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CPM Specifications Document Fontan Aorta - Exercise: OSMSC 0063_1000, 0064_1000, 0065_1000, 0075_1000, 0076_1000, 0077_1000 May 1, 2013 Version 1 Open Source Medical Software Corporation © 2013 Open Source Medical Software Corporation. All Rights Reserved.
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Page 1: PM Specifications ocument ontan Aorta xercise PM Specifications ocument ontan Aorta - xercise: OSMSC 0063_1000, 0064_1000, 0065_1000, 0075_1000, 0076_1000, 0077_1000 May 1, 2013 Version

CPM Specifications Document

Fontan Aorta - Exercise: OSMSC 0063_1000, 0064_1000, 0065_1000, 0075_1000, 0076_1000, 0077_1000

May 1, 2013

Version 1

Open Source Medical Software Corporation

© 2013 Open Source Medical Software Corporation. All Rights Reserved.

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© 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 2

1. Clinical Significance & Condition Congenital heart defects are structural abnormalities present at birth that disrupt normal blood flow through

the heart, affecting 8 of every 1,000 newborns [1]. There are at least 18 documented types of congenital heart

defects, including coarcataion of the aorta, single ventricle defects, and complete atrioventricular canal defect

[2]. A large amount of anatomical variation is present within these individual congenital heart defect types.

In a study that examined congenital heart disease in the general population, the prevalence of single ventricle

defects was found to be 0.13 per 1000 children and 0.03 per 1000 adults [3]. Single ventricle defects cover a set

of cardiac abnormalities that result in one of the two ventricles being underdeveloped. With one ventricle being

of inadequate functionality or size, only one ventricle is available to pump the blood throughout the entire body.

Some examples of single ventricle defects include: hypoplastic left heart syndrome, pulmonary atresia, tricuspid

atresia, and double inlet left ventricle [2] [4]. Single ventricle heart patients are severely cyanotic at birth, and

these conditions are fatal with no interventions.

In order to provide adequate oxygenation, and separate the pulmonary and

systemic blood supplies, the blood returning to the heart is surgically redirected

to the pulmonary arteries, bypassing the heart. This surgical course typically

consists of three staged surgeries, a Blalock Taussig (BT) shunt and/or Norwood

procedure, a Glenn procedure, and finally a Fontan procedure (or total

cavopulmonary connection, TCPC).

The first stage is performed immediately after birth, and can vary among

patients depending on the defect and the pulmonary resistances. A systemic-

pulmonary shunt (BT shunt, central shunt, or Sano shunt) is used to maintain

adequate ventricle volume load and providing sufficient pulmonary blood flow.

This is accomplished by connecting a systemic artery, such as the brachocephalic artery, to the pulmonary

arteries with a tube graft (Figure 1) [4] [5]. For situations where there is too much blood flow to the lungs, the

pulmonary artery can be narrowed with a synthetic band to restrict blood flow [4]. In patients with aortic

atresia, a neo-aorta is also constructed during the first stage of surgery. About 65-80% of hypoplastic left

ventricles have been found to be related to aortic atresia in several reviews [6]. During reconstruction of a neo-

aorta, the distal stump of the pulmonary artery and homograft tissue are used to

direct flow through the ascending aorta to the carotid and subclavian arteries [6, 7].

The second stage is typically completed between the ages of 2-6 months [5]. The

Glenn procedure connects the superior vena cava to the right pulmonary artery in

order to improve oxygenation and decrease ventricle volume load (Figure 2) [8]. If

the patient had previously gone through a stage one procedure, it is removed during

stage two [4]. Oxygen saturation in patients who have undergone the Glenn

procedure typically is between 75-85% [4]. Another variation of the second stage is

the hemi-Fontan, where the pulmonary artery and superior vena cava are connected

through the right atrium and closed off to the rest of heart with a patch.

Figure 1 –Systemic-pulmonary shunt for a single ventricle heart.

Figure 2 –Glenn procedure. Arrows represent blood flow, with blue being deoxygenated blood, red being oxygenated blood, and purple being a mix of both.

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The third stage, a complete Fontan procedure, is typically completed between the ages of 1-5 years [5]. This

final stage redirects the inferior vena cava to the pulmonary artery. In combination with the previous stage,

deoxygenated blood bypasses the heart completely and is routed directly to the pulmonary artery so the single

ventricle is only pumping oxygenated blood throughout the body. A complete Fontan procedure is typically

done through a lateral tunnel or extracardiac method. A lateral

tunnel Fontan incorporates the wall of the atrium with a baffle

from the inferior vena cava to the pulmonary artery. On the

other hand, an extracardiac Fontan connects the inferior vena

cava to the pulmonary artery with a synthetic tube-shaped graft,

bypassing the heart altogether (Figure 3) [4]. In both methods, a

small hole, or fenestration, is often needed between the newly

formed channel and the atrium to reduce pressure in the Fontan

circuit [4] [5]. A complete Fontan procedure increases oxygen

saturation to virtually normal levels [4].

2. Clinical Data Patient-specific volumetric image data was obtained to create physiological models and blood flow simulations.

Details of the imaging data used can be seen in Table 1. See Appendix 1 for details on image data orientation.

Table 1 – Patient-specific volumetric image data details (mm)

OSMSC ID Modality Voxel Spacing Voxel Dimensions Physical Dimensions

R A S R A S R A S

0063_0000 MR 1.0000 0.5469 0.5469 120 512 512 120 280 280

0064_0000 MR 1.5000 1.1719 1.1719 64 256 256 96 300 300

0065_0000 CT 0.3691 0.3691 0.5000 512 512 296 189 189 148

0075_0000 MR 1.5000 0.6836 0.6836 80 512 512 120 350 350

0076_0000 MR 1.5000 0.6836 0.6836 88 512 512 132 350 350

0077_0000 MR 0.5859 1.5000 0.5859 512 52 512 300 78 300

Available patient-specific clinical data collected for resting conditions can be seen in Table 2.

Table 2 – Available patient-specific clinical data

OSMSC ID Age Gender BSA CI Aorta Psys

(mmHg)

Aorta Pdia

(mmHg)

Aorta Pavg

(mmHg)

IVC Pavg

(mmhg)

LPA Pavg

(mmHg)

RPA Pavg

(mmHg)

SVC Pavg

(mmHg)

0063_0000 3 M 0.63 3.8 80 50 63 11 10 10 11

0064_0000 6 F 0.71 2.7 95 63 78 9 6 6 9

0065_0000 5 F 0.68 2.8 - - - 11 7 9 11

0075_0000 17 F 1.55 2.3 102 67 78 18 17 17 18

0076_0000 27 F 0.68 3.8 140 95 108 15 14 14 15

0077_0000 3 F 0.67 2.8 100 61 79 7 6 6 7

Figure 3 – Complete Fontan Circulation: Laterial Tunnel Fontan (leff), Extracardiac Fontan (right). Arrows represent blood flow, with blue being deoxygenated blood and red being oxygenated blood.

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Details for available PCMRI can be seen in Table 3.

Table 3 – Available PCMRI

OSMSC ID Slice Location Number of Frames Voxel Spacing (mm)

X Y

0063_1000

Aorta 20 0.9375 0.9375

IVC 20 0.9375 0.9375

LPA 20 0.9375 0.9375

RPA 20 0.9375 0.9375

RPA_v2 20 0.9375 0.9375

SVC 20 0.9375 0.9375

0064_1000

Aorta 20 1.0938 1.0938

IVC 20 1.0938 1.0938

LPA 20 1.0938 1.0937

PA 20 1.0938 1.0938

RPA 20 1.0938 1.0937

SVC 20 1.0938 1.0938

0075_1000

Aorta 20 1.0938 1.0938

IVC 20 1.0938 1.0938

LPA 20 1.0938 1.0937

RPA 20 1.0938 1.0937

SVC 20 1.0937 1.0938

0076_1000

Aorta 20 1.0938 1.0938

IVC 20 1.0937 1.0938

LPA 20 1.0937 1.0938

RPA 20 1.0938 1.0938

SVC 20 1.0938 1.0937

3. Anatomic Model Description Anatomic models were created using customized SimVascular software (Simtk.org) and the image data

described in Section 2. See Appendix 2 for a description of modeling methods. See Table 4 for a visual summary

of the image data, paths, segmentations and solid model constructed.

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Table 4 – Visual summary of image data, paths, segmentations and solid model.

OSMSC ID Image Data Paths Paths and

Segmentations Model

ID:

OSMSC0063

subID: 1000

Age: 3

Gender: M

ID:

OSMSC0064

subID: 1000

Age: 6

Gender: F

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ID:

OSMSC0065

subID: 1000

Age: 5

Gender: F

ID:

OSMSC0075

subID: 1000

Age: 17

Gender: F

ID:

OSMSC0076

subID: 1000

Age: 26

Gender: F

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ID:

OSMSC0077

subID: 1000

Age: 3

Gender: F

Details of anatomic models, such has number of outlets and model volume, can be seen in Table 5.

Table 5 – Anatomic Model details

OSMSC ID Inlets Outlets Volume (cm3) Surface Area (cm2) Vessel Paths 2-D Segmentations

0063_1000 1 5 15.0166 72.5062 5 67

0064_1000 1 6 23.5916 99.5179 6 70

0065_1000 1 6 26.8316 95.3494 6 57

0075_1000 1 5 64.3892 169.829 5 52

0076_1000 1 5 165.808 272.09 5 62

0077_1000 1 5 20.1973 93.6672 5 54

4. Physiological Model Description

In addition to the clinical data gathered for this model, several physiological assumptions were made in

preparation for running the simulation. See Appendix 3 for details.

5. Simulation Parameters & Details

5. 1 Simulation Parameters

See Appendix 4 and the peer-reviewed publication featuring these models [9] for information on the physiology

and simulation specifications. Solver parameters can be seen in Table 6.

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Table 6 – Solver Parameters

OSMSC ID Time Steps per Cycle Time Stepping Strategy

0063_1000 1600 Fixed step – 3

0064_1000 1600 Fixed step – 3

0065_1000 1600 Fixed step – 3

0075_1000 1653 Fixed step – 3

0076_1000 1600 Fixed step – 3

0077_1000 1600 Fixed step – 3

5. 2 Inlet Boundary Conditions

Ascending Aorta PC-MRI waveform was prescribed to the inlet of the computational fluid dynamics (CFD) model

when available. When PCMRI was not available for adequate, a normalized waveform was applied to the

patient, fitting age and gender norms. See Figure 4 for a plot of inflow for each model and Table 7 for more

inflow details.

Table 7 – Inflow details from waveforms seen in Figure 4

OSMSC ID Period (sec) Mean Flow (L/min) Profile Type

0063_1000 0.66667 2.20928 plug

0064_1000 0.66667 1.71522 plug

0065_1000 0.66667 1.90401 plug

0075_1000 0.66667 3.68463 plug

0076_1000 0.7143 3.60897 plug

0077_1000 0.66667 1.87597 plug

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Figure 4 – Inflow waveforms in L/min

5. 3 Outlet Boundary Conditions

RCR boundary conditions were applied to each outlet. Volumetric flow to each outlet vessel was distributed

based on flow distributions in LaDisa et. al. [10]. Blood flow distributions, calculated as a percentage of resting

volumetric blood flow to the right subclavian artery (RSA), right common carotid artery (RCCA), left common

carotid artery (LCCA), left subclavian artery (LSA), descending aorta (daorta), and neo-aorta (when applicable)

are shown in Table 8, along with target pressure values. See Appendix 5 for more details on RCR calculations

and Exhibit 1 for the values used in each simulation.

Table 8 – Target Flow distributions and Pressures

OSMSC ID neo-aorta RSA RCCA LCCA LSA dAorta Psys

(mmHg) Pdia

(mmHg) Pavg

(mmHg)

0063_1000 n/a 11.3% 11.5% 11.5% 10.7% 55.0% 80 50 63

0064_1000 1.7% 9.6% 9.7% 8.0% 9.6% 61.4% 95 63 78

0065_1000 1.5% 5.3% 7.4% 7.5% 7.6% 71.0% 90 53 66

0075_1000 n/a 8.1% 12.1% 11.7% 11.1% 57.0% 102 67 78

0076_1000 n/a 22.2% 5.2% 6.0% 8.6% 58.0% 140 95 108

0077_1000 n/a 13.6% 10.6% 12.8% 9.5% 53.4% 100 61 79

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6. Simulation Results

Simulation results were quantified for the last cardiac cycle. Paraview (Kitware, Clifton Park, NY), an open-

source scientific visualization application, was used to visualize the results. A volume rendering of velocity

magnitude for three time points during the cardiac cycle can be seen in Table 10 for each model.

Table 9 – Volume rendering velocity during peak systole, end systole and end diastole.

OSMSC ID Peak Systole End Systole End Diastole

ID:

OSMSC0063

subID: 1000

Age: 3

Gender: M

ID:

OSMSC0064

subID: 1000

Age: 6

Gender: F

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ID:

OSMSC0065

subID: 1000

Age: 5

Gender: F

ID:

OSMSC0075

subID: 1000

Age: 17

Gender: F

ID:

OSMSC0076

subID: 1000

Age: 26

Gender: F

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ID:

OSMSC0077

subID: 1000

Age: 3

Gender: F

Surface distribution of time-averaged blood pressure (TABP), time-averaged wall shear stress (TAWSS) and

oscillatory shear index (OSI) were also visualized and can be seen in Table 10.

Table 10 – Time averaged blood pressure (TABP), time-average wall shear stress (TAWSS), and oscillatory shear index (OSI) surface distributions

OSMSC ID Time Averaged Pressure TAWSS OSI

ID: OSMSC0063

subID: 1000

Age: 3

Gender: M

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ID: OSMSC0064

subID: 1000

Age: 6

Gender: F

ID: OSMSC0065

subID: 1000

Age: 5

Gender: F

ID: OSMSC0075

subID: 1000

Age: 17

Gender: F

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ID: OSMSC0076

subID: 1000

Age: 26

Gender: F

ID: OSMSC0077

subID: 1000

Age: 3

Gender: F

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7. References [1] National Heart Blood and Lung Institute, "Congenital Heart Defects," 1 July 2011. [Online]. Available:

http://www.nhlbi.nih.gov/health/health-topics/topics/chd/. [Accessed January 2012].

[2] American Heart Association, "Common Types of Heart Defects," 2 May 2011. [Online]. Available: http://www.heart.org/HEARTORG/Conditions/CongenitalHeartDefects/AboutCongenitalHeartDefects/Common-Types-of-Heart-Defects_UCM_307017_Article.jsp#.TwHuCNQS01I. [Accessed Januaray 2012].

[3] A. Marelli, A. Mackie, R. Ionescu-Ittu, E. Rahme and L. Pilote, "Congenital Heart Disease in the General Population: Changing Prevalence and Age Distribution," Circulation, vol. 115, pp. 163-172, 2007.

[4] Cincinnati Children's, "Single Ventricle Anomalies and Fontan Circulation," March 2010. [Online]. Available: http://www.cincinnatichildrens.org/health/s/sv/. [Accessed January 2012].

[5] S. Nayak and P. Booker, "The Fontan Circulation," British Journal of Anaesthesia, vol. 8, no. 1, pp. 26-30, 2008.

[6] A. M. Rudolph, "Aortic atresia, mitral atresia, and hypoplastic left ventricle," in Congenital Disease of the Heart: Clinical Physioloical Considerations, Hoboken, Blackwell Publishing, 2009, pp. 257-288.

[7] Children's Hospital of Wisconsin, "Norwood Procedure of Hypoplastic Left Heart Syndrome," 2012. [Online]. Available: http://www.chw.org/display/router.asp?DocID=21364#. [Accessed 24 May 2012].

[8] S. Yuan and H. Jing, "Palliative Procedures for Congenital Heart Defects," Archives of Cardiovascular Disease, vol. 102, pp. 549-557, 2009.

[9] A. L. Marsden, I. E. Vignon-Clmentel, F. P. Chan, J. A. Feinstein and C. A. Taylor, "Effects of exercise and respiration on hemodynamics efficiency in CFD simulations of the total cavopulmonary connection," Annals of Biomedical Engineering, vol. 35, no. 2, pp. 250-263, 2007.

[10] J. LaDisa, "Computational Simulations for Aortic Coarctation: Representative Results from a Sampling of Patients," Journal of Biomechanical Engineering, Oct. 2011.

[11] A. L. Marsden, M. Reddy, S. Shadden, F. Chan, C. Taylor and J. Feinstein, "A New Multiparameter Approach to Computational Simulation for Fontan Assessment and Redesign," Congenit Heart Dis., vol. 5, pp. 104-117, 2010.

[12] A. L. Marsden, M. V. Reddy, S. C. Shadden, F. P. Chan, C. A. Taylor and J. A. Feinstein, "A new multiparameter approach to computational simulation for fontan assessment and redesign," Congenital Heart Disease, no. 5, pp. 104-117, 2010.

[13] M. Zamir, P. Sinclair and T. H. Wonnacott, "Relation between diameter and flow in major branches of arch of the aorta," J. Biomechanics, vol. 25, no. 11, pp. 1303-1310, 1992.

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Exhibit 1: Simulation RCR Values

Table 11 – RCR Values for 0063_0000 in cgs units

ID Face Name Rp C Rd

2 LPA_ul1_final 1153 2.20E-05 5975

3 LPA_ul2_final 1362 2.03E-05 6662

4 LPA_ulbr_final 1072 2.07E-05 6354

5 LPA_ul_final 1072 2.07E-05 6354

6 LPA_ml_final 1425 1.79E-05 7274

7 LML_final 1128 2.25E-05 5743

8 LMML_final 1574 1.29E-05 9862

9 LML2_final 1862 1.16E-05 12496

10 LPA_br1_final 1122 2.00E-05 6656

11 LPA 825 3.21E-05 4739

12 LPA_llbr_final 1849 1.03E-05 13671

13 RPA_br3_final 800 4.10E-05 3733

14 RPA_br2_final 1545 1.65E-05 8149

15 RPA_mmbr_final 1355 1.32E-05 9033

16 RUML2_final 1812 1.71E-05 8251

17 RPA_mm_final 1785 1.36E-05 10129

18 RPA_ml_final 922 2.85E-05 5453

19 RPA_mlbr_final 779 4.15E-05 3959

20 RPA_br1_final 581 5.92E-05 2575

21 RPA 557 6.70E-05 2467

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Table 12 – RCR Values for 0064_0000 in cgs units

ID Face Name Rp C Rd

2 LUL2_final 2118 7.92E-06 14631

3 LUL2b_final 2687 4.90E-06 21732

4 LUL 1374 1.20E-05 9945

5 LUML2_final 2434 6.52E-06 18889

6 LPA_2_final 828 3.59E-05 4586

7 LPA_3_final 1121 2.33E-05 5583

8 LML 1174 2.17E-05 6077

9 LPA_4_final 914 2.88E-05 5369

10 LPA_final 773 3.96E-05 3671

11 PA_ex2_final 1856 1.46E-05 9556

12 RUL 872 3.35E-05 4784

13 RUL_3_final 1581 1.57E-05 8551

14 RUL4_final 3523 4.68E-06 23573

15 RUL_2_final 1107 1.95E-05 6852

16 RML_final 580 6.33E-05 2358

17 RML2_final 680 5.93E-05 2628

18 RMML_final 732 4.01E-05 3551

19 RLML_final 831 3.58E-05 4647

20 RLL_2 579 7.43E-05 2179

21 RPA_final 557 6.71E-05 2465

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Table 13 – RCR Values for 0065_0000 in cgs units

ID Face Name Rp C Rd

9 LLL2_final 1010 2.06E-05 6328

11 LLL3_final 1491 2.00E-05 6941

8 LLL_final 1010 2.06E-05 6327

4 LML2_final 928 2.84E-05 5519

5 LML_final 756 4.09E-05 3994

10 LPA_final 731 4.02E-05 3543

2 LUL2_final 1074 2.07E-05 6368

3 LUL_final 872 3.52E-05 4741

7 LUML2_final 1261 2.09E-05 6447

6 LUML_final 1261 2.09E-05 6447

17 RL1_final 739 6.04E-05 2694

18 RL1a_final 911 2.89E-05 5334

23 RL1b_final 1423 1.79E-05 7257

21 RL2_new_final 765 3.17E-05 4392

22 RL2a_final 1112 2.35E-05 5495

20 RL3_final 1655 1.71E-05 7790

19 RL3b_final 1655 1.71E-05 7790

24 RL3c_final 1668 1.45E-05 9228

15 RML4_final 1496 1.70E-05 7666

16 RML_final 757 3.59E-05 4157

14 RPA_final 1799 8.85E-06 12705

12 RUL2_final 1129 2.25E-05 5750

13 RUL_final 888 2.98E-05 5075

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Table 14 – RCR values for 0075_0000 in cgs units

ID Face Name Rp C Rd

2 LUL2_new_final 1615 1.12E-05 11778

3 LUL_new_final 1407 1.99E-05 6917

4 LUML2_final 2403 6.96E-06 17046

5 LUML3_final 2403 6.97E-06 17045

6 LUML_final 1542 1.18E-05 10851

7 LML_final 1621 1.36E-05 9590

8 LML2_final 1859 7.91E-06 15256

9 LML4_final 1859 7.91E-06 15256

10 LML5_final 2328 6.75E-06 17705

11 LLL2_final 1799 8.85E-06 12706

12 LLL3_final 2328 6.75E-06 17705

13 LLL_final 1385 1.16E-05 11737

14 LPA_final 1132 2.24E-05 5783

15 RUL_final 1422 1.38E-05 8825

16 RULbr3_final 4481 2.78E-06 38549

17 RULbr2_final 3849 3.61E-06 30699

18 RULbr4_final 2422 6.92E-06 17247

19 RULbr_final 2703 4.56E-06 23992

20 RML5_final 1863 8.19E-06 15642

21 RML2_final 1796 1.52E-05 9055

22 RML3_final 1476 1.70E-05 7760

23 RML4_final 1146 2.21E-05 5909

24 RML_final 1378 1.17E-05 11634

25 RLL_final 886 2.98E-05 5057

26 RLL2_final 1388 1.16E-05 11780

27 RPA_final 783 4.32E-05 3529

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Table 15 – RCR Values for 0076_0000 in cgs units

ID Face Name Rp C Rd

2 LUL1 1016 2.05E-05 6384

3 LUL2 2408 6.57E-06 18602

4 LML1 1141 2.22E-05 5863

5 LML2 1391 1.16E-05 11827

6 LML3 1939 7.29E-06 16463

7 LML4 1560 1.38E-05 9147

8 LLL1 1920 1.01E-05 13288

9 LLL2 882 3.20E-05 5009

10 LLL3 1260 2.09E-05 6433

11 RUL1 1723 8.38E-06 14014

12 RUL2 2236 7.04E-06 16668

13 RUL3 1826 8.44E-06 14591

14 RUL4 2471 6.44E-06 19291

15 RML1 1555 1.59E-05 8469

16 RML2 1116 2.34E-05 5534

17 RML3 796 3.83E-05 4292

18 RLL1 1806 1.40E-05 9724

19 RLL2 1124 2.26E-05 5706

20 RLL3 1487 1.27E-05 9801

21 RLL4 1302 2.02E-05 6700

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© 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 21

Table 16 – RCR Values for 0077_0000 in cgs units

ID Face Name Rp C Rd

2 LUL 1264 1.99E-05 6636

3 LMA 1709 1.77E-05 7828

4 LMAA 1374 1.17E-05 11589

5 LML 1129 2.25E-05 5757

6 LMB 1408 1.99E-05 6925

7 LMBA 1656 1.71E-05 7803

8 LMC 802 4.55E-05 3491

9 LMCB 875 3.23E-05 4939

10 LLL 819 4.37E-05 3583

11 LPA 888 3.74E-05 3823

12 RUL 766 5.27E-05 3167

13 RULB 1342 2.01E-05 6792

14 RMAB 1257 2.10E-05 6406

15 RMBA 881 3.30E-05 4828

16 RMA 762 4.22E-05 3542

17 RLL 635 5.10E-05 3150

18 RMB 754 5.54E-05 3093

19 RMC 881 3.30E-05 4828

20 RPA 1135 2.23E-05 5805

21 RLL_2 1129 1.99E-05 6725

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© 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 22

Appendix

1. Image Data Orientation The RAS coordinate system was assumed for the image data orientation. Voxel Spacing, voxel dimensions, and

physical dimensions are provided in the Right-Left (R), Anterior-Posterior (A), and Superior-Inferior (S) direction

in all specification documents unless otherwise specified.

2. Model Construction All anatomic models were constructed in RAS Space. The models are generated by selecting centerline paths

along the vessels, creating 2D segmentations along each of these paths, and then lofting the segmentations

together to create a solid model. A separate solid model was created for each vessel and Boolean addition was

used to generate a single model representing the complete anatomic model. The vessel junctions were then

blended to create a smoothed model.

3. Physiological Assumptions Newtonian fluid behavior is assumed with standard physiological properties. Blood viscosity and density are

given below in units used to input directly into the solver.

Blood Viscosity: 0.04 g/cm•s2

Blood Density: 1.06 g/cm3

4. Simulation Parameters Conservation of mass and Navier-Stokes equations were solved using 3D finite element methods assuming rigid

and non-slip walls. All simulations were ran in cgs units and ran for several cardiac cycles to allow the flow rate

and pressure fields to stabilize.

5. Outlet Boundary Conditions

5.1 Resistance Methods

Resistances values can be applied to the outlets to direct flow and pressure gradients. Total

resistance for the model is calculated using relationships of the flow and pressure of the model.

Total resistance is than distributed amongst the outlets using an inverse relationship of outlet area

and the assumption that the outlets act in parallel.

5.2 Windkessel Model

In order to represent the effects of vessels distal to

the CFD model, a three-element Windkessel model

can be applied at each outlet. This model consists of

proximal resistance (Rp), capacitance (C), and distal

resistance (Rd) representing the resistance of the

proximal vessels, the capacitance of the proximal

vessels, and the resistance of the distal vessels

downstream of each outlet, respectively (Figure 1).

Figure 5 - Windkessel model

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© 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 23

First, total arterial capacitance (TAC) was calculated using inflow and blood pressure. The TAC was

then distributed among the outlets based on the blood flow distributions. Next, total resistance (Rt)

was calculated for each outlet using mean blood pressure and PC-MRI or calculated target flow

(Rt=Pmean/Qdesired). Given that Rt=Rp+Rd, total resistance was distributed between Rp and Rd adjusting

the Rp to Rt ratio for each outlet.


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