Aneurysmal Hypertension and its Relationship to SacThrombus: A Semi-qualitative Analysis by Experimental

Fluid Mechanics

A. Chaudhuri,1 L. E. Ansdell,2 A. J. Grass2 and M. Adiseshiah1*

1Vascular Endovascular Unit, University College London Hospitals and 2Department of Civil Engineering,Chadwick Building, University College London, London, UK

Objectives. To ascertain the effect of aneurysm thrombus and luminal diameter on arterial blood pressure within theabdominal aortic aneurysm lumen and at the sac wall.Methods. A life-like abdominal aortic aneurysm was incorporated in a pulsatile flow unit, using systemic bloodpressure settings of 140/100 mmHg and 130/90 mmHg (denoted the high and low settings, respectively). Aneurysmsac pressure was measured in the absence of thrombus within the sac. This was repeated after a thrombus analogue(gelatine) was introduced into the aneurysm model in an asymmetric fashion. Luminal and sac wall pressures werecompared to the systemic pressure, and to each other, in both blood pressure settings. Statistical analysis wasperformed using ANOVA in Minitab 13.Results. In the empty sac, the luminal and sac wall pressures were identical to the systemic pressures at the highand low settings. After introduction of thrombus, pressure was transmitted in a monophasic pulsatile fashion,measuring 166/142/151 mmHg (SP/DP/MP) at the sac wall, while the corresponding intraluminal pressure was164/136/145 mmHg (p , 0.001, high setting). By contrast, in the low setting, these readings were 157/133/141 (sacwall) and 160/128/138 mmHg (lumen; p , 0.001). The sac wall pressures were significantly higher than theluminal pressures for both high and low settings (p , 0.001).Conclusions. Thrombus has a significant effect on the intraaneurysmal lumen itself and causes localisedhypertension with high intraluminal pressures. The differences between the sac wall/luminal pressures may affectregional aneurysm wall biomechanics, but needs further study.

Key Words: Aneurysm thrombus; Aneurysmal hypertension; Pascal’s Law; Bernoulli’s principle.

Introduction

The relationship of AAA thrombus to aneurysm wallbiomechanics has been the subject of several studies.1,2

It has been suggested that aneurysm thrombustransmits pulsatile pressure.2 However, no data existsin the current literature as to the significance of theluminal diameter, or the nature of the pressure wavestransmitted through the blood within the lumen of theaneurysm, in relation to the presence of aneurysmthrombus.

Methods

A life-like latex AAA model3 was incorporated into apulsatile flow unit (PFU) for simulation of the cardiaccycle, achieving a flow velocity of 40 cm/s (confirmedby USS) at a rate of 70 bpm, generated from a pulsegenerator4 (Fig. 1). The latex has a Young’s modulusðEÞ of 5.151872 N/mm2, measured by a Hounsfieldtensometer. A solution of glycerol in water (55:45 v/v,r ¼ 1172 kg=m3; viscosity ¼ 15.53 cP at 25 8C) wasused as a blood analogue. The increased density wascalculated to generate the high-pressure setting withinthe limitations of the solenoid angle seat valve. Flowwithin the PFU had a Reynolds’s number (Re) of4134.74, confirming it to be turbulent. The arterialpressure waves (Fig. 2(a)) generated in the systemwere monitored through a side channel tapped flushinto the PFU just above the AAA. Luminal and sacwall pressures were monitored at the level of the

Eur J Vasc Endovasc Surg 27, 305–310 (2004)

doi: 10.1016/j.ejvs.2003.11.010, available online at http://www.sciencedirect.com on

*Corresponding author. Dr M. Adiseshiah, 149 Harley Street, 2ndfloor, London W1G 6DE, UK.

Abbreviations: SP, systolic pressure; DP, diastolic pressure; MP, meanpressure; PFU, pulsatile flow unit; AAA, abdominal aorticaneurysm; EVAR, endovascular aneurysm repair; USS, ultrasoundscan.

1078–5884/030305 + 06 $35.00/0 q 2003 Elsevier Ltd. All rights reserved.

maximum anteroposterior diameter of the model via a12 G cannula flush on the posterior and anterior aspectof the AAA wall, respectively, to avoid flow distortionartefacts. The cannulae were placed before addition ofthrombus analogue to minimise any artificial increasein the pressure readings. The side channel and thecannula were connected to a pressure transducer (MX960 LogiCal, Medtronic/World Medical, Sunrise, FL,USA). This was displayed on a standard monitor(Hewlett Packard model HP78353A). The transducerreadings on the monitor were calibrated using amercury sphygmomanometer. The waveform wasoutputted to a computer using the Wave Viewplatform (Wave View for DOS 1.16 (1994), multiboard(3), Eagle Appliances Ltd, UK), which sampled theinput over 5 s at a sampling rate of 1000 Hz in volts.This was saved as a text file and then converted to aMicrosoft Excel numerical and graphic file. A conver-sion equation to mmHg was obtainable using logisticregression in SigmaPlot for Windows.

The aneurysm sac was filled anteriorly withgelatine solution (Applefords jelly, Kerry Food Service,Bucks., UK), which solidified by cooling the model to12 8C to produce an aneurysm thrombus analoguelocated asymmetrically within the aneurysm sac.5 Thiswas coated with a membrane of Tivodex 60 (EvodeLtd, Staffs, UK), a solvent based adhesive thatevaporates to leave a latex membrane behind, toprevent it from washing out with the flow. This was re-incorporated into the PFU, and intrasac pressurereadings in two arterial blood pressure settings (140/100 and 130/90 mmHg, denoted the high and lowsettings, respectively) in this scenario were taken. Thepressure obtained in the lumen and at the sac wall wascompared to the systemic pressure at the setting. Thesac wall pressure was compared to the intraluminalpressure. Statistical analysis of the pressure readings(derived from the data points on the pressure curves,including the SP and DP, in volts) was performedusing ANOVA in Minitab 13 (Table 1).

Results

The luminal and sac wall pressures in the emptysac were identical to the systemic pressures atthe high and low settings (140/100/113 and130/90/103 mmHg, respectively, (SP/DP/MP)). Inthe low setting, intraluminal pressure was160/128/138 mmHg whilst the pressure measured atthe sac wall was 157/133/141 mmHg ðp , 0:001Þ:Aneurysm sac wall pressure measured166/142/151 mmHg in the high setting, whilst thecorresponding intraluminal pressure was164/136/145 mmHg ðp , 0:001Þ (Fig. 2(b) and (c)).The aneurysm sac wall pressure was also significantlyhigher than the intraluminal pressure at both bloodpressure settings ðp , 0:001Þ (Fig. 3(a)). This isreflected in the mean pressures. After addition ofthrombus analogue, the pressure waves were blunted,losing their triphasic appearance.

Discussion

The arterial pressure wave contributes to wall stresswithin the AAA sac.1,2 It is therefore important tostudy the role of thrombus in modifying the pressure.The heterogenous nature of thrombus suggests thatthe pressure wave is transmitted in a variable fashion.6

The homogenous nature of the thrombus analogueused in our ‘idealised’ system would result in pressuretransmission in accordance to Pascal’s law and is thebasis for pressure measurement in one position. A

Fig. 1. Schematic representation of the PFU. (1 ¼ bloodanalogue in reservoir, 2 ¼ supply pump, 3 ¼ inflow, 4 ¼outflow, 5 ¼ solenoid angle seat valve coupled to pulsegenerator, 6 ¼ pressure sensing and display, 7 ¼ AAAmodel test section, 8 ¼ WaveView platform.

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Fig. 2. (a) PFU waveforms. A negative excursion is noted due to a water hammer effect as a result of elastic recoil from thelatex model. (b) Pressure waveforms transmitted via thrombus. (c) Pressure waveforms within the AAA model lumen.

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series where it was suggested that thrombus lowerswall stress did not look at the aneurysm size thatmight warrant EVAR.7 It has been suggested thatstresses, and therefore the pressures which generate

the stresses, may vary positionally in the aneurysmsac.8 However, the authors do not take into account thepossibility of Gore-tex patches and suture lines used inthe manufacture of their aneurysm model, which mayhave contributed to the stress differential. In addition,the baseline waveform obtained using fluid onlywithin the AAA sac is identical to the pressureobtained from the PFU above the AAA neck.

The pressures obtained may be explained qualitat-ively. The model exhibits complex geometry due to theasymmetrical shape of the aneurysm.9,10 The presenceof aneurysm thrombus may be causally related to thevarying pressures and stresses that have been noted invivo. However, an idealised situation maybe con-sidered where the AAA might be thought of as adiverging tube with a circular cross section for all ‘x’described (Fig. 3(b)).

The cross sectional area at ‘x’ is given by:

Ax ¼ pðrxÞ2 ð1Þ

As volume flow rate ðQtÞ is a function of time, themean velocity ðuÞ at any given section is denoted by:

u ¼Qt

pðrxÞ2

ð2Þ

This clearly indicates that blood flow velocity isreduced within an arterial channel as it dilates. If itis assumed that Bernoulli’s equation applies approxi-mately along the centre streamline a form of the steadyflow equation can be derived11 (Appendix A).

Fig. 2 (continued )

Fig. 3. (a) Box plots comparing pressure values (volts). Thehorizontals on the boxes represent the 25th and 75thpercentiles and the bar the median. (b) Model of aneurysmalblood flow within an idealised aneurysm sac. The thrombushas not been included for the sake of clarity.

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Multiplying both sides of Eq. (A3) by g, we obtain:

P

rþ

u2

2¼ c2 ð3Þ

As r is a constant for the fluid medium, i.e. blood ittherefore follows, from Eq. (3) that as velocity fallspressure must rise. This may be considered in thecontext of Pillary et al.’s findings, which demonstratedthat aneurysm size was inversely related to thevolume of thrombus, and also that thrombus wasthicker anteriorly.12 This may, in terms of fluidmechanics, therefore form a basis for the risk ofrupture as aneurysmal size, and therefore luminal sizeand pressure increase. In addition, these findingscontradict the preconception that thrombus growth isrelated to eddy currents and secondary velocitypatterns. As we have used only a fixed volume ofthrombus volume, the interaction of the flow andthrombus volume is beyond the scope of this experi-mental setting. However, this will occur only if thediameter of the channel within the AAA is larger thanthat at the neck, and becomes invalid if the lumenbecomes narrowed by thrombus or calcification. Thestudies of Stenbaek and Wolf et al. suggest a higher riskof rupture in small AAAs as thrombus volumeincreases, but they have not correlated the thrombusvolume with the luminal calibre and intraluminalpressures, and excluded the larger aneurysms thatPillary et al. studied.13,14

There is also generation of turbulence following theabrupt increase in aortic calibre (Fig. 3(b)). This givesrise to eddy currents with loss of kinetic energy (KE,also termed the exit loss in this case) from the bloodstream, in accordance with the Borda – Carnotequation.15 We therefore hypothesise that this KE istransmitted through that part of thrombus in contactwith the blood stream and therefore all or part of theexit loss manifests as pressure waves with a higheramplitude at the sac wall, whilst the energy loss fromthe lumen results in a pressure that is comparativelylower than that obtained at the sac wall.

Our findings correlate with other studies, whichhave demonstrated higher intrathrombic sac pressuresin correlation to increased luminal pressures.16 How-ever, Hans et al. demonstrated lower pressure valuesoverall—this is due to the fact that the AAAs had beenclamped proximally and distally, and thereforeexcluded from the systemic pressures. Reduction ofthe intrathrombic pressure after further clamping ofthe inferior mesenteric artery supports our hypothesisthat KE absorbed from arterial flow causes pressurewaves of higher amplitude to be transmitted throughthrombus.T

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Aneurysmal Hypertension and Sac Thrombus 309

Eur J Vasc Endovasc Surg Vol 27, March 2004

Conclusion

Aneurysm thrombus transmits pressure in a pulsatilefashion and may relate to a localised rise in aneurysmintraluminal blood pressure, especially if the aneur-ysmal lumen continues to be wide. This may add tothe risk of rupture, particularly in those aneurysmsincreasing in size, and needs to be studied in greaterdetail both in vivo and in vitro.

Appendix

Derivations of the steady flow equation as applied tothe flow model

P

rgþ

u2

2gþ z ¼ c ðconstantÞ ðA1Þ

Then,

P

rgþ

u2

2g¼ c 2 z ðA2Þ

P

rgþ

u2

2g¼ c1 ðA3Þ

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Accepted 25 November 2003

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