A PRELIMINARY STUDY FOR A BIOMECHANICAL MODEL

OF THE RESPIRATORY SYSTEM

Jacques Saadé, Anne-Laure Didier, Romain Buttin, Jean-Michel Moreau

Michaël Beuve, Behzad Shariat

LIRIS CNRS UMR 5205, Université Claude Bernard Lyon 1, 43 Boulevard du 11 novembre 1918

69622 Villeurbanne, France

Pierre-Frédéric Villard

LORIA, Nancy University, 615 rue du Jardin Botanique, 54602 Villers les Nancy, France

Keywords: Biomechanics, Respiratory system, Finite element method, Motion.

Abstract: Tumour motion is an essential source of error for treatment planning in radiation therapy. This motion is

mostly due to patient respiration. To account for tumour motion, we propose a solution that is based on the

biomechanical modelling of the respiratory system. To compute deformations and displacements, we use

continuous mechanics laws solved with the finite element method. In this paper, we propose a preliminary

study of a complete model of the respiratory system including lungs, chest wall and a simple model of the

diaphragm. This feasibility study is achieved by using the data of a “virtual patient”. Results are in

accordance with the anatomic reality, showing the feasibility of a complete model of the respiratory system.

1 INTRODUCTION

Patients internal motions have large implications in

different domains such as imaging and treatment

(chirurgical operations or radiation therapy).

Thereby the respiratory motion reduces the

efficiency of radiotherapy benefits. Indeed, thoracic

and abdominal tumours can move and deform due to

respiration. It is then essential to know their position

and shape deformation to be able to optimize the

dose to tumour and healthy tissues. Lung tumours

are particularly concerned by this motion (Mori et

al, 2007; Seppenwoolde et al., 2002). Several

management strategies including breath holding

(Gagel et al, 2007; Wong et al, 1999), beam gating

(Ozhasoglu and Murphy, 2002) and tracking have

been discussed in the literature to account for

tumour displacement (Giraud et al, 2006). A

disadvantage of breath holding and beam gating is

that, part of the time, the beam is off. Another

disadvantage is that they do not take into account

some irregularities in the breathing cycle. Indeed,

both methods deduce tumour position from an

external breathing parameter (spirometry, abdominal

or thoracic height...). Ozhasoglu and Murphy (2002)

demonstrated that respiratory compensation

strategies that use an external breathing signal to

infer tumour position lack the ability to detect and

adapt to continuously changing characteristics of

respiratory motion during treatment. Other studies

(Shirato et al, 2006) show that the respiratory motion

has some non-reproducible aspects that need to be

taken into account during radiotherapy. This non-

reproducibility will be explained later in the

anatomy part. Tracking fiducial markers implanted

inside the tumour or tracking the tumour using the

CyberKnife® robotic radiosurgery system are

techniques that take into account the non-

reproducibility of the breathing cycle. While the

implantation of fiducial markers is an intrusive

method that may lead to medical complications such

as pneumothorax (Jiang, 2006), the CyberKnife®

system has also some inconveniences such like the

long treatment time requirement and the irradiation

of the patient by the tracking device.

Alternatively we propose a model based solution

that takes into account the non-reproducible aspects

of breathing motion: a biomechanical modelling of

the respiratory system monitored by at least two

external parameters (Thoracic motion and

509

Saadé J., Didier A., Buttin R., Moreau J., Beuve M., Shariat B. and Villard P. (2010).

A PRELIMINARY STUDY FOR A BIOMECHANICAL MODEL OF THE RESPIRATORY SYSTEM.

In Proceedings of the International Conference on Computer Vision Theory and Applications, pages 509-515

DOI: 10.5220/0002892405090515

 SciTePress

spirometry). Ribs and diaphragm displacements can

be computed out of thorax outer-surface motion and

spirometry measurements. Lungs deformations, and

then tumour displacements, can be deduced

considering the organ interactions. All deformations

and displacements are calculated using continuous

mechanics laws, solved with the finite element

method.

Another requirement, particularly important in

the context of hadrontherapy, is the ability to predict

not only tumour motion but also motions,

deformations and density changes of any tissue

traversed by the beam.

Our group has been active in the biomechanical

modelling of the respiratory system (Villard et al,

2005, Didier et al, 2007, 2009) and the

transformation of biomechanical data into 4D-CT

data (Villard et al, 2006). Previously, we have

validated a chest wall model based on rib kinematics

that enables the computation of rib displacements

out of thorax outer-surface motion (Didier et al,

2009). In this paper, we develop a feasibility study

of a diaphragm model. First, we summarize previous

studies concerning the biomechanical modelling of

the respiratory system. Then we expose a complete

model of the respiratory system, using a "virtual

patient" data, and the preliminary results on the

diaphragm and lung motions.

2 ANATOMY OF THE

RESPIRATORY SYSTEM

Lungs are passive structures that inflate under

muscles action. The increase of thoracic volume, due

to inspiratory muscles action, induces lung

expansion, leading to internal negative pressure and

consequently to inspiration. Contact of the lungs

with the ribcage and the diaphragm is maintained by

the pleura. The pleura is composed of two

membranes (figure 1): the first, referred to as

parietal, covers the chest wall, the mediastinum and

the diaphragm while the second, referred to as

visceral, covers the outer surface of the lungs.

The space in between the parietal and visceral

pleura, known as the pleural space, is filled with an

incompressible fluid which lubricates the pleural

space and allows the lungs to easily slide against the

chest wall and the diaphragm during their expansion.

Lungs mainly expand under the action of the

external intercostal muscles (EIM) and the

diaphragm. The role of the EIM is relatively

important in both quiet and forced respiration. They

are inserted between the ribs from the second to the

twelfth rib and they are responsible for the rib

elevation during inspiration.

Figure 1: Anatomy of the respiratory system.

The diaphragm is a digastric muscle which

separates the thoracic and abdominal cavity. It is

composed of two domes (figure 2): the right dome

comes up to the fourth intercostal space whereas the

left dome remains below the fifth rib. The

diaphragm is constituted of a peripheral part

(muscular fibre) and a central tendon (figure 2). The

peripheral part is linked to the lower thoracic cavity

perimeter and has three major insertions: lumbar,

sternum and ribs. During inspiration, the muscular

contraction fibres bring down the central tendon.

This lowering increases the vertical diameter of the

thorax. As for the lungs, EIM action induces posto-

anterior and transversal inflation while the

diaphragm action causes vertical motion. The EIM

and the diaphragm may act independently, making

respiration a non-reproducible and an unpredictable

movement. Thereby, in general, lung motion cannot

be simply predicted by a correlation with one single

parameter.

Figure 2: A mesh representation of the diaphragm (upper

view). The central tendon is represented in yellow whereas

the peripheral part is in blue.

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510

3 BIOMECHANICAL

MODELLING OF THE

RESPIRATORY SYSTEM

In the past, several studies were achieved to model

the lung environment. A description of these studies

can be found in (Baudet et al. 2003), Villard et al.

(2005) and (Al-Mayah et al. 2007). Thus, we focus

on the more recent studies. (Villard et al. 2005) used

a patient's CT scan images to build the geometry of a

finite element lung model. They also studied lung

motion sensitivity to Poisson’s ratio, elastic modulus

(Young modulus) and contact conditions at the

pleura. It appeared that Poisson's ratio has an effect

on the amplitude and the orientation of the

displacements while Young modulus should be

carefully chosen because a change in its value may

either induce a faulty implementation of contact

conditions or increase the computing time needs.

(Brock et al. 2005) developed a platform to perform

multi-organ deformable image registration using

finite element modelling. The model was developed

using images from magnetic resonance (MR)

scanning. The lungs were included in this model and

good agreement was found between the finite

element simulation using orthogonal displacement

(OD) and the MR data. (Didier et al. 2007) showed

the significant role of the pleura and the necessity to

include its effect in the model. The role of the pleura

is simulated by applying contact conditions that

allow sliding on the lungs surface (contact without

friction). The results of this model were compared to

those of the OD model and showed an improvement

in predicting the position of the lungs while the

computing time requirement was higher. (Al-Mayah

et al. 2007) included the role of the pleura and two

other nonlinearities to the model (hyperelastic

nonlinear materials and nonlinear geometry due to

large displacements). They also added the chest wall

and the tumour to the model and achieved a good

precision on lung and tumour position. An

inconvenience of adding the nonlinearities was the

increase in the computation time needed to complete

the simulation. All the models mentioned above,

focused on deformable registration of soft tissues in

the thorax and did not invest in the bone tissues of

the rib cage. Going from the fact that the bones of

the rib cage can relatively be considered as rigid

bodies, (Didier et al. 2007) introduced a rigid

transformation that simulates the kinematic

behaviour of the rib cage intead of simulating the

action of each intercostal muscle. The

transformation is based on the Finite Helical Axis

(FHA) method. (Didier et al 2009) developped this

method in order to build a model of the chest wall.

This model proposed a correlation between ribs

motion and thorax-outer surface motion and

achieved a good precision on lungs position in the

upper thorax. This model is essential to enable

monitoring of lung motion out of thorax motion.

Thus, to be able to build a complete model of the

respiratory system and to include a second parameter

to the monitoring process of the lungs, we introduce

in this paper a biomechanical study of the diaphragm

and some preliminary results concerning a finite

element simulation of its motion.

4 DIAPHRAGM

BIOMECHANICAL MODEL

In order to build a complete model of the respiratory

system, the diaphragm is modeled and added to the

thorax and the lung models. As mentioned in the

anatomy part, the diaphragm is composed of a

peripheral part (muscular fibre) and a central tendon.

During inspiration, muscular fibres contract under

the action of a force F and the ribs undergo a

displacement Dc. Both actions cause the lowering of

the central tendon (figure 3).

Figure 3: An illustration of the diaphragm motion.

Figure 4: Anatomic elements of the model.

Since most thoracic medical imaging data cover

only the lungs and big parts of the diaphragm are not

included in the imaging protocol, we chose to carry

out our study on a “virtual model” data. We chose

A PRELIMINARY STUDY FOR A BIOMECHANICAL MODEL OF THE RESPIRATORY SYSTEM

511

the data of a virtual patient that include surface

meshes of the skin, the ribcage, the lungs and the

diaphragm. Figure 4 shows the different mesh data.

We apply on this geometrical model the

mechanical laws and boundary conditions and

material properties as follow.

4.1 Mechanical Behaviour Laws

We use continuous mechanics laws to compute the

deformations with a non-linear behaviour law that

allows large displacements. We considered elastic

materials. Calculations were made in the static mode

which means that only the initial and final states of

deformations are computed after the application of

boundary conditions.

4.2 Boundary Conditions

The boundary conditions of our model are illustrated

in figure 5. They are the same as described in Didier

et al (2009), but we add the boundary conditions at

the diaphragm. Lungs are fixed near the trachea and

the pleura behaviour is simulated by applying

contact conditions allowing lungs surface to slide

against the chest wall (parietal pleura). These

contact conditions permit us to model the negative

intra-pleural pressure, and the sliding surface

represents the pleural fluid. According to reality,

parietal pleura is directly linked to the ribs or fat

tissue. A particular rigid transformation (Dc)

computed with the finite helical axis method is

applied to each rib. Ribs are directly linked to the fat

tissues which are also directly linked to the skin. The

diaphragm boundary conditions are as follow:

4.2.1 Diaphragm / Ribcage

As mentioned in the anatomy part, the diaphragm is

attached to the ribcage. In our simulation, we made

sure, in the attached region, that the corresponding

nodes were linked together.

4.2.2 Diaphragm / Fat tissues, Diaphragm /

Parietal Pleura

The diaphragm is directly linked to the fat tissues

and to the parietal pleura. This is an approximation

because normally the fat tissues can slide against the

diaphragm. The soft tissues that lie under the

diaphragm represent a resistance to the force that

tends to lower the diaphragm. They are simply

modelled like the fat tissues and they are affected the

same biomechanical parameters.

4.2.3 Contraction of the Muscular Fibres

To mimic the contraction, we apply the force F

illustrated on figure 5. This force should be parallel

to muscle orientation. In a first approximation, we

apply vertical (cranio-caudal) forces that are

oriented downwards. These forces are applied on

each node of the muscular part of the diaphragm.

This choice was motivated by the goal of this work,

which aims at demonstrating that it is possible to

propose a complete model of the respiratory system

as soon as a diaphragm model is available.

Figure 5: Boundary conditions.

4.3 Material Properties

Table 1 illustrates the biomechanical parameters

(Young modulus and Poisson’s ratio) of the lungs,

ribs, fat tissues, skin and diaphragm. The diaphragm

has two different parts (muscle and tendon) and each

part has different mechanical properties. All

parameters are taken from the bibliography

(Handriks, 2001; Promayon and Baconnier, 2008).

Table 1: The biomechanical properties of the different

organs.

Lungs Ribs & vertebrae

Young Modulus (MPa) 700*10

-6

5000

Poisson’s ratio 0.3 0.3

Fat tissues Skin

Young Modulus (MPa) 3 3

Poisson’s ratio 0.4 0.4

Diaphragm

Muscle)

Diaphragm

(Tendon)

Young Modulus (MPa) 5.32 10

Poisson’s ratio 0.3 0.3

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5 RESULTS

The “virtual patient” data are available for only one

respiratory state (we consider it arbitrarily as the

exhalation state). Because we need at least two

respiratory states to be able to compute rib

kinematics parameters (Didier et al, 2009), we apply

the rib parameters computed for a real patient in a

previous study (Didier et al, 2009). We apply the

force F as explained in 4.2.3, then we compare the

diaphragm at the initial state with the diaphragm at

the computed state to deduce its deformation and the

displacement fields. All calculations are made using

Code-Aster finite element software

(http://www.code-aster.org). The results

(deformations and displacement fields) are

visualised using GMSH software

(http://www.geuz.org/gmsh) and MESH (Aspert et

al, 2002).

Figure 6 shows the diaphragm deformations

between the initial state (wireframe mesh) and the

computed final state (colored mesh). We can

observe that the central tendon goes down due to the

action of the force applied to the muscular part. We

observe also a lateral augmentation of the diaphragm

diameter due to the rib motion.

Figure 6: Frontal view of the diaphragm motion between

exhalation (wireframe mesh) and computed inhalation

state (coloured mesh). The deformations are illustrated in

colours on the computed mesh with red representing the

highest deformation value and blue its lowest value. The

colour scale is proportional to the motion amplitude.

Figure 7 represents the displacement vectors at

different locations on the diaphragm. The two red

vectors represent the mean orientation of the

displacement vectors at the level of the central

tendon (upper view) and at the level of the lower

muscular part (lower view). On the muscular part,

the displacement is lateral, oriented downwards

while the displacement on the level of the central

tendon tends to be more vertical. Globally, these

results are in accordance with the anatomy. Indeed,

the central tendon is relatively rigid, and therefore

less influenced by the ribs motion. However, after

the contraction of the muscular part, the central

tendon goes down while preserving the form of its

domes. This result is in accordance with the

bibliography and the observations made by Boriek

and Rodarte (1997).

Figure 7: Motion of the diaphragm.

We also present the results of our model

concerning lungs motion. Figure 8 represents the

displacement vectors at different locations on the

lungs. The two red vectors represent the mean

orientation of the displacement vectors at a high

level of the lungs (upper view) and at a low level of

the lung near the diaphragm (lower view). On the

upper level, the displacement is lateral, oriented

upwards while the displacement on the lower level

tends to be more vertical and is oriented downwards.

These results are in accordance with the anatomy.

Indeed, the higher parts of the lungs are influenced

by the ribs motion (lateral motion with elevation)

and the lower parts are more influenced by the

motion of the diaphragm central part (downwards).

A PRELIMINARY STUDY FOR A BIOMECHANICAL MODEL OF THE RESPIRATORY SYSTEM

513

Figure 8: Lungs motion.

6 CONCLUSIONS

We have developed a complete model of the

respiratory system built from “virtual patient” data.

A simple model of the diaphragm, which was

missing in our previous studies, has been introduced.

We showed preliminary results, which are in

accordance with the anatomical reality. The central

part of the diaphragm tends to move downwards,

while the muscular part motion tends to be lateral

oriented downwards due to rib motions. In future

works, the model should be applied on a real

patient’s data to enable quantitative comparisons of

the results. The applied nodal forces should be

replaced by more appropriated formulations. In

particular, the forces could be parallel to muscular

fibres in agreement with anatomy and derived from

biomechanical considerations. Last, the forces

should be correlated to thoracic motion and air flow

to the lungs.

ACKNOWLEDGMENTS

We thank the French League against Cancer and

PRRH ETOILE for their financial support.

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