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Eur J Cardiothorac Surg 2008;34:623-629. doi:10.1016/j.ejcts.2008.02.032
Copyright © 2008, European Association for Cardio-thoracic Surgery. Published by Elsevier. All rights reserved.
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Blunt trauma and acute aortic syndrome: a three-layer finite-element model of the aortic wall

Aihong (Rachel) Zhaoa,*, Mark L. Fieldb,*, Kennerly Diggesa, David Richensc

a The George Washington University, Washington, DC, United States
b The Cardiothoracic Centre, Liverpool, United Kingdom
c The Trent Cardiac Centre, Nottingham, United Kingdom

Received 21 September 2007; received in revised form 20 February 2008; accepted 24 February 2008.

* Corresponding authors. (Email: aihongzhao{at}yahoo.com; mlfield{at}doctors.net.uk).


   Abstract
Top
 Abstract
1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 References
 
Objective: The exact process by which blunt trauma to the aorta produces a typical characteristic lesion set of primary, transverse, intimal injury remains unknown. The likely cause is a combination of intraluminal hypertension and mechanical deformation. We set about creating a three-layer finite-element model of the aorta. We hypothesised that deformation of the aorta through tension, torsion and bending would have differential effects on the constitutive layers of the aorta and this differential stress strain pattern would help to explain the mechanism of this injury. Methods: A finite-element model of the aorta was created with three distinct layers representing tunica intima, media and adventitia. A rubble-like material model in the commercial dynamic finite-element package LS-DYNA was adopted. Numerical methods for considering the interaction between aortic tissue (solid) and blood (fluid) were defined using arbitrary Lagrangian Eulerian methods. Simulations of mechanical deformation including tension, torsion and bending were applied with loading set at 1 m/s and intraluminal blood pressure rising from 86.6 mmHg to 146 mmHg. The simulations were run until material failure. The role of blood within these simulations was explored. Result: Our initial simulations confirmed the functionality of the three-layer finite-element model of the aorta with behaviour as expected from previously published experimentation. The addition of mechanical loading through torsion, tension and bending resulted in failure of the aorta at significantly lower mean blood pressures than without. Temporal and spatial aspects of failure were distinct for each method of loading. Bending resulted in rapid primary adventitial failure while tension and torsion resulted in a relatively delayed primary intimal failure. Blood flow altered the stress strain characteristics within the model. Conclusions: This work confirms the feasibility of using a three-layer FE model of the aorta. Our data suggest that the relative contribution of intraluminal hypertension to BTAR is lower in the presence of complex loading by tension, torsion and bending. In addition, failure of the aorta is load dependent with bending causing a relatively early primary adventitial failure, while tension and torsion result in a relatively delayed primary intimal failure.

Key Words: Aorta • Trauma • Finite-element model


   1. Introduction
Top
 Abstract
 1. Introduction
2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 References
 
Blunt traumatic aortic injury following road traffic accidents typically has a dismal outcome. We have previously published an analysis of the UK-based Co-operative Crash Injury Study [1], a detailed database of vehicle related injury, indicating that blunt aortic trauma accounts for approximately 20% of vehicle related deaths. The literature [2] describes a scene survival of approximately 5% and an overall survival of less than 2%, suggesting most victims sustain immediate and catastrophic aortic failure with exsanguination and death at the site of trauma; so-called blunt traumatic aortic rupture (BTAR). A small number of victims sustain a lesser partial mural injury, which allows transfer to hospital and definitive treatment; so-called blunt traumatic aortic injury (BTAI). Aortic injury is now considered as part of a spectrum of diseases (acute aortic syndrome), with blunt aortic trauma being at one end of the disease continuum, and including other process such as classical dissection, intimal flap, sub-intimal haematoma, intra-mural haematoma, and penetrating atherosclerotic ulcer, through BTAI to BTAR [3]. While the characteristics of BTAI/R have been well documented, including the circumstance under which it occurs, the transduction of impact energy through the thorax, and the evolution of the injury to the aortic wall, the exact aetiology, which accounts for injury characteristics remains unclear [2]. In particular, it is uncertain why despite a range of trauma scenarios, the injury profiles of victims are very similar with the majority of tears being initiated in the intima and occurring in a transverse fashion in the peri-isthmus region. Several hypotheses have been put forward to account for these characteristic sets of lesions and these broadly centre on mechanical deformation and intraluminal hypertension. Mechanical deformation and injury of the peri-isthmus aorta during trauma may occur by a number of mechanisms including tension, torsion, bending, and their combinations [4–6]. These forces may result from a complex combination of both relative motion of structures within the thorax and local loading of tissues either as a result of their anatomy or the nature of the impact. Compounding mechanical deformations in loading the aorta following trauma are a number of mechanisms resulting in intraluminal hypertension including luminal compression, either by osseous [7] or diaphragmatic pinch [8], sympathetic discharge and the Valsalva effect [9]. We believe however that suprapressurisation of the aorta occurs during anticipation of impact and the brace response, and simply serves to place the aorta in a high tensile, vulnerable state, with vessel deformation ultimately initiating injury. The exact process by which some or all of these mechanisms are channelled through a final common pathway to cause consistent injury to the isthmus, despite a wide range of trauma scenarios, remains unknown. We have previously published a finite-element model of the thorax and its contents, simulating blunt trauma, in order to study the complex interplay of multiple forces causing BTAI/R [10]. This experience highlighted the difficulty of examining a vast number of dynamic variables simultaneously leading us to the conclusion that in order to understand the aetiology of this disease we would need a detailed and sophisticated understanding of aortic wall mechanics first. Previous studies in isolated aortic wall samples have documented simple wall mechanics [11], however no data exist describing complex loading conditions. We hypothesised that a histologically and physiologically representative three aortic wall finite-element model would allow us to examine in detail how predominant loading modes (tension, torsion and bending) may lead to the initiation of an acute aortic syndrome, and therefore better understand the aetiology of BTAI.


   2. Methods
Top
 Abstract
 1. Introduction
 2. Methods
3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 References
 
2.1 The three-layer finite-element model of the thoracic aorta
2.1.1 The finite-element method
The finite-element method (FEM) is a numerical technique, which can be applied to model the dynamic response of anatomical structures under load such as the aorta following blunt trauma [10]. Mathematically, the FEM is used for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. In order to present unlimited degrees of freedom of structures by limited degrees of freedom, the structures are divided into many elements. Each individual element is joined to its adjacent element by interconnected common points (nodes). The displacements of common points provide the complete numerical description of the structure under examination. In the case of the thoracic aorta a simplified anatomical structure was created assuming a three-layer model to represent the tunica intima, tunica media and tunica adventitia. The thicknesses of the three layers are 0.33, 1.32 and 0.96 mm, respectively, while the internal diameter was assumed to be 18 mm and the length of the tube 44 mm [12]. Loads applied included tension, torsion and bending.

2.1.2 Material properties of the three-layer finite-element model
To develop an aortic FE model, there are a number of issues, which require addressing. Firstly, an accurate representation of the complex aortic material characteristics through constitutive equations is necessary to capture stresses and strains that would lead to aortic rupture during a crash simulation. In addition, apart from the constitutive equations, material failure criteria are important for predicting the rupture of this vessel. Ideally, to fulfill these obligations, an orthotropic material model is required. We have previously [13] created a three-layer orthotropic aorta FE model for special cases such as tension and inflation of an artery as a circular cylindrical tube. However, due to the lack of experimental data and a theoretical basis, an isotropic model in nonlinear dynamic finite-element software LS-DYNA was employed for complex loading cases. A rubber-like material model (material type 181) with a rate-dependent hyperelasticity characteristic was chosen in LS-DYNA and the theory behind this approach has been defined by Du Bois [14]. This material model provides rate-dependency by defining a single uniaxial curve or by a family of curves at discrete strain rates. In addition, this material model reproduces the quasi-static uniaxial tension and compression tests exactly. Under quasi-static arbitrary 3D loading the response of MAT_SIMPLIFIED_RUBBER is identical to MAT_OGDEN based on parameters that would allow an exact fit of the uniaxial test results. The generalised form of the partial derivative of Ogden's hyperelastic strain energy density functional, with respect to the principal stretches {lambda} is shown in equation 1. In this equation, K is the bulk modulus, J is the volume ratio (V/V 0), {lambda}* is the modified stretch ratio ({lambda}* = {lambda}J – 1/3) and f({lambda}) is a generalised function of Ogden coefficients. The simplified rubber model assumes a different form of f({lambda}) than the conventional polynomial form. The alternative form of f({lambda}) is shown in Eq. (2). In this form, the uniaxial stress and strain data provided is used to directly calculate the function. Strain is calculated from the stretch ratio provided by the user via equation (3) and the corresponding force is read from the uniaxial data. Stress is calculated by dividing the force by the undeformed specimen cross-sectional area.


Formula

(1)


Formula 1

(2)


Formula 2

(3)

A series of aortic simulations using this model was performed and it was found to be stable. Apart from constitutive equations of the material model, considering the test results and numerical stability, the first principal strain at failure was chosen as the criterion of material failures. Under the assumption that the aortic model is isotropic, the strain–stress curve in either circumferential or longitudinal direction can be chosen to present the strain stress curve of the aorta material in the FE aorta model. However, since the intima in circumferential direction, which is most vulnerable layer of the aortic failure, is stiffer than that from longitudinal direction, the strain–stress curves in circumferential direction are assumed as the strain–stress curve of the three layers of the aorta, respectively (Fig. 1 [12]). Nevertheless, as indicated in Table 1 [15,16], the ultimate strains in circumferential direction of three layers are not always bigger than those from longitudinal direction respectively. Conservatively, the maximum ultimate strains in either direction are chosen as failure criterion of each layer separately. The data utilised from Holzapfel's work is based on results from the human cadaver.


Figure 1
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  		Fig. 1. Strain–stress curves of the layers of the aorta [12].

 

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  		Table 1 Ultimate tensile stress and strain characteristics of three-layer model [15] (stress unit: kPa)
 
2.1.3 The interaction between artery and blood
Blood pressure is assumed to be an important contributory factor in BTAR, and hence the interaction between blood and aortic tissue was included in the FE model. In this work, arbitrary Lagrangian Eulerian (ALE) was chosen for considering the interaction between aortic tissue (solid) and blood (fluid). The main material parameters of blood are dynamic viscosity and density. They were taken to be 4 kPa s, and 1060 kg/m3, respectively. The coupling method of solid and fluid is used by specifying the parameters in *CONSTRAINT_LAGRANGIN_IN_SOLID. The blood is allowed in a Eulerian mesh space defined by *INITIAL_VOID. Simulations were undertaken to define the effect of blood flow on the behaviour of the three-layer aortic model. During this analysis blood is confined to the artery at the ends of the aorta.

2.1.4 FE model of aorta under loading
Several modes of loading were simulated including tension, torsion and bending. Torsion was included to mathematically determine the ultimate shear stress at the point of failure. Tension was modelled by effectively stretching the model. Each load was applied at a rate of 1 ms–1 over the duration of 1 s. During this period the intraluminal representation of blood pressure was increased from a mean of 86.6 mmHg to 146 mmHg. The ultimate strains of three layers are adopted from Holzapfel's test [15]. The relative failure profiles of the three layers under different loading conditions were compared. The first principal strain means the maximum principal strain. Under the tensile and bending loading the direction of the first principal strain is the circumferential direction of aorta tubes, while the direction of the principal strain is between the longitudinal and circumferential direction of the aorta tube under the torsion loading. The first failed element is assumed to fracture in the direction that is perpendicular to the first principal strain because the first principal strain is chosen as the failure criterion in this model.


   3. Results
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
4. Discussion
 5. Conclusion
 Appendix A
 References
 
3.1 Tension
Following the application of a tension load at 1 m s–1 for 1 s with a simulated pressure, the pressure rises from 86.6 mmHg to 146 mmHg (Fig. 2a and b), we witnessed the first failed element in the intima at 100 ms. This is represented graphically in Fig. 6 along side other loading modes showing tension results in the longest time to failure.


Figure 2
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  		Fig. 2. (a) First principal stresses under tension at initial mean blood pressure. (b) Maximum principal strain under tension loading at the onset of failure of aorta FE model.

 

Figure 6
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  		Fig. 6. The history of maximum strain of tension, bending and torsion at the first failed elements.

 
3.2 Bending
Similarly, the application of a bending load at 1 ms–1 for 1 s with a simulated pressure, the pressure rises from 86.6 mmHg to 146 mmHg (Fig. 3a and b), we saw the first failed element in the adventitia at 50 ms. This is also represented graphically in Fig. 6 along side other loading modes showing that bending results in the quickest time to failure.


Figure 3
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  		Fig. 3. (a) Maximum principal strain under bending loading at the onset of failure of aorta FE model. (b) von Mises stresses. The maximum principal strain under bending loading at the onset of failure of aorta FE model.

 
3.3 Torsion
Again, during the application of a torsion load (1 ms–1 for 1 s with a simulated pressure, the pressure rises from 86.6 mmHg to 146 mmHg) (Fig. 4a and b), we observed the first failed element in the intima at 96 ms. This is also represented graphically in Fig. 6 along side other loading modes.


Figure 4
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  		Fig. 4. (a) The maximum principal stresses under torsion loading at the onset of failure of aorta FE model. (b) Maximum principal strain under torsion loading at the onset of failure of aorta FE model.

 
3.4 Behaviour of the three-layer FE aorta model in the presence of blood
In order to understand the influence of blood flow on the stresses and strains of the aortic wall under complex loading, we conducted the model under a bending load with blood flow. The model consisted of a steel guillotine (2.4 kg), top and bottom foams, fluid-filled three-layer aortic model and blood Eulerian space, which is shown schematically in Fig. 5 . The FE model is created to represent the descending thoracic aorta. The thickness of intima, media and adventitia is 1.81 mm, 2.10 mm and 1.91 mm respectively. The initial velocity of the indenter is 3700 mm/s. The material properties are adopted from Gayzik et al. [17]. We demonstrated the effect of blood flow within the aorta during a bending load with the aorta fully occluded and with the aorta partially occluded (data not shown). A second experiment was run with the aorta partially occluded. These simulations demonstrate higher intimal stress during total occlusion and at the point of narrowest radius due to intimal compression. The experiments illustrate that the deformation of the foams and aorta are reasonable and reveals that the maximum first principal stress occurs in the intima. In addition, they demonstrate that when the top of the intima contacted the bottom of the intima and blood is blocked to flow, the maximum strain appears in the media. These results show that the maximum stress always happened in the intima because the material of the intima is much stiffer than the other two layers. The maximum strain always occurred in the media and adventitia.


Figure 5
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  		Fig. 5. The first principal stresses of aorta FE model with intraluminal blood.

 

   4. Discussion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
5. Conclusion
 Appendix A
 References
 
The exact aetiology of blunt traumatic aortic rupture has remained elusive, with a large number of putative mechanisms described in the literature [2]. At the centre of the controversy is a desire to explain the injury profile of BTAR which typically occurs at the isthmus as a circumferential tear initiated in the intimal layer, despite a wide range of trauma scenarios. To date, all the hypotheses around blunt trauma and aortic injury are based on a variable contribution from mechanical deformation and intraluminal hypertension. We believe however that suprapressurisation of the aorta occurs during anticipation of impact and the brace response, and simply serves to place the aorta in a high tensile, vulnerable state, with vessel deformation ultimately initiating injury. In addition, deformation is not mechanically simple but must correspond to a complex combination of both relative motion of the structures within the thorax and local loading of the tissues either as a result of their anatomy or due to the nature of the impact. With this hypothesis in mind we created and used the three-layer FE model to examine the effect of complex loading scenarios of the layers of the aorta simulating motion during trauma.

4.1 Mechanics of the aorta
Detailed biomechanical experimentation has provided some insight into the injury profile of this condition [11]. Early investigators excluded a sudden rise in blood pressure as a cause for BTAR rationalising that if the aorta were an isotropic cylindrical vessel under pressure it would rupture axially rather than transversely. However, the aorta is anisotropic and several authors point out that the scenario is further complicated by the fact that the aorta is unlikely to be a perfect cylinder during blunt trauma and this may be contributory in the observed transverse tear [11,18,19]. Creating such loading conditions in tissue experimentation is challenging and is an area where a finite-element model is applicable.

4.2 Simulations of complex loading
The novel aspect of the approach described in this manuscript is that we can use an anatomically representative three-layer model of the aorta, with biofidelic models, and simulate complex loading conditions. This allows us to study layer specific mechanical behaviour during deformation and study the relative vulnerability of the aorta to different modes of loading. In addition the effect of intraluminal blood flow and partial versus complete occlusion of the aorta may be examined. Several aspects of this work are noteworthy:

(a) Feasibility of FE process. This work establishes the credentials of the finite-element process to recreate a biofidelic three-layer aorta model whose behaviour reflects published experimental data. This data will be central to the development of a more sophisticated model to study the behaviour of the aspects of acute aortic syndrome including intramural haematoma.
(b) Relative contribution of intraluminal hypertension and mechanical load. We have previously suggested that BTAR results from a combination of intraluminal hypertension and mechanical deformation. The nature of the relative contribution in different circumstances has been unknown. Previous data have questioned the importance of intraluminal hypertension on two grounds [20,21]. Firstly, if it were the principal mode of failure the aorta would rupture at multiple points. The literature tells us the primary site of rupture is the isthmus. Secondly, exceedingly high pressures have been required to rupture ex vivo aortic tissue in the range of several thousand mmHg. The present work suggests that rupture may occur at mean pressures in the range of hundreds of mmHg in the presence of a load like tension, torsion and bending. This underlies the importance of mechanical load in the aetiology of this condition and helps explain why rupture may occur following low impact trauma with minimal intraluminal hypertension.
(c) Load dependent modes of failure. Clearly, (compared with tension, bending and torsion at the same loading speed), bending results in relatively early failure with primary adventitial injuries, compared to tension and torsion where primary intimal injury is seen. Traditionally the literature has told us that BTAR results from a primary intimal injury. However, clinical experience has shown us that some patients suffer a primary adventitial injury with no medial or intimal disruption; a finding which has up until now been difficult to understand. Within the limits of the model it may be possible to conclude that such injuries are caused by a principal bending mechanism of injury.
(d) Delamination injury. The principal foci of stress during bending in the presence of blood are seen to be in areas of compression at the narrowest radius. This suggests a possible point of delamination or partial thickness injury, which may be important in understanding acute aortic syndrome.
(e) Intimal injury. From the view of material properties, the reason why the intima ruptures first is that the material is stiffer than other two layers. Due to the fact that the fibres are oriented in longitudinal direction, the ultimate strain and stress of intima in longitudinal is smaller than that from circumstantial direction. This is one reason for intimal rupture in the circumstantial direction.
(f) Influence of blood flow. This work illustrates that the deformation of the foam reveals that the maximum first principal stress occurs in the intima. However, our data shows that the top of the intima contacted the bottom of the intima and blood is blocked to flow indicating that the maximum strain appears in the media. Our results show that the maximum stress always happened in the intima because the material of the intima is much stiffer than the other two layers. The maximum strain always occurred in the media and adventitia (Fig. 7).


Figure 7
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  		Fig. 7. Schematic representation of the forces acting through the aorta during blunt trauma [23].

 
4.3 The FE process and its limitations and possibilities
In this paper, a simplified three-layer aorta model is created with physiological material properties adopted from the human cadavers. It is an essential step in the development of a method to understand the complexities blunt traumatic aortic rupture. Constitutive equations are critical for obtaining a deeper insight into the physiological and the pathological load carrying mechanisms in aortic tissues. To establish orthotropic material models under complex quasi-static and dynamic loading is the key to developing a material model of the aorta. In order to validate the predictive capability of the models with respect to physiological loading states, comparisons between data from corresponding multi-axial tests and FE model responses must be performed. Furthermore, the residual stresses and deformations at zero-load state are very important factors that will have significant influence on the results and therefore residual stresses and strains at zero loading needs to be considered in future models. Considering the marked differences in the mechanical properties of the constitutive layers, the mechanical interplay between the three layers in the intact arterial wall must also be mediated by (large) residual deformations related to each arterial layer. Experimental studies on aged human arteries have demonstrated significant layer-specific residual strains in the intact arterial wall for femoral and iliac arteries [22]. The influence of the pressure and flow wave of blood on deformability of aortic tissues needs to be studied further. For considering the interaction between fluid and solid, the numerical methods necessitate comparison. The ultimate goal is to identify and describe the potential mechanisms of injury in various impact modes and to determine ways to identify the crash characteristics that produce aortic injuries. Furthermore, to ascertain injury tolerances and injury risk in vehicle collisions, an entire thorax model containing main parts around the aorta needs to be created. In order to get the correct impact loading to the aorta in real vehicle crashes, full vehicle collisions should be simulated. The results of aortic injury should be comparable with cadaver tests. Although much work must be performed to reach our final goal, the development of an appropriate layer-specific artery FE model is essential, which was the aim of this analysis. Ultimately we aim to produce a dynamic and anatomically detailed complex FE model, which simulates the behaviour of partial thickness injuries to large vessels, and acts as a clinically useful predictive tool. Such a model should give us important information on mechanism of injury and victim profile in vehicle related trauma. We are performing concurrent laboratory investigation of the behaviour of aortic tissue during mechanical deformation in an attempt to validate the results of this finite-element analysis.


   5. Conclusion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
Appendix A
 References
 
This work confirms the feasibility of using a three-layer FE model of the aorta, with representation of intraluminal blood flow, to study complex loading patterns during blunt trauma. Our data suggest that the relative contribution of intraluminal hypertension to BTAR is lower in the presence of complex loading by tension, torsion and bending. In addition, failure of the aorta is load dependent with bending causing a relatively early primary adventitial failure, while tension and torsion result in a relatively delayed primary intimal failure. This indicates that the form of mechanical loading may be primarily responsible for the particular features of a given aortic injury.


   Appendix A
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 Appendix A
References
 
Conference discussion

Dr C. Yankah (Berlin, Germany): Did you consider also diastolic hypertension as an important factor for aortic rupture is concerned. Were the diastolic pressures higher as normal?

Dr Zhao: In this model we considered mean pressure. The purpose of the simulations is to find severe external impact loadings causing aorta blunt trauma rupture.

Dr S. Schueler (Newcastle Upon Tyne, UK): Is there any sort of follow-up on this model? Are you planning to use the human aorta as well, like a piece of healthy human aorta? Is that something which you are planning as well?

Dr Zhao: Our current model is a human aorta model including material properties and the geometry of the model. We have studied aorta blunt trauma aorta rupture by three approaches, including aorta injury impact case analysis, computer modeling and cadaver tests. We have developed a full body model. We will continue developing three-layer aortic models, such as introducing residual stresses and deformations, orthotropic material model. And then we will include an updated aorta model into the full human body model to study acute aorta syndromes, either following trauma or aneurysms.


   Acknowledgments
 
Authors greatly appreciate Dr G.A. Holzapfel for his support in references.


   Footnotes
 
{star} Presented at the 21st Annual Meeting of the European Association for Cardio-thoracic Surgery, Geneva, Switzerland, September 16–19, 2007.

{star}{star} The funding for this research has been provided [in part] by private parties, who have selected Dr Kennerly Digges [and FHWA/NHTSA National Crash Analysis Center at the George Washington University] to be an independent solicitor of and funder for research in motor vehicle safety, and to be one of the peer reviewers for the research projects and reports. Neither of the private parties have determined the allocation of funds or had any influence on the content of this report.


   References
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 References
 

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