hemodynamic determinants of aortic dissection propagation by 2d computational modeling: implications...

Vol. 53 - No. 5 THE JOURNAL OF CARDIOVASCULAR SURGERY 631

Aortic dissection (AD) is a life threatening cardio-vascular disorder characterized by separation of

the aortic wall layers with formation of a false lu-men.1 Propagation of AD results in a variety of fatal complications including aortic rupture, aortic valve insufficiency, myocardial ischemia, and end-organ ischemia. Despite significant improvement in treat-ment strategies, in-hospital mortality rate remains overall very high at 27% based on current data from the International Registry of Acute Aortic Dissection (IRAD).2 Although AD has a relatively low incidence (approximately 3 cases in 100,000 per year), it is one of the most common aortic catastrophes.1, 3-5

Thoracic endovascular aortic repair (TEVAR) has significantly reduced mortality and become an ac-ceptable alternative to open surgery for patients pre-senting with complicated type B aortic dissection.6-8 However, TEVAR has shown no advantage over medical therapy in non-acute uncomplicated type B aortic dissection and the procedure itself carries its own risks of complications.9 The role of TEVAR in reducing mortality of acute uncomplicated type B dissection is not yet clear.10

Mechanical factors play a substantial role in de-velopment of AD. Typically, AD begins with an inti-mal tear within the aortic wall.11 Blood pressure ex-

1Division of Cardiothoracic Surgery, Department of Surgery, University of California at San Francisco

Medical Center and San Francisco VA Medical Center San Francisco, CA, USA

2Division of Vascular Surgery, Department of Surgery, University of California at San Francisco Medical

Center and San Francisco VA Medical Center San Francisco, CA, USA

J CAR DI O VASC SURG 2012;53:631-40

S. CHITSAZ 1, A. N. AZADANI 1, P. B. MATTHEWS 1, T. A. CHUTER 2, E. E. TSENG 1, L. GE 1

Hemodynamic determinants of aortic dissection propagation by 2D computational modeling: implications for endovascular stent-grafting

Aim. Aortic dissection is a life-threatening aortic ca-tastrophe where layers of the aortic wall are sepa-rated allowing blood flow within the layers. Propaga-tion of aortic dissection is strongly linked to the rate of rise of pressure (dp/dt) experienced by the aortic wall but the hemodynamics is poorly understood. The purpose of this study was to perform computational fluid dynamics (CFD) simulations to determine the relationship between dissection propagation in the distal longitudinal direction (the tearing force) and dp/dt.Methods. Five computational models of aortic dissec-tion in a 2D pipe were constructed. Initiation of dis-section and propagation were represented in 4 single entry tear models, 3 of which investigated the role of length of dissection and antegrade propagation, 1 of which investigated retrograde propagation. The 5th model included a distal re-entry tear. Impact of pressure field distribution on tearing force was de-termined.Results. Tearing force in the longitudinal direction for dissections with a single entry tear was approxi-mately proportional to dp/dt and L2 where L is the length of dissection. Tearing force was much lower under steady flow than pulsatile flow conditions. In-troduction of a second tear distally along the dissec-tion away from the primary entry tear significantly reduced tearing force.Conclusion. The hemodynamic mechanism for dissec-tion propagation demonstrated in these models sup-port the use of β-blockers in medical management. Endovascular stent-graft treatment of dissection should ideally cover both entry and re-entry tears to reduce risk of retrograde propagation of aortic dis-section.Key words: Aortic diseases - Molecular dynamics simula-tion - Aneurysm.

Corresponding author: E. E. Tseng, MD, Division of Cardiothoracic Surgery, Department of Surgery, UCSF Medical Center, 500 Parnassus Ave Suite 405W Box 0118, San Francisco, CA 94143, USA. E-mail: [email protected]

Anno: 2012Mese: OctoberVolume: 53No: 5Rivista: THE JOURNAL OF CARDIOVASCULAR SURGERYCod Rivista: J CAR DI O VASC SURG

Lavoro: titolo breve: Hemodynamic determinants of aortic dissection propagationprimo autore: CHITSAZpagine: 631-40

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CHITSAZ HEMODYNAMIC DETERMINANTS OF AORTIC DISSECTION PROPAGATION

632 THE JOURNAL OF CARDIOVASCULAR SURGERY October 2012

ble 1. There were four single-entry tear models and one double-entry tear model. One single-entry tear model was designed to show hemodynamics of a retrograde propagated dissection (Figure 1A). The other three single-entry tear models were designed to investigate the impact of dissection length on the tearing force. The only geometric difference among these three models was length of the intimal flap (l

pands the tear longitudinally within the media and eventually leads to formation of a false lumen. Un-derstanding mechanical factors associated with de-velopment of AD are critical for improving clinical management. A strong link exists between propaga-tion of AD and rate of rise of pressure (dp/dt).12 On this basis, β-blockers known clinically to control dp/dt have been the mainstay of therapy for uncompli-cated type B dissection with good results.13-15 How-ever, the mechanics by which dp/dt propagates AD is not clear.16 In this paper we examined the rela-tionship between dp/dt and AD propagation distally in the longitudinal direction by 2D computational fluid dynamics.

Materials and methods

In order to investigate the relationship between dp/dt and distal tearing force in the longitudinal direction, we constructed five 2-dimensional (2D) aortic dissection models, and conducted compu-tational fluid dynamics (CFD) simulations of flows through these models. Complex 3D shear stresses were excluded. Each model was characterized by one straight pipe that modeled the true lumen, and one side channel that modeled the false lumen. True and false lumens were interconnected with one or two entries (Figure 1), modeling dissections with ei-ther single- or double-entry tears. In the latter, one tear was the primary and the other one was the re-entry tear. Since these models were designed to primarily focus on the effects of flow acceleration and deceleration on aortic dissection propagation distally in the longitudinal direction, effects of blood flow shear stress were neglected. Thus, the com-plex 3D geometry and spiral nature of dissection were ignored and simplified 2D simulation enabled isolation of the impact of dp/dt on aortic dissection propagation distally for investigation.

A detailed list of the models is presented in Ta-

Figure 1.—Geometry and grid used in this study; A) single entry tear retrograde propagation model A4; B) single entry tear antegrade propagation model A2; C) double-tear model with entry and re-entry intimal tears.

Flow direction

Flow direction

Flow direction

A

B

C

Table I.—�Dissection models used in this study.

Model No. Number of Tears Length of Tear (mm) Dissection Propagation Direction

A1 1 35 AntegradeA2 1 70 AntegradeA3 1 120 AntegradeA4 1 70 RetrogradeA5 2 65 N/A

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HEMODYNAMIC DETERMINANTS OF AORTIC DISSECTION PROPAGATION CHITSAZ


sure difference, defined as: Δpmax(t) = Δp(x0, t) where x0 is the location of maximum magnitude of cross-membrane pressure difference (i.e. Δp(x0, t) = max |Δp (x, t)|), was examined for each model. x=0,l

Results

The focus of the current paper is on the pressure field. A representative pressure field distribution of a single entry tear antegrade dissection model subjected to pulsatile incoming flow is shown in Figure 2A, B. The pressure field of model A2 is shown at two time instants, one in the acceleration phase or systole (t=0.05s) and one in the middle of the deceleration phase or diastole (t=0.3s), re-spectively. At both time instants, the pressure dif-ference between the entry tear (point A in Figure 2) and the end of the false lumen (point B in Fig-ure 2) was less than 5 Pa. Such low pressure dif-ference was observed throughout the full systolic phase. The most significant feature of the pressure distribution, however, was the very large cross-membrane difference of surface pressure exerted on the intimal flap. During the acceleration phase, represented by t=0.05s, the pressure on the false lumen side was much higher than the true lumen side. During the deceleration phase, this trend re-versed. Subjecting the same geometrical model to a steady rather than pulsatile inflow, however, yielded a very different pressure field. The pres-sure difference between entry tear (point A) and end of dissection (point B) was still very low simi-lar to the pulsatile flow model. The cross-mem-brane pressure difference between the two sides of the intimal flap, however, was much lower with steady than pulsatile flow. The maximum pressure difference observed for the steady flow condition was 10 Pa.

The distribution of false-lumen side surface pres-sure, pf (x), true-lumen side pressure, pt(x), and cross-membrane pressure difference Δp(x) along the length of intimal flap of model A2 during pulsatile flow at the same time instants, is illustrated in Figure 3 (3a. t=0.05s and 3b. t=0.3s). Near the entry tear, the cross-membrane pressure difference was very low while the largest value of pressure difference was always observed at the end of the intimal tear. The overall tearing force acting on the intimal flap

in Figure 1B). The two-tear model geometry is illus-trated in Figure 1C.

In this study blood was assumed to be a Newto-nian fluid, and flow to be incompressible. Kinematic viscosity of blood was specified as 3×10-6 m2/s. The aortic wall was assumed to be noncompliant, i.e., no fluid-structure interaction effect was considered. A half-sine flow velocity waveform was specified at the inlet to model aortic pulsatile flow. Duration of systolic flow was 250 ms and cycle duration was 857 ms, corresponding to a heart rate of 70 beats per minute. Peak bulk velocity for pulsatile flow was set to match physiologic conditions of peak flow, 0.8 m/s. Peak Reynolds number, a dimensionless number of the ratio of inertial forces to viscous forc-es, was 6000, based on peak pulsatile flow velocity U and aortic diameter D (R = UD/ν) where ν is kinet-ic viscosity. Outlet pressure was specified as zero. Steady flow conditions with inlet velocity of 0.8m/s and outlet pressure of 0 were compared to pulsatile flow conditions. Flow was studied only during the systolic phase of the cardiac cycle.

The CFD simulation was conducted using Open-FOAM, an open-source CFD code (http://www.opencfd.co.uk). The effect of turbulence was not considered in our simulation. In OpenFOAM in-compressible flow solver, the governing equations for incompressible flows are solved using the PISO algorithm.17 The equations are discredited with a finite volume method. The distribution of false-lu-men side surface pressure, pf (x), true-lumen side pressure, pt(x), and cross-membrane pressure dif-ference, defined as Δp(x) = pf (x)-pt(x), along the length of intimal flap was determined in each of the models. The cross-membrane pressure differ-ence leads to a pressure force normal to the intimal flap. A positive pressure difference creates a pres-sure force that could tear the dissected flap from the rest of the wall, i.e., a tearing force; a nega-tive pressure difference, on the other hand, would lead to a pressure force that pushes the flap toward the outer wall. The local tearing force per unit flap width, denoted as T(Δx), acting on a small portion of intimal flap located as x with a length of Δx (Fig-ure 1) can be calculated as T(Δx) = Δp·Δx. Inte-gral of the local tearing force over length of intimal flap L leads to the overall tearing force acting on

the intimal flap: T=0∫LΔPdx. The time history of the

instantaneous maximum cross-membrane pres-

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Figure 2.—A) pressure distribution of model A2 subject to pulsatile flow condition, t=0.05s; B) pressure distribution of model A2 subject to pulsatile flow condition, t=0.3 s; C) pressure distribution of model A5 subject to pulsatile flow condition, t=0.05s; A, entry tear; B and C, two sides of intimal flap at the end of dissection in true and false lumen, respectively.

A

B

C p (Pa): 554 685 806 902 1003 1109

p (Pa): 554 685 806 902 1003 1109

A

A

B

B

C

C

p (Pa): -1043 -934 -819 -682 -559

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the retrograde dissection, model A4, and antegrade dissection, models A1-A3. During the acceleration phase, model A4 had a negative pressure difference where the pressure force pushed the flap toward the outer wall, while the tearing force and positive pres-sure difference pulled the flap away from the outer wall during the deceleration phase. The reverse was true of the antegrade dissection models.

Model A5 examined the pressure field with intro-duction of a distal re-entry tear. A re-entry tear at the distal end drastically reduced the cross-membrane pressure gradient between the two sides of the flap (Figure 4). The maximum pressure gradient of mod-el A5 was less than 20 Pa.

Discussion

Mechanical factors play a substantial role in the development of AD. Factors investigated thus far in

T= ΔPdx

was determined over time for each model during pul-satile flow (Figure 4 and Table II). Model A3, which had the longest dissection, exhibited the largest tear-ing force. There was a clear phase difference between

Figure 4.—Time history of tearing force acting on the intimal flap (T) obtained from model A1-A4 subject to pulsatile flow condition; for description of each model please see Table I; t, time during one flow waveform.

Figure 3.—Distribution of surface pressure pt (true lumen), pf(false lumen), and cross-membrane pressure difference (Δp), obtained from model A2 subject to pulsatile flow condition. x Axis is di-mensionless and defined as distance from the entry tear along the intimal flap divided by the aortic diameter at the same point; A) t=0.05s; B) t = 0.3s.

-500

-800

p (P

a)

Δp (Pa)-900

-1000

-1200

-1100

-500

-400

200

0

100

-100

-300

-200

0.01x

0.02 0.03 0.04 0.05 0.06

-700

-600

PƒPtΔp

1200

900

p (P

a)

Δp (Pa)800

700

500

600

0

100

700

500

600

400

200

300

0.01x

0.02 0.03 0.04 0.05 0.06

1000

1100

PƒPtΔp

A

B

60

0

T (

mN

/mm

)

-20

-40

-600.05

t (s)

0.1 0.15 0.2 0.25 0.3 0.35

20

40

A1A2A3A4

Table II.—�Maximum tearing tension values observed during a cardiac cycle for the four single-entry models. The tearing force directions are antegrade during systole and retrograde during diastole. All values are in mN/mm.

Model A1 Model A2 Model A3 Model A4

Phase during which the maximum tension happened Systole Systole Systole DiastoleMaximum tearing tension observed 55 20 5 17

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blood. For pulsatile flows through the aorta, since the Womersley number of aortic flows is much larg-er than 1 (α ~ 18), the viscous effects are very small and thus can be neglected. The governing equation of u under pulsatile flow conditions can therefore be approximated as:

(2)

where t is time. Equations (1) and (2) reveal differ-ences in fluid mechanics governing luminal pressure distribution under steady vs. pulsatile flow condi-tions. Under steady flow, luminal pressure gradient is dominated by the viscous effect. However, un-der pulsatile flow conditions, stream-wise pressure gradient in the true lumen is primarily determined by the acceleration rate of intraluminal flow. The large flow acceleration typically seen in aortic blood flows creates a very large streamwise pressure gra-dient within the true lumen (i.e., between points A and C in Figure 2). Thus, the magnitude of pres-sure gradient is significantly higher under pulsatile flow than steady flow. Meanwhile, pressure within the false lumen is practically uniform and equals the entry tear pressure, due to the extremely low flow acceleration. The pressure distribution between true and false lumen sides leads to the cross-membrane pressure difference. As seen in our results, the large pressure gradient created by the pulsatile flow leads to a much higher cross-membrane pressure differ-ence. These results are consistent with the experi-mental findings of Prokop et al who demonstrated in vitro that AD propagation occurred only during pulsatile but not steady flow conditions.21

In our rigid wall model the tearing force acting on the intimal flap may be approximated as:

2 (3)

where L is the length of the tear and T is the over-all tearing force acting on the intimal flap. Equation (3) above indicates that the longer the intimal tear, the larger the tearing force. This equation may ex-plain why the onset and propagation of AD often happens very acutely and rapidly. During very early stages of AD progression, propagation rate could be slow and undetectable. Once the length reaches a critical value, where the tearing force is greater than the aortic wall strength, the process becomes irre-versible and propagation speeds up exponentially.

the pathogenesis of AD include blood pressure, tear depth, aortic root motion, aortic wall material prop-erty, and the rate of rise of pressure (dp/dt). Tam et al. studied the relationship between propagation pressure and the number of elastin layers in the outer dissection wall as well as depth of intimal tear.18 Using finite-element modeling, Beller et al. assessed the contribu-tion of aortic root motion and blood pressure, to wall stress distribution.19 Sommer’s group conducted peel-ing experiments on the media of human abdominal aorta to quantify the material strength of aortic wall subjected to a dissection force.20 Finally, Prokop’s team constructed an in vitro loop to study AD under both steady and pulsatile conditions, and found that dissec-tion of aortic wall occurred only under pulsatile but not steady flow conditions.21 Propagation of AD was subsequently found to be dependent on peak growth rate of pressure, (dp/dt)max.12 Clinically β-blockers have been used effectively to medically manage acute type B dissection by reducing the rate of rise of pressure, dp/dt. Probably one of the strongest contributers to AD propagation is dp/dt; however, the hemodynamic mechanism is unclear. This study utilizes 2D CFD to illustrate the relationship between distal AD propaga-tion in the longitudinal direction and dp/dt.

Relationship between tearing force and tear length during pulsatile flow

Our numerical results demonstrate that for aortic dissection the local, as well as overall tearing force acting on the intimal flap is directly related to: 1) length of the tear; 2) unsteadiness of the flow; and 3) number of intimal entry tears. This CFD simula-tion did not include fluid-structure interaction and as such, did not take into account aortic wall material properties and assumed aortic dissection with rigid walls. The tearing force was very large for dissec-tions with a single entry tear, but was very low for dissections with two tears. The fluid dynamic mecha-nism for this phenomenon can be explained by con-sidering the governing equations for incompressible fluid flows. Stream-wise velocity is denoted as u. The governing equation of u in a 2D steady flow, when neglecting the convective effect, reads as:

(1)

where x is the streamwise coordinate, ν is kinetic viscosity, p is dynamic pressure, and ρ is density of

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not a sole factor known to be the main cause of determining antegrade vs. retrograde propagation. Microscopic architecture and overall strength of elastin layers in either direction may play a role in this regard. Number and thickness of elastin layers constructing the media decrease along the thoracic aorta.12 The less the number of elastin layers in the media, the lower the pressure needed for dissection propagation.18 Rarely, retrograde propagation of an intimal tear in the descending thoracic aorta can oc-cur and be a cause of type A dissection. However, numerous cases of retrograde propagation have been reported as a complication of previous TEVAR, although its overall frequency as a complication of TEVAR is low, roughly between 0.75% to 2.5% in dif-ferent studies.24, 26-28

Implications for TEVAR in type B dissection

Limited studies have been performed on the fluid mechanics of aortic dissection using CFD. Tse et al. studied the hemodynamics through the aorta of a patient with a single-entry aortic dissection.29 They observed high pressure difference between the true and false lumen during systole and suggested this pressure difference could be responsible for the de-velopment of a dissecting aortic aneurysm clinically observed in their patient. Karmonic et al. created a 3D model of a patient specific aortic dissection with two entry tears and artificially closed one of the tears to study the impact of tear location on the he-modynamic forces acting on dissected flap.30 They observed high negative pressure-difference between the true and false lumens when the primary entry tear was closed. A more recent study conducted by the same group showed that, after TEVAR of aor-tic dissection, high pressure existed on the partially thrombosed false lumen side.31 Our 2D CFD simula-tion results agree well with these patient-specific 3D simulations and suggest these results may be more broadly applicable to most patients regardless of specific anatomic geometry.

The tear propagation mechanism illustrated by our computational simulations may build a theoreti-cal skeleton for managing AD with β-blockers. The effect of β–blockade is to reduce heart rate and de-crease contractility which effects dp/dt in two ways; increasing the duration of the cardiac cycle and reducing the amplitude of the flow wave, both of which diminish dp/dt. The approach was pioneered

Propagation could end with onset of a re-entry tear which significantly reduces tearing force, or the tear-ing force can result in rupture of the outer wall and/or collapse of the true lumen.22 The reduction in tearing force by a re-entry tear may be necessary for patient survival in chronic dissection where al-most all chronic ADs have been noted to have at least one clearly identifiable re-entry tear.23 Tearing force is cyclic, largest during acceleration phase for antegrade propagation and zero during decelera-tion phase (negative T in figure 4 means no tearing force). The cyclic nature of tearing force correlates well with the pulsatile pain typically reported by dis-section patients.

Relationship between tearing force and dp/dt

Equation (3) shows that tearing force is propor-tional to flow acceleration rate but indicates no link-age to dp/dt because in the current study we as-sumed the aortic walls were non-compliant solids. Real aortic walls, however, are compliant and blood travels through the vascular system as propagated waves. Based on previous studies, the pressure gra-dient in the aorta is proportional to dp/dt.17 Peak pressure gradient between the two sides of intimal tear with a single entry tear is thus proportional to dp/dt. This analysis should be interpreted with cau-tion though, because it assumes the pressure is uni-form in the false lumen.

Antegrade vs. retrograde propagation

Retrograde propagation to the ascending aorta with transformation to type A dissection is a known reported complication of TEVAR and, to a lesser de-gree, medical management of type B dissection.24,

25 The tearing mechanism works in both antegrade and retrograde directions. The only difference is that the major tearing force for antegrade propagation occurs during acceleration phase or systole, where-as for retrograde propagation it happens during deceleration phase or diastole (Figure 4). Since the duration of systole is approximately half that of dias-tole in a normal cardiac cycle, dp/dt is higher during systole than diastole. As a result, the effective tear-ing force causing antegrade propagation is larger than the force causing retrograde propagation. This may explain why propagation occurs mainly in the antegrade direction naturally. Nevertheless, there is

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force then converts to a single entry tear mechanism which may propagate the dissection antegrade dur-ing systole or retrograde during diastole. Thus, these fluid mechanical factors yield an alternative expla-nation of retrograde type A dissection after TEVAR other than the device-induced mechanism.

These mechanical explanations for retrograde type A dissection after TEVAR are supported by experi-mental data by Tsai et al. and others.25, 38 Closing an entry tear significantly increases the pressure gradi-ent between the false and true lumens. It should be noted, however, that the pressure gradient reported by Tsai is not the cross-flap pressure gradient we calculated, because their study measured pressures of the false and true lumen at different locations.

Current opinion is that acute type B dissections are better treated with a shorter endograft to seal only the entry tear, which results in favorable remodeling of the aorta. Shorter endografts significantly reduce the risk of paraplegia, a devastating complication associated with long coverage of the descending thoracic aorta.39-41 Closing only the primary entry tear by TEVAR without consideration of the re-entry tears can result in unsatisfactory outcomes due to further opening of re-entry tears and AD propaga-tion. Given the potentially fatal 42, 43 complication of retrograde type A dissection, which endangers critical anatomic structures including coronary arter-ies, aortic valve, and aortic arch vessels, decision on whether to cover only the entry tear or all intimal tears during TEVAR of type B AD should be made af-ter balancing the risk of retrograde dissection versus the risk of paraplegia and unfavorable remodeling. When coverage of all entry tears is considered, use of covered stents may not be feasible since re-entry tears may involve or be in proximity to the orifice of visceral organ blood supply. Attempted closure of the tears with bare metal stents may be sufficient to close the re-entry tears and support the dissected aortic wall.

Limitations of the study

In general, aortic dissection propagates in 3D in-cluding both longitudinal and circumferential direc-tions due to the laminated structure of aortic me-dia. However, in this study, we only considered the impact of dp/dt on propagation of dissection dis-tally along the longitudinal direction. Complex fluid-structure interaction simulation would be required

by Wheat et al.13 and is currently accepted as the treatment of choice for uncomplicated type B AD. Patients with complicated type B AD, i.e., those with impending rupture or end-organ ischemia, require prompt surgical treatment by either replacing the dissected aorta including the entry tear with a graft or TEVAR 32 with or without balloon fenestration.33 The major goal of TEVAR is to cover the primary intimal tear through which blood enters the false lu-men. Sealing off the intimal tear triggers a thrombot-ic cascade within the false lumen, while maintaining patency of true lumen. TEVAR has significantly re-duced the mortality of complicated type B dissec-tion and become an accepted alternative to open type B dissection repair under these circumstances.8 Despite short term success of TEVAR, the procedure has been accompanied with an unexpected and rare but potentially fatal complication: retrograde type A dissection.24, 28, 34 This complication has typical-ly been attributed to damage to the inner layers of the aortic wall during implantation of the device, particularly those with partially uncovered stents.35,

36 In a retrospective study, at least 73% of patients with post-TEVAR retrograde dissection were ini-tially treated using stent grafts with proximal bare spring.28 However, retrograde type A dissection has been seen with various devices including reported cases without a bare stent.37

The risk of a retrograde type A dissection follow-ing TEVAR may also be explained by the fluid dy-namics mechanism illustrated in this paper. As seen in Figures 2 and 4, dissections with multiple entries are typically associated with low cross-membrane pressure difference and low tearing force on the in-timal flap. In ADs with a single entry tear, the intimal flap is exposed to a very large tearing force (Figure 4), which under certain situations can cause retro-grade type A dissection. One possible scenario for this type of retrograde dissection is when the stent is implanted such that the entry tear is incompletely covered and part of the dissected intimal layer is not supported by the stent. This unsupported area is subjected to large intraluminal pressure force and can lead to rapid retrograde dissection. If the dis-sected aortic wall is fully supported by the stent, this pressure load will be primarily offset by the stent to reduce risk of retrograde propagation. Another scenario occurs when an entry and re-entry tear exist, which reduces the tearing force, but the TE-VAR covers only the primary entry tear. The tearing

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that the dynamic nature of dissection propagation has to be considered during clinical management of dissection, especially with application of endovascu-lar stent grafting.

References

1. Hagan PG, Nienaber CA, Isselbacher EM, Bruckman D, Kara-vite DJ, Russman PL et al. The International Registry of Acute Aortic Dissection (IRAD): new insights into an old disease. JAMA 2000;283:897-903.

2. Golledge J, Eagle KA. Acute aortic dissection. Lancet 2008;372: 55-66.

3. Tsai TT, Evangelista A, Nienaber CA, Trimarchi S, Sechtem U, Fattori R et al. Long-term survival in patients presenting with type A acute aortic dissection: insights from the Interna-tional Registry of Acute Aortic Dissection (IRAD). Circulation 2006;114:I350-6.

4. Tsai TT, Fattori R, Trimarchi S, Isselbacher E, Myrmel T, Evange-lista A et al. Long-term survival in patients presenting with type B acute aortic dissection: insights from the International Regis-try of Acute Aortic Dissection. Circulation 2006;114:2226-31.

5. Meszaros I, Morocz J, Szlavi J, Schmidt J, Tornoci L, Nagy L et al. Epidemiology and clinicopathology of aortic dissection. Chest 2000;117:1271-8.

6. Hiratzka LF, Bakris GL, Beckman JA, Bersin RM, Carr VF, Ca-sey DE Jr. et al. 2010 ACCF/AHA/AATS/ACR/ASA/SCA/SCAI/SIR/STS/SVM Guidelines for the diagnosis and management of patients with thoracic aortic disease. A Report of the American College of Cardiology Foundation/American Heart Association Task Force on Practice Guidelines, American Association for Thoracic Surgery, American College of Radiology, American Stroke Association, Society of Cardiovascular Anesthesiologists, Society for Cardiovascular Angiography and Interventions, Society of Interventional Radiology, Society of Thoracic Sur-geons, and Society for Vascular Medicine. J Am Coll Cardiol 2010;55:e27-e129.

7. Mustafa ST, Sadat U, Majeed MU, Wong CM, Michaels J, Tho-mas SM. Endovascular repair of nonruptured thoracic aortic aneurysms: systematic review. Vascular 2010;18:28-33.

8. Coady MA, Ikonomidis JS, Cheung AT, Matsumoto AH, Dake MD, Chaikof EL et al. Surgical management of descending thoracic aortic disease: open and endovascular approaches. A Scientific Statement From the American Heart Association. Cir-culation 2010;121:2780-804.

9. Nienaber CA, Rousseau H, Eggebrecht H, Kische S, Fattori R, Rehders TC et al. Randomized comparison of strategies for type B aortic dissection: the INvestigation of STEnt Grafts in Aortic Dissection (INSTEAD) trial. Circulation 2009;120:2519-28.

10. Tang DG, Dake MD. TEVAR for acute uncomplicated aortic dis-section: immediate repair versus medical therapy. Semin Vasc Surg 2009;22:145-51.

11. Larson EW, Edwards WD. Risk factors for aortic dissection: a necropsy study of 161 cases. Am J Cardiol 1984;53:849-55.

12. van Baardwijk C, Roach MR. Factors in the propagation of aor-tic dissections in canine thoracic aortas. J Biomech 1987;20:67-73.

13. Wheat MW, Jr., Palmer RF, Bartley TD, Seelman RC. Treatment of dissecting aneurysms of the aorta without surgery. J Thorac Cardiovasc Surg 1965;50:364-73.

14. Shores J, Berger KR, Murphy EA, Pyeritz RE. Progression of aortic dilatation and the benefit of long-term beta-adrenergic blockade in Marfan’s syndrome. N Engl J Med 1994;330:1335-41.

that includes 3D geometry, material properties, and fluid shear stresses in order to fully model the prop-agation of the tear in three dimensions. However, our 2D model allowed us to investigate and isolate the role of dp/dt on distal (longitudinal) propaga-tion of aortic dissection in order to understand the mechanical importance of beta blockers used clini-cally. A second study limitation was that aortic wall material properties were not included such that the aortic wall was assumed to be noncompliant even though the dissected flap in patients can be rela-tively thin and compliant. In some respect, this mod-el resembles chronic dissection where the intimal flap has a more non-compliant nature and TEVAR is performed for aneurysmal dilatation over time as opposed to complicated malperfusion. TEVAR in those circumstances is far less successful with mere sealing of the entry tear. On the other hand, the non-compliant nature of our intimal flap in this model is also representative of TEVAR in acute dis-section where the stent against the flap functions as a non-compliant entity. As such, the implications for TEVAR treatment of aortic dissections are none-theless relevant since TEVAR functionally makes the dissected flap non-compliant. Inclusion of material properties would be particularly important in simu-lations that examined the impact of circumferential dissection on risk of rupture which was not the fo-cus of this study. Complicated fluid-solid interaction simulation of flow and stress patterns in the aortic wall may alter the pressure distribution in the false lumen. However, our results of the relative pressure gradient between the false and true lumen would nonetheless be expected to be similar and clinically relevant.

Conclusions

We performed 2D computational fluid dynamic simulations of aortic dissection models to illustrate the mechanism by which hemodynamic determi-nants impact dissection propagation distally in the longitudinal direction. We demonstrated that the intimal flap of a dissection with single entry tear experiences a very large tearing force when sub-jected to pulsatile flow conditions. Tearing force is drastically reduced with the introduction of a sec-ond entry (re-entry) tear or changing to steady flow conditions. The mechanism illustrated here reveals

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31. Karmonik C, Bismuth J, Davies MG, Shah DJ, Younes HK, Lumsden AB. A computational fluid dynamics study pre- and post-stent graft placement in an acute type B aortic dissection. Vasc Endovascular Surg 2011;45:157-64.

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Funding.—This work was supported by American Heart Association and Northern California Institute for Research and Education.

Received on November 25, 2010.Accepted for publication on April 19, 2012.Epub ahead of print on July 23, 2012.

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