels (0.01, 0.1 and 0.15 min1) are illustrated in (Fig. 1). As expected, the PS values were higher than the Ktrans values at lower Fp and approached the Ktrans values as Fp increased. Under- and overestimation of Ktrans values caused errors in the derived PS in the same directions, with the amounts relatively insensitive to Fp values. Figure 2 shows the relationships between PS and Ktrans at three Fp levels (0.1, 0.3 and 0.8 min1). At low Ktrans, the derived PS values were not affected by errors in Fp values. At higher Ktrans, under- and over-estimation of Fp values caused errors in the derived PS values in the opposite directions. The proportional constants between the fractional errors of PS values and those of Ktrans and Fp values are shown in (Fig. 3), as the results of Equations [7] and [8]. They increased dramatically with E and were approximately one order of magnitude higher for Ktrans than for Fp. Table 1 lists the mean tumor Ktrans, PS and Fρ values of each patient. The mean Ktrans values were found to be significantly lower than the PS values using a paired t-test (p < 0.05). The values averaged across patients (Ktrans = 0.041 min1, PS = 0.050 min1) exhibited an 18% difference, and the greatest discrepancy of 25% was found for the patient with the highest Ktrans (0.162 min1) and PS (0.217 min1) values. (Additional statistical data from ROI analysis of Ktrans and PS values are listed in Tables S1 and S2, respectively.)
Copyright © 2015 John Wiley & Sons, Ltd.
NMR Biomed. 2015; 28: 642–649
MR PERMEABILITY IMAGING
Figure 1. Relationships between permeability × surface area product per unit mass of tissue (PS) and blood plasma flow per volume of tissue trans (Fp) at three forward volumetric transfer constant (K ) values: (a) 1 1 1 0.01 min ; (b) 0.1 min ; (c) 0.15 min . The gray curves show the trans changes in the relationships when K is under- and over-estimated trans . by 10%, 20% and 30%. The broken lines represent PS = K
NMR Biomed. 2015; 28: 642–649
Figure 3. The proportional constants between fractional errors of permeability × surface area product per unit mass of tissue (PS) and of trans ) and blood plasma flow per forward volumetric transfer constant (K volume of tissue (Fp) as a function of the extraction ratio (E).
Copyright © 2015 John Wiley & Sons, Ltd.
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Figure 4 shows post-contrast T1-weighted images and Ktrans, Fρ and PS maps obtained from two patients: one had a sellar germ-cell tumor (top row) and the other had a medulloblastoma (bottom row). The top row images show prominently elevated values in most parts of the tumor on the PS map compared with that on the Ktrans map. The bottom row images show elevated values in only the left portions of the tumor on the PS map compared with that on the Ktrans map. In general, the PS values were higher than the Ktrans values in the tumors. This trend was more apparent in the patient shown in the top row, who had a tumor with low blood flow. Figure 5a illustrates a scatter plot of the estimated PS and measured Ktrans values obtained by averaging across the tumor ROIs of the 14 patients. The results showed that the PS values were increasingly higher than the Ktrans values for tumors with higher Ktrans values. However, for most of the tumors, such as those with Ktrans values of less than 0.04 min1, the Ktrans values appeared approximately equal to the PS values. Figure 5b shows the scatter plot of the intratumoral voxel-by-voxel PS and Ktrans values of two patients (patients 1 and 2 in Table 1). The discrepancies between PS and Ktrans appeared heterogeneous within
Figure 2. Relationships between permeability × surface area product per unit mass of tissue (PS) and forward volumetric transfer constant trans (K ) at three blood plasma flow per volume of tissue (Fp) values: (a) 1 1 1 0.1 min ; (b) 0.3 min ; (c) 0.8 min . The gray curves show the changes in the relationships when Fp is under- and over-estimated by 10%, 20% and 30%.
H.-L. LIU ET AL. Table 1. Physiological parameters [forward volumetric transfer constant (Ktrans), permeability × surface area product per unit mass of tissue (PS) and blood flow per volume (Fρ)] obtained from tumor regions of interest in patients Patient 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mean
Tumor diagnosis
Ktrans (min1)
PS (min1)
Fρ (mL/100 mL/min)
Glioneural tumor Germinoma Germinoma Medulloblastoma Brain-stem glioma Medulloblastoma Atypical teratoid/rhabdoid tumor Brain-stem glioma Anaplastic ependymoma Pilocytic astrocytoma Medulloblastoma Atypical teratoid/rhabdoid tumor Choroid plexus papilloma Germinoma
0.031 0.084 0.018 0.006 0.008 0.011 0.162 0.020 0.101 0.015 0.024 0.023 0.069 0.006 0.041
0.033 0.102 0.019 0.006 0.008 0.011 0.217 0.021 0.130 0.016 0.026 0.025 0.080 0.006 0.050
47.3 47.8 39.6 70.2 46.5 72.0 64.2 65.5 45.1 72.7 36.9 32.7 48.7 27.8 51.2
trans
Figure 4. Post-contrast T1-weighted (T1w) images and forward volumetric transfer constant (K ), permeability × surface area product per unit mass of tissue (PS) and cerebral blood flow (CBF) maps obtained from an 11-year-old girl with pineal gland germ-cell tumor (top row) and a 9-year-old boy with medulloblastoma (bottom row).
the tumors. Some PS values were more than two-fold higher than the Ktrans values for voxels with high K trans levels (see Fig. S1 for time curves from the two voxels with the largest K trans values in Fig. 5b).
DISCUSSION
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This study proposes the use of the PCASL technique for the separation of flow weighting from the Ktrans measurement by DCE MRI in brain tumors. It is well understood that Ktrans, the forward volumetric transfer constant of a tracer between the blood plasma and EES, depends on both blood flow and vessel permeability, two crucial but independent parameters that can be used to characterize tumor neovasculature (18). In the PS-limited condition, i.e. PS 20) were required to ensure minimal bias (
