JOURNAL OF MAGNETIC RESONANCE IMAGING 23:554 –563 (2006)
Original Research
Comparative Study into the Robustness of
Compartmental Modeling and Model-Free Analysis
in DCE-MRI Studies
Caleb Roberts, BSc,1 Basma Issa, MD,1 Andrew Stone, MSc,2
Alan Jackson, MBChB, PhD1 John C. Waterton, PhD,2 and Geoffrey J.M. Parker, PhD1*
Purpose: To evaluate and compare the reproducibility of
the preferred phenomenological parameter IAUC60 (initial
area under the time-concentration curve [IAUC] defined
over the first 60 seconds postenhancement) with the preferred modeling parameter (Ktrans), as derived using two
simple models, in abdominal and cerebral data collected in
typical Phase I clinical trial conditions.
Materials and Methods: Dynamic contrast enhanced MRI
(DCE-MRI) time series were acquired at two imaging centers from a group of patients with abdominal tumors and a
group with gliomas. At both imaging centers, precontrast T1
was calculated using a variable flip angle three-dimensional spoiled gradient echo acquisition that was used to
quantify tissue contrast agent concentration, allowing voxelwise definition of summary DCE-MRI parameters.
Results: A comparison of reproducibility showed that there
was no statistically significant difference in reproducibility
between IAUC60 and Ktrans, although there was a trend
towards better reproducibility for Ktrans (P ⫽ 0.0782). The
95% confidence intervals (CIs) for individual changes
showed that for IAUC60 and Ktrans, changes in excess of
47% and 31%, respectively, are outside the range of normal
variability.
Conclusion: Although modeling is more complex and more
computationally intensive than an IAUC parameterization,
our data suggest this approach to be preferable to a modelfree approach since it provides greater physiological insight
without a reduction in statistical power for Phase I/II clinical drug trials.
Key Words: contrast-enhanced MRI; reproducibility; pharmacokinetic modeling; microvascular endothelial permeability; quantitative analysis; semiquantitative analysis
J. Magn. Reson. Imaging 2006;23:554 –563.
© 2006 Wiley-Liss, Inc.
1
Imaging Science and Biomedical Engineering, University of Manchester, Manchester, UK.
2
AstraZeneca, Alderley Park, Macclesfield, Cheshire, UK.
*Address reprint requests to: G.J.M.P., Imaging Science and Biomedical
Engineering, Stopford Building, University of Manchester, Oxford
Road, Manchester, M13 9PT, UK.
E-mail: geoff.parker@manchester.ac.uk
Received February 16, 2005; Accepted December 28, 2005.
DOI 10.1002/jmri.20529
Published online 27 February 2006 in Wiley InterScience (www.
interscience.wiley.com).
© 2006 Wiley-Liss, Inc.
DYNAMIC CONTRAST-ENHANCED MRI (DCE-MRI) is
finding increasing application in preclinical and clinical
trials of antivascular cancer treatments. It has been
established that tumors cannot grow beyond 1 cm3 in
size and rely on the recruitment of a vascular supply to
generate further growth and for metastasis (1,2). This
blood supply is the target of a number of putative anticancer treatments that aim to impede tumor growth by
either stopping the process of angiogenesis or by destroying existing tumor vasculature. Many such treatments may be expected to be cytostatic rather than
cytotoxic when applied in isolation and are unlikely to
produce immediate reductions in tumor size. In these
cases arresting tumor growth is a more likely initial
indication of successful treatment. In this situation,
established radiological measures of response to treatment, based around measurements of tumor size reduction (3), may be unhelpful, especially when assessing short-term drug effects. Methods that are sensitive
to the blood supply of tumors at the microvascular
level, and that are able to quantify features such as
blood flow and capillary wall permeability, are likely to
be of value as biomarkers as these features match the
targets of the therapies. A method that can be shown to
be reproducible and sensitive to such features will
therefore be of great value in assessing the efficacy of
new antivascular treatments.
Quantitative T1-weighted DCE-MRI methods have
been shown to demonstrate significant changes in the
presence of malignancies (see for example Ref. 4 and
references therein), multiple sclerosis (5), rheumatoid
arthritis (6), atherosclerosis (7,8), Crohn’s disease (9)
and other inflammatory conditions (10), and are potentially able to provide information concerning the blood
volume of the tissue, microvessel permeability, and lesion interstitial space. These parameters may be extracted from a DCE-MRI time course via the application
of models that describe the distribution of contrast
agent in vivo. There is a range of methods that are
currently used to characterize contrast agent uptake
and distribution by the neovasculature. Due to its easy
implementation it is common practice to apply a modelfree approach, initial area under the time-concentration curve (IAUC), to characterize tumor microvasculature. IAUC is a model-free parameter that describes the
554
Reproducibility of IAUC and Ktrans
555
Table 1
Patient Information for Patients that Fulfilled Acceptance Criteria*
Sex
Age
Scanning site
Tumour type
Tumour location
Tumour size (mL)a
M
M
M
M
M
F
F
M
M
F
M
F
F
41
76
56
59
45
50
54
54
60
54
65
69
50
1
1
1
1
2
2
2
2
2
2
2
2
2
Anaplastic astrocytoma
Anaplastic astrocytoma
Glioblastoma multiforme
Glioblastoma multiforme
Alveolar sarcoma
Colon carcinoma
GE junction carcinoma
Renal cell carcinoma
Renal cell carcinoma
Renal cell carcinoma
Colon carcinoma
Liver carcinoma
Breast carcinoma
Brain
Brain
Brain
Brain
Soft tissue
Liver
Liver
Soft tissue
Soft tissue
Bone
Pelvic
Liver
Bone
73
27
33
59
309
60
2
363
222
14
127
52
9
*See text for details.
a
Tumor size calculated as the average measurement over two visits.
uptake of contrast agent in a tissue of interest (11). The
relationship between IAUC and microvascular physiology is not clear—it is in general not possible to determine whether a particular value of IAUC is, for example,
indicating a particular level of capillary permeability or
blood volume. However, potentially more specific physiological information can be derived using tracer kinetic
modeling methods. In this study we implemented two
commonly-applied kinetic models (5,12) to attempt to
extract specific information regarding the characteristics of the tumor microvasculature. The model we applied is that introduced by Tofts and Kermode (5) and
further developed by Tofts (12), which provides estimates of the volume transfer coefficient, Ktrans (min⫺1),
between the blood pool and the extracellular extravascular space (EES). It also provides estimates of the
volume occupied by the EES, ve (no units), as a fraction
of total tissue volume. This model may be extended to
additionally estimate the fractional volume of the
plasma space, vp (no units), and this extension (13)
represents our second model implementation.
It might be argued that IAUC should be more reproducible than Ktrans, as it does not involve a fitting
process and so is less error-prone in generation. However, this has not been shown explicitly in the literature. Compartmental modeling, although potentially
giving more specific information regarding the true
underlying physiology, might be assumed to be less
robust since the modeling process is sensitive to data
noise and fitting instabilities. Furthermore, comparisons of compartmental modeling parameters across
institutions have proven difficult due to the varying
data acquisition techniques used. Therefore, the hypothesis that we set out to test is that the model-free
parameter, IAUC, will produce a more reproducible
assessment of tumor microvasculature than parameters such as Ktrans, ve, or vp.
The aim of this work was to evaluate the reproducibility of the IAUC parameter and model-derived parameters obtained from DCE-MRI data acquired using protocols designed for use in multicenter clinical trials of
new antivascular agents. Data acquisition in this study
was performed at two sites in different countries with
scanners made by different manufacturers. Both cerebral and abdominal tumors were investigated, and repeat scans were acquired to assess the reproducibility
of the methods. Data analysis was performed at a single
center.
MATERIALS AND METHODS
Patients and Data Acquisition
Patients were scanned at two imaging centers with protocols that were designed to be as similar as possible
within hardware and software constraints. Table 1 provides patient details, including gender, tumor type, size
and location.
Site 1
Eleven patients with known intracranial neoplasms
were scanned twice (mean interscan interval 1.5 days)
at the University of Manchester, UK. The study was
approved by the Central Manchester medical ethics
committee and all patients gave informed consent. The
clinical diagnoses were: glioblastoma multiforme (N ⫽
7) and anaplastic astrocytoma (N ⫽ 4). Diagnoses were
confirmed histologically in nine patients. Of these patients, four were ultimately included in the study (see
below and Table 1).
Imaging was performed using a 1.5-T Philips ACS NT
Gyroscan scanner. T1-weighted DCE-MRI was performed using an axial radiofrequency (RF)-spoiled
three-dimensional fast field echo (gradient echo) sequence. Sequence parameters: TR ⫽ 4.3 msec; TE ⫽ 1.1
msec; field of view (FOV) ⫽ 230 ⫻ 230 mm; in-plane
reconstruction matrix ⫽ 128 ⫻ 128; reconstructed partitions ⫽ 25; and reconstructed partition thickness ⫽ 3
mm. The three-dimensional volume was acquired with
reduced k-space coverage and the 25 partitions were
interpolated from 13 axial phase encoding steps. These
strategies allowed rapid volume acquisition, suitable
for DCE-MRI studies. Native tissue T1 values were determined prior to contrast agent administration from
three acquisitions with three different flip angles (␣ ⫽
2°, 10°, 35°) (14,15). The dynamic series utilized the
556
Roberts et al.
same three-dimensional acquisition (TR, TE, FOV, matrix identical), with ␣ ⫽ 35°, repeated to cover between
three and six minutes. The temporal resolution of the
acquisition was approximately eight seconds, and images were acquired contiguously in time. Scanner
transmitter and receiver gains were kept constant
throughout both the baseline T1 calculation and the
dynamic series to facilitate signal comparisons for determination of contrast agent concentration (15,16).
Contrast agent (0.1 mmol/kg of gadodiamide: GdDTPA-BMA [Omniscan, Nycomed, Norway]) was administered manually by an experienced neuroradiologist
following the seventh dynamic scan. The injection was
administered through a 16 –18-gauge cannula inserted
into a large antecubital vein and the injection rate was
standardized by use of a metronome so that the contrast injection took between three and four seconds,
and the injection rate was kept as constant as possible
through this period. The injection was immediately followed by a similar volume of normal saline injected at
the same rate. This injection protocol has previously
been shown to be reproducible in this patient group
(17). All patients received steroid therapy from diagnosis (4 mg of dexamethasone four times a day, no other
treatment was given prior to or during the study).
Acceptance Criteria
Site 2
Tissue Concentration and Arterial Input Function
Sampling
Twelve patients with known abdominal neoplasms were
scanned twice, with a mean interscan interval of 3.5
days, at Wayne State University, Detroit, MI, USA.
Studies were carried out following ethical approval from
Wayne State University Institutional Review Board. Of
these patients, nine were ultimately included in the
study (see below and Table 1).
Imaging was performed using a 1.5-T Siemens Vision
scanner. Axial T1-weighted DCE-MRI was performed
using an RF-spoiled three-dimensional FLASH (gradient echo) sequence. Sequence parameters: TR ⫽ 3.8
msec; TE ⫽ 1.4 msec; field of view (FOV) ⫽ 230 ⫻ 230
mm; in-plane reconstruction matrix ⫽ 256 ⫻ 256; reconstructed partitions ⫽ 32; and reconstructed partition thickness ⫽ 4 mm. Native tissue T1 values were
determined prior to contrast agent administration from
three acquisitions with three different flip angles (␣ ⫽
2°, 13°, 28°). The dynamic series utilized the same
three-dimensional acquisition (TR, TE, FOV, matrix
identical), with ␣ ⫽ 13°, repeated to cover 8.85 minutes.
The time series was split in two to allow for restricted
image capacity on this scanner. For the first series,
which lasted for approximately 70 seconds, each acquisition lasted approximately 8 seconds, and images were
acquired contiguously in time. For the second series, 6
volumes were acquired at 75-second intervals. Scanner
transmitter and receiver gains were kept constant
throughout both the baseline T1 calculation and the two
dynamic series to facilitate signal comparisons for determination of contrast agent concentration (0.1
mmol/kg gadopentate dimeglumine: Gd-DTPA [Magnevist, Schering, Germany]) (15,16).
Data from the two sites were screened in order to maintain a uniform compilation of comparable data. The
data acquisition was expected to comply exactly with
the acquisition protocol outlined above. Additionally,
any data that contained errors that were responsible for
an inaccurate T1 calculation, contained significant patient motion during dynamic acquisition, or misregistered baseline and dynamic images was rejected from
the study. As a result, seven brain data sets and three
abdominal data sets were rejected. Table 1 shows the
remaining data sets that were used in this study.
In four of the data sets, the entire tumor volume was
not captured in the imaging volume on one or both of
the visits and therefore could not be used. In one patient the tumor margins were deemed too difficult to
define accurately (see below for details on tumor outlining) on both visits. In three data sets a poor baseline
T1 calculation, which was most likely due to operator
error in acquiring baseline T1-weighted images, prevented them from being used. In one patient, contrast
agent was administered prior to (rather than during)
the dynamic acquisition and in another patient the
dynamic images were not acquired in the same anatomical location as the baseline T1-weighted images. The
overall yield of acceptable datasets was 57 %.
Contrast Agent Concentration Calculation
Native T1 at each voxel r in the three-dimensional imaging volume was determined from the three-flip-angle
baseline data by fitting the standard relationship describing signal, S, from a spoiled gradient echo acquisition at short TE (14)
冉
冉 冊冊
冉 冊
⫺TR
T1共r兲
⫺TR
1 ⫺ cos ␣ exp
T1共r兲
S0共r兲sin ␣ 1 ⫺ exp
S共r,␣,T1兲 ⫽
(1)
where S0 is a factor proportional to the proton density of
the tissue and scanner and image gain settings that is
also generated during the fitting process. We neglect
errors from radiofrequency inhomogeneity in the transmitter, and from misset pulses. T1 at each time point, t,
during the dynamic series was estimated by rearranging Eq. [1] (15):
冉
T 1 共t,r兲 ⫽ ⫺TR ln
冊
S0共r兲sin ␣ ⫺ S共t,r兲
S0共r兲sin ␣ ⫺ S共t,r兲cos ␣
(2)
Concentration of contrast agent was then estimated
using the standard relationship:
1
1
⫺
T1共t,r兲 T1共0,r兲
关CA兴共t,r兲 ⫽
r1
(3)
Reproducibility of IAUC and Ktrans
557
Table 2
Summary of the Analysis Methods Used in This Study and the
Information They Produce*
Method
number
Analysis method
IAUC60
1
2
3
Model-free analysis
Tofts model
Tofts model extended
⻫
✕
✕
n⫽0
trans
ve
vp
✕
⻫
⻫
✕
⻫
⻫
✕
✕
⻫
K
冘
N
IAUC 60 ⫽
*(⻫) indicates a parameter that may be calculated from the analysis.
where r1 is the longitudinal relaxivity of the contrast
agent, which was assumed for all experiments to be 4.5
seconds–1mM–1.
Arterial Input Function Sampling
Due to differences in data acquisition procedures at the
two imaging sites, mainly the extended temporal resolution of abdominal data, the arterial input function
(AIF) could not be accurately defined from the data for
each individual. Therefore an assumed AIF was used for
all modeling analysis procedures (5,18).
Data Analysis
Tumors were manually outlined in two dimensions on
each image slice containing tumor using the Dispimage
software package (19). This was performed by a trained
radiologist (BI) on one of the postcontrast dynamic time
series volumes. IAUC and model fitting was performed
on a voxel-by voxel basis within the volume and the
mean and median values of each time series parameter
were obtained, in addition to the total tumor volume at
each visit. On occasions when more than one tumor
was wholly-enclosed within the imaging volume, each
tumor was treated individually.
A voxel within a volume of interest was defined as
showing enhancement if the peak signal intensity after
contrast agent arrival was more than 3 SD away from
the mean baseline (prearrival) signal. The volume occupied by all such voxels within the manually defined
tumor volume was then calculated as the enhancing
tumor volume. Time series analysis was only performed
in tumor voxels classed as enhancing.
Three analysis methods were applied to the tissue
contrast agent concentration time course. These methods are summarized in Table 2 and are described in
detail below.
Method 1
The IAUC method has been developed to provide a robust indicator of tumor vascular characteristics. This
approach does not attempt to directly estimate physiological parameters related to tumor vasculature; instead it provides a measurement of the initial arrival of
contrast agent in the tissue of interest after intravenous
bolus administration that reflects blood flow, vascular
permeability and the fraction of interstitial space (20).
We calculate IAUC60 (units mmol.kg–1.second) using
trapezoidal integration of the contrast agent concentration with time over the first 60-second postcontrast
agent arrival in the enhancing voxels of interest:
共C t 共n兲 ⫹ C t 共n ⫺ 1兲兲共t共n兲 ⫺ t共n ⫺ 1兲兲
2
(4)
where Ct(n) is the tissue concentration of contrast
agent, at dynamic time point n, t(n) is the time at time
point n, and N is the last time point before t(n) ⱖ 60
seconds t(0) was defined manually as the first image
volume to exhibit signal enhancement.
Method 2
Low molecular weight contrast media available for clinical MRI studies diffuse from the blood pool into the
tissue extracellular space at a rate determined by the
blood flow to the tissue, permeability of the microvessel
walls, and the surface area of the perfusing vessels.
Clinical MRI contrast agents do not cross cell membranes and its volume of distribution is therefore effectively the interstitial space, which can be defined as the
volume of the EES per unit volume of tissue, ve (13).
The rate of accumulation and washout of a contrast
medium in ve, under the assumption that contrast
agent is well-mixed in the vascular plasma space, vp,
and in ve, can be described by a general rate equation
(see for example Ref. 21):
ve
dC e 共t兲
⫽ K trans共Cp共t兲 ⫺ Ce共t兲兲
dt
(5)
where Ce is the concentration of agent in ve, Cp is the
concentration of agent in vp, and Ktrans is the volume
transfer coefficient between vp and ve (13).
In many normal tissues (in particular in the brain),
the vascular volume is a small fraction of total tissue
volume, and it is often assumed that the tracer concentration in the tissue as a whole, Ct, is not influenced by
the concentration in the vessels (that Ct ⬇ veCe) (5). This
allows us to express the concentration of contrast agent
observed in a DCE-MRI experiment as
C t 共t兲 ⫽ K trans
冕
t
0
冉
Cp共t⬘兲exp
冊
Ktrans共t ⫺ t⬘兲
dt⬘.
ve
(6)
Equation [6] requires the concentration of contrast
agent in the blood plasma, Cp (the AIF), to be provided.
As with previous applications of this method, we assume an AIF derived from the normal washout characteristics measured in a normal population (5,18).
Method 3
While method 2 provides a model that is likely to be
acceptable in tumors with no large increase in blood
volume, it is likely to be invalid in many contexts, as
blood volume can increase markedly in neoplasms.
Models of additional sophistication are required to allow these cases to be described adequately, and a number of investigators (see for example Refs. 22–24) have
attempted to incorporate the effects of a significant vas-
558
Roberts et al.
cular signal. We choose to extend Eq. [6] to include the
concentration of contrast agent in the blood plasma,
giving Ct ⫽ vpCp ⫹ veCe. We then have
C t 共t兲 ⫽ v p C p 共t兲 ⫹ K trans
冕
冉
t
Cp共t⬘兲exp
0
冊
Ktrans共t ⫺ t⬘兲
dt⬘
ve
(7)
We apply the model described in Eq. [7] using the same
assumed AIF as used in method 2.
Parameter Estimation
Methods 2 and 3 were applied to the DCE-MRI data
volume on a voxel-by-voxel basis using a simplex fitting
algorithm incorporated in software written in-house.
The time of arrival of contrast agent to the tissue was
included as a variable in the fit. Fitting was performed
only in the previously defined tumor ROIs in voxels
identified as enhancing, and three-dimensional maps of
the parameters listed in Table 2 were generated. Median summary parameter values were then extracted
from these maps.
Statistical Analysis
Median values were chosen for analyses since they are
less sensitive to data outliers within the tumor volume.
For each subject in both study cohorts, the percentage difference between two measurements of each parameter was calculated:
冉
冊
measurement 1 ⫺ measurement 2
⫻ 100%
measurement 2
(8)
The reproducibility of each pairwise comparison was
assessed using the test–retest root mean square (RMS)
coefficient of variation (CoV). For each subject, i, the
CoV is the standard deviation, ␴i, for the two measurements on that subject, divided by their mean, ␮i
CoV i ⫽
␴i
␮i
(9)
The overall test-retest RMS CoV for a group of N subjects is then
冑
冉冊
␴i
␮i
N
¥ i⫽1
(10)
This provides an estimate of the intrasubject test–retest
CoV and can further be used to calculate the 95% confidence interval (CI) for the observation of genuine
changes in each parameter for a single individual from
the group:
冑
N
¥i⫽1
95% CI ⫽
冉冊
␴i
␮i
N
2
共1.96 冑2兲 ⫻ 100%
RESULTS
For all time course parameters we report the median
values of the various parameters of interest from the
manually defined volumes of interest for each tumor.
We also present the difference in the parameter values
between the two scanning time points with the calculated intra subject test–retest CoV and individual 95%
CIs for each parameter of interest. The results have
been divided into two groups based on the anatomical
location of the tumor.
Tumor Volume
Figure 1 shows the changes in measured whole and
enhancing tumor volume between visits in the brain
and abdominal tumor cases. Mean whole tumor volumes at each visit for the brain were 48.5 mL and 47.7
mL, for measurement one and two, respectively. Similarly in the abdominal data group, mean whole tumor
volumes were 107.3 and 105.4 mL. The mean magnitude change between visits was 5%, compared with 7%
in the abdominal tumor group. When looking at whole
tumor volume as a marker of treatment effect our results show that a change in an individual of more than
16% is outside the range of normal variability (95% CI).
However, a change of 73% in enhancing tumor volume
is required in order for the change to be significant. This
dramatic change in the variability of enhancing tumor
volume is due to two outliers in the data set, without
which a change of 23% in enhancing tumor volume
would be outside the range of normal variability.
Summary Kinetic Parameters
2
N
To compare the reproducibility of each parameter, we
first calculated the log of the ratio of measurement one
to measurement two, for both IAUC60 and Ktrans (this
approach is consistent with using a CoV). We then calculated, for each subject, both the sum of and difference between the log IAUC60 ratio and log Ktrans ratio.
We then performed a linear regression of the sum of the
parameters on the difference in parameters. A test of
whether there was a significant correlation in such a
model is equivalent to testing whether there was a difference in reproducibility in correlated samples (25).
The null hypothesis of the reproducibility being the
same for both parameters would result in a regression
coefficient of zero.
(11)
Values of IAUC60 from measurements one and two
ranged from 1.2 to 10.1 mmol.kg–1.second in the brain
data and from 7.7 to 44.6 mmol.kg–1.second in the
abdominal data (Fig. 2). Using method 2, values of
Ktrans range from 0.35 to 2.04 minute–1 in the brain and
from 0.37 to 1.45 minute–1 in the abdomen. Values of ve
(no units) ranged from 0.019 to 0.19 in the brain and
from 0.21 to 0.78 in the abdominal data sets. In Fig. 3
an additional parameter to method 2, vp, is also shown.
This model (method 3) produced values of Ktrans in the
range of 0.075 to 0.299 minute–1 in the brain data and
from 0.242 to 0.759 minute–1 in the abdominal tumors.
These values are considerably lower than Ktrans calcu-
Reproducibility of IAUC and Ktrans
559
Figure 1. Summary of measurements at visit
1 and visit 2 for whole tumor volume (a) and
enhancing tumor volume (b).
lated from method 2. ve as calculated using method 3
shows values in the brain from 0.014 to 0.246. In the
abdominal data set values of ve range from 0.22 to 1.01.
For ve, the range of values was similar in both methods
2 and 3. The additional parameter, vp (no units), which
defines the space per voxel occupied by blood plasma,
ranges between 0.001 to 0.005 in the brain and 0.016
to 0.311 in the abdomen.
At first glance, the most reproducible parameter is
Ktrans calculated using method 2 in the brain data, with
a mean magnitude change (derived from the group of
median parameter values) of 9.77% between measurements (Table 3). In this case the individual 95% CI
indicates that changes in the order of 21% need to be
seen to conclude a significant change due to treatment
(Fig. 4). However, since Ktrans values in the abdominal
data are less reproducible, with mean percentage
changes of 16% and 23% in method 2 and 3, respectively, the overall 95% confidence limit for individual
changes for the combined group is reduced to 31%
using method 2 and 44% using method 3 to calculate
Ktrans (Fig. 4).
The mean magnitude change in IAUC60 for combined
data was 20%. The individual 95% CIs for IAUC60 show
that a change of 47% is required in order for significance to be indicated. Table 3 shows that ve is approx-
Figure 2. Measurements at visit 1 and
visit 2 for IAUC60 (a), Ktrans (b), and ve (c).
Both Ktrans and ve were estimated using
method 2.
imately as robust as Ktrans derived using method 2 and
perhaps more so than Ktrans derived using method 3,
with a mean percentage change of 15% and 17%, respectively. The individual changes in ve outside the
range of normal variability are 35% using method 2 and
41% using method 3. Vascular space (vp) can only be
calculated using method 3. This parameter showed relatively poor reproducibility across both data sets. Although there was only a mean of 33% difference between measurements for vp, the RMS, as reported in
Table 3, of 0.371 meant that a change of over 100%
could be expected by chance.
When exploring how IAUC60 is correlated with both
Ktrans and ve (Fig. 5), we see in the abdominal tumor
group that IAUC60 is more correlated with Ktrans (R2 ⫽
0.81) than with ve (R2 ⫽ 0.73). However, in the Glioma
tumor group IAUC60 is more strongly correlated with ve
(R2 ⫽ 0.98) than Ktrans (R2 ⫽ 0.31).
Specific tumor characteristics can be illustrated
through calculated parameter maps (Fig. 6) that highlight the heterogeneity of the tumor. These maps for
IAUC60, Ktrans, ve, and vp (the later three parameters
calculated using method 3, the extended Tofts model),
indicate that modeling can provide multiple tracer kinetic parameters that are distributed in a spatially complementary manner; for example, the Ktrans distribution
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Roberts et al.
Figure 3. Summary of measurements
at visit 1 and visit 2 for Ktrans (a), ve (b),
and vp (expressed in % for clarity) (c), all
estimated using method 3.
the biomarker for individual patients involved in a clinical trial.
Kinetic model-based assessments of the DCE-MRI
time series have an advantage over model-free approaches in that the measurements of tumor microvascularity that are made attempt to represent the true
underlying physiology of the pathology concerned.
However, model-based approaches are generally
thought to be more susceptible to the effects of noise
and fitting errors than the simpler model-free approaches, and are therefore often assumed to be less
robust. In a multicenter clinical trial there may be large
variation in the methods of data acquisition, including
acquisition parameters and pulse sequences that can
produce significant differences in the determination of
kinetic parameters (11). Furthermore, it is often difficult to form a comparison of physiologically modeled
parameter values such as Ktrans, ve, and vp, if the data
analysis methods are different across institutions. A
model-free approach, such as IAUC60, might be assumed to be less variable, as there is no data-fitting
process involved. This method can be easily implemented across institutions and successfully compared.
It is therefore useful to know whether this parameter,
IAUC60, is indeed a more robust marker of tumor characteristics than the more physiological parameters
Ktrans, ve, and vp.
Modeling output provides additional information—
Fig. 6 shows that this can be complementary in its
in the abdominal tumor (Fig. 6) is markedly different to
the ve distribution. The distributions of none of the
modeling parameters appear to match the IAUC60 distribution particularly well.
A linear regression of the sum of the log IAUC60 and
log Ktrans ratios on the difference between the log
IAUC60 and log Ktrans ratios shows that although there
was a correlation between the two parameters (R2 ⫽
0.26), this was not significant (P ⫽ 0.0782) (Fig. 7). The
95% CIs for the ratio of variances between IAUC60 and
Ktrans are 0.90 and 6.67. These findings are therefore
compatible with the null hypothesis that the two parameterizations have the same reproducibility. However, the trend in the data suggests that the reproducibility of IAUC60 may be slightly worse than Ktrans.
DISCUSSION
An assessment of tumor microvasculature prior to and
during the course of antivascular or antiangiogenic
treatment is valuable in Phase I clinical trials. It is
essential to have knowledge of the reproducibility of a
technique prior to embarking on a clinical trial in order
to determine the statistical power, and thus to include
sufficient patients to detect changes due to drug effect
and not to measurement error in the biomarker. The
test–retest coefficient of variation (CoV) and the individual 95% CIs give a good indication of what can be
expected to be a significant drug-induced change in of
Table 3
Summary of Test–Retest Root Mean Square (RMS) CoV (see Eq. [10]), Magnitude Mean (⫾ SD) and Mean Magnitude % Change
Between Measurements for Each DCE-MRI Kinetic Parameter Studied
Abdominal (N ⫽ 9)
Parametera
Method 1
IAUC60
Method 2
Ktrans
ve
Method 3
Ktrans
ve
vp
a
Brain (N ⫽ 4)
Combined (N ⫽ 13)
Mean mag.
change
Mean mag.
% change
RMS
CoV
Mean mag.
change
Mean mag.
% change
RMS
CoV
Mean mag.
change
Mean mag.
% change
RMS
CoV
3.27 ⫾ 2.9
22.4
0.19
0.65 ⫾ 0.58
15.7
0.11
2.47 ⫾ 2.7
20.3
0.17
0.12 ⫾ 0.09
0.06 ⫾ 0.07
16.3
11.5
0.13
0.11
0.14 ⫾ 0.1
0.02 ⫾ 0.01
9.8
21.9
0.08
0.15
0.13 ⫾ 0.09
0.05 ⫾ 0.06
14.3
14.7
0.11
0.13
0.1 ⫾ 0.07
0.08 ⫾ 0.1
0.027 ⫾ 0.021
22.9
13.9
31.4
0.19
0.14
0.30
0.02 ⫾ 0.016
0.02 ⫾ 0.017
0.001 ⫾ 0.002
11.5
23.8
35.8
0.08
0.17
0.49
0.075 ⫾ 0.07
0.06 ⫾ 0.09
0.019 ⫾ 0.02
19.4
16.9
32.7
0.16
0.15
0.37
Parameter units: IAUC60 (mmol/kg second), Ktrans (minute⫺1), ve and vp (no units) mag. ⫽ magnitude.
Reproducibility of IAUC and Ktrans
Figure 4. Individual patient smallest detectable difference expressed as 95% confidence interval values for each calculated
parameter (Eq. [11]). Tumors grouped in the brain, abdomen
and combined.
spatial distribution. Figure 5 also shows that IAUC60
cannot be used as a simple surrogate for Ktrans, as the
relationship between the parameters (and with ve) varies between tumor types and/or anatomical site. Therefore, the only argument for not using a modeling approach is that it may be less robust than a model-free
approach. However, we have shown using the regression of the sum on the difference of log-ratios for Ktrans
and IAUC60 that neither IAUC60 nor Ktrans gives a significantly superior reproducibility. This indicates that
modeling should be applied wherever the data acquisition allows it.
The transfer coefficient, Ktrans, as defined using
method 2, has been shown in this study to be a reasonably reproducible parameter. Our results show that for
an individual enrolled in a clinical trial cohort of N ⫽
13 a measured change in Ktrans (using method 2) in
excess of 31% can be attributed to a significant druginduced effect, rather than to measurement error. However, method 2 does not account for any contribution of
a vascular component in the tumor and a more accurate physiological model should include a term for the
vascular plasma fraction, vp. Method 3 incorporates
this into its approach; here Ktrans values are lower than
observed using method 2, which probably indicates a
closer representation of the true contrast agent kinetics. However, the results of using method 3 are also less
reproducible due to the additional degrees of freedom in
the fitting process. In any individual a change of the
order of 45% is required to be significant. Therefore,
although this measurement of Ktrans has been derived
from a more accurate model of the true underlying
tumor physiology, it is less precise, reflecting the general tradeoff between the level of modeling detail and
robustness.
Our estimations of the model-free parameter IAUC60
show an average of 20% variability between measurements across both tumor type groups. In comparison
with Ktrans, in which the variabilities between measurements were on average 14% and 19% for methods 2 and
3, respectively, the measurements of IAUC60 are marginally less reproducible, although this does not reach a
statistically significant level. This is somewhat at odds
with the previously discussed relationship between
561
analysis complexity and analysis robustness; if this
applied to our measurements of IAUC60, this would be
expected to be more reliable than the modeling results,
as it is the simplest method investigated. We believe
this result is caused by the fact that the modeling approaches exploit the entire time series of the data acquisition, whereas IAUC60 is defined over the first 60
seconds only. It is therefore likely that the marginally
better performance of the modeling methods is a result
of reduced overall noise influence. This is consistent
with a study using deuterium-labeled water as a contrast agent that showed a modeling benefit in precision
that increases with increasing noise levels (26).
Our results compare reasonably well with other DCEMRI reproducibility studies by Jackson et al (27), Galbraith et al (28), and Evelhoch et al (20). Jackson et al
(27) studied kinetic parameters calculated in the brain
and report CoV values of 7.7% for Ktrans and 6.7% for ve,
compared with 7.8% and 14.8% for Ktrans and ve, respectively, in our brain data. Our current study bears
similarities with Galbraith et al (28) in that we have
studied a selection of abdominal tumors and applied
the standard Tofts model (our method 2). They found
that the individual 95% CI for Ktrans was approximately
64%, 17% for ve, and 61% for IAUC90. This compares
with our results of 35%, 30%, and 55%, respectively, for
our abdominal data. Our IAUC60 results are similar to
the IAUC90 results in Galbraith et al (28), implying that
our data may have had a better signal to noise ratio, as
this was achieved with a 50% shorter dynamic time
series. Our tighter 95% CI for Ktrans may be caused by
our use of a longer data acquisition. The worse performance of our ve measurement is likely to be caused by
the fact that both Galbraith et al (28) and Jackson et al
(27) discarded ve values above 1.0, as these indicate an
unphysiological estimate of the EES volume (similarlymotivated thresholds were applied to Ktrans in these
studies). However, we chose to keep these high values
in our voxel-by-voxel analysis, as we judge these to be a
genuine output from the modeling process. While they
reflect the fact that the model is imperfect, they are
often required for adequate parameterization of contrast kinetics in certain voxels; these are likely to be
those with high blood volume—an effect not accounted
Figure 5. Correlation of IAUC60 with Ktrans and ve for both
glioma and abdominal tumor groups.
562
Roberts et al.
Figure 6. Parameter maps of
IAUC60 (mmol.kg–1.second) (a),
Ktrans (minute–1) (b), ve (c), and
vp (d) in a renal tumor. Arrow i
shows an area of high IAUC60
(a) corresponding to high vp (d).
Arrow ii demonstrates the hypoperfused core of this tumor,
which leads to low IAUC60 (a),
Ktrans (b), and vp (d).
for using the standard Tofts model. Our results therefore reflect the full instability/inadequacy of the modeling and experimental process without truncation. A
direct comparison of IAUC in Evelhoch et al (20) shows
our CoV to be marginally better. We believe that this is
due to our more stringent data acceptance criteria.
Figure 7. Linear regression of the sum of log IAUC60 and Ktrans
ratios on the difference between log IAUC60 and Ktrans ratios.
IAUC601 and Ktrans1 refer to measurement 1 and IAUC602 and
Ktrans2 to measurement 2.
A limitation of this study is the lack of a calculated
AIF for each individual. AIF calculation was only possible in the brain data and since it could not be performed
in the abdominal data due to acquisition problems we
did not include these findings in the study. If an AIF
could be calculated the reproducibility of the DCE-MRI
analysis would depend largely on the AIF calculation. If
the AIF calculation contained minimal errors due to
noise in the data and reproducible AIFs could be produced, then we expect both the reproducibility and precision of the kinetic analysis to improve. However, if
data quality and AIF reproducibility is poor, the overall
reproducibility of kinetic analysis would be degraded.
This study highlights the importance for good data
acquisition and screening. From the number of discarded datasets, it is apparent that careful data acquisition is needed for this type of study in order to prevent
a buildup of rejected data sets. Some of the data could
in theory be recovered by the use of image registration
techniques, a general application of which would reduce errors in analysis due to patient or physiological
motion and perhaps improve overall reproducibility for
all parameters. Furthermore, rigorous quality assurance procedures are able to decrease the rejection rate
significantly (see for example Ref. 29).
In conclusion, we have demonstrated the statistical
limits that should be acknowledged when employing
DCE-MRI in assessing antitumor therapy in which biomarkers such as Ktrans, ve, vp, and IAUC can be calculated. These parameters offer insight into underlying
Reproducibility of IAUC and Ktrans
tumor physiology, although the usefulness of the data
depends on the detail included in the parameterization
process. This study shows that since the reproducibility
of model-based analyses (generating parameters such
as Ktrans) is statistically no worse than an IAUC parameterization, a model-based approach is likely to be more
useful in clinical trial settings since further information
that more closely reflects the true underlying physiology may be obtained.
563
11.
12.
13.
14.
15.
ACKNOWLEDGEMENTS
We thank Jeffrey Evelhoch and Pat LoRusso for provision of data from Wayne State University, Detroit, MI,
USA. Also Xiao Ping Zhu, Ka-Loh Li, Dave Clarke, and
Yvonne Watson for work on the data acquisition protocol in Manchester. We also thank Nikki Fernandes and
Andrew Holmes for work on statistical analyses of the
data and David L. Buckley for valuable input into the
study.
16.
17.
18.
19.
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