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Ann Thorac Surg 2005;80:623-630
© 2005 The Society of Thoracic Surgeons

Original article: Cardiovascular

Numerical Simulation Techniques to Study the Structural Response of the Human Chest Following Median Sternotomy

Raimund Bruhin, MD a , * , Ulrich Alfred Stock, MD a , Jan-Peter Drücker b , Tarek Azhari, MD c , Jens Wippermann, MD a , Johannes Maximilian Albes, MD a , Dagmar Hintze, PhD b , Stephan Eckardt b , Carsten Könke, PhD b , Thorsten Wahlers, MD a

a Department of Cardiothoracic and Vascular Surgery, Friedrich-Schiller-University, Jena, Germany
b Institute of Structural Mechanics, Bauhaus University, Weimar, Germany
c Department of Radiology, Friedrich-Schiller-University, Jena, Germany

Accepted for publication March 3, 2005.

* Address reprint requests to Dr Bruhin, Department of Cardiothoracic and Vascular Surgery, Friedrich-Schiller-University Jena, Erlanger Allee 101, 07747 Jena, Germany (Email: raimund.bruhin{at}med.uni-jena.de).


   Abstract
Top
 Abstract
Introduction
 Material and Methods
 Results
 Comment
 References
 
BACKGROUND: The optimal closure technique of median sternotomy remains controversial. The objective of this study was to analyze the structural response of the separated sternum using computer-based numerical discretization techniques, such as finite element methods.

METHODS: Thoracic computer tomographic scans (2.5-mm slices) were segmented, analyzed by image processing techniques, and transferred into a three-dimensional finite element model. In a first approach a linear elastic material model was used; neglecting nonlinear and damage effects of the bones. The influence of muscles and tendons was disregarded. Nonlinear contact conditions were applied between the two sternal parts and between fixation wires and sternum. The structural response of this model was investigated under normal breathing and asymmetric leaning on one side of the chest. Displacement and stress response of the segmented sternum were compared regarding two different closure techniques (single loop, figure-of-eight).

RESULTS: The obtained results revealed that for the normal breathing load case the single loop technique is capable of clamping the sternum sufficiently, assuming that the wires are prestressed. For asymmetric loading conditions, such as leaning on one side of the chest, the figure-of-eight loop can substantially reduce the relative longitudinal displacement between the two parts compared with the single loop.

CONCLUSIONS: The application of numerical simulation techniques using complex computer models enabled the determination of structural behavior of the chest regarding the influence of different closure techniques. They allowed easy and fast modifications and therefore, in contrast to a real physical model, in-depth parameter studies.


   Introduction
Top
 Abstract
 Introduction
Material and Methods
 Results
 Comment
 References
 
Median sternotomy remains the standard approach in cardiothoracic surgery. Failure of postoperative sternal closure remains a serious issue, including complications such as sternal instability and mediastinitis.

Throughout the years, a variety of sternal closure techniques [1–7] as well as different devices (wires, metal plates, stainless steel bands, nylon bands, metal plates in combination with wires) [7–13] have been applied. None of them were able to reduce or eliminate the failure rate. Recently, an article by Khasati and colleagues [14] discussed different literature sources, which compared two different sternal closure techniques, ie, simple wire and figure-of-eight technique. The authors selected seven relevant articles, out of which four were reporting on experimental studies and three represented retrospective cohort studies. The authors concluded from their review that the figure-of-eight technique reveals no significant advantage compared with the simple wire technique. All experimental in-vitro studies cited addressed the ultimate limit state of wires. Therefore, only the forces causing the fracture of wires or sterna were reported. No study has been reported on numerical simulation techniques investigating this problem.

Despite the importance of this surgical access and its associated problems, few biomechanical studies [7, 15–19] have been conducted presenting quantitative results for the structural response of different sternal closure techniques.

Casha and coworkers [18] studied the load displacement behavior of different closure techniques—straight, figure of eight, and Sterna-band (Stony Brook Surgical Innovations, Stony Brook, NY)—using two plates replacing the two sternal parts. McGregor and colleagues [15] and Trumble and coworkers [16] investigated structural responses of sternums using whole cadavers as well as artificial sternal models formed from polyurethane foam. Global displacements and local separation of the sternum parts were measured and correlated with applied forces. Jutley and associates [20] and Glennie and colleagues [21] determined the load displacement behavior of single wires and groups of wires with respect to wire dimension and wire twists. Except for the publication of McGregor and colleagues [15], all previously published models simplified this issue by extracting the sternum from the chest and studying the sternum separately. Experimental studies were restricted to general response parameters, such as applied global forces and total displacements.

The application of modern numerical discretization techniques allows physicians, in collaboration with engineers, to investigate displacement and stress distribution of the sternum embedded in the human chest in general response values. This includes displacements, forces, as well as local response values, such as strains and stresses.

The objective of this study was to analyze the structural response of the separated sternum with a specially designed computer model of the complete human chest. In addition, two different closure techniques (single loop and figure-of-eight) were compared with respect to displacement and stress response of the segmented sternum. The structural model was based on the finite element method (FEM) [22, 23], widely used for structural analysis problems in engineering research and practice. This study investigated the potential of numerical simulation techniques for the different sternal closure techniques. Therefore the authors have restricted their investigations to two particular types of wire closures and did not consider other closure techniques, such as Sterna-band or bone gluing.


   Material and Methods
Top
 Abstract
 Introduction
 Material and Methods
Results
 Comment
 References
 
Two-dimensional (2D) thoracic computer tomographic scans (CT scans), which have been grabbed in 2.5-mm slices, were segmented and analyzed by image processing techniques [24] and transferred into a three-dimensional (3D) finite element model by an automated procedure [25]. The stepwise modelling is illustrated below. In each slice of the thoracic CT scan, the different grey values were analyzed. The image processing software [24] detected closed areas of similar grey values and bounded them by polygonal borders. This concept was applied to each of the 250 pictures, taken over the entire height of the investigated human chests. Figure 1A presents a CT scan with an orange line, which has been used to study different filter effects. Figure 1B illustrates the same slice with red marked and bounded areas of bony and cartilage structures. By manual interaction, different grey values in the CT scans were assigned to specific material zones in the model. This technique allowed us to distinguish between ribs, cartilage and sternum, and to assign different material parameters to each of these structural components.



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  		Fig 1. (A) Computer tomographic (CT) scan; (B) CT scan with segmented subregions for ribs, cartilage, and sternum.

 
Using an image processing program and applying a marching-cube algorithm [24], the 2D slices were assembled into a 3D volume model describing the geometry and the different material subregions. This model will be referred to as computer aided design (CAD) model in the following. This assemblage was done without user interaction. Figure 2A depicts the generated 3D boundary surface model, describing the enclosed volume of all parts by a patched surface. Different colors were assigned to the three different material sections of the chest ribs (light blue), cartilage (red), and sternum (purple).



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  		Fig 2. (A) Computer aided design model of chest, different material subregions; (B) finite element method model of chest with different material subregions and five simple wire loops marked in blue.

 
Based on the CAD, model an automated meshing procedure transfers this geometrical information into a finite element discretization, shown in Figure 2B. Taking into account the tubular structure of both structural elements the chest ribs and the sternum were modelled by shell elements. The shell geometry, as well as the 5 degrees of freedom per node (ux, uy, uz, {phi}x, {phi}y) of the chosen shell element, are shown in Figure 3. The varying shell thickness of ribs and sternum was received from the CT scans and automatically included in the CAD model. Although the cartilage is a solid, it was also modeled with the described shell elements. This simplification can be justified as long as no detailed strain and stress information should be obtained for the cartilage. A comparison between two numerical models indicated that models with 3D volume or shell representation of the cartilage revealed similar overall global responses (data not presented). Even so sensitive to the stiffness distribution in the model, local strain and stress distribution in the sternum were hardly influenced by the type of modeling of the cartilage. All three model subregions are rigidly bonded to their neighboring subregions.



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  		Fig 3. Finite element shell with nodal degrees of freedom.

 
In a first investigation all three zones (ribs, cartilage, and sternum) were modeled by a linear-elastic material law, with material parameters taken from Furusu and Kato [26] (Table 1). Therewith no physical nonlinear effects, such as plasticity or damage, are taken into account. In order to consider the influence of the flexible backbone, the spinal column was modeled by a straight beam structure with constant cross-section and linear-elastic material. The lower end of this spinal beam was clamped. Figure 4 depicts the backbone beam and the beam connections between spinal ends of ribs and spinal column. These connections model fixed constraint conditions with respect to relative displacements between ribs and backbone and allow rotations around the longitudinal axis of the ribs [25]. The upper free end of the backbone has been used to apply different translational displacements for the two load cases of dorsal and lateral bending. For the dorsal bending case a displacement of uy= 100 mm and for the lateral bending case a displacement of ux = 100 mm were applied to the free backbone end.


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  		Table 1. Linear-Elastic Material Parameters for Sternum, Chest, and Cartilage (Furusu and Colleagues 26 )
 


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  		Fig 4. Backbone beam structure with attached chest ribs.

 
Nonlinear contact conditions, describing stiff contact under pressure and zero cohesive forces under tension contact, were chosen in the contact zone between the two sternum parts and for the contact between fixation wires and sternum. The fixation wires with a diameter of d = 0.45 mm have been described by a linear-elastic material law with a Young’s modulus of E = 2.0 105 N/mm2. Coulomb friction with an estimated friction coefficient of 0.2 was taken into account. Accordingly, tensile stresses from one part of the sternum to the other can only be transferred by the wires, whereas compressive forces might be transferred by contact over the intersection. Shear forces for a closed contact surface will be transferred by a combination of coulomb friction and forces in the fixation wires. The influences of muscles and tendons were neglected in this initial study.

Three different loading conditions were applied. The first load case simulates normal breathing and was described by prescribed rotations at the spinal ends of the ribs. The applied rotation angles at the connections points between spinal beam and chest ribs were estimated by comparison of the displacements of the chest ribs with expected values for a normal breathing cycle. The applied rotation angles for 10 chest ribs are listed in Table 2, starting with chest rib number 1 from top.


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  		Table 2. Applied Rotation Angles for Load Case Breathing
 
The second load case describes a lateral bending, and the third load case a dorsal bending of the spinal column. The latter two load scenarios were applied in order to model asymmetric loading conditions, such as leaning on one chest side and modeled by prescribed displacements assigned to the free end of the spinal column (see Fig 4).

In the first instance we intended to obtain relative information about different closure techniques of median sternotomy, comparing the same chest geometry and a similar numerical discretization and varying only the closure devices. Two particular closure techniques, a simple wire loop and a more sophisticated figure-of-eight loop were compared for the three described load case conditions.

A first partial model, representing only the sternum divided into two parts, was used to perform a simple plausibility test of the model. The left part of the sternum was fixed by appropriate boundary conditions while on the right sternum part pure shear forces were applied as loads, in order to simulate a dorsal load case. Figure 5 is illustrating this model. Two different closure techniques, a simple wire loop and figure-of-eight loop, were compared. For the first case two simple wire loops were applied to the centre region of the sternum, for the latter case one figure-of-eight loop was applied to the sternum. In both cases no prestress forces were applied to the wires. The entire chest model, consisting of ribs, sternum, cartilage, and spinal beam was investigated in a second step and is depicted in Figures 2A and 2B. For the full model a fixation of 5 simple wire loops, as shown in Figure 2B, was compared with a combined fixation of 2 figure-of-eight wires at the top of the sternum and 1 simple wire loop fixation at the lower end.



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  		Fig 5. (A) Simplified (partial) sternum model with single wire loop [25]; (B) simplified (partial) sternum model with figure-of-eight wire loop [25].

 
All FEMs were calculated with a commercial general purpose FE-package (ANSYS 5.7; CAD-FEM GmbH, Munich, Germany) performing static incremental-iterative nonlinear computations. It should be mentioned once again that the nonlinearity of the problem was introduced only by the contact conditions between the two sternum parts and the fixation wires and sternum.


   Results
Top
 Abstract
 Introduction
 Material and Methods
 Results
Comment
 References
 
The displacement situation for the partial model, shown in Figure 6, demonstrates that the figure-of-eight-loop clearly reduces the relative lateral displacement between the two sternum parts. The maximal relative displacements (lateral slip between the two sternum parts) was reduced from umax = 4 mm for the simple wire loop (Fig 6A) to umax = 1.55 mm for the figure-of-eight-loop (Fig 6B), indicating a better shear stress transformation in the latter case. The model furthermore revealed that the algorithm was able to simulate contact conditions between the two sternum parts as well as the contact between fixation wires and sternum.



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  		Fig 6. (A) Vertical displacement uz [mm] for the sternum with single wire loop; (B) vertical displacement uz for the sternum with figure-of-eight wire loop.

 
For the full chest model the intact chest, without sternal cut, was compared with the simple wire fixation technique and the figure-of-eight-fixation as described above. Figures 7A-7C compare the effective or von-Mises stresses of the three models for the load case breathing. It can be seen that the two fixation techniques lead to stress concentrations along the contact zones between sternum and wire. The wire stresses are in the same range of {sigma} = 20 N/mm2 for both fixation techniques, which is less than the assumed yield stress of {sigma} = 360 N/mm2, indicating that no wire will show plastic effects or damage. The zone of maximum stresses can be observed at the lower end of the sternum, indicating that the last simple wire is enforcing the closure of the sternum cut. Zooming into this region shows that the last parallel wire fixation at the sternal end is not capable to enforce the complete closure of the sternal. Figure 8 illustrates the gap that is evolving at the lower sternal end.



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  		Fig 7. Illustration of (A) von-Mises stress for intact sternum [N/mm2]; (B) von-Mises stress for simple-wire loop [N/mm2]; and (C) von-Mises stress for figure-of-eight loop [N/mm2].

 


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  		Fig 8. Gap at lower sternal end for simple wire fixation and load case breathing.

 
A slightly different behavior was seen in the lateral bending case (Fig 9A-9C). In this particular condition a tendency for a lateral gap at the sternal contact surface occurred, leading to relative lateral displacements along the sternal contact zone. Both investigated fixation techniques indicate similar stress distribution in the sternal bone. Once again the stress concentration along the contact zones between sternum and wire can be observed.



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  		Fig 9. Illustration of (A) von-Mises stress for intact sternum [N/mm2]; (B) von-Mises stress for simple-wire loop [N/mm2]; and (C) von-Mises stress for figure-of-eight loop [N/mm2].

 
Differences in load transfer were observed, when comparing the differences in the displacement components between the two sternal parts, as shown in Table 3. The relative difference of the displacements in the three cartesian directions is describing the relative slip between the two sternal parts and can be interpreted as a statement for the quality of the fixation techniques under different load cases. The x direction is defining the lateral, the y direction is defining the dorsal direction, and the z axis is parallel to the sternal length. The results reveal that for the load cases breathing and lateral bending the relative slip between the two sternal parts is clearly reduced for the figure-of-eight fixation compared with the simple wire fixation. The only exception is the relative slip in y direction for the lateral bending, which is increased by about 25% for the figure-of-eight fixation technique. For the dorsal bending all relative displacements demonatrate larger values for the figure-of-eight technique as for the simple-wire fixation. This might be a result of the missing prestressing forces in the wires. The figure-of-eight wires, which are longer, need higher relative displacements between the two sternal parts before a substantial transaction force can be activated. In subsequent studies the effect of prestressing forces in all fixation techniques has to be investigated. The wire stresses are {sigma} = 24 N/mm2 for the simple wire fixation and {sigma} = 2 N/mm2 for the figure-of-eight fixation technique. This also indicates that the figure-of-eight fixation technique needs a prestressing force to activate the force transfer via wires in the lateral bending load case. As for the first load case breathing, both stress values are much below the yield stress.


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  		Table 3. Relative Displacements {Delta}u [mm] Between the Two Sternal Parts
 

   Comment
Top
 Abstract
 Introduction
 Material and Methods
 Results
 Comment
References
 
Median sternotomy remains the preferred approach of most cardiac surgeons [1]. Severe complications such as sternal dehiscence, with or without combination of deep sternal wound infections vary from 0.15% to 8% with an average incidence of 1% to 2% [27–34]. If they occur they carry a high mortality rate of 5% to 47% [5, 35, 36].

Most of the previous studies on sternal closure focused on either risk factors for such complications [27, 33, 37, 38] or different surgical techniques [1–7], technical modifications and different closure materials [7–13]. The biomechanical studies that have been published analyzed more objectively conventional closure techniques [7, 15–19]. They all failed to influence clinical practice. Steel wire remains the standard closure material.

A stable fixation remains one of the prerequisites for an undisturbed bone healing [39]. Moreover, sternal instability seems to precede and promote bacterial infections [40]. A recent study revealed that complete healing of the sternum was observed in only half of the patients after 6 months [41].

Therefore, we believe that in depth knowledge of the strain and stress distribution as well as force transfer will be helpful to determine the optimal sternal closure technique. This numerical sternum model mimics quantitatively realistic conditions regarding traction forces at any point of the sternum. All parameters, such as chest geometry, bone characteristics and prestressing force of the different sternal closure techniques allow the comparison of the potential benefit of the varying procedures.

For that reason the first step was to create a computer model of the chest, as described above. This is a novel approach to study sternal closure stability. As a result digital 2D information of the chest (CT scan) was converted into a 3D model (CAD volume model) with the final transformation of the geometrical information into a FEM of the chest. The numerical discretization method FEM allowed a quantitative investigation of the structural behavior of the chest, taking into account the effects of different fixation techniques. Strain and stress distribution in the sternal wires can be investigated in detail. This concept clearly has some advantages in comparison to cadaver specimens and artificial polyurethane models. The proposed numerical model eliminates the biological variability of in vitro experiments and simplifies the interpretation and comparison of different closure techniques. It furthermore allows fast and easy modifications. Accordingly it is less time consuming with the possibility to perform intensive in depth parameter studies. In contrast, real physical models require each time a new model. Considering the entire chest geometry, the numerical model allows an increase of accuracy due to a higher flexibility and the potential to determine individual stress distributions on the basis of individual patient CT scans.

With respect to different loading cases the two most commonly used sternal closure techniques (single loop and figure-of-eight loop) were simulated and compared on the basis of this structural model. The application of this model enabled the simulation of effective stresses, strength of forces, force transfers, and displacements at the sternum as well as activation of the wires in the contact zones between wires and sternum. It furthermore allows the calculation of maximal total displacements (in mm) and relative slips between sternal parts (in mm) or maximal effective stresses (in N/mm2) under different loading cases at any point of the sternum (Table 4). Revealing a tendency to form a lateral gap at the sternum contact surface it finally shows a significant reduction of relative longitudinal displacement between the sternal parts using the figure-of-eight loop technique. Even if the absolute results of numerical models remain to be judged cautiously due to still missing sensitivity studies for different material parameters, the comparison of the same model with different closure techniques can give some valuable insight into basic stress distribution and force transfer mechanisms of the chest.


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  		Table 4. Effective Stresses {sigma} [N/mm2] in Sternum
 
Due to different objectives it was not possible to compare our own results with reported in vitro results quantitatively. The reported in vitro results are focussing on ultimate-limit loads for wires whereas our model is intending to compare different closure techniques for three simplified load scenarios (breathing, lateral, and dorsal bending), which all have been not leading to failure loads in the wires.

The described multidisciplinary approach enables the comparison of different closure techniques for specific patient situations. Future studies with respect to all influencing parameters, such as sternum and chest geometry, stiffness and strength of the bone and cartilage, influence of muscles and tendons, will be conducted efficiently. These studies will potentially result in an optimization of sternal closure techniques following median sternotomy.

Conclusions
This study is a first step towards realistic numerical models, which allow the prediction of the structural behavior of the human chest in context with median sternotomy. A numerical computer model, based on the FEM, demonstrated the general feasibility to model displacement and force transfer behavior of different closure techniques for median sternotomy. Numerical simulation models have to take into account a number of governing physical effects, such as nonlinear contact conditions between sternum parts and wires, or the interaction between the different parts of the chest. As a first quantitative outcome of the proposed approach, it was shown that the figure-of-eight loop sternal closure substantially reduced the relative longitudinal displacement (lateral slip) between the two sternum parts compared with a single loop wire. Future studies will need to focus on the sensitivity of the obtained results with respect to material parameters and material models including tendons and muscles and with respect to the sensitivity of displacements and stresses depending on prestressing forces in the wires.


   References
Top
 Abstract
 Introduction
 Material and Methods
 Results
 Comment
 References
 

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C. Schimmer, W. Reents, S. Berneder, P. Eigel, O. Sezer, H. Scheld, K. Sahraoui, B. Gansera, O. Deppert, A. Rubio, et al.
Prevention of Sternal Dehiscence and Infection in High-Risk Patients: A Prospective Randomized Multicenter Trial
Ann. Thorac. Surg., December 1, 2008; 86(6): 1897 - 1904.
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