Evaluation of an automated deformable matching method for
quantifying lung tumor motion in respiration-correlated CT
images
Gig Mageras1, Sarang Joshi2, Brad Davis2, Alex Pevsner1, Agung Hertanto1, Ellen Yorke1, Kenneth Rosenzweig1,
Yusuf Erdi1, Sadek Nehmeh1, John Humm1, Steven M Larson1, C Clifton Ling1
1
Departments of Medical Physics, Radiation Oncology, and Radiology, Memorial Sloan-Kettering Cancer Center, New York, NY, USA; and
Departments of Computer Science and Radiation Oncology, University of North Carolina, Chapel Hill, NC, USA
2
Abstract
We have investigated an automated procedure of deformable CT-to-CT matching for determining lung tumor motion in CT data sets
at different respiration phases of the same patient. The deformable matching procedure uses a high-dimensional transformation to
map voxels between two CT data sets; the transformation is then used to transfer delineated organs from one CT data set onto the
other, thus quantifying organ motion and shape changes. We have evaluated the accuracy of the procedure in predicting the GTV
motion between CT data sets at end expiration and end inspiration of six patients treated for nonsmall cell lung carcinoma.
Preliminary results comparing the model prediction with manual delineation as a reference indicate an estimated accuracy in
determining the GTV boundary of 0.7 mm (median) and 3.1 mm (95% confidence); the latter number is comparable to the estimated
uncertainty of one CT slice thickness (2.5 mm) in the manual delineation along the superior-inferior direction.
Keywords
Segmentation, image fusion, radiation treatment planning, respiration, 4D computed tomography, lung cancer
Introduction
It is well known that respiration induces significant anatomic
motion in the thorax. Recently CT imaging techniques have
been developed, variously referred to as respiration-correlated
CT or 4D-CT, that provide 3D image sets at multiple
respiration phases from a single CT scan [1,2,3,4]. These
imaging techniques provide valuable information on tumor and
other anatomic motion with respiration that may improve the
accuracy of precision radiotherapy by determining appropriate
planning target volume margins and assessing the need for
respiration management at treatment, such as breath hold or
respiration gating.
A hurdle in realizing these gains is the need to define
the gross tumor volume (GTV) in the large number of images,
from 2 to 10 times more than standard practice, depending on
the number of respiration phases sampled. It is therefore
highly desirable to have software tools that automatically
segment the GTV in the image sets at different phases, using
the physician-drawn contours at one phase as a starting point.
To this end, the University of North Carolina has developed an
automated deformable CT-to-CT matching tool that can predict
changes in organ shape between image data sets. In this paper,
we evaluate the application of this tool to defining GTV motion
in respiration-correlated CT image sets of patients treated for
nonsmall cell lung carcinoma (NSCLC).
Material and methods
The deformable matching model quantifies anatomical
variation by constructing a high-dimensional registration
transformation h that brings a study CT data set of a patient (in
this case, a CT at the end inspiration [EI] phase) into
correspondence with a reference CT image set Ip(x) of the same
patient (i.e., the planning CT at the end expiration [EE] phase).
The model assumes that the reference and study CT data sets
are previously registered by alignment of the skeletal anatomy.
The deformable transformation has dimensions on the order of
the
image
resolution,
according
to
h : x  ( x1 , x2 , x3 )  h( x) ( x1 , x2 , x3 )  (u1 ( x), u 2 ( x), u3 ( x))
with the vector field u(x) = (u1(x) ,u2(x), u3(x)) describing the
local tissue displacement. Registration is defined using a mean
squared error distance measured between the transformed study
image Is(h(x)) and the reference image Ip(x), i.e.,
D(h) = ∫ |Ip(x)–Is(h(x))|2 dx, where the integration is over the
coordinate system of the study image. The transformation h is
estimated in a manner that minimizes the distance D(h) while
at the same time constraining the transformation to satisfy the
laws of continuum mechanics, derived from viscous fluid
modeling using the Navier-Stokes equations. Further details of
viscous fluid modeling are given in [5,6]. Having computed
the transformation h that maps the study CT onto the planning
CT, the segmentation of the study CT is accomplished by
applying the inverse transformation to the segmentations (i.e.
physician-drawn contours) of the planning CT. The
transformation h thus quantifies the organ motion and fine
featured organ shape changes between the two CT data sets.
Data for evaluating the automated procedure consist of CT
image sets of patients treated for NSCLC, acquired at different
respiration phases on a 4-slice scanner (LightSpeed GX/i, GE
Medical Systems, Waukesha, WI). The CT acquisition uses a
cine mode, in which CT data are acquired for a complete
respiratory cycle at each couch position while simultaneously
recording the patient’s respiration with a monitor (Real-time
Figure 1: (Left, center) Axial and coronal sections of superimposed CT data sets of a patient at end expiration (EE) and end inspiration (EI),
prior to deformable matching. Axial section shows manually delineated GTV at EE (green) and EI (red). (Right) Surface rendering of GTV
at EE (green) and EI (red).
Position Management System, Varian Medical Systems, Palo
Alto, CA) consisting of a passive reflective marker placed on
the patient’s thorax, which is observed by a CCD camera
mounted on the CT couch. CT slices are retrospectively
resorted according to respiration phase (Advantage 4D, GE
Medical Systems). To provide a standard against which to
compare the registration model, the GTV is manually
delineated in the CT images at end expiration, and then the
contours are used as a visual guide to delineate the GTV at end
inspiration. The GTV surface differences between the model
prediction and manual delineation are analyzed with a software
tool developed for this purpose, which is an adaptation of the
method of Remeijer et al [7]. The analysis tool constructs a
triangular tiled surface of the reference object (i.e., the
manually delineated GTV in the EI data set) and reads in a tiled
surface of the study object (i.e., the model prediction of the
GTV in the EI data set given the manual delineation in the EE
data set). The analysis tool then casts rays radially outward
from the centroid (origin) of the reference object, determines
the intersection of the ray with the surface (reference or study)
furthest from the origin, and from the intersection point finds
the nearest distance to the surface of the other (study or
reference) object. The distances are plotted on a polar map of
angles theta (polar angle with 0 and 180 corresponding to the
superior and inferior directions) and phi (azimuthal angle with
90 and 270 corresponding to the posterior and anterior
directions).
Results and discussion
We have evaluated the automated procedure on respirationcorrelated CT images from six patients treated for NSCLC.
Figure 1 shows an example prior to the application of the
deformable matching. Axial and coronal views of the two CT
data sets (left, center panels) are overlaid and blended; regions
where the anatomy differs between the two data sets show up
as darker gray, such as in the diaphragm, mediastinum and
GTV (at center of cross hairs). The two CT data sets come
from the same cine acquisition, thus are already rigidly
matched according to the patient’s stationary skeletal anatomy.
The respiration-induced changes in internal anatomy are
clearly evident. The right panel shows a surface display of the
manually delineated GTV at EE (green) and EI (red). The
rectangle in the left and center panels indicates the volume of
interest (VOI) in which deformable matching will be done.
Figure 2 shows the result after the deformable matching. Note
the improved correspondence of the CT data inside the VOI
(left and center panels), compared to the rest of the image
where deformable matching was not applied. The same
transformation is applied to deform the delineated GTV from
the EE data set into the EI data set (right panel, green), note the
good agreement with the manually delineated GTV at EI (red).
Figure 2: (Left, center) Axial and coronal sections of superimposed CT data sets after deformable matching is applied inside the rectangular
region. (Right) Surface rendering of model predicted (green) and manually delineated GTV (red) at end inspiration.
0
Superior
4
Theta (degrees)
30
6
60
42 0
90
Post
-2 Ant
120
-4
-6
150
180
8 mm
6
4
2
0
-2
-4
-6
-8
Inferior
0
60
Conclusion
120 180 240 300 360
Phi (degrees)
Figure 3: Polar map of surface differences between GTV at EE and
EI, prior to deformable matching. Positive (negative) values
indicate that GTV surface at EI is outside (inside) the GTV at EE
along those directions.
Figure 3 shows a polar map of the GTV surface differences
between the manually delineated GTV at EE and EI,
corresponding to the right panel of Figure 1. One observes
differences up to 8 mm, with the largest differences occurring
at the inferior and superior GTV borders, owing to the GTV
motion primarily in the superior-inferior direction. Figure 4 is
a polar map of the surface differences between modelprediction and manually drawn GTV and EI, corresponding to
the right panel of Figure 2. The agreement is very good, with
surface differences of about 2 mm or less over all angles in this
example. Analysis of surface difference data over all angle and
patients yields median and 95 percentile values for the absolute
surface difference of 0.7 mm and 3.1 mm, respectively. The
latter number is comparable to the estimated uncertainty of one
CT slice thickness (2.5 mm) in the manual delineation along
the superior-inferior direction.
0
-2
Superior
-1
30
3mm
Theta (degrees)
2
60
1
90
Post
0
0
Ant
-1
120
-2
1
150
2
180
0
60
-3
2
Inferior
120 180 240
Phi (degrees)
300
plus a margin for microscopic disease) is not underdosed at any
phase, one strategy would be to design a volume for intrafractional motion that encloses the CTV at all phases. For
gated treatments, one can identify the phase interval of the
respiratory monitor corresponding to minimum GTV motion,
then design an intra-fractional motion volume to enclose the
CTV for only that phase interval. To form the planning target
volume, an additional margin will be required for interfractional variations in target position [8] as well as patient
positioning errors.
360
Figure 4: Polar map of surface differences between model
prediction and manually drawn GTV at EI and EI, following
deformable matching
Once the GTV is defined at each respiration phase, the
information can be used in different ways in planning
treatment. The extent of GTV motion so determined can be
used to assess whether respiration management at treatment,
such as breath hold or gating techniques, is warranted. If the
intent is to treat without respiratory gating and one wants to
ensure that the clinical target volume (CTV, enclosing the GTV
We have investigated an automated procedure of deformable
CT-to-CT matching for determining tumor motion in lung with
CT data sets at different respiration phases. Preliminary results
comparing the model prediction with manual delineation as a
reference indicate an estimated accuracy in determining the
position of the GTV boundary that is comparable to the CT
resolution. Further plans are to evaluate the procedure in larger
numbers of patient data sets, and to evaluate its applicability to
other disease sites, such as CT-guided treatment of prostate.
Acknowledgements
This work was supported in part by U.S. National Institutes of
Health grant P01-CA59017, Varian Medical Systems, and
General Electric Medical Systems.
References
[1] Ford E C, Mageras G S, Yorke E and Ling C C 2003
Respiration-correlated spiral CT: a method of measuring
respiratory-induced anatomic motion for radiation treatment
planning. Med Phys 30 88-97
[2] Vedam S S, Keall P J, Kini V R et al 2003 Acquiring a
four-dimensional computed tomography dataset using an
external respiratory signal. Phys Med Biol 48 45-62
[3] Low D A, Nystrom M, Kalinin E et al 2003 A method for
the reconstruction of four-dimensional synchronized CT
scans acquired during free breathing. Med Phys 30 1254-63
[4] Rietzel E Chen G T Doppke K P et al 2003 4D computed
tomography for treatment planning Int J Radiat Oncol Biol
Phys 57 (Suppl 1) S232-3
[5] Christensen G E, Joshi S C and Miller M I 1997 Volumetric
transformation of brain anatomy. IEEE Trans Med Imaging
16 864-877
[6] Joshi S and Miller M I 2000 Landmark matching via large
deformation diffeomorphisms. IEEE Trans Image
Processing 9 1357-1370
[7] Remeijer P, Rasch C, Lebesque J V et al 1999 A general
methodology for three-dimensional analysis of variation in
target volume delineation. Med Phys 26 931-940
[8] Ford E, Mageras G S, Yorke E et al 2002 Evaluation of
respiratory movement during gated radiotherapy using film
and electronic portal imaging. Int J Radiat Oncol Biol Phys
52 522-531