Eur J Cardiothorac Surg 2004;25:1039-1047
© 2004 Elsevier Science NL
A finite element model of blunt traumatic aortic rupture
David Richensa*,
Mark Fielda,
Shahrul Hashima,
Michael Nealeb,
Charles Oakleyb
a Department of Cardiothoracic Surgery, Nottingham City Hospital, Hucknall Road, Nottingham NG5 1PB, UK
b Transport Research Laboratory Limited, Old Wokingham Road, Crowthorne, Berkshire RG45 6AU, UK
Received 21 October 2003;
received in revised form 17 January 2004;
accepted 21 January 2004.
* Corresponding author. Tel.: +44-115-969-1169; fax: +44-115-840-2605
e-mail: drichens{at}ncht.trent.nhs.uk
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Abstract
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Objective: Blunt traumatic aortic rupture has a scene survival of 2–5% and is present in 20% of all automobile fatalities. The manner in which the forces from a range of thoracic impacts are transduced through the thoracic cavity to produce consistent injury to the aortic isthmus remains uncertain. Our objective was to create and evaluate a computer based finite element (FE) model of the aorta and observe its behavior during blunt traumatic impacts. Methods: A finite element model of the thorax including details of the heart, aorta and pertinent thoracic structures was created and run under the FE code LS-DYNA3D. The motion response of the heart following a simulated thoracic impact was extracted from the thorax model and applied in a second more detailed model of the heart and aorta in order to investigate the stresses acting through the aortic isthmus during simulated thoracic impacts. Results: Simulated impact studies show that the predicted peak chest compression of the thorax model matched the measured responses from non-embalmed human cadaver impact studies by Kroell et al., 1974. The more detailed heart–aorta model predicted maximum stresses at the isthmus and pulmonary artery bifurcation the sites of most common trauma injury. Conclusions: Analysis of the response of the finite element heart–aorta model during blunt thoracic trauma demonstrates its potential for predicting major vessel injury. The model will be helpful in the design of impact protection systems.
Key Words: Trauma • Aorta • Rupture • Finite-element models and impact protection systems
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1. Introduction
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A multitude of trauma scenarios are known to result in Blunt Traumatic Aortic Rupture (BTAR). However, the most detailed data available in the United Kingdom, and worldwide, relates to vehicle related trauma. In the UK, Transport Research Laboratories (TRL) Limited have participated in the development of an injury database that has been funded by the UK Government's Department for Transport and several commercial automotive companies entitled, The Co-operative Crash Injury Study. We have formerly appraised this source [1] and the data suggests that BTAR has a <2% overall survival and a scene survival of around 2–5%. Interestingly, BTAR occurs in approximately 20% of all road accident fatalities. This equates to approximately 684 road accident deaths per year in the United Kingdom (pop. 55 million). Studies from the USA and Canada suggest around 7500–8000 victims die from BTAR each year in those countries [2].
The presentation, investigation and treatment of BTAR are well described and accepted in the literature. However, there remains considerable uncertainty regarding the pathogenic aetiology of this injury. We have recently published a review on the mechanisms of BTAR and the reader is referred for a detailed analysis [3]. In essence, the manner in which the forces from a range of thoracic impacts are transduced through the thoracic cavity to produce consistent injury to the aortic isthmus remains uncertain. Early investigators supported the view that the injury resulted from one of a number of specific mechanisms. The first suggested mechanism was of sudden stretching of the aorta with rupture at the point of presumed weakness, the isthmus. An additional factor in this aetiology was the suggestion that the distal descending aorta is relatively fixed while the proximal aorta is mobile. A second suggested mechanism was based on the assumption of a sudden spike in blood pressure during trauma, which causes wall tension and rupture at the isthmus. It is further speculated that this mechanism may be augmented by a water hammer effect created by diaphragmatic occlusion of the aorta during trauma. Entrapment of the aorta by boney structures within the thorax, so-called ‘osseous pinch’ is a further suggested mechanism of aortic rupture. Other multivariate hypotheses have been suggested. These mechanisms are based on a combination of the above mechanisms and typically suggest that the heart is squeezed as the chest is compressed by trauma, creating a dramatic rise in blood pressure. This together with occlusion of the aorta at the diaphragm creates a water hammer effect. The displacement of the heart upward, or ‘shoveling effect’, creates stress in the aorta since the descending aorta is tethered. These forces conspire at the point of anatomical weakness, commonly the isthmus.
In summary, a number of conflicting unsubstantiated hypotheses have been suggested to account for BTAR, however there is no obvious evidence to support any one mechanism and the multivariate hypotheses seems most probable. It seems likely that the injury results from a multitude of forces: tension, torsion, shear, stretching, bending and water hammer, acting within a haemo-dynamic, pulmonary dynamic and structural dynamic, to converge on the aortic isthmus. The relative importance of deceleration, acceleration and crushing injuries in the aetiology of BTAR also remains uncertain. As suggested by Richens et al. [3], ‘given the number of variables and computations in a complex dynamic system, it is reasonable to conclude that the future lay in computer based modeling systems’. This present work represents our initial data from the development of a finite element (FE) model of the aorta to investigate the mechanical initiators of BTAR.
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2. Methods
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2.1. The FE method
The FE method is a numerical technique, which can be applied to model the dynamic response of structures under load. Chosen structures for examination are idealized by a mesh of much smaller regular shaped structural elements with known mathematical characteristics. Each individual element is joined by its adjacent element by interconnected common points (nodes). It is the connection between elements that provide the complete numerical description of the structure under examination. (Fig. 1a and b)
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2.2. The FE heart–aorta model
A detailed FE model of the heart and aorta was created in order that intricate examinations of the aorta's dynamic response under loading could be made. The geometry for the heart aorta model was commercially available. The mesh for the model was developed using the proprietary pre and post processing software code Hypermesh. Fig. 2
shows the structure of the resulting model. The main features of the model include the aorta, pulmonary vessels, blood, bronchi, heart, ligamentum arteriosum and a generic cylindrical spine. The model was constructed from 7355 elements and 4281 nodes. Shell elements were used to construct all the anatomical details in the model.
2.3. The FE thorax model
Although providing a detailed description of the aorta, the heart–aorta model lacked the peripheral anatomical structures of the chest such as the skin, ribs, and lungs, through which trauma would be transduced to the heart and aorta during chest impacts. Ultimately these additional structures would be added, but currently there existed limitations in applying a representative load in the model in order to test its response. This difficulty was overcome by developing a less detailed FE model of the thorax with simplified details of the heart, aorta and other pertinent thoracic structures. The intention of this model was to provide information on the motion response of the heart during blunt trauma to the chest (Fig. 3)
. The motion response of the heart was taken from the thorax model (Fig. 4)
and applied in the more detailed FE heart–aorta model so that a more detailed examination of the aortas dynamic response under loading could be made.
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Fig. 3. The thorax impactor model used to establish the motion of the heart during a typical frontal impact to the thorax.
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The basic structure and form of the thorax model was established from anatomical geometric data on the heart, aorta, spine, trachea and pulmonary trunk available at TRL Limited. The lung, heart, skin, ribs and impactor are made out of shell elements. The vertebra is made out of solid element and the vertebral discs, heart's blood and surrounding tissue are of solid elastic elements. Overall, 2883 elements and 2045 nodes were used to construct the FE thorax model. Table 1 details the material properties of the anatomical structures simulated in the thorax model.
2.4. Material characteristics of the heart–aorta model
As the dynamic response of the aorta was the principal focus of the study a considerable amount of effort was placed on getting the material properties of this aspect of the model correct. Mohan and Melvin [4] acquired the loading response of the aorta from an autopsy-based study involving uniaxial tensile tests on samples of human aortic tissue. We approached the problem of simulating the dynamic response of the aorta by examining various material models for coherence with the experimental data obtained from the tests described by Mohan and Melvin [4] and reviewed in Section 4. The methodology of this approach involved the construction of a FE uniaxial tensile test model matching the setup of the tests completed by Mohan and Melvin [4]. A series of material models were then applied in the uniaxial tensile model in an attempt to match the model's predictions to the uniaxial test results. Initially an elastic material model was applied in the uniaxial test model as a first attempt to model the aorta's response. It was anticipated prior to investigating this material model that unlike the loading response of the aorta it would provide a linear stress–strain response. However, it was also discovered during runs of the uniaxial test model that the elastic material model was only able to operate up to strains of 10%, after which the modeling code became unstable. A second, non-linear orthotropic material model was evaluated. However, it was also found to be unstable demonstrating erratic stress–strain behavior when strained beyond 10%. Further attempts to replicate the material characteristics of the aorta using Frazer Nash and Ogden rubber models failed due to instability of the simulation at high strain values. The most stable system was found using a Blatz-Ko rubber model and this was the chosen material model applied in the heart–aorta model. Although possessing linear isotropic material characteristics the Blatz-Ko rubber model had a stable response when strained up to 80%. This material model is defined by two parameters: material density and shear modulus. For the heart aorta model the mass density of the Blatz-Ko material was approximated to that of water 1000 kg m–3) and the shear modulus (0.51 MPa) was derived using a value for the Young's modulus of the aorta, established from the initial linear stress strain response. Table 2 details the complete material properties of the individual components of the heart aorta model including those of the aorta. Blood within the aorta was modeled using an elastic fluid material model. The limitations of such an approach are covered in Section 4. The material characteristics of the pulmonary trunk were made equivalent to the aorta while the ligamentum arteriosum was made relatively weaker. The Young's modulus of the trachea and bronchi were made ten times greater than that of the aorta. In order to simulate the action of the left lung pressing the descending aorta onto the spine, a sheath of elements was attached to the generic cylindrical spine to envelop the descending aorta.
2.5. Boundary conditions of the FE heart–aorta model and the thorax model
A number of assumptions were associated with the heart–aorta model in order to obtain the most representative response from the model. In the human anatomy the ends of the pulmonary vessels and bronchi feed into the lungs. The lungs were not simulated in the detailed heart aorta model and so it was necessary to make a decision on the boundary conditions that should be placed on the ends of these vessels. As such it was decided to tie the end motion of the left pulmonary vessel to that of the terminal end of the left bronchi. Similarly the end motion of the right pulmonary vessel was tied to the motion of the terminal end of the right bronchi. The coupling was achieved by tying the motion of the nodal points at the ends of the vessels together in what is defined within the FE software code as a ‘rigid nodal constraint’. For the studies conducted with the thorax model there were no boundary conditions placed on the model. The thorax model was impacted by an impactor and the thorax model responded accordingly. For the detailed heart aorta model the spine and the proximal end of the bronchi was fixed in space and a displacement boundary condition was placed on the rigid heart. The generic cylindrical spine was modeled as a rigid body and its position, in addition to the proximal end of the trachea, were locked in position. The heart was modeled as a rigid body so that the motion response of the heart obtained from a run of the thorax model could be applied in the heart–aorta model.
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3. Results
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The thorax model was validated by comparing peak chest deflection predictions from thorax model runs against comparable data obtained from impact studies on cadavers [5]. Table 3 contains the results from the comparisons that were made and shows that the predicted chest compression of the thorax model broadly matches the measured responses except for Test 5 where the disparity is over 40%. The motion response of the heart in the test 3 validation run of the thorax model (Table 3) was obtained and applied in the heart–aorta model. This particular run of the thorax model was chosen, as the comparison between measured and predicted peak chest deflections was the closest match of all the comparisons made. Fig. 4 shows captured images of the heart–aorta model run at 10 ms intervals and Fig. 5
shows the same series of images with the Von Mises stresses predicted by the model. Regions of high stress are observed at the isthmus region of the aorta and at the point of bifurcation of the pulmonary aorta.
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4. Discussion
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The manner in which the forces from a range of thoracic impacts are transduced through the thoracic cavity to produce consistent injury to the aortic isthmus remains uncertain. Given the large number of variables and the dynamic nature of the system, our objective was to create and evaluate a computer-based FE model of aortic rupture during blunt traumatic impacts. Our preliminary data suggests that it is feasible to generate a FE model of the thorax, which following a simulated blunt trauma, behaves in a manner consistent with published experimental data. Several limitations have been highlighted, the solution to which should allow the creation of a truly biofidelic model which may be used to study a variety of trauma scenarios. Discussions of the issues surrounding this pathology are given below.
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5. Blunt traumatic aortic rupture
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We have reviewed the mechanisms proposed for BTAR in Richens et al. [3] and these were briefly covered in Section 1. Putting aside specific mechanisms, it is clear that several processes underlie all proposals, whether alone or in combination. These include tension, torsion, shear, stretch and bending or buckling. Irrespective of the mechanism or the net force, a number of consistent observations have been reported on the nature of the rupture:- The rupture frequently occurs on the inner side of the aortic arch;
- The rupture is a very clean separation of the aortic wall;
- The rupture is circumferential around the aorta;
- The rupture appears to initiate on the inner wall of the aorta and develop towards the outer wall.
Typically, the aorta ruptures at the isthmus, however, other sites of rupture have been documented including the ascending aorta just proximal to the braciocephalic artery and occasionally the distal descending aorta [6]. Moar [7] reviewed 21 individuals with multiple ruptures, three of whom were found to have eight tears in the aorta. Our study has gone some way to creating a detailed FE model of the thorax and simulating the stresses and strains experienced by the aorta during an impact. A number of limitations exist within the model and these are discussed below.
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6. Limitations of the heart–aorta model's material characteristics
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The relative characteristics of contiguous tissue systems is likely to be the key to understanding the dynamics within the chest during an impact. It is thus necessary to model these characteristics precisely in order to have confidence in the models predictions. Development of the simulated aortic material was based on the results of the uniaxial tensile tests conducted by Mohan and Melvin [4]. The authors investigated the failure properties of samples of human autopsy aorta. Their work details a series of uniaxial tensile tests on 32 autopsy samples of aorta from a group of subjects with a mean age of 54.6 years (4–89). The aortic samples were opened, cleaned and dumbbell shaped specimens were stamped out from the mid-thoracic section of the descending aorta in both transverse and axial directions. The uniaxial tensile tests were conducted under both quasi-static (0.21 mm s–1) and high strain (1533.33 mm s–1) conditions. These investigators showed that aortic tissue has a non-linear stress strain response. It was further discovered in the investigations that aortic tissue is anisotropic having an ultimate tensile strength in the transverse direction 50% larger than it is in the axial direction. Furthermore, the strength of the aorta is strain rate dependent having a dynamic ultimate tensile strength around 80% larger than under quasi-static loading conditions. We approached the problem of constructing a biofidelic simulation of an aorta by examining various material models for coherence with results from the uniaxial tensile tests. Of the material models investigated the most stable was found to be the Blatz-Ko rubber model, which provided a stable response when strained up to 80%, which is typical of the strain that the aorta can sustain prior to failure. However, in comparison to the loading behavior of the aorta this material model is linear, isotropic and strain rate independent in its response and the characteristics defined for the material only consider the initial linear response of the aorta. The simulation is thus not representative of the aorta's response at higher tensions and further work is needed to develop a comprehensive material model that can simulate the non-linear, anisotropic and strain rate dependent behavior of the aorta.
Similarly, relatively simple material models were used to describe the loading behavior of the other anatomical structures of the heart–aorta model such as the pulmonary vessels, ligamentum arteriosum and trachea, which potentially have complex loading behaviors matching that of the aorta. There is thus a need to develop complex material models for these components of the heart–aorta model also. Furthermore, the blood in the aorta was simulated with an elastic fluid material model. Although the elastic fluid material model provides a simulated structure that has bulk properties of a fluid unable to sustain deviatoric stresses, it is incapable of sustaining large deformations which would be expected from a fluid such as blood under loading. This may place a limit on the types and magnitudes of load that could be placed on the model to investigate aortic rupture. Further work is thus needed to more accurately simulate the response of the blood in the model. This may require the application of such techniques as Arbitrary Lagrangian Eulerian methods or Smooth Particle Hydrodynamics, which can be employed to simultaneously model the response of fluids and sold structures within the same simulation.
6.1. Impact simulation in the heart aorta model
A chest impact was simulated with the heart–aorta model by applying a representative motion response on the heart of the model as obtained from a previous simulation completed with the thorax model. For the run completed with the heart–aorta model a number of assumptions were made in order to obtain a representative response from the model. These included a rigid generic cylindrical spine and the proximal end of the trachea fixed in position and coupling the motion response of the terminal ends of the pulmonary arteries and bronchi. All these assumptions placed an artificial boundary condition on the heart–aorta model and would contribute to the results obtained. It is uncertain how much these artificial boundaries influence the accuracy of the model's predictions. The model results do provide a promising insight into the response of the aorta during a blunt chest impact and there is no reason to suggest that the artificial boundary conditions have enhanced these observations in the model. However, on account of the many limitations currently associated with the model it is too early and possibly would be misleading to speculate on the mechanisms that cause aortic rupture.
Ultimately, developing the outstanding anatomical features of the thorax in the heart–aorta model would eliminate the need for the artificial boundary conditions placed on the model in this study. When such a position is reached there would be more confidence in the accuracy of the model's predictions and it would then be more pertinent based on predictions from the model to suggest the mechanisms that cause aortic rupture. Other factors which must form part of any representative model include victim related characteristics such as age, hypertension, diabetes, and atherosclerotic disease.
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7. Future work
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Having established the feasibility of FE modeling the thorax during blunt traumatic rupture, and validated its basic behavior with published experimental data, we intend to proceed to create a more sophisticated and biofidelic model. This will involve developing in detail the outstanding anatomical structures of the chest with correctly defined material models describing the material behavior of the anatomical structures. In addition to these considerations it is speculated that an additional key to understanding BTAR and creating a model, which may be used for experimentation, is the cardiopulmonary dynamic. As cited by Kivity and Collins [8] and McDonald and Campbell [9] proposed that the injury is more likely at the start of diastole when the aorta is full of blood and in its maximum state of pressurization. In addition, the lungs in a state of full inspiration could potentially provide additional cushioning or conversely greater loading of the aorta during impacts to the chest. Loading of the aorta during an impact, and therefore susceptibility to BTAR, is possibly dependent on:- the position within the cardiac cycle;
- the position within the pulmonary cycle;
- the volume loading of the vasculature.
The developed model should therefore be able to consider the cardiopulmonary dynamic in its predictions. It could then be applied to investigate the importance of the cardiopulmonary dynamic on BTAR and potentially the key states within the cardiopulmonary cycle that BTAR is most likely. One may speculate that given this information, it may be possible to develop an automobile ‘intelligent impact protection system’ allowing the point of maximum impact to be modified by 100 or 200 ms, and therefore to a point of least susceptibility in the cardiopulmonary dynamic. The expectation is that a computer system could modify the impact profile, through the co-ordinated deployment of the crumple zone, seat belt and airbag, thereby phasing the dispersment of energy to a safe point. This work is on going.
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8. Conclusions
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The manner in which the forces from a range of thoracic traumas are transduced through the thoracic cavity to produce consistent injury to the aortic isthmus remains uncertain. Given the large number of variables and the dynamic nature of the system, our objective was to create and evaluate a computer-based FE model of aortic rupture during blunt traumatic injury. Our preliminary data suggest that it is feasible to generate a FE model of the thorax, which following a simulated blunt trauma, behaves in a manner consistent with published experimental data. Several limitations have been highlighted, the solution to which should allow the generation of a truly biofidelic model which may be used to study a variety of trauma scenarios. The model will be helpful in the design of impact protection systems.
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Footnotes
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Presented at the joint 17th Annual Meeting of the European Association for Cardio-thoracic Surgery and the 11th Annual Meeting of the European Society of Thoracic Surgeons, Vienna, Austria, October 12–15, 2003.
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Appendix A. Conference discussion
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Dr J. Tsai (Pingtung, Taiwan): Did you consider the ductus arteriosus ligament in your study of a finite element mode of blunt aortic traumatic injury?
Mr Field: This was included in the model.
Dr Tsai: Yes, because the ductus arteriosus ligament may be fibrotic. Sometimes blunt injury may tear the aortic arch. So would you like to take it into your consideration?
Mr Field: Yes, this was included in the model, and a number of additional things also need to be included in terms of risk factors for the rupture, such as age and diabetes and sclerosis as well. These things also need to be included.
Mr D. Richens (Nottingham, UK): To answer that, yes, the ligament is included in the anatomical model. In all the cycles we have got a finite element model of the ligament.
Dr E. Baudet (Bordeaux, France): Did you take into consideration only vertical deceleration or blunt trauma or also horizontal deceleration?
Mr Field: Just blunt trauma at the present time. We have a lot of work to do improving our model before going on to do this sort of work.
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References
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- Richens D., Field M., Neale M., Oakley C. The mechanism of injury in blunt traumatic rupture of the aorta. Eur J Cardiothoracic Surg 2002;21:288-293.[Abstract/Free Full Text]
- Mohan D., Melvin J.W. Failure properties of passive human aortic tissue. I. Uniaxial tension tests. J Biomech 1982;15(11):887-902.[CrossRef][Medline]
- Kroell C., Schneider D., Nahum A. Impact tolerance and response of human thorax. Eighth Stapp Car Crash Conference. Pennsylvania: Society of Automotive Engineers, 1974.
- Symbas P.N. Fundamentals of clinical cardiology-great vessel injury. Am Heart J 1977;93:518-522.[Medline]
- Moar J.J. Traumatic rupture of the thoracic aorta. An autopsy and histopathological study. S Afr Med J 1985;67(10):383-385.[Medline]
- Kivity Y, Collins R. Non linear wave propagation in viscoelastic tubes: application to aortic rupture 1974;7:67–76.
- McDonald J.B., Campbell W.A. Traumatic rupture of the normal aorta in young adults. Am Heart J 1945;30(4):321-324.[CrossRef]
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Abstract
1. Introduction
