EJCTS Click here to go to Edwards website
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Eur J Cardiothorac Surg 2008;33:995-1001. doi:10.1016/j.ejcts.2008.02.029
Copyright © 2008, European Association for Cardio-thoracic Surgery. Published by Elsevier. All rights reserved.
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to Personal Folders
Right arrow Download to citation manager
Right arrow Author home page(s):
Michael P. Poullis
Aung Oo
Right arrow Permission Requests
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Poullis, M. P.
Right arrow Articles by Poole, R. J.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Poullis, M. P.
Right arrow Articles by Poole, R. J.
Related Collections
Right arrow Great vessels

Ascending aortic curvature as an independent risk factor for type A dissection, and ascending aortic aneurysm formation: a mathematical model

Michael P. Poullisa,*, Richard Warwicka, Aung Ooa, Robert J. Pooleb

a Department of Cardiothoracic Surgery, Thomas Drive, Liverpool L14 3PE, United Kingdom
b Department of Engineering, University of Liverpool, United Kingdom

Received 23 August 2007; received in revised form 12 February 2008; accepted 14 February 2008.

* Corresponding author. Address: The Cardiothoracic Centre, Thomas Drive, Liverpool L14 3PE, United Kingdom. Tel.: +44 151 293 2456/2398; fax: +44 151 293 2254. (Email: mike.poullis{at}ctc.nhs.uk).


   Abstract
Top
 Abstract
1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 Appendix B
 References
 
Objective: To develop a mathematical model to demonstrate that ascending aortic curvature is an independent risk factor for type A dissections, in addition to hypertension, bicuspid aortic valve, aneurysm of ascending aorta, and intrinsic aortic tissue abnormalities, like Marfan's syndrome. Methods: A steady state one-dimensional flow analysis was performed, utilising Newton's third law of motion. Five different clinical scenarios were evaluated: (1) effect of aortic curvature; (2) effect of beta-blockers, (3) effect of patient size, (4) forces on a Marfan's aorta, and (5) site of entry flap in aortic dissection. Results: Aortic curvature increases the forces exerted on the ascending aorta by a factor of over 10-fold. Aortic curvature can cause patients with a systolic blood pressure of 80 mmHg to have greater forces exerted on their aorta despite smaller diameters and lower cardiac outputs, than patients with systolic blood pressures of 120 mmHg. In normal diameter aortas, beta-blockers have minimal effect compared with aortic curvature. Aortic curvature may help to explain why normal diameter aortas can dissect, and also that the point of the entry tear may be potentially predictable. Aortic curvature has major effects on the forces exerted on the aorta in patients with Marfan's syndrome. Conclusions: Aortic curvature is relatively more important that aortic diameter, blood pressure, cardiac output, beta-blocker use, and patient size with regard to the force acting on the aortic wall. This may explain why some patients with normal diameter ascending aortas with or without Marfan's syndrome develop type A dissections and aneurysms. Aortic curvature may also help to explain the site of entry tear in acute type A dissection. Further clinical study is needed to validate this study's finding.

Key Words: Cardiac • Aortic • Dissection • Aneurysm


   1. Introduction
Top
 Abstract
 1. Introduction
2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 Appendix B
 References
 
The imbalance between the forces exerted on the ascending aorta and its biological strength determine its fate, be it a normal ageing process, aneurysmal dilatation or acute dissection.

Risk factors for dissection of the ascending aorta include hypertension, bicuspid aortic valve [1], aneurysm of ascending aorta, and intrinsic aortic tissue abnormalities, like Marfan's syndrome [2], Loeys–Dietz syndrome [3], or Ehlers–Danlos syndrome [4]. Risk factors for aneurysm formation of the ascending aorta are essentially identical.

Elective surgery of the ascending aorta is solely dictated by its diameter [5] (in the absence of concomitant valvular or coronary disease); however, with the recent widespread introduction of 3D CT reconstruction [6] of the ascending aorta becoming widespread, the degree of curvature of the ascending aorta can now be easily evaluated (Fig. 1 ). Previously invasive investigations like aortography would have been the only investigation available. Cardiac surgeons are well aware of the differing curvatures of patients ascending aorta immediately upon entering the pericardial space.


Figure 1
View larger version (67K):
[in this window]
[in a new window]

  		Fig. 1. 3D CT reconstructions allow non-invasive assessment of aortic curvature.

 
Calculating the forces imparted on the aortic wall secondary to blood flow provides a quantitative assessment of the force that the aorta is under due to its 3D geometric shape. The greater the forces exerted on the aorta the more likely it is to dissect or become aneurysmal, due to Laplace's law.

To determine the possible clinical importance of aortic curvature, five different clinical scenarios were evaluated: (1) effect of aortic curvature and its relative effect compared with (2) beta-blockers; (3) patient size; (4) a Marfan's aorta; and (5) site of entry flap in aortic dissection.

Due to the large number of variables studied a mathematical model was developed to provide proof of principle (Fig. 2 ).


Figure 2
View larger version (11K):
[in this window]
[in a new window]

  		Fig. 2. Aortic curvature model.

 

   2. Methods
Top
 Abstract
 1. Introduction
 2. Methods
3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 Appendix B
 References
 
2.1 Aortic curvature definition
As currently no definition exists of aortic curvature, we define it as the angle between the perpendicular to the plane of the aortic valve, and the perpendicular to the cross section at the origin of the innominate artery (Fig. 2).

2.2 Cardiovascular values utilised in the models
To maintain clinical relevance, for calculation purposes the cardiac output was varied between 3 and 6 l/min, the systolic blood pressure 110–150 mmHg, and ascending aortic diameter 20–40 mm (i.e. non-aneurysmal). Aortic curvature was varied from 10° to 90°. The body's natural negative intrathoracic pressure was not included in this model. The aortic valve was assumed to be anatomically normal for analysis, with blood ejected at right angles to the plane of the valve.

2.3 Steady state model
A steady state one-dimensional flow analysis was performed, utilising Newton's third law of motion (Fig. 7). Mathematical derivation is detailed in Appendix B, but the force exerted on the aorta can be summarised in Eq. (1).


Formula 1

(1)
where p, blood pressure; B, atmospheric pressure; A, cross sectional area of aorta; {theta}, aortic curvature; Formula mass flow rate within lumen of aorta; V, Velocity of flow; Rx, force on aortic wall in x direction; Ry, force on aortic wall in y direction; Rz, resultant force on aortic wall.


Figure 7
View larger version (16K):
[in this window]
[in a new window]

  		Fig. 7. Diagrammatic representation of mathematical model, and the variables utilised.

 
2.4 Effect of beta-blockers
Previous work has demonstrated that beta-blockers reduce the peak velocity of blood in the ascending aorta from 130 cm/s to about 80 cm/s [7]. In addition beta-blockers reduce systolic blood pressure and cardiac output. We assumed a 10% reduction in blood pressure (140 mmHg vs 126 mmHg) and cardiac output (5 l/min vs 4.5 l/min) for these calculations. By inserting these values into Eq. (1), the effect of beta-blockade can be modelled. The aortic diameter was 4 cm for all calculations.

2.5 Effect of patient size
To model for the effects of patient size, the effects of aortic curvature was compared in 50, 70, 90, and 110 kg patients. The associated ascending aortic diameters, cardiac outputs, and blood pressures utilised are shown in Table 1 .


View this table:
[in this window]
[in a new window]

  		Table 1 Variables utilised in calculating forces acting on ascending aorta for different body sizes.
 
2.6 Forces on a Marfan's aorta
Previous work has demonstrated that the elasticity of a Marfan's aorta has two components separated by a threshold point [8]. Up to the threshold point the elasticity is determined by elastin, and above the threshold it is determined by collagen. The blood pressure determines on which point of the elasticity curve a particular patient is. Typically a pressure of 120 mmHg ensures that the aortic elasticity is due to collagen, and a blood pressure of 80 mmHg ensures the aortic elasticity is due to elastin. The forces in a Marfan's aorta was thus modelled at 120 and at 80 mmHg, with a cardiac output of 5.0 l/min, and ascending aortic diameters of 4.0 cm (i.e. non-aneurismal).

2.7 Site of aortic dissection
The height of impact of the blood above the aortic valve ejected was calculated. This can be shown to be

Formula (2)
where H, height above the aortic valve; R, radius of aortic curvature; {theta}, aortic curvature.


   3. Results
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
4. Discussion
 5. Conclusion
 Appendix A
 Appendix B
 References
 
3.1 Steady state model
3.1.1 Aortic curvature
As the curvature in the ascending aortic increases (Fig. 3a) from straight to curved (90°–10°), the force on the aortic wall increases by a factor of over 10, this is despite a normal aortic diameter, normal blood pressure and normal cardiac output.


Figure 3
View larger version (28K):
[in this window]
[in a new window]

  		Fig. 3. (a) Effect of aortic curvature on the reaction force acting on the ascending aorta. Model variables: aorta was 3.5 cm in diameter, systolic blood pressure was 140 mmHg, and the cardiac output 5 l/min. (b) Effect of diameter on the reaction force acting on the ascending aorta. Model variables: systolic blood pressure was 140 mmHg, and the cardiac output 5 l/min.

 
3.1.2 Diameter effects
As would be predicted, as the diameter of the ascending aorta increases so does the reaction force acting on the ascending aorta (Fig. 3b). As the ascending aorta diameter increases in size from 3.5 to 5.5 cm it can be seen that the magnitude of increase in force on the wall increases by about four times. However, the absolute increase in force is greatest the more curved the ascending aorta is, with over 10-fold increase in the total force exerted on the ascending aorta as curvature increases from straight to curved.

3.1.3 Blood pressure
It can be seen from Fig. 4a that as the blood pressure increases so does the reaction force acting on the ascending aorta. As the patient's systolic blood pressure increases from 110 to 150 mmHg, it can be seen that the increase in force on the wall is 1.3-fold. However, as the curvature increases the force increases to over 10-fold.


Figure 4
View larger version (17K):
[in this window]
[in a new window]

  		Fig. 4. (a) Effect of Blood pressure on the reaction force acting on the ascending aorta. Model variables: aortic diameter was 3.5 cm, and the cardiac output 5 l/min. (b) Effect of cardiac output on the reaction force acting on the ascending aorta. Model variables: aortic diameter was 3.5 cm, and the blood pressure 140 mmHg.

 
3.1.4 Cardiac output
From Fig. 4b it can be seen that as the cardiac output increases from 4 to 7.5 l/min the reaction force acting on the ascending aorta is virtually unchanged. However, as the aortic curvature increases the force acting on the ascending aorta increases to over 10-fold.

3.2 Effect of beta-blockers
Beta-blockers had a relatively small effect, (Fig. 5a), on reducing the force acting on the ascending aorta by a factor of 1.2. It should be noted that in the calculations for the effect of beta-blockers the blood pressure, cardiac output and aortic blood flow velocity were all reduced appropriately, but despite this, beta-blockers have a relatively small effect compared to aortic curvature. As aortic curvature increased this had greater than 10-fold increase in the force acting on the ascending aorta.


Figure 5
View larger version (15K):
[in this window]
[in a new window]

  		Fig. 5. (a) Effect of beta-blockers on the reaction force acting on the ascending aorta. Model variable: aortic diameter was 3.5 cm. (b) Effect of patient size on the reaction force acting on the ascending aorta. Model variables: aortic diameter, blood pressure and cardiac output are detailed in Table 1.

 
3.3 Effect of patient size
It can be seen, (Fig. 5b), that the larger the patient the greater the forces acting on their aorta for a given aortic curvature. However, patients who are 50 kg can have forces exerted on their aorta that are greater than those experienced in a 110 kg patients, depending on their aortic curvature. A 50 kg patient with an aortic curvature of 10° has the same force on their aortas as a 110 kg patient with a curvature of 65°. This is despite the 110 kg patient having a higher systolic blood pressure (140 mmHg vs 110 mmHg), a larger aortic diameter (4.5 cm vs 3.0 cm), and a higher cardiac output (5.5 l/min vs 4.0 l/min). Patients who are 110 kg only start to have greater forces exerted on their aortas when their aortic curvature is less than 60°.

3.4 Forces on a Marfan's aorta
It can be seen, (Fig. 6a), that patients who have a systolic blood pressure of 80 mmHg can have forces exerted on their aorta that are greater than those experienced in a patient with a systolic blood pressure of 120 mmHg. Patients with a systolic blood pressure of 120 mmHg only start to have greater forces exerted on their aortas when their aortic curvature exceeds 45°.


Figure 6
View larger version (10K):
[in this window]
[in a new window]

  		Fig. 6. (a) Effect of blood pressure on the reaction force acting on a Marfan's ascending aorta. Model variables: cardiac output was 5.0 l/min, and ascending aortic diameter of 4.0 cm (i.e. non-aneurismal). (b) Effect of aortic curvature on height of impact above the aortic valve of blood being ejected through the aortic valve.

 
3.5 Site of aortic dissection
The height above the aortic valve where the aorta receives the greatest impact from blood being ejected through the aortic valve increases the straighter the ascending aorta (Fig. 6b). This calculated variable is independent of blood pressure, cardiac output, beta-blocker therapy, intrinsic aortic tissue abnormality and ascending aortic diameter (Fig. 7 ).


   4. Discussion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
5. Conclusion
 Appendix A
 Appendix B
 References
 
We have shown that aortic curvature is, potentially, a more important factor than diameter, blood pressure or cardiac output with regards to the forces on the aortic wall. With the introduction of 3D CT reconstructions the curvature of the ascending aorta can now be easily measured. Conventional 2D CT plane films are not adequate to calculate aortic curvature.

The force exerted on the ascending aorta is dependent on the 3D geometry of the vessel and the pressure and flow within the vessel. Assuming a smooth walled rigid vessel, the tensile physical characteristics of the vessel have no effect on determining this force. However, the vessels’ physical properties determine its fate due to the forces imposed on it.

Aortic rupture and aortic dissection are known adverse effects that occur to patients on surgical waiting lists. The frequency is increased with patients with known aneurysms. Demonstration of the importance of aortic curvature will enable clinicians to prioritise surgical intervention with regard to aortic diameter, extent of aneurysm, and aortic curvature. In the past the aortic diameter was the major risk factor for aortic rupture or dissection. Up to a third of aortic dissections occur in patients with no demonstrable tissue defect and with normal ascending aortic diameters. Aortic curvature may help to explain this.

Beta-blockers are the mainstay of medical management in aortic dissections; however, it can be seen that their effect is only modest compared to the effect of aortic curvature. The cumulative effect of beta-blockers on peak aortic blood flow velocity (130 cm/s vs 80 cm/s), cardiac output (5 l/min vs 4.5 l/min) and systolic blood pressure (140 mmHg vs 126 mmHg) can result in the forces on the ascending aorta being reduced by 1.2-fold. Aortic curvature reduced the force by a factor of over 10-fold.

Patient size is an important consideration with regard to the forces acting on the aortic wall. For any given aortic curvature a 110 kg patient will have greater forces acting on their ascending aorta than a 50 kg patient; however depending on the aortic curvature, the 50 kg patient (aortic curvature between 0° and 10°) may potentially have more than double the forces acting on their aorta than a 110 kg patient (aortic curvature greater then 80°).

Interpretation in the medical literature of the stresses and strains exerted on the ascending aorta in normal and Marfan patients is difficult due to the variable use of the following terms: Young's modulus, Petersons's pressure–strain elastic modulus, arterial stiffness constant, stiffness [9], static aortic compliance, compliance [10], elasticity, distensibility, and extensibility, when referring to essentially the same physical property of the aorta. We based our calculations on previously published elastance data [8].

Aortic elasticity is determined by its elastin and collagen content. At higher pressure (>120 mmHg) collagen is relatively inelastic, and consequently increases the stresses experienced by the ascending aorta. The Young's modulus (the ratio between stress and strain) in a Marfan's aorta is twice that of a normal aorta. We have shown that the forces exerted in a Marfan's aorta can be greater with a blood pressure of 80 mmHg, compared to a pressure of 120 mmHg, depending on the aortic curvature. Patients with Marfan's syndrome can dissect despite normal aortic diameter [11]. To date the only risk factor for this occurrence is familial history of dissection [12]. Aortic curvature may thus help to partially explain dissection in a non-aneurysmal Marfan's aorta.

The most common site of an entry tear in type A dissection is just above the sinotubular junction. The second most common site is just before the innominate artery. We have shown that the aortic curvature affects the site of impact of the ejected blood. Thus aortic curvature in a non-diseased aorta may help predict the entry site of a future aortic dissection.

Aortic elongation can occur in the absence of dilatation. As the aortic valve position is relatively fixed by the cardiac geometry and the innominate artery is relatively fixed by the head and neck structures, increased aortic curvature is the only possible result. Anecdotally this can be sometimes observed at surgery in Marfan's patients with isolated root dilation. Patients with Loeys–Dietz syndrome develop elongated tortuous and dilated arteries that are prone to dissection and rupture [13]. Elongation and tortuosity are synonymous with increased curvature.

Aortic stenoses with or without a bicuspid valve are known risk factors for dissection or aneurysm formation in the ascending aorta. Our model could be extended to analyse these scenarios, via modelling the effects of jet flow through the valve, but the same principle of the effects of aortic curvature still holds regardless of angle and direction of jet.

The geometry of the ascending aorta affects the fluid dynamics of the blood flow in the arch. Having demonstrated that the geometry of the ascending aorta is potentially crucial to the development of dissections or aneurysms, the aortic arch now needs to be studied. Aortic arch curvature has recently been shown to be associated with enhanced systolic wave reflection, central aortic stiffness, and increased left ventricular mass [14].

4.1 Clinical implications
Aortic curvature in addition to aortic diameter may need to be considered when deciding on when to operate on the ascending aorta, should this mathematical treatise prove to be correct in humans.

4.2 Study limitations
This study was a mathematical treaty to apply a basic science concept in fluid dynamics to cardiac surgery. The mathematical analysis assumed Newtonian flow in a rigid tube, which was steady state. Future work in a clinical setting is now needed to validate this work.


   5. Conclusion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
Appendix A
 Appendix B
 References
 
Aortic curvature is relatively more important than aortic diameter, blood pressure, cardiac output, beta-blocker use, and patient size with regard to the force acting on the aortic wall. This may explain why some patients with normal diameter ascending aortas with or without Marfan's syndrome develop type A dissections, and aneurysms. In addition aortic curvature may help to explain why some patients dissect just above the sinotubular junction, and others just proximal to the innominate artery.

Aortic curvature should now be studied in humans as a possible risk factor for dissection and potentially influencing timing of ascending aortic replacement surgery.


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

Dr L. von Segesser (Lausanne, Switzerland): Everybody knows that dissection can occur at any diameter, and in small patients you can have it and in bigger ones, of course, also. We also know that when we drive a car in a narrow curve, that there is a lot of centrifugal force, and you have to fight against it.

We, I think, also know that the human body is quite complex machinery. We have non-Newtonian fluid. We have the compliant vessels. We have pulsatile flow, and the pattern of the flow in the ascending aorta has a spiral form.

So when you did your analysis, you had to make some assumptions and simplifications, and you have already told us that you did a two-dimensional analysis. I have also observed that your aorta has a straight inflow and a straight outflow, which is a major simplification, of course.

And I would like to know what your assumptions were with regard to compliance, what your assumptions were with regard to the flow pattern. And finally, with regard to longitudinal compliance, there is also a problem that you have to answer.

Dr Poullis: You are exactly right in everything you said. The blood, as an argument, it's almost certainly a non-Newtonian fluid. And when you analyse, you have pulsatile flow, non-pulsatile flow, it could be steady state and non-steady state, and you can have turbulent and non-turbulent, and you can have a rigid vessel and you can have an elastic vessel. And elasticity, exactly as you said, can be longitudinal and circumferential.

We had to take our advice from the engineer who did the analysis for us. And he said yeah, yeah, I can do all of that, but you’ve got so many variables too that are not really known, things like the Young's modulus of the aorta, it's just not known. Because, of course, it is known in healthy people and it is known in a patient that has died, but the variation is so enormous, he said you need to look at this in simple terms. So he did the analysis the way he did where we looked at the force acting on the wall of the aorta assuming it's a rigid vessel because then the material of the wall of the aorta is immaterial to the mathematical analysis.

He said, of course, you will have more error, but he said you will get an error between 10 and 20% by ignoring all of the factors which you quite correctly stated are important. And he thinks if you’ve got an important point, the 20% error was okay. Because our differences that we found in curvature were so great, the 20% error he thinks is not so important for the conclusion.

You’re exactly right, though. For working out the exact force on the aorta, you need all the variables you said.

Dr von Segesser: There is another point which I would like to stress: if you have rapid increase in diameter for the aorta, and you look at this like a balloon, which is another simplification, then the overall mass of wall is constant. But the larger the diameter, of course, the thinner the wall. Can you comment on that?

Dr Poullis: Yes. That's partly why we picked a rigid tube because you’re exactly right. The stresses and the strains, the strain will change as stress will change in that situation. And that's why we picked the simpler version of doing it because it's the principle of curvature we wanted to say was important.

Dr J. de Hart (Eindhoven, Netherlands): I do have two questions. The first one is you state that you’ve used the similar cardiac outputs in the different aortic diameters; is that correct?

Dr Poullis: We used the same kind of cap with the different diameters, yes.

Dr de Hart: Yes.

Dr Poullis: We kept the cardiac output constant.

Dr de Hart: Yes. But that means that you have a lower velocity in your aorta.

Dr Poullis: Yes.

Dr de Hart: Which has a huge impact on the actual force that you’re calculating because it's probably much less than we would expect.

Dr Poullis: The engineer, he tells me he altered the velocity dependent on the cross-section of the aorta because if you varied the cardiac output – well, if you have the same cardiac output and a different diameter, you are exactly right, the bigger the aorta, the lower the velocity. And he included that in his calculation he tells me.

Dr de Hart: But if I’m not mistaken, you showed that the force was much higher in the larger aorta whereas you have a lower velocity?

Dr Poullis: Yes.

Dr de Hart: So you have a lower impact?

Dr Poullis: Because you have a wider diameter, so you have greater Laplace forces as well. There's two components to the force that acts on the wall of a vessel. There's the diameter – well, there's a number of factors actually. There's the diameter of the vessel that's important but also the velocity of the blood.

And that's been the problem with a number of the analyses. They do steady-state analysis even though they have a pulsatile pressure waveform. There's no flow in the vessel, so they’ve missed the second component.

Dr de Hart: The other question that I have is you are ignoring elasticity of the aortic wall?

Dr Poullis: Yes.

Dr de Hart: I think it is really important because the interaction of the blood flow with the wall is important for the actual force that you’re going to calculate.

And the other thing is, what about rigid body motion of the aorta?

Dr Poullis: I’ll come back. There's two points there.

Dr de Hart: Okay.

Dr Poullis: With regard to the elasticity of the aorta, you’re completely correct. We decided not to include it, though, for simplicity of the analysis.

Dr de Hart: Yeah, yeah, I understand that. I mean ...

Dr Poullis: But we did include it for the Marfan's, and that's important for two components to the elasticity of the aorta. That's why I picked the 80 systolic to prove the point. No one has an 80 systolic walking around who has got Marfan's. It was just to prove the point.

Your second point was?

Dr de Hart: The rigid body motion of the aorta.

Dr Poullis: Yes. That's one of the theories for how you get aortic dissection, isn’t it? And there's a bit of a debate as to whether or not that's correct. I know it was published in Circulation about two or three years ago. And one of the problems is it doesn’t explain the risk of dissection being higher in people who have had previous cardiac surgery where the motion is reduced.

And also, the one condition that should be associated with a high rate of dissection is aortic regurgitation because you have a massively increased root motion, but that's not the case clinically. So there are a couple of flies in the ointment of that theory.

Dr de Hart: Yeah.

Dr Poullis: But it must be one – aortic curvature is not going to be the only cause of dissection. I’m not deluding myself. I think this is a possible factor that has not been considered so far to add to all the other factors we already know about. And there's probably more we still haven’t worked out.

Dr de Hart: You know, from an engineer point of view ...

Dr Bachet: Gentlemen, sorry, but we are running short of time, so maybe you can go on with that discussion in the corridor later on.


   Appendix B
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 Appendix A
 Appendix B
References
 
Basic fluid mechanic theory dictates that the force exerted on fluid in aorta due to fluid motion (Fig. 7) (change of momentum) can be calculated from Eq. (3).

Formula 2(3)

Assumptions

• Quasi steady flow (peak values)
• Two-dimensional

Formula 3(4)

Eq. (3) simplifies to (see Fig. 6), Eq. (4) in x-axis, and Eq. (5) in y-axis

Formula 4(5)
Forces on aorta must be in static equilibrium, Eq. (6)

Formula 5(6)
Combining Eq. (4) and (6), yields Eq. (7)

Formula 6(7)

Similarly, combining Eqs. (5) and (6), yields Eq. (8)

Formula 7(8)

Further assumptions

(a) Pressure loss across aorta is small, therefore p1 ~ p2.
(b) Diameter change along aorta is small, therefore A1 ~ A2.
where p – B = systolic blood pressure; A = ascending aorta cross-sectional area; Formula (cardiac output) in Kg/s.

Total force (N) acting on aorta, combining Eqs. (7) and (8), yields Eq. (9)

Formula 8(9)


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


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

  1. Januzzi JL, Isselbacher EM, Fattori R, Cooper JV, Smith DE, Fang J, Eagle KA, Mehta RH, Nienaber CA, Pape LA. Characterizing the young patient with aortic dissection: results from the International Registry of Aortic Dissection (IRAD). J Am Coll Cardiol 2004;43(4):665-669.[Abstract/Free Full Text]
  2. Devereux RB, Roman MJ. Aortic disease in Marfan's syndrome. N Engl J Med 1999;340(17):1358-1359.[Free Full Text]
  3. Akutsu K, Morisaki H, Takeshita S, Sakamoto S, Tamori Y, Yoshimuta T, Yokoyama N, Nonogi H, Ogino H, Morisaki T. Phenotypic heterogeneity of Marfan-like connective tissue disorders associated with mutations in the transforming growth factor-beta receptor genes. Circ J 2007;71(8):1305-1309.[CrossRef][Medline]
  4. Gleason TG. Heritable disorders predisposing to aortic dissection. Semin Thorac Cardiovasc Surg 2005;17(3):274-281.[CrossRef][Medline]
  5. Bonow RO, Carabello BA, Kanu C, de Leon Jr. AC, Faxon DP, Freed, MD, Gaasch WH, Lytle BW, Nishimura RA, O’Gara PT, O’Rourke RA, Otto CM, Shah PM, Shanewise JS, Smith Jr. SC, Jacobs AK, Adams CD, Anderson JL, Antman EM, Faxon DP, Fuster V, Halperin JL, Hiratzka LF, Hunt SA, Lytle BW, Nishimura R, Page RL, Riegel B. ACC/AHA 2006 guidelines for the management of patients with valvular heart disease: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (writing committee to revise the 1998 Guidelines for the Management of Patients With Valvular Heart Disease): developed in collaboration with the Society of Cardiovascular Anesthesiologists: endorsed by the Society for Cardiovascular Angiography and Interventions and the Society of Thoracic Surgeons. Circulation 2006;114(5):e84-e231.[Free Full Text]
  6. Alkadhi H, Wildermuth S, Desbiolles L, Schertler T, Crook D, Marincek B, Boehm T. Vascular emergencies of the thorax after blunt and iatrogenic trauma: multi-detector row CT and three-dimensional imaging. Radiographics 2004;24(5):1239-1255.[Abstract/Free Full Text]
  7. Singer M, Allen MJ, Webb AR, Bennett ED. Effects of alterations in left ventricular filling, contractility, and systemic vascular resistance on the ascending aortic blood velocity waveform of normal subjects. Crit Care Med 1991;19(9):1138-1145.[Medline]
  8. Nollen GJ, Westerhof BE, Groenink M, Osnabrugge A, van der Wall EE, Mulder BJ. Aortic pressure-area relation in Marfan patients with and without beta blocking agents: a new non-invasive approach. Heart 2004;90(3):314-318.[Abstract/Free Full Text]
  9. De Backer J, Nollen GJ, Devos D, Pals G, Coucke P, Verstraete K, van der Wall EE, De Paepe A, Mulder BJ. Variability of aortic stiffness is not associated with the fibrillin 1 genotype in patients with Marfan's syndrome. Heart 2006;92(7):977-978.[Free Full Text]
  10. Kuecherer HF, Just A, Kirchheim H. Evaluation of aortic compliance in humans. Am J Physiol Heart Circ Physiol 2000;278(5):H1411-H1413.[Free Full Text]
  11. Neri E, Barabesi L, Buklas D, Vricella LA, Benvenuti A, Tucci E, Sassi C, Massetti M. Limited role of aortic size in the genesis of acute type A aortic dissection. Eur J Cardiothorac Surg 2005;28(6):857-863.[Abstract/Free Full Text]
  12. Antman EM. Current diagnosis and prescription for Marfan syndrome: when to operate. J Card Surg 1994;9(2 Suppl.):174-176.[CrossRef][Medline]
  13. Williams JA, Loeys BL, Nwakanma LU, Dietz HC, Spevak PJ, Patel ND, Francois K, DeBacker J, Gott VL, Vricella LA, Cameron DE. Early surgical experience with Loeys–Dietz: a new syndrome of aggressive thoracic aortic aneurysm disease. Ann Thorac Surg 2007;83(2):S757-S763.[Abstract/Free Full Text]
  14. Ou P, Celermajer DS, Raisky O, Jolivet O, Buyens F, Herment A, Sidi D, Bonnet D, Mousseaux E. Angular (gothic) aortic arch leads to enhanced systolic wave reflection, central aortic stiffness, and increased left ventricular mass late after aortic coarctation repair: Evaluation with magnetic resonance flow mapping. J Thorac Cardiovasc Surg 2008;135:62-68.[Abstract/Free Full Text]



This article has been cited by other articles:


Home page
 HeartHome page
A. F Bolger
Aortic intramural haematoma
Heart, December 1, 2008; 94(12): 1670 - 1674.
[Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to Personal Folders
Right arrow Download to citation manager
Right arrow Author home page(s):
Michael P. Poullis
Aung Oo
Right arrow Permission Requests
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Poullis, M. P.
Right arrow Articles by Poole, R. J.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Poullis, M. P.
Right arrow Articles by Poole, R. J.
Related Collections
Right arrow Great vessels

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
ANN THORAC SURG ASIAN CARDIOVASC THORAC ANN EUR J CARDIOTHORAC SURG
J THORAC CARDIOVASC SURG ICVTS ALL CTSNet JOURNALS