Download Incorporation of functional imaging data in the evaluation of dose

INSTITUTE OF PHYSICS PUBLISHING
PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 49 (2004) 1711–1721
PII: S0031-9155(04)74792-2
Incorporation of functional imaging data in the
evaluation of dose distributions using the generalized
concept of equivalent uniform dose
Moyed M Miften, Shiva K Das, Min Su and Lawrence B Marks
Department of Radiation Oncology, Duke University Medical Center, Durham, NC 27710, USA
E-mail: [email protected]
Received 15 January 2004
Published 1 April 2004
Online at stacks.iop.org/PMB/49/1711 (DOI: 10.1088/0031-9155/49/9/009)
Abstract
Advances in the fields of IMRT and functional imaging have greatly increased
the prospect of escalating the dose to highly active or hypoxic tumour
sub-volumes and steering the dose away from highly functional critical
structure regions. However, current clinical treatment planning and evaluation
tools assume homogeneous activity/function status in the tumour/critical
structures. A method was developed to incorporate tumour/critical structure
heterogeneous functionality in the generalized concept of equivalent uniform
dose (EUD). The tumour and critical structures functional EUD (FEUD) values
were calculated from the dose–function histogram (DFH), which relates dose
to the fraction of total function value at that dose. The DFH incorporates
flouro-deoxyglucose positron emission tomography (FDG-PET) functional
data for tumour, which describes the distribution of metabolically active
tumour clonogens, and single photon emission computed tomography (SPECT)
perfusion data for critical structures. To demonstrate the utility of the method,
the lung dose distributions of two non-small cell lung caner patients, who
received 3D conformal external beam radiotherapy treatment with curative
intent, were evaluated. Differences between the calculated lungs EUD and
FEUD values of up to 50% were observed in the 3D conformal plans. In
addition, a non-small cell lung cancer patient was inversely planned with a
target dose prescription of 76 Gy. Two IMRT plans (plan-A and plan-B) were
generated for the patient based on the CT, FDG-PET and SPECT treatment
planning images using dose–volume objective functions. The IMRT plans
were generated with the goal of achieving more critical structures sparing in
plan-B than plan-A. Results show the target volume EUD in plan-B is lower
than plan-A by 5% with a value of 73.31 Gy, and the FEUD in plan-B is
lower than plan-A by 2.6% with a value of 75.77 Gy. The FEUD plan-B
values for heart and lungs were lower than plan-A by 22% and 18%,
respectively. While EUD values show plan-A is marginally better than plan-B
in terms of target volumetric coverage, the FEUD plan-B values show adequate
0031-9155/04/091711+11$30.00 © 2004 IOP Publishing Ltd Printed in the UK
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target function coverage with significant critical structure function sparing. In
conclusion, incorporating functional data in the calculation of EUD is important
in evaluating the biological merit of treatment plans.
1. Introduction
Recent advances in the field of intensity modulated radiation therapy (IMRT) and
positron emission tomography/single photon emission computed tomography/functional MRI
(PET/SPECT/fMRI) imaging have greatly increased the prospect of escalating the dose to
tumour sub-volumes with high activity or low radiosensitivity and steering the dose away from
critical structure regions with high function (Xing et al 2002, Alber et al 2003).
FDG-PET images provide functional data regarding the distribution and proliferative
potential of metabolically active tumour clonogens and SPECT perfusion images provide
information on blood flow in critical structure sub-units, thus complementing the CT-derived
information. Recent articles have shown that higher pre-treatment flouro-deoxyglucose
(FDG) uptake, as measured by the specific uptake value, correlates to worse outcome, as
measured by local control and survival (Halfpenny et al 2002, Jeong et al 2002, Eary et al
2002). This makes FDG-PET an effective tool for diagnosing and staging of malignant
lesions. Radiotherapy (RT) treatment plans can be designed based on the ability of FDG-PET
data to detect the lesion metabolic activity. For organs at risk, SPECT imaging maps the
perfusion distribution, and thus identifies regions of high and low function (Boersma et al
1993, Marks et al 1993). Treatment plans can be designed using SPECT data to avoid critical
structure regions with high function which is usually not detected on CT scans (Das et al
2003). Seppenwoolde et al (2002) demonstrated that lung treatment plans generated based on
perfusion-weighted optimization result in less radiation damage to functioning lung, compared
to geometrically optimized plans, for patients with large perfusion defects. This is based on
the premise that poorly perfused lung regions (for example, before the RT treatment of lung,
lymphoma or breast cancer) of a heavy smoker patient or a patient with chronic obstructive
pulmonary disease will not recover after RT (Theuws et al 1999).
Several authors suggested incorporating biological information in the evaluation of dose
distributions (Niemierko 1997, Lu et al 1997). The linear-quadratic-based equivalent uniform
dose (EUD) formalism, introduced by Niemierko (1997) for tumours, explicitly allowed
for spatial variation of clonogen density. Lu et al (1997) suggested calculating functional
normal tissue complication probability (fNTCP) from functional dose volume histogram
data. Nonetheless, current clinical treatment planning and evaluation tools still assume
homogeneous activity/function status in the tumour/critical structures. For tumours, this
assumption is not valid since tumour growth/function is heterogeneous. On the other hand,
in most organs, functional status is relatively homogenous, such as the normal liver and
normal lung. Such organs are constituted from many relatively identical and homogeneously
distributed functional sub-units which are arranged in a parallel architecture (Yorke et al
1993, Staverv et al 2001). However, for example, functional heterogeneity within the lung is
present in many patients with lung cancer. Furthermore, for many other organs the function
is not uniformly distributed. For example, there are dominant and non-dominant portions
of the brain, and the left ventricle of the heart is functionally the most important chamber.
The biological/physiological outcome of tumour and critical structures (heart, lung, brain
etc) irradiation may correlate better with predictions from biological models that incorporate
Incorporation of functional imaging data in equivalent uniform dose
1713
dose–function and dose–volume information, compared to models that incorporate dose–
volume information only (Marks et al 1997, Choi et al 2002). In this work, a method was
developed to incorporate tumour and critical structure heterogeneous activity/functionality in
the calculation of the generalized equivalent uniform dose (EUD).
2. Materials and methods
2.1. Functional EUD calculation
The generalized EUD concept proposed by Niemierko (1999) is a phenomenological model
based on the power law dependence of the response of a biological system to a stimulus. The
EUD can be calculated from the differential dose–volume histogram (DVH) of an anatomical
structure as
N
N 1/a
a
EUD =
vi Di
vi
(1)
i=1
i=1
where N is the number of DVH bins, Di and vi are the dose and volume in the ith bin, a
is a tumour or critical structure specific parameter which describes the dose–volume effect
and can be obtained from clinical outcome data (Emami et al 1991, Wu et al 2002). The
generalized EUD can be used to evaluate dose distributions in the tumour and surrounding
critical structures. It reports the generalized mean value of the non-uniform dose distribution,
which represents the homogenous dose distribution that produces the same local control as
that obtained with an inhomogeneous dose distribution for the case of tumours. For the case
of critical structures, the generalized EUD reports the homogeneous dose distribution which
results in the same probability of complication as that of an inhomogeneous dose distribution.
The optimal IMRT plan is the plan that maximizes the EUD in the target and minimizes the
EUD in critical structures. The formalism in equation (1) assumes functional uniformity in
the response of tumour and critical structures to irradiation.
Wu et al (2002) described that for partial organ irradiation the parameter a is related to
the parameter n of the Lyman and Wolbarst (1987) partial volume irradiation effect model
by a = 1/n. Furthermore, Wu et al (2002) explained that in the context of partial organ
irradiation, where a fractional volume of the organ receives a certain dose and the rest of the
volume receives no dose. The generalized EUD reduces to the power law model of Lyman
and Wolbarst (1987) and to the effective uniform dose formula of Mohan et al (1992) which
reports non-uniform dose distribution as an effective uniform dose. Kutcher and Burman
(1989), Kutcher et al (1991) used the power law model to reduce the DVH into an effective
volume (Veff ) for the calculation of complication probabilities. The a parameter values in this
work were calculated based on the work of Burman et al (1991) using the clinical outcome
data of Emami et al (1991). Specifically, we used the tolerance dose values to the whole organ
and partial volumes that would result in a 5% complication probability in 5 years (TD5/5)
TD5/5 (1) = TD5/5 (v) v 1/a .
(2)
Modifying the EUD formalism by replacing volume weighting with function weighting
in equation (1), the tumour and critical structures activity/function can be incorporated in the
calculation of EUD (FEUD). The FEUD can be calculated from the differential dose–function
histogram (DFH) as
N 1/a
N
a
fi Di
fi
(3)
FEUD =
i=1
i=1
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where Di and fi are the dose and value of function in the ith bin and N is the number of DFH bins.
Unlike the DVH which assumes functional homogeneity, the DFH provides quantitative 3D
functional information by incorporating the heterogeneous functionality of tumour or critical
structure volumes (Marks et al 1995, 1999).
In the DFH calculation and FEUD formalism, the activity/function of tumour/critical
structures sub-units was assumed proportional to the number of counts/volume on FDG-PET
and SPECT functional images. The assumption was made based on recent papers which have
demonstrated that there is strong evidence linking the magnitude of FDG uptake in target to
tumour grade (Berlangieri et al 1999, Albes et al 2002, Shon et al 2002, Chin et al 2002) and
linking higher uptake to poorer post-therapy response (Kole et al 1999, Saunders et al 1999,
Dhital et al 2000, Shiomi et al 2001, Choi et al 2002, Oyama et al 2002, Wong et al 2002).
A number of studies have established that FDG uptake and tumour proliferation rate are well
correlated (Smith and Titley 2000, Higsashi et al 2000, Dimitrakopoulou-Strauss et al 2001,
Jacob et al 2001, Avril et al 2001, Nerini-Molteni et al 2001, Vesselle et al 2000, Buck et al
2002, Pugsley et al 2002, Bos et al 2002). This suggests that the level of FDG-PET activity
correlates to tumour aggressiveness and, consequently, the spatial distribution of FDG-PET
activity correlates to the spatial distribution of tumour aggressiveness. For SPECT perfusion
data, phantom and animal studies (Osborne et al 1982, 1985) have shown that SPECT count
rates are linearly correlated with blood flow. Moreover, clinical data using SPECT perfusion
imaging to predict pulmonary function following surgery suggest that regional function is
approximately linearly related to regional perfusion (Kristersson et al 1972, Wernley et al
1980, Bria et al 1983).
The DFHs used in the calculation of FEUD were generated as follows (Marks et al 1999).
First, the PET/SPECT images were registered with the 3D planning CT scan, and hence
with the RT dose distribution. The number of PET/SPECT counts at each dose level was
calculated to generate PET/SPECT count histograms. As the number of FDG-PET counts
is proportional to tumour proliferation and SPECT counts is proportional to the amount of
perfusion, and using FDG-PET activity as the measure of tumour aggressiveness/proliferation
and perfusion as the measure of function, the PET/SPECT count histograms may be termed
dose function histograms (DFH). The FDG-PET/SPECT scans provide quantitative data
regarding the relative function/activity of one region compared to other regions and therefore
can be summed to calculate DFHs in a manner similar to DVHs.
The optimal plan is the plan that maximizes the FEUD in the target and minimizes the
FEUD in each critical structure. The higher target FEUD value implies higher tumour activity
is targeted and this may result in improved local control. A lower critical structure FEUD
value implies more sparing of functional sub-units, which may result in lower complications.
2.2. Treatment planning
To demonstrate the utility of the FEUD formalism, the lung dose distributions of two nonsmall cell lung cancer patients, who received 3D conformal external beam RT treatment at our
institution with curative intent, were evaluated. Both patients were treated with 15 MV AP-PA
fields to include the gross tumour volume (GTV) and the elective nodal volume followed by
off-cord oblique boost to the GTV. The GTV of the first patient (patient-1) was treated to a
prescription dose of 62 Gy to the 100% isodose volume, and the GTV of the second patient
(patient-2) was treated to a prescription dose of 73.6 Gy to the 93% isodose volume. In both
patients, the elective nodal areas were treated to 45 Gy. The treatment plans were generated
using the PLUNC (Plan University of North Carolina) treatment planning system. The lungs
SPECT scans were registered with the 3D planning CT scans, and consequently the RT dose
Incorporation of functional imaging data in equivalent uniform dose
1715
distribution, using the image registration software of the PLUNC system. The lungs dose
distributions were evaluated using the generalized EUD and FEUD models with a lung a value
of 0.96.
Furthermore, a non-small cell lung cancer patient, who had previously received 3D
external beam RT treatment at our institution, was inversely planned using the optimization
algorithm of the PLUNC treatment planning system (Chang et al 2002). The target (PET-CTGTV) was defined as the union of the FDG-PET avid regions of the GTV and the CT-outlined
GTV, both segmented by the radiation oncologist. A target dose prescription of 76 Gy to the
PET-CT-GTV was used. PET and SPECT scans of the patient were registered with the 3D
planning CT scan using the PLUNC system. Then, based on the CT, FDG-PET and SPECT
treatment planning images of the target and critical structures, two IMRT plans (plan-A and
plan-B) were generated using dose–volume objective functions.
The IMRT plan-A and plan-B were generated with the same objective function and using
the same dose–volume constraints but with different importance weighting parameters. The
IMRT plan-B was generated with the goal of achieving more critical structures sparing and
more functional volume target coverage than plan-A. To achieve this goal, higher importance
weighting was used for the PET-GTV, lungs and heart dose–volume objective functions. A
four coplanar 15 MV field set-up was used for the IMRT plans. The IMRT plans were
compared using the generalized EUD and FEUD models. The calculated a values of –10, 0.96
and 3.1 were used for the target, lung and heart, respectively.
For both the 3D and IMRT conformal plans, the dose distributions were calculated using
the differential scatter-air ratio algorithm (Sontag and Cunningham 1978) and were corrected
for tissue inhomogeneities using the Batho power law model (Batho 1964).
3. Results and discussion
Figures 1(a) and (c) show the relative dose distributions on a transverse SPECT image along
with the target, lungs and skin contours for patient-1 and patient-2, respectively. Figures 1(b)
shows the lungs DVH and DFH with the EUD value of 21.13 Gy and the FEUD value of
10.48 Gy for patient-1. Figure 1(d) shows the DVH and DFH for patient-2 with the EUD
value of 11.84 Gy and FEUD value of 20.61 Gy. The dose distributions superimposed on the
SPECT image along with the DFH plot for patient-1 show a significant amount of the perfused
right lung was spared. Most of the dose delivery was confined to the left non-functional lung
where very large SPECT perfusion defects were present next to the CT-defined lung tumour,
as shown in figure 1(a). The lungs FEUD value was lower than the EUD value by a factor of 2.
The physiological outcome of the lung irradiation would be better quantified by reporting the
DFH and FEUD data which are lower than the DVH and EUD data, indicating more sparing
of the functional lung.
On the other hand, the lungs dose distribution and DFH data of patient-2 shown in
figures 1(c) and (d) demonstrate that a large functional volume is treated to a significant
amount of dose, compared to the DVH. For this patient, the lungs FEUD value was higher
than the EUD by a factor of 2. Results suggest that by providing the additional lungs
functional data and FEUD value, one may re-plan the patient using other co-planar or noncoplanar beam set-ups to spare more functioning lung regions as much as possible. This may
be accomplished by selecting beam directions that traversed low-functioning lung regions
and/or less lung volume, versus another that traversed high-functioning lung regions and/or
more lung volume. The FEUD and DFH data show that the possibility of radiation-induced
damage measured by the reduction in the function of lungs volume in the high dose region is
higher, a fact that is not revealed by the DVH and EUD data.
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M M Miften et al
100
(a)
DVH
DF H
(b)
50
50
30
30
Volume (%)
SPECT Perfusion (%)
80
Target
100
100
90
90
90
70
70
Lungs
60
EUD = 21.13 Gy
FEUD = 10.48 Gy
40
20
0
0
20
40
60
80
Dos e (Gy)
100
30
30
50
50
100
100
Target
70
70
90
90
DVH
DF H
(d)
80
Volume (%)
SPECT Perfusion (%)
(c)
Lungs
60
EUD = 11.84 Gy
FEUD = 20.61 Gy
40
20
0
0
20
40
60
80
100
Dos e (Gy)
Figure 1. (a) Relative dose distributions of patient-1 superimposed on a SPECT transverse slice
with the CT-defined target, lungs and skin contours. (b) Lungs DVH and DFH for patient-1.
(c) Relative dose distributions of patient-2 superimposed on a SPECT transverse slice with the
CT-defined target, lungs and skin contours. (d) Lungs DVH and DFH for patient-2.
Figure 2(a) shows a CT transverse slice of the inversely planned patient with the target
outlines from CT and FDG-PET, and figure 2(b) shows an FDG-PET transverse slice with
the outlined PET-avid regions (treatment regions). Figure 2(c) shows beam’s eye view of the
target on a digitally constructed radiograph, and figure 2(d) shows the lungs pre-treatment
SPECT perfusion data. The PET and SPECT data show the regions with high activity and
function (darker regions) respectively, as shown in figures 2(b) and (d). The FDG-PET image
in figure 2(b) shows that there is an avid area located posteriorly in the right lung. The radiation
oncologist and radiologist at our institution diagnosed this area as being atelectatic lung with
consripation and inflammation (non-aerated inflamed lung) and therefore was not considered
in the 3D treatment of the patient.
Figure 3 shows plan-A and plan-B relative isodose distributions on a CT transverse slice.
Figure 4 shows the PET-CT-GTV DFH and DVH along with the lungs and heart DFHs. Both
IMRT plans show that a relatively homogeneous dose delivery is achieved where the high
dose regions are conforming to the target. The dose distributions of the IMRT plans show
more critical structure sparing is achieved in plan-B than plan-A at the expense of ‘slightly’
losing some target volumetric coverage. While the dose distributions in figure 3 and the
PET-CT-GTV DVH in figure 4(a) show that IMRT plan-A achieved more target volumetric
coverage than plan-B, the PET-CT-GTV DFH in figure 4(b) shows that plan-B was more
Incorporation of functional imaging data in equivalent uniform dose
(a)
(a )
1717
(b)
CT
FDG-PET
FDG-PET
PET
PE
TAv
Avid
id
Reg ion s
Regions
PET-GTV
PET-GTV
CT-GTV
(c )
(c)
(d)
BEV
BEV
SPECT
SPECT
Hig h Perfusion
High
Pe rfusio n
CT-GTV
PET-GTV
PET-GTV
Low Pe
Perfusion
rfusio n
Figure 2. (a) A CT transverse slice of the patient with the target outlines from CT and FDG-PET.
(b) An FDG-PET transverse slice from the FDG-PET image dataset of the patient showing the
outlined PET-avid regions (treatment regions). (c) An anterior beam’s eye view on a digitally
constructed radiograph showing the target which is the union of the CT treatment volume and the
FDG-PET treatment volume. (d) A transverse slice from the SPECT image dataset showing the
patient high and low perfusion regions in lungs.
Plan-A
PET-GTV
CT-GTV
100
90
100
70
50
Plan-B
100
90
90
100
100
70
50
Figure 3. Relative IMRT dose distributions of plan-A and plan-B superimposed on a CT transverse
slice.
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M M Miften et al
100
100
80
PET Activity (%)
80
Volume (%)
DFH
(b)
DVH
(a)
PET-CT-GTV
60
40
Plan_A
Plan_B
PET-CT-GTV
60
40
Plan_A
Plan_B
20
20
0
0
0
20
40
60
80
100
0
120
20
40
Dose (%)
100
80
100
120
100
DFH
(c)
DFH
(d)
80
80
Plan_A
Plan_B
SPECT Perfusion (%)
SPECT Perfusion (%)
60
Dose (%)
60
Lungs
40
20
0
Plan_A
Plan_B
60
40
Heart
20
0
0
20
40
60
Dose (%)
80
100
0
20
40
60
80
100
Dose (%)
Figure 4. The IMRT plan-A and plan-B dose–volume histogram (DVH) and dose–function
histograms (DFH). (a) Target DVH; (b) target DFH; (c) lungs DFH; (d) heart DFH.
effective at target activity/function coverage than volumetric coverage. Significantly higher
functional volumes of perfused lungs and heart are spared in plan-B than in plan-A, as shown in
figures 4(c) and (d).
Table 1 lists the EUD and FEUD values for the target and FEUD values for heart and lungs
of IMRT plan-A and plan-B. The results in table 1 show that the target volume EUD in plan-B
is lower than plan-A by 5%, with a value of 73.31 Gy, which is within 3.5% of the prescription
dose. However, the target FEUD in plan-B is lower than in plan-A by only 2.6%, with a
value of 75.77 Gy, which is within 0.3% of the prescription dose. The PET-CT-GTV EUD
and FEUD values of plan-A are within 1.6% and 2.3% of the prescription dose. The heart and
lungs plan-B FEUD values are lower than plan-A by 22% and 18%, respectively. While the
EUD values, which assume functional uniformity of the target and critical structures, show that
plan-A is marginally better than plan-B for target coverage, the FEUD values of plan-B show
adequate target activity/volume coverage with significant critical structure function sparing.
For both IMRT plans, beam directions were selected to achieve optimal sparing of the heart
and left lung functions. This resulted in FEUD values that are slightly smaller than the EUD
values (within 1 Gy) for heart and lungs in both plans.
Incorporation of functional imaging data in equivalent uniform dose
1719
Table 1. EUD and FEUD values of target (PET-CT-GTV), heart and lungs for IMRT plan-A and
plan-B.
EUD (Gy)
Plan-A
Plan-B
FEUD (Gy)
PET-CT-GTV
Heart
Lungs
PET-CT-GTV
Heart
Lungs
77.18
73.31
15.63
12.18
23.39
19.16
77.78
75.77
15.02
11.61
22.66
18.45
The FEUD model, unlike the TCP and NTCP models, provides a tool for the evaluation of
dose distributions which takes into account the non-linearity of tissue dose–function response
without attempting to make predictions of absolute outcome. This makes FEUD an attractive
method for the evaluation and comparison of dosimetrically guided and biologically guided
dose distributions. The FEUD concept can be used for the evaluation of conventional dose
distributions and is not limited to 3D conformal and/or IMRT plans. We applied the concept
of FEUD to 3D conformal and IMRT plans to stress the importance of using biological metrics
for the evaluation of conformal dose distributions. The FEUD concept can also be used to
evaluate dose distributions with pre- and post-treatment functional imaging data of the patient.
For example, by examining the pre- and post-treatment FEUD values, additional information
on tumour shrinkage/reduced activity and radiation-induced damage in normal tissue can be
used in the assessment of local control and long-term morbidity at follow-up.
The IMRT treatment plans in this work were steered by dose–volume objective functions
and evaluated by FEUD. In a future work, we are planning to perform IMRT planning using
objective functions that include functional imaging data information and evaluate the dose
distributions using the FEUD model. We will report the results in a future article.
4. Conclusions
A method to incorporate functional status in the calculation of EUD for radiotherapy dose
distributions was developed. The method accounts for the functional heterogeneity of
tumour and critical structures volumes by calculating the functional EUD using dose–function
histograms. Results from 3D conformal and IMRT plans for lung cancer patients show that
incorporating functional imaging data in the calculation of EUD is important in evaluating the
biological merit of dosimetrically guided or functional-guided IMRT dose distributions.
Acknowledgments
The authors would like to thank Dr Su-Min Zhou, Dr Mike Munley and Dr Andrzej Niemierko
for helpful discussions. This work is partially supported by NIH grant no. 69579 and Varian
Medical Systems.
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