Original contributions Quantitative pharmacokinetic analysis of DCE-MRI data without an arterial input function: a reference region model Thomas E. Yankeelov a,b, T , Jeffrey J. Luci a,b , Martin Lepage a,b , Rui Li b,c , Laura Debusk d , P. Charles Lin d,e , Ronald R. Price a,b , John C. Gore a,b a Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232-2675, USA b Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232-2675, USA c Department of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37232-2675, USA d Department of Cancer Biology, Vanderbilt University, Nashville, TN 37232-2675, USA e Department of Radiation Oncology, Vanderbilt University, Nashville, TN 37232-2675, USA Received 17 February 2005; accepted 17 February 2005 Abstract Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can assess tumor perfusion, microvascular vessel wall permeability and extravascular–extracellular volume fraction. Analysis of DCE-MRI data is usually based on indicator dilution theory that requires knowledge of the concentration of the contrast agent in the blood plasma, the arterial input function (AIF). A method is presented that compares the tissues of interest (TOI) curve shape to that of a reference region (RR), thereby eliminating the need for direct AIF measurement. By assigning literature values for K trans (the blood perfusion-vessel permeability product) and v e (extravascular–extracellular volume fraction) in a reference tissue, it is possible to extract the K trans and v e values for a TOI without knowledge of the AIF. The operational RR equation for DCE-MRI analysis is derived, and its sensitivity to noise and incorrect assignment of the RR parameters is tested via simulations. The method is robust at noise levels of 10%, returning accurate (F20% in the worst case) and precise (F15% in the worst case) values. Errors in the TOI K trans and v e values scale approximately linearly with the errors in the assigned RR K trans and v e values. The methodology is then applied to a Lewis Lung Carcinoma mouse tumor model. A slowly enhancing TOI yielded K trans = 0.039F0.002 min 1 and v e = 0.46F0.01, while a rapidly enhancing region yielded K trans = 0.35F0.05 min 1 and v e = 0.31F0.01. Parametric K trans and v e mappings manifested a tumor periphery with elevated K trans ( N 0.30 min 1 ) and v e ( N 0.30) values. The main advantage of the RR approach is that it allows for quantitative assessment of tissue properties without having to obtain high temporal resolution images to characterize an AIF. This allows for acquiring images with higher spatial resolution and/or SNR, and therefore, increased ability to probe tissue heterogeneity. D 2005 Elsevier Inc. All rights reserved. Keywords: DCE-MRI; Arterial input function; Pharmacokinetics; Reference region model 1. Introduction Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) involves the serial acquisition of MR images of a tissue of interest (TOI) (e.g., a tumor locus) before, during and after an intravenous injection of contrast agent (CA). As the CA perfuses into the tissue under investigation, the T 1 and T 2 values of tissue water decrease to an extent that is determined by the concentration of the agent. By considering a set of images acquired before, during and after a CA infusion, a region of interest (ROI) or individual voxel will display a characteristic signal intensity time course that can be related to CA concentration. This time course can be analyzed with an appropriate mathematical pharmacokinetic model. By fitting the DCE-MRI data to such model, physiological parameters can be extracted that relate to, for example, tissue perfusion, microvascular vessel wall perme- ability and extracellular volume fraction [1]. It has been shown that both healthy and pathologic tissues exhibit characteristic signal intensity time courses as well as pharmacokinetic parameter values (see, e.g., Ref. [2– 4]). Furthermore, since these parameter values are probes of 0730-725X/$ – see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.mri.2005.02.013 * Corresponding author. Institute of Imaging Science, Vanderbilt University, Nashville, Tennessee 37232-2675, USA. E-mail address: [email protected] (T.E. Yankeelov). Magnetic Resonance Imaging 23 (2005) 519 – 529
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Magnetic Resonance Im
Original contributions
Quantitative pharmacokinetic analysis of DCE-MRI data without
an arterial input function: a reference region model
Thomas E. Yankeelova,b,T, Jeffrey J. Lucia,b, Martin Lepagea,b, Rui Lib,c,
Laura Debuskd, P. Charles Lind,e, Ronald R. Pricea,b, John C. Gorea,b
aInstitute of Imaging Science, Vanderbilt University, Nashville, TN 37232-2675, USAbDepartment of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN 37232-2675, USA
cDepartment of Electrical Engineering and Computer Science, Vanderbilt University, Nashville, TN 37232-2675, USAdDepartment of Cancer Biology, Vanderbilt University, Nashville, TN 37232-2675, USA
eDepartment of Radiation Oncology, Vanderbilt University, Nashville, TN 37232-2675, USA
Received 17 February 2005; accepted 17 February 2005
Abstract
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can assess tumor perfusion, microvascular vessel wall permeability
and extravascular–extracellular volume fraction. Analysis of DCE-MRI data is usually based on indicator dilution theory that requires
knowledge of the concentration of the contrast agent in the blood plasma, the arterial input function (AIF). A method is presented that
compares the tissues of interest (TOI) curve shape to that of a reference region (RR), thereby eliminating the need for direct AIF measurement.
By assigning literature values for Ktrans (the blood perfusion-vessel permeability product) and ve (extravascular–extracellular volume fraction)
in a reference tissue, it is possible to extract the Ktrans and ve values for a TOI without knowledge of the AIF. The operational RR equation for
DCE-MRI analysis is derived, and its sensitivity to noise and incorrect assignment of the RR parameters is tested via simulations. The method
is robust at noise levels of 10%, returning accurate (F20% in the worst case) and precise (F15% in the worst case) values. Errors in the TOI
Ktrans and ve values scale approximately linearly with the errors in the assigned RR K trans and ve values. The methodology is then applied to a
Lewis Lung Carcinoma mouse tumor model. A slowly enhancing TOI yielded K trans=0.039F0.002 min�1 and ve=0.46F0.01, while a rapidly
enhancing region yielded Ktrans=0.35F0.05 min�1 and ve=0.31F0.01. Parametric K trans and ve mappings manifested a tumor periphery with
elevated Ktrans (N0.30 min�1) and ve (N0.30) values. The main advantage of the RR approach is that it allows for quantitative assessment of
tissue properties without having to obtain high temporal resolution images to characterize an AIF. This allows for acquiring images with higher
spatial resolution and/or SNR, and therefore, increased ability to probe tissue heterogeneity.
D 2005 Elsevier Inc. All rights reserved.
Keywords: DCE-MRI; Arterial input function; Pharmacokinetics; Reference region model
1. Introduction
Dynamic contrast-enhanced magnetic resonance imaging
(DCE-MRI) involves the serial acquisition ofMR images of a
tissue of interest (TOI) (e.g., a tumor locus) before, during
and after an intravenous injection of contrast agent (CA). As
the CA perfuses into the tissue under investigation, the T1 and
T2 values of tissue water decrease to an extent that is
determined by the concentration of the agent. By considering
0730-725X/$ – see front matter D 2005 Elsevier Inc. All rights reserved.
doi:10.1016/j.mri.2005.02.013
* Corresponding author. Institute of Imaging Science, Vanderbilt
where S- is the steady-state pixel-averaged intensity before
CA was injected. In the computation of the R1 time course
from Eqs. (20) and (21), we again took TEbT2*.
R1 (
s-1)
0.5
1.0
1.5
2.0
2.5
time (min)0 10 20 30 40
R1
(s-1
)
0.5
1.0
1.5
2.0
2.5
R1 (
s-1)
0.5
1.0
1.5
2.0
2.5
3.0
RRTOIfit
RRTOIfit
RRTOIfit
no noise
5% noise
10% noise
A
B
C
Fig. 3. Results of fitting the RR model (Eq.(13)) to simulated TOI curves
with 0% (A), 5% (B) and 10% (C) noise added to the bdataQ sets. See
Table 1 for the returned parameter values.
T.E. Yankeelov et al. / Magnetic Resonance Imaging 23 (2005) 519–529524
We then input the RR and TOI R1(t) curves with the RR
model (Eq. (16)) into the curve-fitting routine. Again, the
Ktrans,RR and ve,RR values were fixed at their assigned
muscle values (0.1 min�1 and 0.1, respectively), while the
Ktrans,TOI and ve,TOI values were allowed to vary. For the
ROI analysis, a cluster of nine (3�3) contiguous voxels was
selected, averaged and input into the curve-fitting routine.
To compute parameter uncertainties for this analysis, we
Table 1
Summary results of the RR fits to simulated data with 0%, 5% and 10% noise a
Parameter 0% Noise 5% No
Actual Returned Accuracy Precision Return
Ktrans (min�1) 0.25 0.25 – – 0.23
ve 0.40 0.40 – – 0.40
first find the average absolute deviation of the data points
from the best-fitted curve returned by Eq. (16); that is, we
compute du 1n
Ptnti¼t0
je tiÞjð , where e(ti)ufit(ti)�data(ti).
Then each point in the best-fitted curve is summed with a
random value from �d to +d, yielding a new bdataQ set.
This new curve is then fit with Eq. (16) to yield a new set of
parameters. Repeating this process 100 times yields
100 values each for Ktrans,TOI and ve,TOI from which means
and standard deviations are computed.
Voxel-by-voxel analysis allows for the production of
pharmacokinetic parameter maps to probe tumor heteroge-
neity. For the Ktrans parametric map, each voxel was then
assigned a color based on the Ktrans value returned from the
fit routine. An identical procedure was used to construct the
ve map. Voxels for which the model either did not converge
or converged to unphysical values (i.e., Ktransb0.0 min�1,
KtransN2.5 min�1; veb0.0, veN1.0) were displayed as black.
Each slice in which the tumor was visible was mapped
(slices 4–8).
4. Results
4.1. Simulations
As stated previously, the R1,TOI(t) and R1,RR(t) curves of
Fig. 2B (the two data sets that would actually be measured
in a DCE-MRI experiment) were discretized with 1-min
temporal resolution and input into a curve-fitting routine for
extraction of Ktrans,TOI and ve,TOI. The results of those
simulations are presented in Fig. 3A and Table 1. The fit is
good and the parameters returned (Ktrans,TOI=0.25 min�1,
ve,TOI=0.4) are identical to the values used to construct the
simulated curve. Next, we tested the model’s sensitivity to
noise as described previously. The data and the subsequent
curve fits are seen in Fig. 3B (5% noise) and C (10% noise),
while the parameters output by themodel are given in Table 1.
Again, the fits are good and the model returns
Ktrans,TOI=0.25F0.02 min�1, ve,TOI=0.4F0.02, for the 5%
case and Ktrans,TOI=0.25F0.04 min�1, ve,TOI=0.42F0.05,
for the 10% case. The v2 for the slowly and rapidly enhancingregions were 6.32�10�4 and 6.05�10�4, respectively. These
results indicate that the RR model is robust enough to
accommodate reasonable experimental noise levels. We next
investigate the systematic errors that can enter if an incorrect
assignment of Ktrans,RR and/or ve,RR is made.
Fig. 4 displays three-dimensional plots of the errors in
the returned Ktrans,TOI and ve,TOI values if incorrect RR
values are assigned. A horizontal plane at 0% on the ver-
tical axis indicates zero error in the returned parameter.
dded to the TOI (see Fig. 3)
ise 10% Noise
ed Accuracy Precision Returned Accuracy Precision
0.92 F0.03 0.20 0.80 F0.03
1.00 F0.01 0.40 1.00 F0.01
-30
-20
-10
0
10
20
30
-30-20
-100
1020
30
-30-20
-100
1020
Ktr
ans,
TO
I err
or
Ktrans,RR error
ve,RR error
Ktrans,TOI error
-30
-20
-10
0
10
20
30
-30-20
-100
1020
30
-30-20
-100
1020
v e,T
OI e
rro
r
ve,RR error
ve,TOI error
0
30
Error scale
KKtrans,RR error
-10 0
20
-30-20
10
Fig. 4. Three-dimensional renderings of systematic errors resulting from incorrect assignment of the RR parameters K trans,RR and ve,RR. The vertical axis
represents the degree to which the incorrect RR parameter assignments affects the Ktrans,TOI (left panel) and ve,TOI (right panel) output parameters.
T.E. Yankeelov et al. / Magnetic Resonance Imaging 23 (2005) 519–529 525
Considering the ve,TOI error plot, maximum ve,TOI errors
occur at the points where ve,RR is at its maximum incorrect
value. In particular, the ve,TOI errors scale linearly with error
in ve,RR; that is, a �30% error in ve,RR yields a �30% error
in ve,TOI, and a +30% error in ve,RR yields a +30% error in
ve,TOI. The ve,TOI error is almost completely independent of
the Ktrans,RR value; if we pick any ve,RR error threshold, the
error introduced into the ve,TOI value is essentially the same
as we move along the Ktrans,RR error axis. Thus, the ve,TOIparameter is extremely stable to incorrect Ktrans,RR assign-
ment. This is reasonable because Ktrans determines the initial
uptake portion of the enhancement curve [1,31] and has
very little effect on the washout slope, whereas vedetermines the washout slope (and to a lesser extent, the
peak height achieved by the enhancement curve). Thus, it is
reasonable that mischaracterizing the uptake portion of the
curve (through assigning an incorrect value to Ktrans,RR) will
have little effect on the ve value. Eq. (16) essentially
calibrates the TOI curve to the RR curve, so errors in
Fig. 5. Panel A displays the slice 4 t =0 MR image, while panel B displays the t =
the tumor periphery, and to a much lesser extent, the tumor core, from panel B. T
and slowly enhancing TOIs, respectively, depicted in Fig. 6. Panel C displays the T
T10 map.
Ktrans,RR will translate into the Ktrans,TOI parameter almost
exclusively with little effect on ve,TOI. Similarly, error in
ve,RR effects both ve,TOI and (to a lesser extent) Ktrans,TOI
since (as mentioned previously) ve determines the washout
slope and influences the ultimate height achieved by the
enhancement curve. Consequently, the plot of Ktrans,TOI
error demonstrates more structure. Maximum errors again
occur only at the points where ve,RR and Ktrans,RR are both
off by +30% of their true values, and when they are both off
by �30% of their true values. However, when ve,RR is off by
�30% and Ktrans,RR is off by +30%, the error in Ktrans,TOI
approximately vanishes. A similar pattern occurs when ve,RRand Ktrans,RR are off by +30% and �30%, respectively, with
K trans,TOI error dipping to ~17%. This increases the
robustness of the returned Ktrans,TOI parameters as there is
a smaller area within the Ktrans,TOI error plot for which
Ktrans,TOI is significantly affected by incorrect assignments
of the RR parameters. These results are encouraging as the
amount of systematic error inherent in the model is tractable
40 min image obtained from this study. Note the significant enhancement in
he red and blue circles in panels A and B represent the rapidly enhancing
10 map from this same slice. A grayscale is provided at the far right for the
Fig. 7. The results of RR parameter mappings for (representative) slices 4–6
(panels A, C and E, respectively) and the associated color scale on the far
right. The superior portion of the displays many red voxels on both the
K trans (the left panels) and ve map (right panels), indicating K trans values
z0.27 min�1 and 0.20bveb0.45. These voxels are most likely associated
with highly perfused and leaky vessels with increased extravascular–
extracellular space volume fractions over healthy tissue (vec0.10).
T.E. Yankeelov et al. / Magnetic Resonance Imaging 23 (2005) 519–529526
and directly related to the amount of error in the RR
parameters. Many literature values for muscle Ktrans and veare within the 0.1 min�1 F30% and 0.1F30% explored
here. Neither parameter returns values worse than F30% of
the true value even in those cases when both Ktrans,RR and
ve,RR are off by that amount. In an elegant series of
experiments, Simpson et al. [16] showed that incorrect
characterization of the AIF can lead to errors in perfusion
estimation by as much as 60%. Nevertheless, these errors
are still of concern and we therefore propose a variation on
Eq. (16) in the Discussion.
4.2. Experimental
Fig. 5 displays an axial slice through the tumor hind limb
at t=0 (panel A) and 40 min obtained from this study, as well
as the corresponding T10 map (panel C). The tumor volume
was calculated at 536.0F26.8 mm3. The signal-to-noise ratio
is approximately 52 and 35 for a 20-voxel TOI and an
arbitrary voxel, respectively — both above the range
explored in the above simulations. There is a significant
change in signal intensity from panels A to B in the tumor
periphery, and to a much lesser extent, in the tumor core. The
T10 map is reasonable (for 7.0 T) with most muscle voxels
between 1.45 and 1.85 s, while most tumor voxels are
between 1.8 and 2.2 s. The t=4-min frame indicates two
voxel groups used for TOI analysis (red circles denote a
rapidly enhancing region, while the blue circle indicate a
slowly enhancing region), as well as the RR (white circle)
that was used for both the ROI and voxel analysis. The Fig. 6
circles, triangles and squares indicate the RR, a slowly
enhancing TOI (blue circle in Fig. 5) and a rapidly enhancing
TOI (red circle in Fig. 5), respectively. The results of the
fitting routines are displayed as solid (slowly enhancing) and
dashed (rapidly enhancing). Again, the fits are good and the
parameters are well within the range of reported values for a
9 pixel TOIs22 pixel RR
time (min)
0 10 20 30 40
R1
(s-1
)
0.4
0.8
1.2
1.6
RR slowly enhancing TOIrapidly enhancing TOI
Fig. 6. The results of the RR model fits to data taken from the TOIs labeled
in Fig. 5. The model accommodates both the rapidly enhancing data (filled
squares) and the slowly enhancing data (filled triangles). The data curve
used as the RR for every slice in the study is depicted as the filled circles.
number of tumor types [3,4,9,32]: Ktrans=0.039F0.002
min�1 and ve=0.46F0.01 for the slowly enhancing region,
Ktrans=0.35F0.05 min�1 and ve=0.31F0.01 for the rapidly
enhancing region. We proceed to voxel-by-voxel analysis to
construct pharmacokinetic parameter maps of Ktrans and ve.
As noted previously, the tumors were manually outlined
and each voxel within the outline was fit with Eq. (16) and
characterized by a Ktrans and ve value. These parameter
values are then assigned a color. All voxels for which the
fitting routine did not converge or return physical values are
colored black. The results of these mappings for slices 4–6
(representative slices) and the associated color scale are
displayed in Fig. 7. (The bottom slice is that depicted in
Fig. 5). First, consider the Ktrans parametric map of panel A.
The superior portion of the tumor displays many red voxels
indicating Ktrans values z0.27 min�1. These voxels are
most likely associated with highly perfused and leaky
vessels where angiogenesis-mediated neovascularization is
occurring, as is commonly the case in the periphery of many
tumor types [33,34]. A similar pattern, though not as
pronounced, is also seen in the inferior portion of the tumor.
Both regions slowly fade into the central portion of the
T.E. Yankeelov et al. / Magnetic Resonance Imaging 23 (2005) 519–529 527
tumor, which is characterized by reduced perfusion and/or
permeability (Ktransb0.15 min�1) and many black voxels.
Since nearly all of these voxels occur within the tumor core,
we assume that these are located in dense necrotic regions that
are poorly vascularized as well as containing high intra-
tumoral pressure to prevent both active and passive delivery,
respectively, of the CA to those voxels. As mentioned in the
Discussion, this is a presumption that needs to be verified by
comparison with histology (which we are actively pursuing).
Moving from panel A to C to E, the number of red pixels
greatly diminishes in the superior portion of the tumor, while
the inferior portion of the tumor maintains high perfusion
and/or vessel permeability. All slices seem to display a central
necrotic zone as manifested by many black pixels for which
there was little or no enhancement.
The ve parameter map of slice 4 (panel B) displays, in the
superior and inferior portions of the tumor, increased
extravascular–extracellular space volume fractions
(0.20bveb0.45) over healthy tissue (ve~0.10). Again, the
values reach a maximum in the tumor periphery and begin
to decrease toward the tumor core. This pattern is seen in
both panels D and F as well, though the central necrotic
zone appears to expand just as in the Ktrans maps.
5. Discussion
We have presented a method by which DCE-MRI data
can be quantitatively analyzed on a voxel-by-voxel basis for
the extravasation transfer constant, Ktrans, and extravascular–
extracellular space, ve, without direct measurement of the
AIF. The assumptions inherent in the method are those
common to all compartmental models (Eq. (1)); principally,
that the subject’s body may be represented by one or more
pools, or bcompartments,Q into and out of which the CA
dynamically flows, and that each compartment is assumed
to be bwell mixedQ in the sense that CA entering the
compartment is immediately distributed uniformly through-
out the entire compartment. The method is fast [the results
presented here indicate that the method can analyze an entire
1282 DCE-MRI data set in less than 5 min on a Pentium P4
(Intel, Santa Clara, CA) running at 2.4 GHz], easily applied
and straightforward in implementation, thereby making it
useful in, for example, experiments to measure tumor
kinetics before and after treatment. The results are reason-
able and consistent with other methods that attempt to
measure the AIF directly. We now discuss some of the
assumptions inherent in the RR model.
It should be noted that an additional assumption inherent
in Eqs. (11) and (12) (and, indeed, nearly all of the DCE-
MRI literature), though simplifying, may not be accurate. It
has recently been shown that there frequently exists signi-
ficant water exchange effects between separate compart-
ments, and this can lead to errors in the analysis of dynamic
MR data. Significant transendothelial water exchange
effects have been seen in arterial spin labeling [35,36] and
DCE-MRI data [37,38], while significant transcytolemmal
water exchange effects have been seen in diffusion-
weighted [39] and DCE-MRI [24,25,28] data. We acknowl-
edge that the theory presented here does not account for
those complicating factors, and we are currently working to
modify Eq. (16) to account for water exchange affects. We
also note that though Fig. 1 implies that the RR and TOI are
in close spatial proximity, they are actually separated by tens
of millimeters as indicated by Fig. 5. Thus, water exchange
between the RR and TOI compartments should not be
incorporated into the model.
The simulations reveal that systematic errors in Ktrans,TOI
and ve,TOI may be caused by incorrect assignments of
Ktrans,RR and ve,RR. That is, there could be both intra- and
interanimal variation in RR parameter values, and by
assigning literature reported values (particularly to
Ktrans,RR), systematic error will be introduced as manifested
by the above simulations. Thus, both the assignment of RR
parameters (interanimal variation) and the selection of the
RR itself (intraanimal variation) can confound the results
obtained by the RR model. An alternate approach would be
to formulate Eq. (16) in terms of ratios of Ktrans,TOI to
Ktrans,RR and ve,TOI to ve,RR, thereby allowing for the
production of relative Ktrans and ve maps. This could
potentially reduce the model’s systematic error due to
incorrect RR parameter assignments since a model reporting
relative parameter values requires no assignments on the
RR. If we make the following assignments:
R1uRuK trans;TOI=K trans;RR ð22Þ
R2uK trans;RR=ve;RR ð23Þ
R3uK trans;TOI=ve;TOI ð24Þ
then Eq. (18) may be expressed as Eq. (25):
R1;TOI Tð Þ ¼ R1bðR1;RRðTÞ � R10;RRÞ
þ R1½R2 � R3�bZT
0
ðR1;RRðtÞ � R10;RRÞ
� expð � R3 T � tð ÞÞdt þ R10TOI: ð25Þ
By noting that (R1/R3)R2=ve,TOI/ve,RR, Eq. (25) can pro-
vide a three-parameter fit to a DCE-MRI time course to
extract rKtrans(R1), rve((R1/R3)R2) and rkep(R
3) values (kepis the rate constant describing the flow of CA from the
extravascular–extracellular space to the blood plasma [1]),
where brQ denotes relative. Such relative measurements have
been shown to be of clinical value, perhaps most noticeably
in investigations of cerebral perfusion. Our preliminary
results have shown that Eq. (25) is very robust to exper-
imental noise, returns accurate values and slightly increases
standard deviations over the Eq. (16) model — as one would
expect for a model with an additional degree of freedom.
Furthermore, we have made some progress on applying an
iterative approach in which Eq. (25) is used to first fit an
T.E. Yankeelov et al. / Magnetic Resonance Imaging 23 (2005) 519–529528