On-line Table 1: Hemodynamic parameters most

On-line Table 1: Hemodynamic parameters most commonly defined in the IA literature Parameter Abbreviation Parameter Name Unit WSS or TAWSS Time-averaged wall shear stress Pa

Definition T

WSS ⫽

1 T

冕

兩wss兩 dt

0

wss, instantaneous shear stress vector; T, cycle period Normalized WSS

Time-averaged wall shear stress, normalized by parent vessel WSS4

None

冕 冕

1 T WSS ⫽

T

兩wss a 兩dt

0

1 T

T

兩wss v 兩dt

0

wssa, wssv, instantaneous shear stress vector for the aneurysm and parent artery; T, cycle period OSI

Oscillatory shear index4

None

冏冕 冏 冕

冦

T

wssdt

1 OSI ⫽ 1 ⫺ 2

0

T

兩wss兩dt

0

冧

wss, instantaneous shear stress vector; T, cycle period WSSG

Wall shear stress gradient4

Pa/m WSSG ⫽

1 T

冕

T

0

⭸wss dt ⭸m

wss, instantaneous shear stress vector; m: flow direction GON

Gradient oscillatory number60

None

冕 冕

T

兩

GON ⫽ 1⫺

WSSGdt兩

0 T

兩WSSG兩dt

0

WSSG, instantaneous wall shear stress gradient vector; T, cycle period MWSS

Maximum time-averaged aneurysmal wall shear stress5

Pa MWSS ⫽ maxAa

冉冕 冊 T

1 T

兩wss a 兩dt

0

Aa, aneurysmal area Normalized MWSS

Maximum time-averaged wall shear stress, normalized by parent vessel WSS4

None

MWSS ⫽ maxAa

冕 冕

冢 冣 1 T

T

兩wss a 兩dt

0

1 T

T

兩wss v 兩dt

0

Aa, aneurysmal area LSA

Low shear-stress area percentage

None

RRT

Relative residence time4

Pa⫺1

LSA ⫽ Al/Aa A1, low WSS aneurysmal area ⬍10%4,13 or 1 standard deviation5 of parent vessel WSS, or ⬍0.4 Pa30 RRT ⫽

1

1 T

冏冕 冏 T

wssdt

0

wss, instantaneous shear stress vector; T, cycle period AJNR Am J Neuroradiol 35:●

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On-line Table 1: Continued Parameter Abbreviation Parameter Name NV Number of vortices4 Inflow concentration index5

ICI

Unit None None

Definition Count on the velocity field of the representative cross-sectional plane Qin/Qv Ain/Ao Qin, inflow rate to aneurysm; Qv, vessel flow rate; Ain, area of inflow region; Ao, area of ostium surface ICI ⫽

Shear concentration index5

SCI

None

Fh/Fa Ah/Aa Fh and Fa, shear forces over high WSS (Ah, ⬎1 standard deviation of parent vessel WSS) and entire aneurysm (Aa) SCI ⫽

VDR

Viscous dissipation ratio5

None

VDS ⫽

冕 冕

2␮/␳(eijeij)dV/Va

Va

2␮/␳(eijeij)dV/Vnear

Vnear

eij, strain rate tensor; Va, aneurysm volume; Vnear, near vessel volume Kinetic energy ratio5

KER

None

KER ⫽

冕 冕

1/2 䡠 u2dV/Va

Va

1/2 䡠 u2dV/Vnear

Vnear

Va, aneurysm volume; Vnear, near vessel volume; u, velocity Low shear index5

LSI

None

F1 䡠 A1 Fa 䡠 Aa F1 and Fa, shear forces over high WSS (A1, ⬎1 standard deviation of parent vessel WSS) and entire aneurysm (Aa) LSI ⫽

Energy loss28,31

EL

Pa/s

Pressure loss coefficient28,31

PLc

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None

冊 冉

再冉

1 2 1 2 ␳v ⫹ Pin ⫺ ␳vout ⫹ Pout 2 in 2 EL ⫽ Vm vin and vout, inlet and outlet vessel velocity; Ain and Aout, inlet and outlet vessel area vinAin 䡠

冉

冊 冉

冊

1 2 1 2 ␳v ⫹ Pin ⫺ ␳vout ⫹ Pout 2 in 2 PLc ⫽ 1 2 ␳v 2 in vin and vout, inlet and outlet vessel velocity; Pin and Pout, inlet and outlet pressure

冊冎

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7 Growing

2008

2011

2012

Boussel17

Sugiyama3

Sforza19

1⬃3 y

1y

ICA: 3 MCA: 1 PICA

5y

BA: 3

BA

Note:—BA indicates basilar artery; PICA, posterior inferior cerebellar artery.

25: 7 ⫹ 18

2 Growing

1 Growing fusiform

Acevedo-Bolton2 2006

TAWSS

TAWSS

WSS

Typical pulsatile inflow WSS

Patient-specific inflow

Patient-specific inflow

Patient-specific inflow

⬎0.5 mm/y

Growing aneurysms could be in the high WSS impact zone and also low WSS and high OSI region 3 Growing aneurysms in high WSS regions; 2 in lower region and the remaining 2 with the same WSS as non-growth region

Main Findings Growth at very low WSS (⬍0.1 Pa) No change in flow pattern with time Pressure uniformly distributed Altering flow ratio of 2 vertebral arteries reduces low WSS in the growth region CFD validated in vivo and in vitro ⬎0.3 mm during followed time Significant relationship between WSS and surface displacement Growth probably occurs at low WSS

On-line Table 2: Summary of literature investigating the relationship between aneurysmal hemodynamics and aneurysm growth No. of Aneurysms Follow-Up Inlet Boundary Definition of Growth and First Author Year (Total: Growing + Stable) Location Time Condition Parameters Analytic Method 2005 2 Fusiform: 1 ⫹ 1 BA 2y Patient-specific inflow WSS, pressure Plot histograms of WSS area Jou1 at different WSS level

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2005

2005

2005

2008

Shojima33

Cebral20

Hassan21

Valencia34 Not specified

34: 15 ⫹ 14

Pulsatile, same mean flow velocity: 0.37 m/s

Pulsatile

MCA, ACA, AcomA

68: 45 ⫹ 23

Pulsatile, same mean flow velocity

Pulsatile, same mean flow rate

ICA, MCA, ACA

62: 25 ⫹ 34

29: 14 ⫹ 15

Vortex, pressure, spatial mean WSS over peak systole

Flow complexity, stability, inflow concentration, impingement WSS at peak systole

Pressure at peak systole

On-line Table 3: Summary of literature investigating the relationship between aneurysmal hemodynamics and aneurysm rupture No. of Aneurysms Inlet Boundary First Author Year (Total: Ruptured + Unruptured) Location Condition Parameters 2004 20: 3 ⫹ 17 MCA Pulsatile, same mean MWSS and mean Shojima12 flow velocity: 0.6 m/s WSS at peak systole

Multiple logistic regression

t Test, ANOVA

Statistical Methods t Test

Main Findings Maximum WSS at neck region, higher than vessel value Mean aneurysmal WSS significantly lower than vessel value Mean WSS at peak: significantly higher for ruptured IAs Tip of ruptured IAs with recirculating flow and markedly low WSS (⬍0.5 Pa), compared with unruptured tip (1.7 Pa) Pressure elevation at the area of flow impact constituted 1⬃2% of systolic pressure Pressure: No significant difference between ruptured and unruptured IAs, also for different locations Pressure elevation has less contribution to rupture Rupture IAs found with complex, unstable, small impingement, and small jet Only impingement size achieved significance Wide-neck IAs: high flow Narrow-neck sidewall IAs: high pressure and flow stasis Highest WSS occurred at neck Very low WSS found in the ruptured IAs WSS correlated with aneurysm-inlet vessel area ratio in both ruptured and unruptured

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2009

2009

2009

2009

Castro23

Castro22

Chien25

Chien24

2010

2008

Chien61

Cebral26

Year 2008

First Author Jou13

AcomA, MCA, BA tip, ICA terminus, ACA Small ICA

42: 25 ⫹ 17

8: 4 ⫹ 4

20

MCA, AcomA, PcomA, ICA, BA

MCA, ICA, BA, AcomA

AcomA

26: 8 ⫹ 18

24

Small ICA

ICA

Location

6: 2 ⫹ 4

No. of Aneurysms (Total: Ruptured + Unruptured) 26: 8 ⫹ 18

On-line Table 3: Continued

Pulsatile, same inlet WSS (1.5 Pa)

Pulsatile, same WSS inlet BC

Pulsatile, same inlet WSS (1.5 Pa for ICA inlet and 1 Pa for BA inlet) Pulsatile, same WSS inlet BC

Pulsatile, same inlet WSS (1.5 Pa)

Pulsatile, same WSS inlet BC

Inlet Boundary Condition Pulsatile, same inlet flow rate (diastole 2.6 mL/s)

WSS

WSS in aneurysmal neck, body and dome circumference at peak systole WSS at peak systole

MWSS at systolic peak

MWSS at systolic peak

Normalized WSS, absolute WSS at peak systole

Parameters Normalized WSS, MWSS, low WSS area% (⬍10% vessel WSS) at the end of diastole

z Test

Spearman rank correlation

Significant test

t Test

Wilcoxon rank sum test

Significant test

Statistical Methods Rank sum test

Lower WSS in aneurysm sac than parent vessel Different aneurysm locations with different WSS 80% Blebs occurred at highest WSS regions Once blebs were formed, 90% progressed to low WSS 77% Blebs located at inflow jet

WSS in aneurysmal sac lower than parent artery WSS Higher WSS in ruptured IAs, compared with unruptured IAs

Main Findings Similar MWSS (26 versus 23 Pa) for ruptured and unruptured Ruptured IAs have larger low WSS area (27% versus 11%, P ⫽ .03) Low WSS found at dome, high WSS found at distal neck Small mean WSS in ruptured IAs, not significant Low WSS in aneurysm compared with parent artery Highest WSS at neck region Absolute aneurysmal WSS value not significant, parent vessel WSS not significant, normalized WSS significant for ruptured and unruptured IAs Higher MWSS in ruptured IAs, P ⫽ .1 High WSS found in dome MWSS significant in ruptured IAs, with P ⫽ .04

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2011

2011

2011

2011

Zhang29

Cebral43

Cebral5

Year 2011

Lu27

First Author Xiang4

210

Not specified

Not specified

ICA, PcomA, AcomA, MCA, BA

54:43 ⫹ 11

210

ICA, MCA, ACA

Location ICA, MCA, PcomA, PCA, AcomA, ACA, BA, PICA, VA

18: 9 ⫹ 9

No. of Aneurysms (Total: Ruptured + Unruptured) 119: 38 ⫹ 81

On-line Table 3: Continued

Pulsatile and steady, same inlet WSS, 1.5 Pa with different heart rates

Pulsatile, same inlet WSS (1.5 Pa)

Pulsatile

Pulsatile, same mean velocity

Inlet Boundary Condition Pulsatile, same flow rate 4.6 mL/s for ICA, aneurysmal WSS normalized by parent vessel WSS

Time-averaged MWSS, SCI, VDR, LSA

Flow complexity, stability, inflow concentration, impingement

WSS, OSI at peak systole

WSS at peak systole, low WSS area % (⬍1.5 Pa), OSI

Parameters Time and spatial mean WSS further normalized by parent vessel WSS, MWSS, LSA, WSSG, OSI, RRT, NV

Student t test

␹2 significant test

␹2 significant test

Wilcoxon test

Statistical Methods t Test, receiver operating characteristic, and multivariate logistic regression

Main Findings Most ruptured IAs had complex flow and multiple vortices Significantly smaller WSS, MWSS and larger OSI, RRT, LSA, NV in ruptured IAs Normalized TAWSS and OSI were the only independently significant variables in the hemodynamics rupture risk model Larger low WSS area in ruptured IAs (P ⫽ .012) Lower WSS in ruptured IAs Higher OSI in ruptured IAs (P ⫽ .008) No difference between parent vessel WSS in both groups Daughter blebs have significantly lower WSS and higher OSI than primary aneurysms Ruptured IAs had lower WSS Rupture IAs were more likely to have complex flow patterns (P ⬍ .001), stable flow patterns (P ⫽ .0018), concentrated inflow (P ⬍ .0001), and small impingement regions (P ⫽ .0006) Significant: higher MWSS, ICI, and SCI and lower VDR Not significant: LSA, KER, LSI

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2013

16: 8 ⫹ 8

Mirrored PcomA

MCA

106: 43 ⫹ 63

MCA

6: 6 ⫹ 0

MCA, ICA, AcomA, ACA, VA, BA

ICA, MCA

100: 13 ⫹ 87

150: 13 ⫹ 137

ICA-PcomA

MCA

Location

30: 4 ⫹ 26

No. of Aneurysms (Total: Ruptured + Unruptured) 22: 7 ⫹ 15

Pulsatile

Pulsatile

Pulsatile

Pulsatile, same inlet flow rate 3.08 mL/s

Pulsatile, same inlet flow rate

Pulsatile, same inlet flow rate 4.23 mL/s

Inlet Boundary Condition Pulsatile, same flow rate 3.7 mL/s

Normalized WSS, OSI

WSS, Normalized WSS, OSI, WSSG, GON

Time-averaged WSS, OSI

Time-averaged WSS, OSI

Time mean WSS, MWSS, minimum WSS, EL, PLc, OSIMAX, OSIAVE

EL, WSS at peak systole

Parameters Time and spatial mean WSS, low WSS% (⬍0.4 Pa), statistical WSS map

Wilcoxon test

Wilcoxon t test, multivariate logistic regression

Student t test

Wilcoxon t test

t Test or rank sum test, Bonferroni method

Significant test

Statistical Methods Mann-Whitney U test

Main Findings WSS: no significant difference Statistical WSS map: larger continuous area of higher WSS in the dome; larger areas of low WSS; overall significant low WSS with ruptured IAs Significantly higher EL in ruptured IAs Mean WSS: no significant difference ICA: minimum WSS significantly lower in ruptured IAs Higher EL in ruptured IAs, not significant PLc significant in both ICA and MCA IAs TAWSS at rupture point was significantly lower than that at the aneurysm wall without rupture point (P ⫽ .031) OSI at rupture point was lower than that at the aneurysm wall without rupture point (P ⫽ .156) Aneurysm blebs in both ruptured and unruptured aneurysm manifested low WSS and high OSI WSS was significantly lower in ruptured than in unruptured blebs Significant parameters: WSS, Normalized WSS, OSI, WSSG WSS is the only independently significant parameter Significant parameters: normalized WSS

ACA indicates anterior cerebral artery; AcomA, anterior communicating artery; BA, basilar artery; LSA, low shear-stress area; PcomA, posterior communicating artery; PICA, posterior inferior cerebellar artery; VA, vertebral artery; WSSG, WSS gradient; PCA, posterior cerebral artery; BC, boundary condition; OSIMAX, maximum oscillatory shear index; OISAVE, average oscillatory shear index; PLc, pressure loss coefficient; RRT, relative residence time; NV, number of vortices; ICI, inflow concentration index; SCI, shear concentration index; VDR, viscous dissipation ratio; KER, kinetic energy ratio; LSI, low shear index; EL; energy loss.

Xu38

2013

2012

Omodaka35

Miura37

2012

Tako31

2012

2011

Qian28

Kawaguchi62

Year 2012

First Author Goubergrits30

On-line Table 3: Continued