Abstract fed into the EBRT system so that




The need for accurate information on lung tumor motion and
deformation has led to development of biomechanical models of the respiratory system.
The recent progress in biomechanical models of the lung can be translated to more
efficient tumor tracking methods in which the respiratory-induced displacement
and deformation of the tumor during the radiation therapy is accounted for. This
paper reviews the different biomechanical approaches for modeling the
respiratory motion and highlights the progress in the field. We further discuss
the advantages and disadvantages of each method and recommendations that can
improve the performance of these biomechanical models.

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Keywords: lung biomechanical model, tumor tracking, respiratory motion,
patient-specific models










Lung cancer has the highest mortality rate among all other cancer
types with 5-year survival rate of merely 17%. Currently, the main treatment
method for lung cancer in the clinic is external beam radiation therapy (EBRT)
which aims to deliver high-energy beams to the tumor. However, the position and
the shape of the tumor changes significantly due to complex motion of the lungs
and surrounding organs during respiratory activity. Therefore, accurate
delivery of radiation to the cancerous tissue is affected which may result in
irradiating and consequently apoptosis of the lungs’ healthy tissues. As a
result, there is an urgent need in the clinic for a tracking system that can
predict the lungs and tumor’s motion and deformation with high accuracy. The
output data of this system can be subsequently fed into the EBRT system so that
it can track and focus the radiation on the tumor and avoid irradiating the
lungs healthy tissue. One possible method of tracking is to develop a
biomechanical model of the lungs that can predict the displacement and shape of
the tumor in real-time. Several groups have been working on developing a
comprehensive lung biomechanical model from 4D CT images as a core part of an
accurate tracking system to be integrated with EBRT. In this review, three most
outstanding and relevant papers available in the field of biomechanical models
of the lung motion and deformation with applications in tumor radiation therapy
will be reviewed from a technical viewpoint with emphasis on the
characteristics of each biomechanical model. In the following progress report,
we recapitulate the highlights of each article, how they are related to one another,
followed by a discussion and conclusion on the proposed methods.

Lung tumor motion biomechanical models: In 2009, Werner et al.1 modeled
lung ventilation by applying pressure forces to 3D lung surfaces, while the resulting
lung expansion is limited by a second geometry representing an intended final
lung shape. They modeled the whole lung to be isotropic, homogeneous, and
linearly elastic, using finite element modeling (FEM). In the first part of their
study, the geometries are given by a mathematical phantom of the lungs which represents
lung shapes as modifications of quarters of an ellipsoid. They applied a
uniform negative pressure to the lung geometry representing an initial state of
breathing which in this study is the phase of end expiration (EE). Starting
from zero the pressure is increased gradually forcing the lung to expand. The expansion
is limited by a second geometry representing the lung shape at end inspiration
(EI) which denotes the final breathing phase. Since they modeled the lung to be
isotropic, linearly elastic, and homogeneous, Young’s modulus E and Poisson’s
ratio n are constant. They analyzed the influence of E and n on the modeling process by solving the FEM for different values of
these two parameters based on the literature: E varied from 0.1 to 10 kPa and n from 0.2 to 0.45. Other parameters such as solver-specific
settings and meshing quality are kept constant. The FEM is solved using COMSOL
Multiphysics. Finally, given the models satisfying the success criterion, which
is defined as the ratio of the volume of the deformed initial geometry and the
limiting geometry being at least 0.995, the influence of the elastic constants
on the inner lung displacement field is assessed. Their phantom study demonstrated
that the values of the biomechanical parameters are of minor impact on the
estimated motion field.

In order to evaluate the modeling accuracy, 4D CT images of lung
cancer patients were used to generate patient-specific models; the choice of
the values of the elastic constants is based on the results of the phantom
studies. In this case, geometry descriptions are extracted from CT image data.
Lungs are segmented at EE and EI using semi-automatic segmentation techniques
(volume growing, morphological operators). Based on the segmented data,
triangulated 3D surface models of the lungs are generated by the marching cubes
algorithm. Prominent inner lung vascular and bronchial bifurcations are
identified by a medical expert in the CT data sets for each patient in order to
be differentiated into landmarks located in the middle of the lungs, near lung
borders, and close to the tumor. Displacements are determined for each landmark
based on the landmark locations identified by the expert (actual displacement).
As a measure of accuracy, the registration residual is defined as the
difference between the actual displacement and the displacements predicted by the
patient-specific model with E=1kPa and n. They
evaluated modeling accuracy based on a total of 960 landmarks. Averaged over
all patients and landmarks, the registration residual magnitude is 3.32.1 mm where
mean landmark motion is 6.65.2 mm. For
landmarks close to tumors, modeling accuracy is slightly worse: 4.12.5 mm. They
have also analyzed motion non-linearity, accuracy in different regions of
lungs, and effects of size of the tumor on modeling accuracy. These will be further
discussed in detail in the final report.

One shortcoming associated with their approach in modeling the lung
is that they rely on a boundary condition (BC) defined by a secondary geometry
and do not model the physiology to compute the motion which renders this
approach not fully predictive. In addition, their accuracy decreases
significantly with increase in the size of the tumor and in the markers that
are close to it. This implies that explicitly modeling the tumor and assigning
different elastic properties to the cancerous tissue is of considerable

Fuerst et al.2 proposed a generative biomechanical model, which is driven
by patient-specific thoracic and diaphragmatic pressure force fields. In
contrast to the previously described work, the EI image is not used as a BC and
the lung motion is not constrained by any fixed BC. An anatomical model of the
respiratory system is computed from a thoracic 4D CT at EE phase through three
steps: segmentation, mesh generation, and mesh post-processing. Thoracic and
diaphragmatic pressures necessary to load the lung from EE to EI are estimated
automatically by minimizing a multivariate cost function using a trust region
optimizer in which pressures are iteratively improved with respect to the
differences between the simulated lung and the EI image. The applied pressures
were then transformed to the lung surface through a lung/thorax/diaphragm
interaction model. Using the anatomical model, a biomechanical model is
employed and solved using FEM in order to simulate the lung deformation during
respiration based on the estimated pressure values. A collision model of pleural
behavior is proposed to transfer the thoracic pressure force field to the
lungs. The collision model attempts to keep the distance d between thorax and
lung greater than the contact distance equal to 1 mm, as the typical pleural
thickness is reported to be 1-2 mm. Furthermore, a convergence analysis in
terms of spatial and temporal resolution is presented.

The model predictions and their framework are evaluated
by predicting exhale deformations in five 4D CT images. They utilized an
average of 414 landmarks. Landmark errors are defined as the Euclidean distances
between the landmarks’ simulated positions and the positions at the target phase.
Results show that the model is able to predict the respiratory motion with an
average landmark error of 3.401.0 mm over the entire respiratory cycle. However, this model also
considers the lung as a homogenous tissue which is not very realistic since the
tumorous tissue has different elastic properties than the healthy one.

Aiming at diminishing the need for real-time
imaging during EBRT, Karami et al.3 developed a lung biomechanical model designed
specifically for tumor tracking. An overview of this novel algorithm is as
follows: there are two main steps involved, preoperative and intraoperative. In
the former, they obtain chest motion data using optical markers and also
estimate the lung BCs, which are trans-pulmonary pressure and lung-diaphragm
contact surface displacement, using imaging. By utilizing a neural network
(NN), a generative model is built that correlated the chest surface markers to
the BCs. In the intraoperative step, the chest surface motion is measured and
fed into the NN in real-time. The output of the NN, which is the real-time BCs is
then used to predict the tumor motion and deformation using the lung’s FE

4D CT images of three lung cancer patients
were used to develop the lung FE models. The lungs, diaphragm, and the tumor are
segmented from the EE phase images using a fully automatic algorithm. The
ribcage and then the lower respiratory tract are segmented by thresholding. The
bronchial tree is removed from the lungs using region growing algorithm and the
lung surface is smoothened using morphological image closing. The segmented
lung is used for developing the FE model and the segmented diaphragm is used
for defining the boundary conditions at the lung’s bottom surface. The tumor
was segmented manually by an expert radiologist. After segmentation, the lung is
meshed using hexahedral elements in contrast to the other two aforementioned
studies as they have better performance than tetrahedral elements. One other
advantage of this approach over others is that they used a hyperelastic model
with variable Poisson’s ratio during breathing which is more realistic and
accurate, especially with the tumor-bearing lungs.

In this study, two sources of lung motion:
diaphragm and ribcage motions are modeled separately. Free Form Deformation
(FFD) registration method was used to obtain the displacements of the segmented
surface of the diaphragm at each phase of respiration. Diaphragm surface displacement
values were assigned as prescribed displacement boundary conditions in the lung
FE model. To account for the trans-pulmonary pressure created by the ribcage
motion, a non-uniformly distributed and time-variable negative pressure was
applied on the surface. Spatial distribution of the pressure is a linearly
increasing function in the anterior-posterior direction, while the magnitude of
pressure and its temporal variations were obtained through optimization. This new
approach in modeling the pressure distribution and calculation of the pressure
values through optimization has led to more accurate modeling results.

Validation of the model was conducted both
qualitatively and quantitatively. To perform quantitative validation, a total
of 40 landmarks were used where 20, 10 and 10 landmarks were selected in the
middle of the lungs, close to the lung surface and close to the tumor,
respectively. DICE similarity coefficient between the actual and simulated gross
tumor volumes (GTVs) is calculated. The tumor tracking results for exhalation
phase of respiration which was used for developing the model and the tumor
tracking results for inhalation phase of respiration which was used for
validating the model were reported. These results demonstrate that the DICE
similarity coefficient between the actual and simulated tumor volumes ranges
between 0.78 and 0.94 while the average DICE similarity coefficient for all
patients over all phases of respiration is 0.86±0.05. They have also reported
an average error per landmark’s 3D position and the average distance between
the actual and simulated lung surfaces. The mean absolute error in the
landmarks’ 3D position and the average Hausdorff surface-to-surface distance
are 1.74±0.77 mm and 1.60±0.17 mm, respectively. In this study, the technique
proposed by Fuerst et al. is improved by incorporating existing physiological
knowledge about pressure gradients and using more realistic material

Discussion/conclusion: Three biomechanical models of lung tumor
motion were briefly and concisely reviewed. The first article represents a
fundamental and straightforward approach for modeling the lung motion and
assessing the effect of different elastic parameters of the tissue. Although
lacking major aspects of an accurate model of the lung among which are the
hyper-elasticity, non-uniformity of pressure distribution, and tumor’s elastic
properties, it provided insight to the possibility of biomechanical modeling of
the lung using 4D CT image-derived geometries. The approach that was proposed
in Fuerst et al. significantly improved the approach to biomechanical modeling.
They developed a lung/thorax/diaphragm interaction model to transform the
pressure on the lung surface. The sliding between the lung and the surfaces of
thorax cavity and diaphragm was simulated as a frictionless. In the third
study, a novel technique is developed to obtain the BCs in real-time without
the need for intraoperative imaging. This can be counted as a major step toward
online tumor tracking during EBRT to achieve an accurate dose distribution and
consequently a higher rate of successful treatment.