patient-speciﬁc models of human trachea to predict...

Phil. Trans. R. Soc. A (2010) 368, 2881–2896doi:10.1098/rsta.2010.0092

Patient-specific models of human trachea topredict mechanical consequences of

endoprosthesis implantationBY A. PÉREZ DEL PALOMAR1,2,3,∗, O. TRABELSI1,2,3, A. MENA1,2,3,

J. L. LÓPEZ-VILLALOBOS4, A. GINEL4 AND M. DOBLARÉ1,2,3

1Group of Structural Mechanics and Materials Modeling, Aragón Instituteof Engineering Research (I3A), Universidad de Zaragoza (Spain),

C/Maria de Luna 3, 50018 Zaragoza, Spain2Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales yNanomedicina (CIBER-BBN), C/Maria de Luna 11, 50018 Zaragoza, Spain

3Aragón Institute of Health Sciences, and4Department of Thoracic Surgery, Hospital Virgen del Rocío,

Seville, Spain

Nowadays, interventions associated with the implantation of tracheal prostheses inpatients with airway pathologies are very common. This surgery may promote problemssuch as migration of the prosthesis, development of granulation tissue at the edges ofthe stent with overgrowth of the tracheal lumen or accumulation of secretions inside theprosthesis. Among the movements that the trachea carries out, swallowing seems to haveharmful consequences for the tracheal tissues surrounding the prosthesis. In this work,a finite-element-based tool is presented to construct patient-specific tracheal models,introducing the endotracheal prosthesis and analysing the mechanical consequences ofthis surgery during swallowing. A complete description of a patient-specific trachealmodel is given, and a fully experimental characterization of the tracheal tissues ispresented. To construct patient-specific grids, a mesh adaptation algorithm has beendeveloped and the implantation of a tracheal prosthesis is simulated. The ascendingdeglutition movement of the trachea is recorded using real data from each specificpatient from fluoroscopic images before and after implantation. The overall behaviourof the trachea is modified when a prosthesis is introduced. The presented tool has beenparticularized for two different patients (patient A and patient B), allowing predictionof the consequences of this kind of surgery. In particular, patient A had a decreaseof almost 30 per cent in his ability to swallow, and an increase in stresses that werethree times higher after prosthesis implantation. In contrast, patient B, who had ashorter trachea and who seemed to undergo more damaging effects, did not havea significant reduction in his ability to swallow and did not present an increase instress in the tissues. In both cases, there are clinical studies that validate our results:namely, patient A underwent a further intervention whereas the outcome of patient B’s

∗Author for correspondence ([email protected]).

One contribution of 13 to a Theme Issue ‘The virtual physiological human: computer simulationfor integrative biomedicine II’.

This journal is © 2010 The Royal Society2881

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2882 A. Pérez del Palomar et al.

surgery was completely successful. Notwithstanding the fact that there are alot of uncertainties relating to the implantation of endotracheal prostheses, thepresent work gives a new insight into these procedures, predicting their mechanicalconsequences. This tool could be used in the future as pre-operative planning softwareto help thoracic surgeons in deciding the optimal prosthesis as well as its sizeand positioning.

Keywords: trachea; finite-element method; tracheal endoprostheses; Dumon prosthesis;granuloma; deglutition

1. Introduction

The trachea is a cartilaginous and membranous tube, extending from the lowerpart of the larynx, at the level of the sixth cervical vertebra, to the upperborder of the fifth thoracic vertebra, where it divides into two bronchi, onefor each lung. The trachea is nearly, but not quite, cylindrical, being flattenedposteriorly; it measures approximately 11 cm in length; its diameter, from sideto side, ranges from 2 to 2.5 cm, being greater in males than in females. Thetrachea is a fibroelastic tube with 15–20 C-shaped slightly separated cartilaginousrings along its length. Cartilages are aligned with each other, and posteriorly,where the trachea is apposed to the oesophagus, they are deficient. This spaceis filled by the tracheal muscle. The hyaline cartilage helps to maintain thepatency of the central lumen during inspiration (Holzhauser & Lambert 2001;Lyubimov 2001).

The trachea can be exposed to different pathologies that usually lead to acommon effect: the obstruction of air flow, either owing to loss of its wall’s rigidity(malacia) or owing to the decrease in its free section (stenosis). Tracheal stenosis,which is the most common tracheal injury (Grillo et al. 1995), is usually causedby a tracheotomy intubation with unsuitable pressure. Prolonged ischaemia andinfection cause necrosis of the tracheal wall and deterioration of the cartilaginousstructure through the formation of granulation tissue. This granulation may leadto the collapse of the tracheal wall (Huang 2001).

Many methods are available to deal with tracheal stenosis, such as trachealdilation, excision of the stricture and anastomosis (end-to-end joining afterresection of a tracheal part) or reconstruction, but, after treatment, the stenosismay reappear, especially when the stenosis is more than 2 cm long (Rob &Bateman 1949; Belsey 1951; Huang 2001; Grillo 2002).

In 1964, William W. Montgomery used for the first time a two-piece rigidacrylic stent during a surgical reconstruction of the cervical trachea to preventpost-operative tracheal stenosis; 1965, he improved it to a one-piece flexiblesilicone stent, called a T-tube stent, which is still being used today, albeit withsome substantial modifications (Wahidi & Ernst 2003). The theory behind itsuse is to create a support on which the lesion scar can be modelled. Then, whenthe scaring process is stabilized, the prosthesis can be taken away. Since then,these stents have been the object of an unceasing evolution, from the simpletube design to more complex geometries (Noppen et al. 1999; Xavier et al.2008), and from the static silicone stent to dynamic or expandable metallic stents

Phil. Trans. R. Soc. A (2010)



Patient-specific models of human trachea 2883

(Freitag et al. 1994; Madden et al. 2002; Noppen et al. 2005). However, in 1987,Dumon designed a flexible, studded, silicone prosthesis stent, with no metallicreinforcement to enhance flexibility and facilitate placement and removal. Thestuds are designed to prevent migration and limit contact with the mucosa(Dumon et al. 1996). The Dumon stent (Novatech; Aubagne, France; Noppenet al. 1999) is probably the most popular stent used nowadays in managingtracheal obstructive lesions, and is considered to be the most effective airway stentpresently available worldwide based on both cost and safety factors (Mitsuokaet al. 2007).

Because of the clinical interest in the reasons for implantation of tracheal stents,few studies based on numerical models have been carried out on prosthesis/airwayinteraction; generally, research has focused on the experimental and clinicalresults of tracheal stent insertion (Dumon 1990; Grillo et al. 1995; Huang2001). Most numerical studies have focused on the development of analyticalmodels simulating an isolated tracheal ring formed by a cartilaginous ring anda muscular membrane (Holzhauser & Lambert 2001). In this line of research,a finite-element model of a lamb’s windpipe was constructed to predict thebehaviour of the trachea before airway ventilation treatments (Costantino et al.2004). Gustin et al. (1996) analysed the influence of the endotracheal prosthesiscollocation through an axisymmetric model, which also used the finite-elementmethod. Wiggs et al. (1997) presented a finite-element model free from thecartilaginous structure to analyse the mechanism of mucosal folding that occursafter smooth muscle shortening and which explains the difference in airwaynarrowing between asthmatic and control airways, based on the mechanics ofthe tracheal wall structure.

In contrast, the mechanical characteristics of the human trachea have notbeen completely determined; few studies have been carried out to understandthe behaviour of its components (Rob & Bateman 1949; Belsey 1951; Grillo2002; Trabelsi et al. 2010). In some of these studies, cartilage is considered to bea nonlinear material displaying higher strength in compression than in extension(Grillo 2002), but, in most of them, the isolated tracheal cartilage was consideredto be a linear elastic material (Wahidi & Ernst 2003; Xavier et al. 2008). In thework carried out by Rains and colleagues (Rains 1989; Rains et al. 1992; Robertset al. 1998), the stress–strain relations obtained for slices of human trachealcartilage were considered linear for deformations up to 10 per cent of the initiallength of the samples. In fact, there was negligible hysteresis and no residualstrain in the specimens tested to a maximal applied strain of 10 per cent; beyondthis limit, strain hysteresis and residual strain increased progressively (Rob &Bateman 1949). With respect to the mechanical properties of the tracheal muscle,most studies dealt with its plasticity, stiffness and extensibility (Yamada 1970;Maksym et al. 2005). Gunst & Ming-Fan (2001) investigated the effects of itslength on the stiffness and extensibility at contractile time activation. Stephenset al. (1977) analysed the influence of temperature on force–velocity relationships.However, none of them except Trabelsi et al. (2010) analysed the mechanicalproperties of this membrane, which makes the collapse of the rings possible andtherefore affects the pressure balance inside the trachea.

In this study, a patient-specific tool based on the finite-element method toanalyse the behaviour of different tracheas before and after implantation of aprosthesis is described. Moreover, a real constitutive model for the tissues is





presented based on an experimental study of the mechanical behaviour of theprincipal tracheal constituents: cartilage and smooth muscle.

2. How to construct a patient-specific tracheal model

In this section, a complete description of the generation of a patient-specific tracheal finite-element model is presented. First, the experimentalcharacterization of the tracheal tissues and their mathematical modelling issummarized from a previously published paper (Trabelsi et al. 2010). Then, theconstruction of patient-specific tracheal meshes will be explained. Finally, theestimation of the movement of the human trachea during swallowing will bepresented. To collect all data, patients were fully informed about the objectives ofthe project, including information about the clinical and experimental protocols.The patient’s anonymity was guaranteed throughout the process.

(a) Experimental characterization and constitutive modelling of tracheal tissues

First, a histological study was performed in order to relate the microstructureof the different tracheal tissues to their mechanical behaviour. Then, theexperimental tests were carried out for cartilage and smooth muscle samples,and, finally, the experimental curves were fitted to a suitable constitutive model,which could represent their particular behaviour (for an extended description, seeTrabelsi et al. 2010).

The specimens were mounted on a Instron MicroTester 5548 to perform tensiletests. For cartilage, since there is no preferential fibre orientation, a neo-Hookeanmodel with strain density energy function (SEDF), J = C1(I 1 − 3), was usedto fit the experimental results. Regarding the smooth muscle, and taking intoaccount that the histology showed two orthogonal fibre families, Holzapfel SEDF(Holzapfel 2000) for two families of fibres was used,

J = C1(I 1 − 3) + K1

2K2

{exp[K2(I 41 − 1)2] − 1

}

+ K3

2K4

{exp[K4(I 42 − 1)2] − 1

} + 1D

(J − 1)2,

where C1 is the material constant related to the ground substance, Ki > 0 are theparameters that identify the exponential behaviour owing to the un-crimping ofthe two families of fibres and D is the tissue incompressibility volumetric modulus.The invariants Iij are defined as

I 1 = trC , I 2 = 12 [(trC )2 − tr(C 2)], I 41 = a0 · Ca0 and I 42 = b0 · Cb0,

(2.1)where a0 is a unitary vector defining the preferential orientation of the firstfamily of fibres and b0 the direction of the second family, both of which are inthe reference configuration. Finally, C is the modified right Green strain tensordefined as C = J −1/3C , where C = FTF , F is the deformation gradient andJ = det(F).





1.00 1.02 1.04 1.06 1.08

l1.10 1.12 1.14 1.16 1.00 1.02 1.04 1.06 1.08

l1.10 1.12 1.14 1.181.16

6

5

(a) (b)

4

3

2s (×

10–3

MPa

)

1

0 0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Figure 1. Uniaxial tests performed with tracheal muscle samples. (a) Fitting of Holzapfel’s modelto the experimental results obtained in a tensile test in the longitudinal direction of the trachea.(b) Fitting of Holzapfel’s model to the experimental results obtained in a tensile test in thetransversal direction of the trachea. Grey shaded area, experimental data; grey line, Holzapfel’smodel.

Table 1. Parameters of the constitutive models that characterize the mechanical behaviour ofcartilage and muscular membrane.

material parameters C1 (kPa) K1 (kPa) K2 K3 (kPa) K4

cartilage 577.7 — — — —muscular membrane 0.87 0.154 34.15 0.34 13.9

The longitudinal and transverse tensile behaviour of the tracheal musclewas analysed and the parameters of the SEDF were calculated by fitting theconstitutive equation of Holzapfel to the experimental results obtained in ourlaboratory (figure 1); see also table 1 for a summary of the material constantsused for the different tissues.

(b) Construction of patient-specific tracheal meshes

The purpose of this research is to construct a useful tool for surgeons to predictthe consequences of implantation of a tracheal prosthesis in a specific patient.Therefore, it is necessary to create patient-specific meshes taking into accountthe huge geometrical variability among them. To develop these patient-specificmodels, an automatic adaptation of the mesh has been implemented.

First, a set of DICOM images from a CT scan performed on a 70-year-oldhealthy man were obtained. These images were used to configure our ‘referencepatient’ model. The DICOM files from the scan provide a clear picture of theinternal (black) cavity filled with air; however, the outer surface and thereforethe thickness of the wall are difficult to detect. Because of this, a non-automaticsegmentation of the CT scan was carried out to determine the real geometry of thetrachea and to distinguish between the muscle membrane and the cartilage rings.The segmentation of the DICOM data was made using MIMICS. An IGES file of





cartilage rings

P

A

cricoid cartilage

thyroid cartilagelamina

muscle membrane

finite-elementmodel of a humantrachea

Figure 2. Finite-element mesh of the trachea of our ‘reference patient’. The cartilaginous parts ofthe trachea are plotted separately from the muscular membrane. (A denotes the anterior part andP the posterior part.)

the segmented geometry was created to construct the associated computationalgrid. Then, a full hexahedral mesh of 29 250 elements was made using PATRAN(figure 2), in which the different tissues (cartilage and muscular membrane) canbe distinguished. Both the internal and external surfaces of this ‘reference patient’are then used to construct the new patient-specific meshes.

Once this ‘reference mesh’ has been constructed, it can be adapted tothe actual geometry of the patient’s trachea to produce the patient-specificmesh. This adaptation process is based on the geometry of the internal andexternal tracheal surfaces of each patient. Thus, the geometry of these newsurfaces can be detected using the DICOM files, as for the ‘reference’ ones.First, the geometry of the reference is scaled in length to the new geometry.Then, to adapt the mesh, only the external and internal surfaces are deformedslice by slice (0.6 mm distant), that is, each slice of the three-dimensionalimage of the ‘reference’ geometry is adapted to the patient-specific geometry(figure 3).

Finally, the previously applied transformations to the three-dimensional imageslices are applied to the nodes of the reference mesh to achieve a new patient-specific mesh. As the definition of elements and nodes does not vary in thisprocess, the same groups for the different tissues are conserved during adaptation,and, therefore, the resulting patient-specific mesh also includes the cartilage rings(the same number as in the reference patient) and the muscular membrane.Figure 4 shows two different patient-specific meshes from two datasets, calledpatients A (male, age 28) and B (male, age 62) in the following sections. Thesemeshes were subsequently checked and sufficient accuracy was found.





referencegeometry

patient-specificgeometry

adaptation of thetotal length

adaptation of eachslice

Figure 3. Adaptive algorithm to construct the patient-specific mesh using a reference mesh.

referencemesh

(a) (b)

zxy

patient A patient B

zxy

zxy

Figure 4. (a) The reference mesh used for adaptation. (b) Two examples of adaptation for twodifferent patients.

(c) Implantation of the tracheal prostheses

The purpose of this work is to analyse the influence of a tracheal endoprosthesison the overall behaviour of the trachea. Therefore, the prosthesis has to beaccurately located inside the tracheal wall. The thoracic surgeons decide whichkind of prosthesis is suitable for each patient. The most common one is the Dumonprosthesis that basically consists of a cylinder that can be of several diametersand lengths. Therefore, this information is available for every patient and, inparticular, in this article for patients A and B. The prosthesis diameter has to belarge enough to fit inside the trachea, remaining fixed to the wall and avoidingmigration; thus, the surgeon chooses a prosthesis with a diameter a little greaterthan the tracheal diameter (for patient A, a Novatech Dumon prosthesis 16 × 50;for patient B, a Novatech prosthesis 14 × 30).





model of thereferencehuman trachea

trachealprosthesis

initial diameter ofthe externalsurface of theprosthesis

imposed radial displacement to obtain the realdiameter of the prosthesis

final (real) diameter ofthe external surface ofthe prosthesis

Figure 5. Implantation of a tracheal prosthesis. First, a smaller diameter stent is placed inside thetrachea and then this prosthesis is deformed to reach its real diameter.

To be able to numerically simulate this process, the commercial softwareABAQUS v6.9 (Hibbit, Karlsson and Sorensen Inc. 2009) was used. First, asmaller prosthesis than the one needed is located inside the trachea in the specifiedposition, then the prosthesis is radially deformed to its real diameter (for patientA, 16 mm; for patient B, 14 mm) (figure 5) contacting the inner tracheal wall. Thecontact definition was defined element by element and a friction coefficient of 0.1was defined in order to avoid migration and to represent the studs that firmlyjoined the prosthesis to the wall. With this new configuration, the real stressdistribution in the tracheal walls due to the prosthesis insertion can be obtained.

(d) Tracheal movement

It has been seen clinically that the most dangerous tracheal movement whena prosthesis is implanted is swallowing. During swallowing, three steps can bedistinguished: lip–mouth time, laryngeal time and oesophagus time (Robert2004). It is during the second step that the pharyngolarynx and the trachea moveupwards by the contraction of the larynx elevating muscles. This movement canbe simulated by introducing the force exerted by these elevating muscles, but,although their directions can be estimated, the value of the developed active forceis very diffcult to measure. Therefore, in this study, these forces were estimatedby measuring the displacement that different tracheas undergo during swallowingin different patients.





patient A

before surgery after surgery

patient A

patient B patient B

–20

Z

Y

–15 –10

Y (mm)

Y (mm) Y (mm)

Y (mm)

Z (

mm

)

Z (

mm

)

Z (

mm

)

Z (

mm

)

–5 0

–10 –5 5 100 –10–15 –5 50

–20 –15 –10 –5 –5 500

51015202530

5101520253035

05

–5

101520253035

05

–5

1015202530

Figure 6. Measurement of the swallowing movement. Marking of the thyroid cartilage to detect themovement in patients A and B before and after implantation of a Dumont prosthesis.

35(a) (b)

30

25

20

15

disp

lace

men

t (m

m)

time (s) time (s)

10

5

1 24

12

3

4

53 5

0

25

20

15

10

5

01 1

Figure 7. The magnitude of the displacement of the thyroid cartilage is plotted for patient A(a) before and (b) after implantation of the prosthesis. It can be seen that patient’s ability toswallow decreases when the prosthesis is implanted (the maximum displacement decreases byapproximately 28% after implantation).

The displacements were obtained by capturing the tracheal movement with asequence of fluoroscopic images. Here, the displacements of two different patients(patient A and patient B) will be reported both before and after implantation ofthe prosthesis (figure 6). Both patients underwent a long-term intubation (morethan 15 days) that caused poor healing and left a fibrous stenosis. The totaldisplacement that the trachea underwent during swallowing could be measuredby marking the superior end of the thyroid cartilage in each image, which is a validreference to track the movement along the antero-posterior and proximal–distaldirections because this cartilage hardly undergoes deformation.

To see how the deglutition movement is performed, we show the magnitudeof displacement for patient A before and after implantation of the prosthesis(figure 7). It can be seen that, when a patient swallows, two different peaks





(points 3 and 5) of movement appear. In every monitored patient, this behaviourwas seen. It can be related to the ‘barium meal’, which is difficult to swallow inonly one deglutition cycle. The same trend could be seen for patient B, in whom,again, the ability to swallow was compromised when the endotracheal prosthesiswas implanted. These movements were introduced as input calculations, tosimulate using ABAQUS the deglutition movement of the trachea before andafter prosthesis implantation.

3. Mechanical consequences of implanting a tracheal prosthesis

In this section, the stresses undergone in the trachea before and after implantationof a prosthesis are shown. First of all, the results for patient A are depicted.The deglutition movement was analysed before and after implantation. Infigure 8, the displacements and the distribution of stresses are presented forthe sequence of deglutition before implantation. It can be seen how themaximum stresses are distributed across the cartilage rings with a maximumvalue of 1.4 MPa for the maximum tracheal elongation. Moreover, it can beseen in the section of the trachea that there is not any stress concentrationduring the movement. The displacement of the trachea before implantationwas 35 mm.

The influence of introducing an endotracheal prosthesis can be seen in figure 9.First, the prosthesis is located and then it is deformed as described in figure 5,then the deglutition movement is applied. In this case, the displacement (notshown in the figure) was 25 mm. The consequences of implanting a prosthesiscan be easily seen in figure 9. The implantation provokes stresses in the internalsurface of the trachea in the initial configuration (as can be seen at instant 0). Infigure 9, the swallowing movement once the prosthesis is properly located is shownin order to compare the tracheal behaviour without and with the prosthesis. Themaximum stresses during the movement are shown, and it can be seen how themaximum stresses (3.4 MPa) when the prosthesis was introduced nearly tripled.In addition, different local stress concentrations appeared in the internal surfaceof the trachea owing to the prosthesis contact.

Regarding patient B, the same analysis was performed. Once the meshis adapted, the movement of the trachea can be analysed before and afterimplantation by introducing the captured displacements (figure 6). In figure 10,a summary of the obtained results before and after implantation is presented.In this case, as can be directly inferred from the fluoroscopic images, theability of patient B to swallow is less compromised than in patient A, but thesame trend is observed. Again, initial stresses owing to the adjustment of theprosthesis are produced in the trachea (figure 10c), but the overall behaviour ofthe trachea after implantation does not differ too much from that of the tracheabefore surgery.

4. Discussion

Based on clinical experience, thoracic surgeons classify swallowing as themovement that causes most harm to the trachea when a prosthesis is implanted.During swallowing, the trachea ascends accompanying the larynx, causing a





U, U3(a)

(b)

U, U3 U, U3 U, U3

S. max. principal(avg: 75%)






zx

zx

zx

zx

zx

zx

U, U3 U, U3

0 1 2 3 4 5

step:

zx

zx

zx

zx

zx

zx

zx0 1 2 3 4 5

0 1 2 3 4 5

Figure 8. (a) Displacement and (b) maximum stresses undergone by patient A’s trachea duringswallowing before implantation. Different stages of the movement (marked from 0 to 5) are plotted(see figure 7 for numbering).

non-homogeneous elongation of its segments. When a prosthesis is implanted,this movement is compromised because the stent stiffens these segments. Thisexplains the inefficiency of the glottis closing that is sometimes observed after theplacement of tracheotomy stents. At present, surgeons use their clinical experienceto choose a suitable stent for each patient, but unfortunately most of the patientshave to be reoperated more than twice.

In this work, the first step to constructing a pre-operative planning toolsuitable for thoracic surgeons is presented. This first approach consists of usingcomplex material models based on the experimental characterization of humantracheal tissues, obtaining patient-specific meshes by using an adaptive algorithm,introducing real movement of the patient-specific tracheas and analysing the





+3.6e-01+3.0e-01+2.4e-01+1.8e-01+1.2e-01+5.8e-02–2.1e-03

zx

zx

zx

zx

zx

zx

+3.6e-01+3.0e-01+2.4e-01+1.8e-01+1.2e-01+5.8e-02–2.1e-03

+2.6e-01+2.2e-01+1.8e-01+1.3e-01+8.7e-01+4.3e-02–1.6e-03

+1.4e+00+1.1e+00+9.1e-01+6.8e-01+4.5e-01+2.2e-01–9.2e-03

+6.1e-01+5.1e-01+4.1e-01+3.1e-01+2.0e-01+9.9e-02–3.8e-03

+1.4e+00+1.2e+00+9.3e-01+6.9e-01+4.6e-01+2.2e-01–1.0e-02


(a)

(b)

0 1 2 3 4 5

0 1 2 3 4 5






Figure 9. (a)Q3 Displacement and (b) maximum stresses undergone by patient A’s trachea duringswallowing after implantation. (a) Location of the prosthesis. Different stages of the movement(marked from 0 to 5) are plotted (figure 7 for numbering).

influence of locating a prosthesis in the exact position defined by the clinician.This procedure has been detailed for two different patients: patient A andpatient B.

The morphology of these tracheas was completely different. Both patients weremale, but patient A was 28 years old while patient B was 62. In addition, patientB’s trachea was significantly shorter than average. The deglutition movementfor each patient was recorded using fluoroscopic images before and after theintervention. It could be appreciated that both of the patients lost some abilityto swallow after the surgery. This consequence was more evident in patientA, who underwent a decrease in his tracheal ascending movement of nearly30 per cent.





initialconfiguration ofpatient B’strachea

(a)

(b)

(c)

cut to thetrachea to seethe location ofthe prosthesis

initial stressesowing to theimplantation ofthe prosthesis

maximumdisplacementduringswallowing

maximumprincipal stressduringswallowing

initialconfiguration ofthe prosthesis

finalconfiguration ofthe prosthesis

maximumdisplacementduringswallowing

U, U3

U, U3

+2.4e+01+2.0e+01+1.6e+01+1.2e+01+8.1e+00+4.0e+00–3.5e–03

+7.5e-01+6.2e-01+5.0e-01+3.7e-01+2.5e-01+1.2e-01+0.0e+00

S, max. principal(avg: 75%)

+3.0e-01+5.0e-02+3.7e-02+2.4e-02+1.1e-02–1.3e-03–1.4e-02–2.7e-02

+2.5e-01+2.1e-01+1.7e-01+1.2e-01+8.3e-00–4.1e-00–4.4e-03

+6.9e-01+5.7e-01+4.6e-01+3.4e-01+2.3e-01+1.1e-01–2.9e-03



maximumprincipal stressduringswallowing

Figure 10. Mechanical consequences of implanting a prosthesis in patient B. (a) Displacement andmaximum principal stresses in patient B’s trachea before implantation. (b) Implantation of theprosthesis, showing the deformation of the prosthesis to reach its actual diameter. (c) Displacementand maximum principal stresses in patient’s B trachea after implantation.

The deglutition movement was simulated for both patients before and afterlocating the stent. The dimensions and location of the stents were defined by thethoracic surgeons. Stresses were located in the tracheal wall tissue in contact withthe superior edge of the stent. Three times higher maximal stress was obtainedafter introduction of the prosthesis in patient A. However, the stresses in patientB were hardly changed. It has been reported that granulation formation can occurat both ends of the stent, suggesting that this anomalous growth can be related tothe mechanical stress (Dumon et al. 1996; Noppen et al. 2005). Therefore, usingthis hypothesis, patient A had developed some fibrous tissue at the superior edgeof the stent, while patient B had not. In both cases, there was clinical validation





of these results because both patients were monitored following implantation ofthe stents. Patient A underwent several reinterventions whereas patient B didnot. Another important result that can be deduced from these simulations is thereaction force related to the imposed displacement. In both cases, the reactionforce (which can be related to the forces exerted by the elevating muscles) wasvery similar. This implies that the same force for each patient could be introduced,and then the displacement of the trachea, which is related to the patient’s abilityto swallow, would be another result of these simulations.

5. Limitations of the study

In spite of the good qualitative results that have been obtained in this work andthe effort that has been made in constructing patient-specific models to predictthe consequences of implanting an endoprosthesis, there are several assumptionsthat have been made and have to be pointed out.

Patient-specific tracheal meshes have been made using a mesh adaptationalgorithm. A reference mesh is adapted to a specific tracheal geometry bytransforming the reference geometry to the real one. This transformation is madeslide by slide, conserving the definition and quality of the reference mesh. Thefirst reason for this is to automate the definition of element groups regarding thedifferent materials, although this implies conserving the same number of cartilagerings among patients, for instance, which would involve a loss of accuracy.Nevertheless, the goal of this work is to construct a tool that allows the thoracicsurgeons to compare the behaviour of the trachea before and after implanting aprosthesis, or using different types of prostheses.

The experimental characterization of the human tracheal tissues has beenmade using samples from elderly people. It is known that biological tissues losewater and collagen with age owing to higher permeabilities and, therefore, theirmechanical properties can be affected, so a wider experimental test with a higherrange of ages should be performed to obtain non-age-dependent results. Moreover,there was a large variability from the mean value of the experimental curves andeach of the isolated curves, a fact that can be related to the use of samples fromdifferent individuals. Therefore, more samples would be necessary to draw moreaccurate conclusions.

The boundary conditions used were based on two real cases of patients beforeand after implantation. The deglutition movement obtained from fluoroscopicimages was obtained by marking the thyroid cartilage in a sagittal plane andtracking its position. Taking into account that the mobility of the trachea inthe transverse plane is negligible, this movement would represent the overallmovement of the trachea during swallowing. To be able to validate the simulateddeglutition movement, the measurement of the movement of each cartilaginousring would be valuable, but at present these rings cannot be distinguished onradiographic images.

Regarding the endoprosthesis itself, a rough approximation has been madeassuming it is a perfect cylindrical surface. The Dumon prosthesis is actually aperfect cylinder; however, it has several studs that are used to fix it to the internalwall of the trachea. This effect has not been simulated, but the friction of theprosthesis–internal wall interface was high enough to avoid migration.





6. Clinical implications

Notwithstanding the fact that there are a lot of uncertainties in implantingan endotracheal prosthesis, the present work provides a new insight into theseprocedures, predicting their mechanical consequences. This tool could be used inthe future as a support decision tool to help in the pre-operative planning of thiskind of surgery.

The support of the Instituto de Salud Carlos III through research project PI07/90023 and theCIBER initiative and of the Platform for Biological Tissue Characterization of the Centro deInvestigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN) ishighly appreciated.

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patient-speciﬁc models of human trachea to predict...

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