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Prediction of Respiratory Motion Using A
Statistical 4D Mean Motion Model
Jan Ehrhardt1, Ren´e Werner1, Alexander Schmidt–Richberg1, and Heinz
Handels1
Department of Medical Informatics, University Medical Center Hamburg–Eppendorf,
Germany, j.ehrhardt@uke.uni-hamburg.de
Abstract. In this paper we propose an approach to generate a 4D sta-
tistical model of respiratory lung motion based on thoracic 4D CT data
of different patients. A symmetric diffeomorphic intensity–based registra-
tion technique is used to estimate subject–specific motion models and to
establish inter–subject correspondence. The statistics on the diffeomor-
phic transformations are computed using the Log–Euclidean framework.
We present methods to adapt the genererated statistical 4D motion
model to an unseen patient–specific lung geometry and to predict individ-
ual organ motion. The prediction is evaluated with respect to landmark
and tumor motion. Mean absolute differences between model–based pre-
dicted landmark motion and corresponding breathing–induced landmark
displacements as observed in the CT data sets are 3.3±1.8mm consid-
ering motion between end expiration to end inspiration, if lung dynamics
are not impaired by lung disorders.
The statistical respiratory motion model presented is capable of provid-
ing valuable prior knowledge in many fields of applications. We present
two examples of possible applications in the fields of radiation therapy
and image guided diagnosis.
1 Introduction
Respiration causes significant motion of thoracical and abdominal organs and
thus is a source of inaccuracy in image guided interventions and in image acqui-
sition itself. Therefore, modeling and prediction of breathing motion has become
an increasingly important issue within many fields of application, e.g in radiation
therapy [1].
Based on 4D images, motion estimation algorithms enable to determine
patient–specific spatiotemporal information about movements and organ defor-
mation during breathing. A variety of respiratory motion estimation approaches
have been developed in the last years, ranging from using simple analytical
functions to describe the motion over landmark–, surface– or intensity–based
registration techniques [2, 3] to biophysical models of the lung [4]. However, the
computed motion models are based on individual 4D image data and their use
is usually confined to motion analysis and prediction of an individual patient.
The key contribution of this article is the generation of a statistical 4D inter–
individual motion model of the lung. A symmetric diffeomorphic non–linear
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intensity–based registration algorithm is used to estimate lung motion from a
set of 4D CT images from different patients acquired during free breathing. The
computed vector motion fields are transformed into a common coordinate sys-
tem and a 4D mean motion model (4D–MMM) of the respiratory lung motion
is extracted using the Log–Euclidean framework [5] to compute statistics on the
diffeomorphic transformations. Furthermore, methods are presented to adapt the
computed 4D–MMM to the patient’s anatomy in order to predict individual or-
gan motion without 4D image information. We perform a quantitative in–depth
evaluation of the model–based prediction accuracy for intact and impaired lungs
and two possible applications of the 4D–MMM in the fields of radiation therapy
and image guided diagnosis are shown.
Few works that deal with the development of statistical lung motion models
have been published. Some approaches exist for the generation of 3D lung at-
lases [6], or the geometry–based simulation of cardiac and respiratory motions
[7]. First steps towards an average lung motion model generated from different
patients were done by Sundaram et al. [8], but their work focuses on 2D+tlung
MR images and the adaptation of the breathing model to a given patient has not
been addressed. First methods for building inter–patient models of respiratory
motion and the utilization of the generated motion model for model–based pre-
diction of individual breathing motion were presented in [9] and [10]. This paper
is an extension of [10] with regard to the methodology and the quantitative eval-
uation. In [9] motion models were generated by applying a Principal Component
Analysis (PCA) to motion fields generated by a surface–based registration in a
population of inhale–exhale pairs of CT images. Our approach is different in all
aspects: the registration method, the solution of the correspondance problem,
the spatial transformation of motion fields, and the computation of statistics
of the motion fields. Furthermore, we present a detailed quantitative evaluation
of a model based prediction for intact and impaired lungs. This offers interest-
ing insights into the prediction accuracy to be expected depending on size and
position of lung tumors.
2 Method
The goal of our approach is to generate a statistical model of the respiratory
lung motion based on a set of Npthoracic 4D CT image sequences. Each 4D
image sequence is assumed to consist of Nj3D image volumes Ip,j :Ω→R
(Ω⊂R3), which are acquired at corresponding states of the breathing cycle.
This correspondance is ensured by the applied 4D image reconstruction method
[11] and therefore, a temporal alignment of the patient data sets is not necessary.
Our method consists of three main steps: First, the subjectspecific motion
is estimated for each 4D image sequence by registering the 3D image frames.
In a second step, an average shape and intensity model is generated from the
CT images. In the last step, the average shape and intensity model is used as
anatomical reference frame to match all subject-specific motion models and to
build an average intersubject model of the respiratory motion.
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Image registration is required in all three steps. We use a non–linear, intensity–
based, diffeomorphic registration method as described in the next section. The
three steps to generate the statistical model of the respiratory motion are de-
tailed in Sect. 2.2. The utilization of the 4D–MMM for motion predicition is
presented in Sect. 2.3.
2.1 Diffeomorphic image registration
Diffeomorphic mappings ϕ:Ω→Ω, (ϕ∈Diff (Ω), Ω ⊂Rd) guarantee
that the topology of the transformed objects is preserved and are therefore used
in computational anatomy to analyze and characterize the biological variabil-
ity of human anatomy [12]. A practical approach for fast diffeomorphic image
registration was recently proposed in [13] by constraining ϕto a subgroup of
diffeomorphisms. Here, diffeomorphisms are parametrized by a stationary veloc-
ity field v, and the diffeomorphic transformation ϕis given by the solution of
the stationary flow equation at time t= 1 [5]:
∂
∂t φ(x, t) = v(φ(x, t)) and φ(x,0) = x.(1)
The solution of eq. (1) is given by the group exponential map ϕ(x) = φ(x,1) =
exp(v(x)) and the significant advantage of this approach is that these exponen-
tials can be computed very efficiently (see [5] for details).
The problem of image registration can now be understood as finding a para-
metrizing velocity field v, so that the diffeomorphic transformation ϕ= exp(v)
minimizes a distance Dbetween a reference image I0and the target image Ijwith
respect to a desired smoothness Sof the transformation: J[ϕ] = D[I0, Ij;ϕ] +
αS[ϕ]. Using S[ϕ] = RΩk∇vk2dx(with ϕ= exp(v)) as regularization scheme,
the following iterative registration algorithm can be derived:
Algorithm 1 Symmetric diffeomorphic registration
Set v0= 0, ϕ=ϕ−1=I d and k= 0
repeat
Compute the update step u=1
2“fI0,Ij◦ϕ−fIj,I0◦ϕ
−1”
Update the velocity field and perform a diffusive regularization:
vk+1 = (Id −τ α∆)−1“vk+τu”(2)
Calculate ϕ= exp(vk+1) and ϕ−1= exp(−vk+1 )
Let k←k+ 1
until kvk+1 −vkk< or k≥Kmax
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The update field uis calculated in an inverse consistent form to assure source
to target symmetry. The force term fis related to Dand is chosen to be:
fI0,Ij◦ϕ(x) = −(I0(x)−(Ij◦ϕ)(x)) ∇(Ij◦ϕ)(x)
k∇(Ij◦ϕ)(x)k2+κ2(I0(x)−(Ij◦ϕ)(x))2(3)
with κ2being the reciprocal of the mean squared spacing. Eq. (2) performs the
update of the velocity field v, where τis the step width. The term (Id −τ α∆)−1
is related to the diffusive smoother Sand can be computed efficiently using
additive operator splitting (AOS).
We have chosen this diffeomorphic registration approach because of three rea-
sons: In the context of the motion model generation, it is important to ensure
that the calculated transformations are symmetric and diffeomorphic because of
the multiple usage of inverse transformations. The second reason is related to
runtime and memory requirements: due to the size of the 4D CT images dif-
feomorphic registration algorithms using non–stationary vector fields, e.g. [14],
are not feasible. Third, the representation of diffeomorphic transformations by
stationary vector fields provides a simple way for computing statistics on diffeo-
morphisms via vectorial statistics on the velocity fields.
For a diffeomorphism ϕ= exp(v), we call the velocity field v= log(ϕ) the
logarithm of ϕ. Remarkably, the logarithm v= log(ϕ) is a simple 3D vector
field and this allows to perform vectorial statistics on diffeomorphisms, while
preserving the invertibility constraint [15]. Thus, the Log-Euclidean mean of
diffemorphisms is given by averaging the parametrizing velocity fields:
¯
ϕ= exp 1
NX
i
log(ϕi)!.(4)
The mean and the distance are inversion-invariant, since log(ϕ) = −log(ϕ−1).
Even though the metric linked to this distance is not translation invariant, it
provides a powerful framework where statistics can be computed more efficiently
than in the Riemannian distance framework. For a more detailed introduction to
the mathematics of the diffeomorphism group and the associated tangent space
algebra, we refer to [5] and the references therein.
2.2 Generation of a 4D mean motion model
In the first step, we estimate the intra–patient respiratory motion for each 4D
image sequence by registering the 3D image frames. Let Ip,j :Ω→R(Ω⊂R3)
be the 3D volume of subject p∈ {1, . . . , Np}acquired at respiratory state j∈
{0, . . . , Nj−1}. Maximum inhale is chosen as reference breathing state and the
diffeomorphic transformations ϕp,j :Ω→Ωare computed by registering the
reference image Ip,0with the target images Ip,j ,j∈ {1, . . . , Nj−1}. In order
to handle discontinuities in the respiratory motion between pleura and rib cage,
lung segmentation masks are used to restrict the registration to the lung region
by computing the update field only inside the lung (see [3] for details).
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In order to build a statistical model of respiratory motion, correspondence
between different subjects has to be established, i.e. an anatomical reference
frame is necessary. Therefore, the reference images Ip,0for p= 1, . . . , Npare
used to generate an average intensity and shape atlas ¯
I0of the lung in the
reference breathing state by the method described in [10]. This 3D atlas image
¯
I0is now used as reference frame for the statistical lung motion model. Each
patient–specific reference image Ip,0is mapped to the average intensity and shape
atlas ¯
I0by an affine alignment and a subsequent diffeomorphic registration.
Let ψpbe the transformation between the reference image Ip,0of subject p
and the atlas image ¯
I0. Since the intra–subject motion models ϕp,j are defined
in the anatomical spaces of Ip,0, we apply a coordinate transformation
˜
ϕp,j =ψp◦ϕp,j ◦ψ−1
p(5)
to transfer the intra–subject deformations into the atlas coordinate space. Such
a coordinate transformation accounts for the differences in the coordinate sys-
tems of subject and atlas due to misalignment and size/shape variation and
eliminates subject–specific size, shape and orientation information in the de-
formation vectors. This enables the motion fields of each of the subjects to be
compared directly quantitatively and qualitatively and the 4D–MMM is gener-
ated by calculating the Log-Euclidean mean ¯ϕjof the mapped transformations
for each breathing state j:
¯ϕj= exp 1
NpX
p
log ( ˜
ϕp,j )!= exp 1
NpX
p
log ψp◦ϕp,j ◦ψ−1
p!.(6)
The method proposed in [16] was used to compute the logarithms log ( ˜
ϕp,j ).
The resulting 4D–MMM consists of an average lung image ¯
I0for a refer-
ence state of the breathing cycle, e.g. maximum inhalation, and a set of motion
fields ¯ϕjdescribing an average motion between the respiratory state jand the
reference state (Fig. 1).
2.3 Utilization of the 4D–MMM for individual motion prediction
The 4D–MMM generated in section 2.2 can be used to predict respiratory lung
motion of a subject seven if no 4D image information is available. Presuming a
3D image Is,0acquired at the selected reference state of the breathing cycle is
available, the 4D–MMM is adapted to the individual lung geometry of subject
sby registering the average lung atlas ¯
I0with the 3D image Is,0. The resulting
transformation ψsis used to apply the coordinate transformation eq. 5 to the
mean motion fields ¯ϕjin order to obtain the model–based prediction of the
subject–specific lung motion: ˆ
ϕs,j =ψ−1
s◦¯ϕj◦ψs.
However, two problems arise. First, breathing motion of different individuals
varies significantly in amplitude [1]. Therefore, motion prediction using the mean
amplitude will produce unsatisfying results. To account for subject–specific mo-
tion amplitudes, we propose to introduce additional information by providing the
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(a) (b)
Fig. 1. Visualization of average lung model ¯
I0(a) and magnitude of mean deformation
¯ϕjbetween end inspiration and end expiration (b). The average deformation model
shows a typical respiratory motion pattern. Different windowing and leveling functions
are used to accentuate inner/outer lung structures.
required change in lung air content ∆Vair. Even without 4D-CT data, this infor-
mation can be acquired by spirometry measurements. Thus, we search a scaling
factor λso that the air content of the transformed reference image Is,0◦λˆ
ϕ−1
s,j
is close to the air content Vair (Is,0) + ∆Vair. In order to ensure that the scaled
motion field is diffeomorphic, the scaling is performed in the Log–Euclidean. To
determine the correct scaling factor λ, a binary search strategy is applied and
the air content is computed using the method described in [17]. ∆Vair can be
regarded as a parameter that describes the depth of respiration. In general, other
measurements can also be used to calculate appropriate scaling factors, e.g. the
amplitude of the diaphragm motion.
Further, a second problem arises when predicting individual breathing motion
of lung cancer patients. Lung tumors will impair the atlas–patient registration
because there is no corresponding structure in the atlas. This leads to distortions
in ψsnear the tumor region and consequently the predicted motion fields ˆ
ϕs,j are
affected. Therefore, we decided to compute ψsby registering lung segmentation
masks from atlas and subject sand by omitting the inner lung structures.
3 Results
To capture the respiratory motion of the lung, 18 4D CT images were acquired
using a 16–slice CT scanner operating in cine-mode. The scanning protocol and
optical–flow based reconstruction method was described in [11]. The spatial res-
olution of the reconstructed 4D CT data sets is between 0.78 ×0.78 ×1.5mm3
and 0.98 ×0.98 ×1.5mm3. Each data set consists of 3D CT images at 10 to 14
preselected breathing phases. Due to computation times, in this study we use
the following 4 phases of the breathing cycle: end inspiration (EI), 42% exhale
(ME), end expiration (EE) and 42% inhale (MI). A clinical expert delineated
left and right lung and the lung tumors in the images.
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Fig. 2. Result of the motion estimatation by intra–patient registration (top row)
and the model–based motion prediction (bottom row) of patient 01. Visualization of
the magnitude of the displacement field computed by intra–patient registration (top
left) and of the displacement field predicted by the 4D mean motion model (bot-
tom left). Right: contours at end inspiration (green), end expiration (yellow) and esti-
mated/predicted contours at end expiration (red).
The aim of the model generation is to create a representation of the mean
healthy lung motion. In a dynamic MRI study by Plathow et al. [18], tumors with
diameter >3cm were shown to influence respiratory lung dynamics. According
to their observations, we divide the lungs into two groups: lungs with intact
dynamics and lungs with impaired motion. Lungs without or with only small
tumors (volume <14.1cm3or diameter <3cm) are defined as intact. Lungs with
large tumors or lungs affected by other diseases (e.g. emphysema) are defined as
impaired. According to this partitioning, we have 12 data sets with both lungs
intact and 6 data sets with at least one impaired lung. Only data sets with intact
lungs are used to generate the 4D–MMM.
3.1 Landmark–based evaluation
Due to the high effort of the manual landmark identification only 10 of the
18 data sets are used for the detailed quantitative landmark–based evaluation.
Between 70 and 90 inner lung landmarks (prominent bifurcations of the bronchial
tree and the vessel tree) were identified manually in the four breathing phases,
about 3200 landmarks in total. An intraobserver variability of 0.9±0.8mm was
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Table 1. Landmark motion amplitudes and target registration errors RE E for the
patients considered (in mm). Values are averaged over all landmarks per lung. Lungs
with impaired motion are indicated by a gray text color.
Landmark Intra-patient Model-based
motion registration prediction
Data set (Lung) [mm] TRE [mm] TRE [mm]
Patient01 left 4,99 ±4,84 1,51 ±1,31 2.43 ±1,64
right 7,25 ±4,47 1,41 ±0,83 3.97 ±2,08
Patient02 left 7,09 ±2,92 2,28 ±1,73 4.26 ±1,28
right 4,21 ±1,75 1,16 ±0,61 3.82 ±1,14
Patient03 left 6,15 ±2,26 1,38 ±0,73 3.68 ±1,31
right 6,28 ±2,01 1,78 ±1,05 3.72 ±1,37
Patient04 left 6,65 ±2,56 1,53 ±0,93 4.01 ±1,60
right 6,22 ±3,52 1,44 ±0,82 2.28 ±1,09
Patient05 left 5,77 ±2,03 1,50 ±0,80 3.17 ±1,34
right 3,18 ±3,36 1,29 ±1,04 3.47 ±1,99
Patient06 left 9,67 ±8,32 1,64 ±1,42 5.85 ±2,65
right 11,85 ±7,08 1,60 ±1,00 4.88 ±2,02
Patient07 left 8,22 ±6,52 2,45 ±2,22 3.99 ±1,79
right 4,99 ±6,65 1,49 ±1,48 3.35 ±1,69
Patient08 left 5,78 ±4,14 1,18 ±0,57 3.15 ±1,70
right 6,28 ±5,63 1,25 ±1,03 3.11 ±2,24
Patient09 left 7,43 ±5,34 1,42 ±1,22 3.05 ±1,39
right 8,41 ±5,22 1,67 ±1,03 4.94 ±3,01
Patient10 left 7,63 ±5,83 1,93 ±2,10 3.16 ±2,29
right 8,85 ±6,76 1,76 ±1,33 5.12 ±2,34
assessed by repeated landmark identification in all test data sets. The target
registration error (TRE) was determined for a quantitative evaluation of the
patient–specific registration method and the model–based prediction. The TRE
Rk
jis the difference between the motion of landmark kestimated by ϕjand the
landmark motion as observed by the medical expert.
The mean landmark motion magnitude, i.e. the mean distance of correspond-
ing landmarks, between EI and EE is 6.8±5.4mm, (2.6±1.6mm between EI and
ME and 5.0±2.8mm between EI and MI). The TRE of the intra–patient reg-
istration is a lower bound for the accuracy of the model–based prediction using
the 4D–MMM. The average TRE REE between the reference phase (EI) and EE
for patient 01 to 10 (averaged over all landmarks and patients) is 1.6±1.3mm
(1.5±0.8mm between EI and ME and 1.6±0.9mm between EI and MI). Details
for all test data sets are shown in table 1.
For each of the 10 test data sets the 4D–MMM is used to predict landmark
motion as described in Sect. 2.3. If both lungs of the test data set are intact,
a leave–one–out strategy is applied to ensure that the patient data is not used
for the model generation. The change in lung air content ∆Vair needed for the
computation of the scaling factor λwas calculated from the CT images IEI and
IEE for each lung side and each test data set. The same factor λwas used to
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scale the predicted motion fields ˆ
ϕEE ,ˆ
ϕME and ˆ
ϕM I . Besides ∆Vair no 4D
information is used for the model–based prediction.
In Fig. 2 the motion field predicted by the 4D–MMM is compared to the
motion field computed by patient–specific registration. A good correspondency
between the motion fields is visible, except in the right upper lobe where small
deviations occur. The prediction accuracy is illustrated by overlayed contours.
The average TREs REE are listed in table 1 for each of the test data sets and
for both the patient–specific and model–based motion estimation. Lungs with
impaired motion are indicated by a gray text color. Regarding table 1, lungs with
impaired motion generally show higher TREs for the model–based prediction
than intact lungs. The average TRE REE for intact lungs is 3.3±1.8mm, which
is significantly lower (p < 0.01) than for lungs with impaired motion (REE =
4.2±2.2mm). Significance is tested by applying a multilevel hierarchical model
with the individual Rkvalues nested within the patient (software: SPSS v.17);
data are logarithmized to ensure normal distribution and the model is adjusted
to landmark motion.
3.2 Model-based prediction of tumor motion
For a second evaluation of the model, we use expert generated tumor segmenta-
tions in two breathing phases (EI and EE) of 9 patient data sets with solid lung
tumors. The 4D–MMM is transformed into the coordinate space of each test
data set (see Sect. 2.3) and then used to warp the expert–generated tumor seg-
mentation at maximum exhale towards maximum inhale. The distance between
the predicted tumor mass center and the center of the manual segmentation
was used to evaluate the accuracy of the model–based prediction. Correspond-
ing results are summarized in table 2. Large tumors with a diameter >3cm are
marked in the table as “large”.
Regarding table 2 accuracy of the model–based predicted motion of the tu-
mor mass center from EI to EE ranges from 0.66mm to 7.38mm. There is no
significant correlation between the tumor motion amplitude and the accuracy
of the model-based predicted mass center (r= 0.19, p > 0.15). Furthermore, it
cannot be shown that the prediction accuracy for small tumors is significantly
better than for large tumors (p > 0.4). In contrast, the model–based prediction
accuracy of non-adherent tumors is significantly better than for tumors adher-
ing to chest wall or hilum (p < 0.05). In these cases the model presumes the
tumour moves like surrounding lung tissue, whereas it rather moves like the ad-
jacent non-lung structure (e.g. chest wall or hilum). In the last column in table 2
those tumors are tagged. Significance is tested by applying a linear mixed model
(software: SPSS v.17) and the model is adjusted to tumor motion.
4 Discussion
In this paper, we proposed a method to generate an inter–subject statistical
model of the breathing motion of the lung, based on individual motion fields
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Table 2. Tumor size and motion amplitude, and the center distances between manually
segmented tumor and predicted tumor position (see text for details).
Tumor Tumor Intra–patient Model–based
size motion registration prediction
Data set (Lung) [cm3] [mm] TRE [mm] TRE [mm]
large
adhere
Patient 01 right 6.5 12.20 0.45 3.54
Patient 02 right 7.6 2.15 1.44 3.90 X
Patient 03 left 12.7 6.74 0.41 3.91 X
Patient 05 right 8.2 2.34 1.95 5.39 X
right 17.3 1.68 1.05 4.44 X X
Patient 06 left 3.4 19.78 2.12 6.87
right 128.2 13.78 0.97 2.99 X
Patient 07 right 2.8 1.31 0.42 0.66
Patient 08 right 18.4 6.24 0.90 1.59 X
Patient 09 right 88.9 8.35 0.29 5.33 X X
Patient 10 right 96.1 1.77 1.01 7.46 X X
extracted from 4D CT images. Methods to apply this model in order to predict
patient–specific breathing motion without knowledge of 4D image information
were presented. Ten 4D CT data sets were used to evaluate the accuracy of the
image–based motion field estimation and the model–based motion field predic-
tion. The intra–patient registration shows an average TRE in the order of the
voxel size, e.g. 1.6±1.3mm when considering motion between EI and EE. The
4D–MMM achieved an average prediction error (TRE) for the motion between
EI and EE of 3.3±1.8mm. Regarding that besides the calculated scaling factor
λno patient–specific motion information is used for the model–based prediction
and that the intra–patient registration as well as the atlas–patient registration
is error prone, we think this is a promising result. Thus we believe that a sta-
tistical respiratory motion model has the capability of providing valuable prior
knowledge in many fields of applications.
Since the statistical model represents intact respiratory dynamics, it was
shown that the prediction precision is significantly lower for lungs affected by
large tumours or lung disorders (4.2±2.2mm). These results indicate (at least for
the 10 lung tumor patients considered) that large tumors considerably influence
respiratory lung dynamics. This finding is in agreement with Plathow et al. [18].
In addition, we applied the 4D–MMM to predict patient–specific tumor motion.
No correlation between prediction accuracy and tumor size or tumor motion
amplitude could be detected (at least for our test data sets). We observed that
tumors adhering to non–lung structures degrade local lung dynamics significantly
and model–based prediction accuracy is decreased for these cases.
To conclude this paper, we present two examples of possible applications of
the statistical respiratory motion model.
Application examples: The capability of the 4D–MMM to predict tumor motion
for radiotherapy planning is exemplarily illustrated for patient 01. This patient
has a small tumor not adherent to another structure, and a therapeutically
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(a) (b)
Fig. 3. (a) Visualization of the internal target volume (ITV) of patient 01 in a coronal
CT slice. The ITV was calculated from expert-defined tumor segmentations (yellow
contour) and from tumor positions predicted by the average motion model (red con-
tour). (b) Visualization of the difference between lung motion estimated by patient–
specific registration and lung motion predicted by the 4D–MMM for patient 09. The
left lung shows intact lung motion; dynamics of the right lung are impaired by the
large tumor. The contour of the tumor is shown in black.
relevant tumor motion of 12.2mm. An important measure for planning in 3D
conformal radiotherapy is the internal target volume (ITV), which contains the
complete range of motion of the tumour. For this patient, the ITV is calculated
first from expert-defined tumor segmentations in the images acquired at EI, EE,
ME and MI. In a second step, the expert segmentation in EI is warped to EE,
ME and MI using the 4D–MMM and the ITV is calculated based on the warped
results. The outlines of both ITVs are shown in Fig. 3(a).
A second example demonstrates that the 4D–MMM could be helpful from
the perspective of image-guided diagnosis. Here, the motion pattern of individual
patients are compared to a “normal” motion, represented by the 4D–MMM. To
visualize the influence of a large tumor to the respiratory motion, the difference
between the individual motion field computed by intra–patient registration and
the motion field predicted by the 4D–MMM is shown in Fig. 3(b). The left
lung shows differences of only about 3mm, whereas the large differences to the
intact lung motion indicate that the respiratory dynamics of the right lung are
influenced by the large tumor.
Currently, the statistical motion model represents the average motion in the
training population. A main focus of our future work is to include the variability
of the motion into the model. Here, the Log–Euclidean framework provides a
suitable technique for more detailed inter–patient statistics.
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Second International Workshop on
Pulmonary Image Processing
