CPM Specifications Document Aortofemoral Normal:

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1 CPM Specifications Document Aortofemoral Normal: OSMSC 0003_ _0000 May 24, 2013 Version 1 Open Source Medical Software Corporation 2013 Open Source Medical Software Corporation. All Rights Reserved.

2 1. Clinical Significance & Condition Studying the hemodynamics of the vasculature distal to the abdominal aorta may be important in understanding common diseases in peripheral arteries downstream of the thoracic aorta. Diseases in the peripheral vasculature affect millions of people in the U.S and can have a profound effect on daily quality of life. Peripheral arterial disease is the build-up of fatty tissue, or atherosclerosis, in lower extremity arteries. By 2001 at least 10 million people in the U.S were estimated to have peripheral arterial disease. The prevalence of peripheral arterial occlusive disease increases with age and can increase to up to 20% of the population in the geriatric population [1]. Up to 4 million people in the U.S suffer from intermittent claudication causing pain in the legs during exercise. Atherosclerotic occlusive disease of the lower extremity arteries is a major cause of walking impairment, pain, ulcerations and gangrene. Renal artery stenosis can have a prevalence of up to 45% in selective populations, specifically populations with other vascular disease. Prevalence can be from 1-6% in hypertensive patients to 30-45% in patients with aortoiliac occlusive disease or abdominal aortic aneurysms [1]. It is most often caused by atherosclerosis in the renal arteries and is often undetected until symptoms become severe. The most common symptom of renal artery stenosis is hypertension, which can have significant effects on the entire vascularture. Up to 24% of patients with renal insuffiency, which can lead to end-stage renal disease renal disease, had renal artery stenosis, suggesting that renal artery stenosis may play an important role in kidney failure [1]. 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). Voxel Spacing, voxel dimensions, and physical dimensions are provided in the Right-Left (R), Anterior-Posterior (A), and Superior-Inferior (S) direction. OSMSC ID Modality Voxel Spacing Voxel Dimensions Physical Dimensions R A S R A S R A S 0003_0000 CT _0000 MR Open Source Medical Software Corporation. All Rights Reserved. Page 2

3 Patient specific clinical data can be seen in Table 2.Note that no patient specific clinical data other than age and gender were available for patient 0003_0000. Table 2 Available patient-specific clinical data OSMSC ID Age Gender Height Weight DP (mmhg) MP (mmhg) SP (mmhg) 0003_ F _ M Anatomic Model Description Anatomic models were created using customized SimVascular software (Simtk.org) and the image data described in Section 2. Aortofemoral models extend from the ascending or thoracic aorta to the femoral arteries. See Table 3 for a visual summary of the image data, paths, segmentations and solid model constructed. Table 3 Visual summary of image data, paths, segmentations and solid model. OSMSC ID Image Data Paths Paths and Segmentations Model ID: OSMSC0003 subid: 0000 Age: 21 Gender: F 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 3

4 ID: OSMSC0006 subid: 0000 Age: 30 Gender: M Details of anatomic models, such has number of outlets and model volume, can be seen in Table 4. OSMSC ID Inlets Outlets (cm 3 ) Table 4 Anatomic Model details Volume (cm 2 ) Surface Area (cm 2 ) Vesel Paths 2-D Segementations 0003_ _ 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 for information on the physiology and simulation specifications. Simulation Parameters are shown in Table 5. Table 5- Simulation Parameters OSMSC ID Time Steps per Cycle Time Stepping Strategy 0003_ fixed_step _ fixed_step Open Source Medical Software Corporation. All Rights Reserved. Page 4

5 5. 2 Inlet Boundary Conditions For 0003_0000 the inflow waveform was adapted from Olufsen et. al. and then smoothed [2]. The mean value of the inflow waveform was reasonably in the range of mean cardiac output of 4.6 L/min given for women in Collis and the standard 5.0 L/min given in Berne and Levy [3, 4]. For 0006_0000, clinically acquired patient height and weight were used to calculate patient BSA based on the Moseller equation. The BSA was then used to calculate the cardiac output based on the Baker equation. Flow to the supraceliac aorta was assumed to be 66% of the cardiac output [5, 6]. Patient-specific inflow waveforms were created by scaling a gender-matched representative supraceliac aortic waveform. Inflow waveforms were prescribed to the inlets of the computational fluid dynamics (CFD) models (Figure 1). See Table 6 for the period and prescribed cardiac inflow for each simulation. Table 6 Period and Cardiac Output from waveforms seen in Figure 1 OSMSC ID Period (s) Cardiac Output (L/min) Profile Type 0003_ Womersley 0006_ Womersley 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 5

6 Figure 1 Inflow waveforms in L/min 5. 3 Outlet Boundary Conditions A three element Windkessel model was applied at each outlet. For more information refer to Exhibit 1 and Appendix 5. To define the parameters in the Windkessel model the mean flow to each outlet was calculated. For both 0003 and 0006 various literature sources were used to calcite the outflow to each artery. Target flow splits are shown in 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 6

7 Table _0000: It is thought that 10-18% of total cardiac output goes to the brain [7, 8, 9, 10, 11]. From this range, 13% of cardiac output to the brain was selected (6.5% to each carotid artery). Because 65% of cardiac output is thought to go down the descending thoracic aorta, then the remaining 22% of cardiac output was assumed to enter the subclavian arteries (11% to each subclavian) [12]. The thoracic aortic flow (65% of the total cardiac output) is equal to the flow entering the abdominal aorta at the supraceliac level. The amount of flow entering the infrarenal aorta was determined from a ratio of infrarenal to supraceliac flow from Cheng and colleagues [13]. Because the supraceliac and infrarenal flow were calculated, the total amount of flow exiting the upper branch vessels (the hepatic, splenic, SMA, and left and right renal arteries) could be determined. This flow to the upper branch vessels was distributed to each upper branch vessel according to measurements made by Moore and Ku [14]. The remaining aortic infrarenal flow was divided equally to the right and left common iliac arteries. From each common iliac artery, each external iliac artery received 70% and each internal iliac received 30% of the common iliac flow flow [15]. The desired flow to the right and left femoral, profunda, and external circumflex arteries was based approximately on the areas of their outlets. 0006_0000: Flow to the supraceliac aorta was taken as 66% of the cardiac output [5, 6]. From the supraceliac flow 21.7% was prescribed to the celiac artery and 14.7% to the superior mesenteric artery [16]. The flow to the celiac artery was split evenly between the hepatic and splenic artery. About 23.3% of cardiac output is thought to go to the kidneys [17]. This flow was also split evenly between the right and left renal arteries. This leaves 29.8% of the remaining flow from the supraceliac aorta to flow through the infrarenal aorta, which is consistent with findings from Cheng et. al. based on PCMRI flow data collected in healthy male subjects ages 20 to 24 years [18]. The remaining flow to the infrarenal aorta was then split evenly between the left and right common iliac arteries. That flow was then distributed to the external iliac and internal iliac arteries at a 70% and 30% of the common iliac artery flow respectively. Target Pressures for 0003_0000 were set based on typical pressures for healthy adults, while target pressures for 0006_0000 were based on clinically-acquired pressure measurements. See Table 6 for target pressures Open Source Medical Software Corporation. All Rights Reserved. Page 7

8 Table 7 Flow distributions and Pressures OSMSC ID 0003_ _0000 Hepatic 7.6% 10.8% Left External Iliac % Left Femoral 2.6% - Left Internal Iliac 2.8% 4.5% Left Profunda 1.3% - Left Renal 10.4% 16.9% Left Common Carotid 6.6% - Left External Circumflex 2.6% - Left Subclavian 11.0% - Right External Iliac % Right Femoral 2.6% - Right Internal Iliac 2.8% 4.5% Right Profunda 1.3% - Right Renal 10.5% 16.9% Right Common Carotid 6.6% - Right External Circumflex 2.6% - Right Subclavian 11.0% - Superior Mesenteric 10.3% 14.7% Splenic 7.5% 10.8% Systolic Pressure (mmhg) Diastolic Pressure (mmhg) Mean Pressure (mmhg) Simulation Results Simulation results were quantified for the last cardiac cycle. Paraview (Kitware, Clifton Park, NY), an opensource 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 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 8

9 Table 8 for each model Open Source Medical Software Corporation. All Rights Reserved. Page 9

10 Table 8 Volume rendering velocity during peak systole, end systole, and end diastole. All renderings have the scale below with units of cm/s OSMSC ID Peak Systole End Systole End Diastole ID: OSMSC0003 subid: 0000 Age: 21 Gender: F ID: OSMSC0006 subid: 0000 Age: 30 Gender: M 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 10

11 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 9. Table 9 Time averaged blood pressure (TABP), time-average wall shear stress (TAWSS), and oscillatory shear index (OSI) surface distributions OSMSC ID TABP TAWSS OSI ID: OSMSC0003 subid: 0000 Age: 21 Gender: F ID: OSMSC0006 subid: 0000 Age: 30 Gender: M 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 11

12 7. References [1] W. R. Hiatt, A. T. Hirsch and J. Regensteiner, Peripheral Artery Disease Handbook, Boca Raton, FL: CRC Press LLC, [2] M. Olufsen, C. Peskin, W. Kim, E. Pedersen, A. Nadim and J. Larsen, "Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions," Annals of Biomediacl Engineering, vol. 28, pp , [3] T. Collis, R. Devereux, M. Roman, G. de Simone, J. Yeh, B. Howard, R. Fabsitz and T. Welty, "Relations of stroke volume and cardiac output to body composition - the strong heart study," Circulation, vol. 103, pp , [4] R. Berne and M. Levy, " Cardiovascular Physiology," no. 8th Edition, [5] P. Reymond, F. Merenda, F. Perren, D. Rufenacht and N. Stergiopulos, "Validation of a One-Dimensional Model of the Systemic Arterial Tree," Am J Physiol Heart Circ Physiol, no. 297, pp. H208-H222, [6] B. N. Steele, M. S. Olufsen and C. A. Taylor, "Fractal network for Simulating Abdominal and Lower Extremity Blood Flow During Resting and Exercise Conditions," Comput. Methods Biomech. Biomed Engin., vol. 10, no. 1, pp , [7] L. Williams et. al., "Reference values for resting blood flow to organs of man," Clin. Phys. Physiol. Meas., vol. 10, no. 3, pp , [8] H. Keller at. al., "Noninvasive Measurement of Velocity Profiles and Blood Flow in the Common Carotid Artery by Pulsed Doppler Ultrasound," Stroke, vol. 7, no. 4, pp , [9] P. Scheel et. al., "Color Duplex Measurement of Cerebral Blood Flow Volume in Healthy Adults," Stroke, vol. 31, pp , [10] B. Chu et. al., "Flow Volume in the Common Carotid Artery Detected by Color Duplex Sonography: An Approach to the Normal Value and Predictability of Cerebral Blood Flow.," Radiation Medicina, vol. 18, no. 4, pp , [11] H. Bogren et. al., "Blood Flow Measurements in the Aorta and Major Arteries with MR Velocity Mapping," JMRI, vol. 4, pp , [12] F. Nicoud et. al., "Integral Boundary Conditions for Unsteady Biomedical CFD Applications," Int. J. Numer. Meth. Fluids, vol. 40, pp , [13] C. Cheng, R. Herfkens and C. Taylor, "Comparison of abdominal aortic hemodynamics between men and women at rest and during lower limb exercise," Journal of Vascular Surgery, vol. 37, pp , Open Source Medical Software Corporation. All Rights Reserved. Page 12

13 [14] J. J. Moore and D. Ku, "Pulsatile velocity measurements in a model of the human abdominal aorta under resting conditions," J Biomech Eng., vol. 116, pp , [15] B. Steele, M. Olufsen and C. Taylor, "Fractal network model for simulating abdominal and lower extremity blood flow during resting and exercise conditions," Computer Methods in Biomechanics and Biomedical Engineering, vol. 10, pp , [16] J. E. Moore Jr. and D. N. Ku, "Pulsatile Velocity Meaurements in a Model of the Human Abdominal aorta Under Resting Conditions," ASME Journal of Biomechanical Engineering, vol. 116, pp , [17] W. W. Nichols, M. F. Rourke and C. Vlachopoulos, McDonald's Blood Flow Arteries: Theoretical, Experimental and Clinical Principles, London: Hoddel Arnold, [18] C. P. Cheng, R. J. Herfkens and C. A. Taylor, "Comparison of Abdominal Aortic Hemodynamics Between Men and Women at Rest and During Lowe Limb Exercise," Journal of Vascular Surgery, vol. 37, no. 1, pp , Open Source Medical Software Corporation. All Rights Reserved. Page 13

14 Exhibit 1: Aortofemoral Simulations RCR Values Information on how RCR values were obtained is included in Appendix 5. RCR values for the final simulations are shown on Tables 9 and 10 for 0003_0000 and 0006_0000 respectively. Table 10 RCR Values for 0003_0000 in cgs Solver ID Face Name Artery Name Rp C Rd 2 Brachiocephalic_Right_Subclavian Right Subclavian Right_Common_Carotid Right Common Carotid Left_Common_Carotid Left Common Carotid Left_Subclavian Left Subclavian Celiac_Hepatic Hepatic Splenic Splenic SMA Superior Mesenteric Left_Renal Left Renal Right_Renal Right Renal Left_Internal Left Internal Right_Internal Right Internal Left_Profunda Left Profunda Right_Profunda Right Profunda Left_Profunda_2 Left External Circumflex Right_Profunda_2 Right External Circumflex Aorta_Smoothed Left Femoral Common_External_Femoral Right Femoral Table 11 RCR values for 0006_0000 in cgs Solver ID Face Name Artery Name Rp C Rd 2 hepatic Heptic splenic Splenic SMA Superior Mesenteric right_renal Right Renal left_renal Left Renal right_internal_iliac Right Internal Iliac left_internal_iliac Left Internal Iliac right_external_iliac Right External Iliac left_external_iliac Left External Iliac Open Source Medical Software Corporation. All Rights Reserved. Page 14

15 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 s 2 Blood Density: 1.06 g/cm 3 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 (R p ), capacitance (C), and distal resistance (R d ) 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 2 - Windkessel model 2013 Open Source Medical Software Corporation. All Rights Reserved. Page 15

16 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 (R t ) was calculated for each outlet using mean blood pressure and PC-MRI or calculated target flow (R t =P mean /Q desired ). Given that R t =R p +R d, total resistance was distributed between R p and R d adjusting the R p to R t ratio for each outlet Open Source Medical Software Corporation. All Rights Reserved. Page 16