Flow Physics & Computation Lab engineering.jhu.edu/fsag

III

Flow Effects on Thrombogenesis: Insights from Computational Models

Rajat Mittal & Jung Hee Seo

Mechanical Engineering

Thura Abd & Richard George Division of Cardiology

Formation of Blood Clots in the Heart

• Clot (thrombus) formation flow statis

• Normal ventricles – Ejection fraction ~55% – Avoids flow statis (How???)

• Conditions associated with cardiac thrombus formation – Myocardial infarction (MI) – Heart failure – Arrhythmias – Cardiomyopathies – …

• Clinical significance

– Thomboembolic risk

2

LA

(Rehan et al. Cardiovascular Ultrasound, 2006 )

Platelets + Fibrin +…

Post MI Thrombus Formation

• Patients recovering from MI are generally at higher risk of LVT formation – 720K MIs/yr in the US – Thrombus located in apical region

• Reduced ejection fraction (<40%) • Apical Akinesia/Dyskinesia • Ventricle remodeling • Hypercoagulable endothelium – Tissue factor pathway

3

LV

LVT

LV

AN

LA AO Apical Akinesia/Dyskinesia

+Apical Aneurysm

LVT Risk Stratification & Therapy

• Risk criteria – Antero-apical STE-MI (250K/yr) – EF < 30%

• Implication

– Only 1/10 people who currently receive ‘triple’ therapy in US are actually at risk of LVT formation

– ½ patients receiving triple therapy are at high risk of bleeding.

• Better risk stratification metrics are needed.

• LVT risk determined by a complex coupling between flow dynamics and coagulation biochemistry.

4

• Antithrombotic Therapy – Anticoagulants – Anti platelet – Blood thinners Stroke Vol

End Dias. Vol EF=

Stratification of LVT Risk?

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0Ej

ectio

n Fr

actio

n

CMP Group

NORMAL Group

LVT Group

Group N Description

LVT 25 Patients with diagnosed LVT

CMP 25 Severe cardiomyopathy; no LVT

NORMAL 25 Normal

Approach

6

Computational Modeling

Patient Studies

Imaging

Modeling Approach

Computational Hemodynamics

Biochemistry of

Coagulation

Patient Physiology

• EF, Stroke Volume • LV Geometry & Kinematics • Infarct Size & Location

• Tissue Factor Release • Thrombin Production • Platelet activation • Fibrin polymerization

• LV Flow Patterns • Flow Stasis • Transport of CC biomolecules

Understand how flow mediates coagulation in infarcted LVs

Coagulation Cascade

8

• Extrinsic (Tissue-factor) Pathway • Damaged wall expose tissue

factor (TF) • TF-VIIa initiates reactions • Produce Thrombin • Thrombin activates other factors • Burst of Thrombin Production

TF

VIIa Active TF

IIa

IIa

IX

IXa

X Xa

VIII

VIIIa

IXa:VIIIa

V

Va

Xa:Va II

IIa

Prothrombin

Thrombin

Xa

Xa Damaged Wall

LV

Role of Thrombin

9

Thrombin • activates platelets • converts fibrinogen to fibrin

(Angiolillo et al, European Heart J, 2009)

TF Thrombin Coagulation Cacade (CC)

10

IX

IX : TF : VIIaIXaXX : TF : VIIaXaVIIIa : IXaX : VIIIa : IXaVVaVIIIVIIIa

(Thrombin)II (Pro-thrombin)Va : XaII :

IIa

Va :

TF : VIIa

XamIIa

18 Species

6 11

16

6 12

17

6 13

18

15

1

3

k k

k

k k

k

k k

k

k

k

k

IX IX : TF : VIIa IXa

X X : TF : VIIa Xa

X VIIIa : IXa X : VIIIa : IXa VIIIa : IXa Xa

IX Xa Xa IXaV Xa Xa Va

TF : VIIa TF : VIIa

TF : VIIa TF : VIIa

VIII Xa Xa VIIIaIIaV

→+ → +←

→+ → +←

→+ → +←

+ → +

+ → +

+ → +

+ 2

4

6 14

19

9

7

9

8

10

k

k

k k

k

k

k

k

k

k

VaVIII VIIIa

II Va : Xa II : Va : Xa Va : Xa mIIa

mIIa Va : Xa Va : Xa

VIII

IIa

a IXa

IIa IIa

II

VIIIa : IXa

Va Xa Va Xa

a

:

→ +

+ → +

→+ → +←

+ → +

→+ ←

→+ ←

Reactions (Biasetti et al, 2012)

2( )ii i i

i j

C U C D C Rt

R r

∂+ ⋅∇ − ∇ =

∂= ⋅S

(18 Eqs.)

D ≈ 1e-8 (m2/s) S: Stoichiometric Matrix rj: Reaction rate

Initial concentrations (mol/m3)

IX X

V VIII

VIIIa II

C 9e 5; C 1.7e 4C 2e 5; C 7e 7C 1e 11; C 1.4e 3

(Pro-thrombin)

= − = −= − = −= − = −

TF:VIIa,wallC : Prescribed on infarct

Platelet Activation and Deposition

11

, , 1 ,2

,( () )m u m u P m u m uPT U PT D APTt

IIa PT∂= − ⋅∇ + ∇ −

∂

2, , ,

, max ,

,

,

1(

( )( ) (

( ) )

)adh a b m a coh b

m a m a P m a

m

m

a

u

k

PT U PT D P A IIa PT

h x PT PT PT k g PT PT

Tt∂

= − ⋅∇ + ∇ +

− − − ⋅∂

⋅

, max , ,( )( ) ( )adh a b m a coh bb m ak h x PT PT PT k g PTt

PP T T∂= − +

∂⋅

(Leiderman and Fogelson, 2011)

Inactivated, mobile

Activated, mobile

Bound

Activation by Thrombin

Activation by Thrombin

Adhesion to wall Cohesion to bound platelets

Adhesion to wall Cohesion DP≈1e-9 (m2/s)

1( )*

=+IIa

IIaIIa

CA IIa kC C

Polymerization of Fibrinogen Fibrin

12

2( )f f f t fC U C C CDt

k∂= − ⋅∇ + ∇ −

∂

2 2( ) tm fm p mmC U C D C Ct

k C k∂= − ⋅∇ + +∇ +

∂

Fibrinogen

Fibrin (Monomer)

=+

cat IIat

m f

k CkK C

Conversion by Thrombin

1

3 3

2 3 -1 -1

3 3,0

84s7.2 10 mol/m

8.2 10 (mol/m ) s

9 10 mol/m

−

−

−

=

= ×

= ×

= ×

cat

m

p

f

kKk

C(Neeves et al. 2010, Biophysics J)

Canonical Models- Comparative Study Design

13

Infarcted/Aneurysm

LV

AN

Normal

LV

AN

LV

LA

Large Aneurysm Small Aneurysm

Damaged wall due to the acute infarction

Case ESV (mL)

EDV (mL)

SV (mL)

EF (%) AN

A 105 167 62 37 L

B 105 146 41 28 L

C 70 111 41 37 S

D 70 97 27 28 S

E/A=1.2, HR=60 BPM

Clinical Translation?

14

Damaged wall

0( )NW NW wd U H d ddt tτ τ∂ = + ⋅∇ = − ∂

• What flow metric can be used for the LVT risk prediction – Quantified correlation between flow metrics and coagulation – Could be obtained from echo PI or CMR

Residence Time (RT) -How long blood volume stays in ROI -Near damaged Wall Residence Time (NWRT) -Decreased flow strength leads to high NWRT

Marsden et al.

Predicted Thrombogenic Risk

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SV=62 mL, EF=37% SV=41 mL, EF=28% SV=41 mL, EF=37% SV=27 mL, EF=28%

Fibrin concentration (µmol/m3)

Risk: Low

Risk: High

Risk: Moderate

Risk: High

Peak:1e-5 Mean:3e-7

Peak:15 Mean:0.016

Peak:0.05 Mean:3e-4

Peak:0.5 Mean:0.012

Average Surface Distributions

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SV = 41 mL EF = 37 %

SV = 27 mL EF = 28 %

Thrombin (µmol/m3)

NWRT (sec)

Bounded Platelet (PTb/PTmax)

Hemodynamic Coagulation Small Aneurysm Cases

Distributions on the (damaged) aneurysm wall

Patient-Specific Model from Multimodal Data Registration

Dynamic 4D CT scan

Segmented/Reconstructed Model

Mitral inflow Doppler Outflow tract Doppler

Patient: SV=84 mL, EF=47% Apical Aneurysm Apical Akinesia

time

Q[m

L/s

ec]

0 0.2 0.4 0.6 0.8 1

-200

0

200

Reconstructed LV Flow Profile

E-wave A-wave

Systole Nearly automated Procedure!

Infarct Indentification

Chemo-Fluidic Interaction

Vortex Dynamics

Mixing and Washout

192x192x256 (9.4M) grid points

Time averaged flow and thrombin accumulation

Evolution of flow and thrombin

Hemodynamics and Coagulation

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Averaged flow and thrombin accumulation

LVT01 EDV=178 mL, EF=47%

LVT02 EDV=334 mL, EF=40%

LVT09 EDV=417 mL, EF=39%

Thrombin: 5e-4 µmol/m3 Thrombin: 1e-5 µmol/m3 Thrombin: 1e-6 µmol/m3

Inferior

Sept

al

Late

ral

Anterior

NWRT Bound PT Infarct NWRT Bound PT Infarct NWRT Bound PT Infarct

NWRT as a Predictor for Thrombosis?

Case Correlation

SV=62 mL; EF=37% 0.61

SV=41 mL; EF=28%) 0.75

SV=41 mL; EF=37% 0.55

SV=27 mL; EF=28% 0.58

Correlation between NWRT and Bound PT

NWRT [sec]Th

rom

bin

[µm

ol/m

3 ]

0 0.5 1 1.5 2 2.5

0

0.1

0.2

0.3

0.4

0.5

CannonicalPatient-specific

Residence time of flow in the vicinity of the infarct is a key indicator of LVT risk. How to obtain a clinical measure of NWRT??

Stratification of LVT Risk?

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

Ejec

tion

Frac

tion

CMP Group

NORMAL Group

LVT Group

Group N Description

LVT 25 Patients with diagnosed LVT

CMP 25 Severe cardiomyopathy; no LVT

NORMAL 25 Normal

A New Metric for LVT Risk E-Wave Propagation Distance

Velocity = Time (VTI) Integral

E-Wave Propagation (EPI) = ( VTI / LLV ) Index

Group N Description

LVT 25 Patients with diagnosed LVT

CMP 25 Severe cardiomyopathy; no LVT

NORMAL 25 Normal EF, no cardiomyopathy

EPI = �< 1 → 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑖𝑖𝑤𝑤𝑖𝑖> 1 → 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑖𝑖𝑤𝑤𝑖𝑖

0.0

0.5

1.0

1.5

2.0

2.5

3.0

E-W

ave

Pene

trat

ion

Inde

x

CMP Group

NORMAL Group

LVT Group

LLV

Normal LVs High mixing and washout <1% of blood cells stay in ventricle for >5 cycles

Cited Papers

• Seo, Jung Hee, Thura Abd, Richard T. George, and Rajat Mittal. “A Coupled Chemo-Fluidic Computational Model for Thrombogenesis in Infarcted Left Ventricles.” American Journal of Physiology-Heart and Circulatory Physiology (2016): ajpheart-00855. Published 25 March 2016 Vol. no. , DOI: 10.1152/ajpheart.00855.2015.

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