Shortened acquisition protocols for the quantitative assessment of the 2-tissue-compartment model using dynamic PET/CT 18F-FDG studies.

Abstract

(18)F-FDG kinetics are quantified by a 2-tissue-compartment model. The routine use of dynamic PET is limited because of this modality's 1-h acquisition time. We evaluated shortened acquisition protocols up to 0-30 min regarding the accuracy for data analysis with the 2-tissue-compartment model.
Full dynamic series for 0-60 min were analyzed using a 2-tissue-compartment model. The time-activity curves and the resulting parameters for the model were stored in a database. Shortened acquisition data were generated from the database using the following time intervals: 0-10, 0-16, 0-20, 0-25, and 0-30 min. Furthermore, the impact of adding a 60-min uptake value to the dynamic series was evaluated. The datasets were analyzed using dedicated software to predict the results of the full dynamic series. The software is based on a modified support vector machines (SVM) algorithm and predicts the compartment parameters of the full dynamic series.
The SVM-based software provides user-independent results and was accurate at predicting the compartment parameters of the full dynamic series. If a squared correlation coefficient of 0.8 (corresponding to 80% explained variance of the data) was used as a limit, a shortened acquisition of 0-16 min was accurate at predicting the 60-min 2-tissue-compartment parameters. If a limit of 0.9 (90% explained variance) was used, a dynamic series of at least 0-20 min together with the 60-min uptake values is required.
Shortened acquisition protocols can be used to predict the parameters of the 2-tissue-compartment model. Either a dynamic PET series of 0-16 min or a combination of a dynamic PET/CT series of 0-20 min and a 60-min uptake value is accurate for analysis with a 2-tissue-compartment model.

Full text

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Shortened Acquisition Protocols for the Quantitative
Assessment of the 2-Tissue-Compartment Model Using
Dynamic PET/CT18F-FDG Studies
Ludwig G. Strauss1, Leyun Pan1, Caixia Cheng1, Uwe Haberkorn1,2, and Antonia Dimitrakopoulou-Strauss1
1Clinical Cooperation Unit Nuclear Medicine, German Cancer Research Center, Heidelberg, Germany; and2Department of Nuclear
Medicine, Ruprecht-Karls-University, Heidelberg, Germany
18F-FDG kinetics are quantified by a 2-tissue-compartment
model. The routine use of dynamic PET is limited because of
this modality’s 1-h acquisition time. We evaluated shortened
acquisition protocols up to 0–30 min regarding the accuracy
for data analysis with the 2-tissue-compartment model. Meth-
ods: Full dynamic series for 0–60 min were analyzed using a
2-tissue-compartment model. The time–activity curves and the
resulting parameters for the model were stored in a database.
Shortened acquisition data were generated from the database
using the following time intervals: 0–10, 0–16, 0–20, 0–25, and
0–30 min. Furthermore, the impact of adding a 60-min uptake
value to the dynamic series was evaluated. The datasets were
analyzed using dedicated software to predict the results of the
full dynamic series. The software is based on a modified sup-
port vector machines (SVM) algorithm and predicts the com-
partment parameters of the full dynamic series. Results: The
SVM-based software provides user-independent results and was
accurate at predicting the compartment parameters of the full
dynamic series. If a squared correlation coefficient of 0.8 (corre-
sponding to 80% explained variance of the data) was used as a
limit, a shortened acquisition of 0–16 min was accurate at predict-
ing the 60-min 2-tissue-compartment parameters. If a limit of 0.9
(90% explained variance) was used, a dynamic series of at least
0–20 min together with the 60-min uptake values is required.
Conclusion: Shortened acquisition protocols can be used to pre-
dict the parameters of the 2-tissue-compartment model. Either a
dynamic PET series of 0–16 min or a combination of a dynamic
PET/CT series of 0–20 min and a 60-min uptake value is accurate
for analysis with a 2-tissue-compartment model.
Key Words: PET;18F-FDG; compartment modeling; quantification
J Nucl Med 2011; 52:379–385
DOI: 10.2967/jnumed.110.079798
The standard radiopharmaceutical for PETexaminations
in oncologic patients is18F-FDG, a marker of tumor via-
bility, which has been used with PET for many years now
(1). The basic quantitative assessment of the tracer uptake
is usually calculated using standardized uptake values
(SUVs)—a method introduced by our group more than
19 y ago as a ratio of the local tracer concentration with the
injected dose and body volume (2). SUV is a distribution
value, which is equal to 1 for a homogeneous distribution of
the tracer and exceeds 1 if retention occurs in the tissue.
The SUVor, alternatively, the maximum SUV in a volume
of interest (VOI) has been used in many publications and
was found to be useful as an additional parameter for tumor
diagnosis and assessment of therapeutic effects. However,
the SUV reflects the global uptake of a tracer and is de-
pendent not only on the specific retention of18F-FDG but
also on the fractional blood volume and other parameters
(3). More detailed information can be obtained by compart-
ment modeling. Vriens et al. reviewed the methodologic
aspects of tracer quantification in oncologic patients (4).
The authors concluded that the SUV is helpful despite these
limitations. Pharmacokinetic quantification is mainly con-
fined to application in a research setting. Indeed, the acquis-
ition of a full dynamic PET scan for 60 min is difficult for
routine purposes. Therefore, shortened acquisition proto-
cols may be helpful in solving this problem.
For tracers such as18F-FDG, a 2-tissue-compartment
model is the most appropriate model to assess the tracer
kinetics. It was shown, for example, for colorectal tumors
and lung tumors, that follow-up examinations with18F-
FDG and compartment modeling provide the possibility
of predicting the therapeutic effect individually (5,6). How-
ever, the use of a 2-tissue-compartment model demands a
dynamic PET/CTacquisition for about 60 min, limiting the
use of dynamic imaging for routine purposes because of the
extended time needed for dynamic and whole-body imag-
ing. Thus, new methods to shorten the dynamic acquisition
time and maintain accurate information about the tracer
kinetics would be helpful. Besides compartment analysis,
the shortened acquisition protocols can also be helpful for
the calculation of the global metabolic rate. Visser et al.
evaluated shortened dynamic PET with18F-FDG and con-
cluded that a 30-min data acquisition was sufficient to cal-
culate the glucose metabolic rate (7).
Received Jun. 2, 2010; revision accepted Dec. 13, 2010.
For correspondence or reprints contact: Ludwig G. Strauss, Medical PET
Group–Biological Imaging (E060-1), Clinical Cooperation Unit Nuclear
Medicine, German Cancer Research Center, Im Neuenheimer Feld 280,
D-69120 Heidelberg, Germany.
E-mail: lgs@ads-lgs.de
COPYRIGHT ª 2011 by the Society of Nuclear Medicine, Inc.
DYNAMIC PET/CT • Strauss et al. 379

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The 2-tissue-compartment model is the standard model to
assess the kinetics of18F-FDG; therefore, the software for
the evaluation of shortened acquisition protocols must pro-
vide the compartment parameters for this model, with
acceptable accuracy. Usually, an iterative solution of the
differential equations is preferred, based on the Levenberg–
Marquardt algorithm. A 60-min dynamic data acquisition is
usually preferred for dynamic studies with18F-FDG. The use
of shorter acquisition times, such as 30 min, may provide
false data about the compartment parameters if the standard
iterative solution is applied, because only the acquired data
(0–30 min) are taken into account for the calculation of the
compartment parameters, and data for the 30- to 60-min
interval are lacking. Furthermore, the conventional approach
of calculating the compartment parameters is generally sen-
sitive for overfitting even with a 0- to 60-min data acquisition
and is therefore user-dependent, thus limiting the reproduci-
bility of the compartment data.
Recently, we developed a software program for the 2-
tissue-compartment model based on a database and a
modified support vector machines (SVM) algorithm (8).
The program applies a modified machine-learning algo-
rithm (SVM) to the measured VOI data. The SVM algo-
rithm is a predictive approach; therefore, it is possible to
predict the 0- to 60-min compartment parameters from 0- to
30-min PET time–activity data, in contrast to the iterative
approach, which is confined to the measured time interval.
The purpose of this study was to assess the SVM approach
for shortened dynamic acquisitions to obtain 60-min com-
partment data from dynamic acquisitions of 10–30 min.
The results of the shortened acquisitions were compared
with those results obtained with the standard 0- to 60-min
dynamic series, which served as the reference.
MATERIALS AND METHODS
The study is based on 1,474 time–activity curves obtained from
539 patients in whom dynamic PET studies for 0–60 min were
performed. All patients were scheduled for diagnostic purposes to
undergo dynamic PET because of a known primary or recurrent
tumor. In the cases of recurrent tumors, the patients had undergone
previous surgery. All tumor histologies were accepted for this study;
the selection was based only on the presence of a malignant lesion.
Furthermore, follow-up studies in patients receiving chemotherapy
were included. The dynamic series was focused on the region of the
tumor, followed by a whole-body scan. We used 28 frames as a
standard for the dynamic series (10 · 30, 5 · 60, 5 · 120, and 8 ·
300 s). Iterative image reconstruction was performed (ordered-sub-
set expectation maximization algorithm), and the reconstructed
images were converted to SUVimages and transferred to a database
for further evaluation. The quantitative assessment was done using
multiple VOIs for the tumor, metastatic lesions, normal tissue, and a
large vessel, preferentially the descending aorta. AVOI is based on
multiple regions of interest positioned over the area of interest on
several slices. The time–activity data were obtained by the VOIs by
quantifying the radionuclide concentration for each time frame of
the series. Partial-volume correction was not applied, because all
regions had a diameter of at least 8 mm and the system recovery is
85% for this diameter. The 2-tissue-compartment model uses an
input function for the calculation of the compartment parameters.
It had been already reported by Ohtake et al. that the input function
can be accurately obtained via VOIs (9). Therefore, at least 7 ROIs
were placed over the descending aorta to obtain the blood data for
18F-FDG.
All datasets were evaluated by 2 experienced nuclear medicine
specialists, and a 2-tissue-compartment model was applied to the
data using the standard iterative curve-fitting procedure. We
obtained the following 5 parameters: vB, fractional blood volume,
also named vessel density; k1,k2(also referred to as K1,k2), param-
eters for the transport of18F-FDG into the cells; and k3,k4, param-
eters for the phosphorylation and dephosphorylation of the
intracellular18F-FDG. The influx was calculated from the compart-
ment data using influx 5 k1· k3/(k21 k3). The results of the
compartment fitting (vB, k1–k4) were associated with the corre-
sponding time–activity curves (input curve, target curve) and stored
in a database. Thus, each dataset of the database consists of the data
from a VOI of the input data, a VOI of the target data, and the
resulting kinetic parameters obtained by 2-tissue-compartment fit-
ting using the classic iterative Levenberg–Marquardt algorithm.
The full dynamic datasets for 60 min and their results regarding
the 2-tissue-compartment fit, based on the classic iterative
solution, were used as reference for the shortened acquisition
protocols and the SVM-based compartment fitting. To generate
shortened acquisitions, the 0- to 60-min time–activity datasets
were reduced to smaller dynamic sequences using the following
time intervals: 0–10, 0–16, 0–20, 0–25, and 0–30 min. Then the
shortened dynamic series were evaluated, and a 2-tissue compart-
ment was fitted, now based on the SVM method (8). A 2-step
procedure was performed: first the current combination of an input
and target curve was compared with the database and a subset of
comparable input and target curves were selected from the data-
base of the shortened acquisition data. Then the subset of curves
was used together with the measured data to predict the 60-min
2-tissue-compartment results by the modified SVM algorithm.
If the Levenberg–Marquardt algorithm would be applied, for
example, to a 0- to 20-min dynamic series, the algorithm calcu-
lates the compartment constants only from this time interval.
Because of the limited information compared with a 0- to 60-
min series, the compartment parameters are usually different from
those obtained from a full dynamic series. In contrast, the modi-
fied SVM algorithm predicts the 60-min compartment data results
from the shortened acquisition series.
Two groups were made for the data evaluation of the shortened
acquisition series. The first group consisted of the different
shortened acquisition series and the 60-min uptake value, for
example, 0- to 20-min series and 60-min acquisition. The second
group comprised only the shortened acquisition series, for example,
0- to 20-min series. The grouping was performed to assess whether
the 60-min acquisition affected the accuracy of the results. The
compartment parameters were calculated for both groups with
the SVM approach, using the results of the full dynamic series
as reference. Furthermore, the influx was used as an additional
variable. Correlation coefficients and squared correlation coeffi-
cients were used to assess the accuracy of the prediction.
RESULTS
The basic statistical data (mean, median, minimum, and
maximum) are provided in Supplemental Table 1 (supple-
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mental materials are available online only at http://jnm.
snmjournals.org). K1 has the highest median values,
whereas k3revealed the lowest median values. Mean and
median values are comparable, reflecting a symmetric dis-
tribution of the data.
The correlation coefficients and squares of the correla-
tion coefficients (variance) are shown in Supplemental
Table 2. In Supplemental Table 2, we focused on influx,
vB, k1, and k3, because these are the most important param-
eters of the 2-tissue-compartment model. The use of the 60-
min acquisition in addition to the shortened acquisitions
generally resulted in higher correlation coefficients and a
higher explained variance preferentially for k3. Differences
of dynamic PET plus the 60-min data as compared with
dynamic PET alone were primarily observed for k3and not
for vB and k1.
The square of the correlation coefficients reflects the
fractional total variance, which is explained by an existing
correlation. If 0.8 (corresponding to 80% of the total data
variance) is chosen as a limit for the squared correlation
coefficient, the shortened acquisition protocols for 0–16 up
to 0–30 min provide this accuracy for both groups, with and
without the 60-min data. Only the series based on 0–10 min
has a lower accuracy, with an r2of 0.7430 (0–10 min and
60-min data) and 0.5609 (0–10 min) for k3(Supplemental
Table 2). However, if a higher limit of r2(0.9; 90%
explained variance) is chosen for the squared correlation
coefficient, only the combination of a dynamic PET series
with the 60-min acquisition fulfills this limit for the 0- to
30-, 0- to 25-, and 0- to 20-min series but not for the 0- to
16- and 0- to 10–min series. The dynamic PET series alone
did not achieve the limit of 0.9 for r2for k3for all time
intervals. Therefore, for routine studies a shortened acquis-
ition of 0–20 min, followed by a whole-body acquisition at
60 min, is an alternative to the full dynamic study.
For routine purposes, a shortened acquisition without an
additional 60-min acquisition may be primarily of interest.
The best results for dynamic PET without the 60-min data
were achieved for the 30-min series. k3was the primary
limiting parameter with an r2of 0.8862 for the 0- to 30-min
series. If a limit of 0.8 is chosen for the squared correlation
coefficient, the 0- to 25-, 0- to 20-, and 0- to 16-min series
are acceptable. The variation of the data is demonstrated in
Figures 1–3. The parameters influx, vB, k1, and k3 are
shown for the 0- to 10-, 0- to 16-, and 0- to 30-min series
(Figs. 1–3). The scatterplots demonstrate that k3is the most
critical parameter with the highest statistical noise.
Currently, we use a 30-min dynamic PET/CT study,
followed by a whole-body acquisition at 60 min after the
tracer application. The advantage of this protocol is that the
dynamic PET examination can be performed with most of
the patients holding their arms over their head; this arm
positioning is not possible for a full dynamic series of
60 min. Furthermore, the patient can rest or move after the
30-min dynamic PET before the whole-body study. The
whole-body study is performed with a 2-min acquisition for
each bed position; therefore, only about 12 min are needed
in most of the patients. One example is demonstrated in
Figure 4. This patient has a recurrent hepatocellular carci-
noma. We performed a 30-min dynamic PET/CT, followed
by a whole-body study at 60 min after injection. Data were
evaluated for the dynamic PET/CT and whole-body images
for the tumor and blood. After the evaluation of the
dynamic PET/CT series by VOIs, the whole-body data
are added to the dynamic series by providing the time point
of the acquisition and SUV. Then the 2-tissue-compartment
model was fitted with the SVM-based program and pro-
vided results with high accuracy (Fig. 4A). In contrast, if
the standard Levenberg–Marquardt method is applied, we
obtain an overfitting for k2that exceeds 1 (Fig. 4B). This
result is not acceptable. The kxvalues must be within the
range of 0–1, because they reflect the relative amount of
18F-FDG, which is exchanged with the next or previous
compartment. Therefore, the maximum value is 1, which
is associated with a complete exchange of all the18F-FDG
with the associated compartment. Overfitting not only dete-
riorates kxvalues, such as k2in this case, but has also an
impact on all other k values and vB. Therefore, this method
is not stable enough for routine use when inexperienced
users apply the algorithm. The problem of overfitting is
usually solved by the sequential fitting of vB and kxvalues,
but this solution demands an experienced user who has
long-term experience with compartment models.
DISCUSSION
Dynamic data acquisitions provide the possibility of
gaining details about18F-FDG tracer kinetics. The standard
method is the acquisition of a dynamic series for 1 h—the
time needed to fit a 2-tissue-compartment model to the
dynamic data and calculate the compartment parameters.
Several studies have already demonstrated that the kinetic
data are superior to single SUV measurements for both
tumor diagnostics and therapy management (10–15). It
was shown in soft-tissue sarcomas that the quantitative
parameters of the18F-FDG kinetics help to predict the
grading of the tumor (11). The differentiation of a colo-
rectal tumor from normal colon was quantitatively assessed
in a study by Strauss et al. (3). If the full kinetic data were
used, only 1 false classification was noted and the overall
accuracy was 97.3%.
Comparable results are reported for therapy management
studies. In sarcomas, the combination of the mean SUVand
k1before and after 1 chemotherapeutic cycle was predictive
for therapy outcome, with a correct classification rate of
93.3% for the nonresponding lesions and 80% for the res-
ponders (12). The quantitative evaluation of soft-tissue sar-
comas in 31 patients revealed that the combination of SUV
and influx provided an overall accuracy of 83% for the
differentiation of responders from nonrespnders, whereas
the use of percentage SUV changes was not helpful, with
an accuracy of 58% (13). Okazumi et al. evaluated 79
patients with sarcomas using dynamic PET (14). The data
DYNAMIC PET/CT • Strauss et al.381

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obtained in 71 postoperative patients revealed a sensitivity
of 80.85% and specificity of 87.50% for the detection of
recurrent disease, using SUV, vB, k3, influx, and fractal
dimension as parameters. Kimura et al. evaluated kinetic
modeling in patients with gliomas and lymphomas of the
central nervous system (15). They concluded that kinetic
analysis helps to delineate malignant lesions in the brain.
However, more studies are needed to assess the impact of
dynamic PET in oncology.
Modeling of tracer kinetics is mainly confined to
scientific studies because of the time-demanding procedure
and complex evaluation. Protocols with a shortened acquis-
ition time may be considered for routine use because of the
shortened acquisition time for the dynamic study and faster
processing of the data. Therefore, we evaluated if dynamic
acquisitions up to 30 min may be helpful to cut down the
acquisition time for dynamic studies. However, a key
problem with shortened acquisitions is the use of appro-
priate software to gain accurate information about the tracer
kinetics. The conventional approach using the Levenberg–
Marquardt algorithm for a shortened acquisition protocol,
as compared with a full kinetic series, provides different
results because the algorithm tries to solve the differential
equations for the shortened time interval only. Therefore,
FIGURE
dynamic PET series at 0–10 min after tracer
injection. Full dynamic series (0–60 min)
results are used for reference. dPET 5
dynamic PET; inf 5 influx.
1.
Selectedscatterplotsfor
FIGURE
dynamic PET series at 0–16 min after tracer
injection. Full dynamic series (0–60 min)
results are used for reference. dPET 5
dynamic PET; inf 5 influx.
2.
Selectedscatterplots for
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predictive, regression-based methods are needed to predict
the results of a 60-min series from shortened acquisition
data.
We developed a new approach for the calculation of the
parameters of the 2-tissue-compartment model based on a
modification of the SVM algorithm. The SVM algorithm is
a machine-learning method, which is usually applied for
data classification (16). The method had been used for the
detection of prostate cancer with MRI and the classification
of lymph nodes (17,18). Ozer et al. assessed the MRI data
of 20 patients with biopsy-proven prostate cancer using
different methods for classification analysis. The SVM
method provided the highest accuracy and detected more
than 80% of the tumors (17). Sattlecker et al. applied the
SVM method for the diagnosis of involved lymph nodes.
These authors used different linear and nonlinear kernels
for the SVM method and were able to identify 100% of the
independent test data using a radial basis function (18).
Jayasurya et al. compared a Bayesian network with the
SVM model to predict 2-y survival in 322 lung cancer
patients (19). The results demonstrate that the SVM method
demands a complete dataset and was accurate for the pre-
diction, whereas the Bayesian network was more helpful if
incomplete patient data were available. However, with PET
we always have the full dataset, and the problem of limited
or missing data does not exist for the dynamic series. We
used the SVM algorithm together with a complete database
of 1,474 reference datasets for the prediction of the kinetic
parameters from the shortened acquisition series. The SVM
prediction of the 60-min kinetic parameters from the short-
ened acquisition series provided, overall, an acceptable
accuracy. If a squared correlation coefficient of at least
80% is accepted, even a single dynamic PET series for
0–16 min is adequate to predict the kinetic parameters
(Supplemental Table 2). Usually a 60-min whole-body
acquisition is performed in oncologic patients. In this case,
the combination of a 20-min dynamic PET series with the
whole-body data provides an accuracy exceeding 90%,
which is acceptable for both routine and scientific PET
studies. We currently use at our center a combination of a
30-min dynamic PET series with a whole-body acquisition
at 60 min after tracer injection to the compartment param-
eters and achieve an accuracy exceeding 95% regarding the
explained variance of the data (Supplemental Table 2).
The data acquisition for 1 h is a problem for most PET
centers because of the limited number of patients who can
be studied per day. Furthermore, the data fitting with
standard software demands experienced users and may be
time consuming. Therefore, simplified methods such as the
calculation of the global metabolic rate and the SUV have
found use for tracer uptake quantification. However, the
SUV has some limitations, and, especially for therapy
follow-up studies, we prefer the kinetic analysis to achieve
more detailed, accurate information. The SUVs summarize
nonmetabolized tracer in the vessels, transported but not
metabolized tracer in the tissue, and phosphorylated18F-
FDG. Actually, the phosphorylated18F-FDG is of major
importance, especially for therapy-monitoring studies, but
this fraction cannot be assessed accurately with the SUV
alone. We have used the conventional compartment fitting
based on the Levenberg–Marquardt algorithm for several
years now. However, the problem of overfitting limits the
method for use in routine applications and with inexper-
ienced users. To avoid overfitting, the compartment param-
eters must be sequentially fitted, which is usually time
consuming. In contrast, the modified SVM method is
user-independent and provides results based on a predictive
approach. One parameter that determines the accuracy of
FIGURE
dynamic PET series at 0–30 min after tracer
injection. Full dynamic series (0–60 min)
results are used for reference. dPET 5
dynamic PET; inf 5 influx.
3.
Selectedscatterplots for
DYNAMIC PET/CT • Strauss et al.383

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FIGURE 4.
increasing over time because of high metabolism in lesion. Data from 0 to 30 min are obtained from dynamic PET/CT series, and 60-min
value is retrieved from whole-body examination. x2is 0.389, demonstrating high accuracy of curve fit based on modified SVM method.
These results meet biologic requirements of compartment model (kx# 1) and are obtained without any setting of initial values for model
parameters; therefore they are user-independent. (B) A 2-tissue-compartment model fit of data shown in A using Levenberg–Marquardt
algorithm. Results demonstrate overfitting of k2with k25 1.487. This result is not usable despite good curve fit, because it does not match
model assumptions (e.g., k2# 1). This algorithm is dependent on selection of initial compartment parameters for model. Therefore, it is
dependent on experience of user, which may introduce bias.
(A) Fitting of kinetic model for hepatocellular carcinoma of liver. Input curve was retrieved from abdominal aorta. Target curve is
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the SVM method is the size of the database. Currently, we
have nearly 1,500 datasets, and the database is further
expanded by adding new dynamic PET studies. However,
the current results demonstrate that the dataset of 1,474
time–activity curves is accurate enough to predict the
60-min compartment parameters. We assume that we can
improve the accuracy further by adding more time–activity
curves to the database. The software used in this study is
part of a new software package that we are developing for
quantitative dynamic PET/CT studies to provide for its
routine use with dynamic PET/CT.
CONCLUSION
Short acquisition protocols are helpful in the acquisition
of dynamic PET data. The evaluation with modified 2-
tissue-compartment model software, based on the modified
SVM algorithm, provides accurate results for shortened
acquisition protocols and avoids overfitting problems.
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