Theoretical and Experimental Assessment of Aortic Stiffness … · 2013. 9. 6. · propagation...
1
The lab member, Dr. S. Nandlall, for providing helpful discussions. Dr. K. Myers and M. Fernandez, Department of Mechanical Engineering, Columbia University, for helping with mechanical testing design and facilities. Drs. T. McGloughlin and B. Doyle, Dept of Mechanical and Aeronautical Engineering, Univ of Limerick, Limerick, Ireland, for providing the patient-specific silicone phantoms. Arterial stiffness has been shown as a reliable indicator of cardiovascular diseases such as hypertension and aneurysms [1-2] Large variability in existing measurements of aortic stiffness: • Human healthy abdominal aorta: Young’s modulus: 120-1150kPa [3,4,5] • Human aneurysmal abdominal aorta: Pressure-diameter modulus:100-800kPa [6], Ultimate tensile strength: 480-910kPa [7] Available methods for aortic stiffness estimation: • Based on central pressure vs. diameter data; either via catheterization [8] (invasive ), or via tonometry along with empirical pressure transfer functions [9] (inaccurate ) • Based on pulse pressure profiles usually between carotid-femoral arteries to obtain average pulse wave velocity (PWV) for stiffness estimate [10] (nonlocal ) Pulse wave imaging (PWI) has been developed as an effective method for noninvasive , accurate and local estimation of PWV, and its reliability has been shown on experimental aortic phantoms as well as on human and mouse healthy and aneurysmal aortas in vivo [4,11]. Various numerical methods have been used to solve one-dimensional pulse wave propagation [12,13,14] and to simulate wave propagation in cardiovascular system [15,16,17]. Just recently, finite element simulation models have been proposed as an effective method to study pulse wave propagation [18,19,20]. The objective of this study is to implement PWI on finite element simulated models of aorta and to measure PWV under different material stiffness Theoretical and Experimental Assessment of Aortic Stiffness using Pulse Wave Imaging Danial Shahmirzadi 1 , Ronny X. Li 1 , Jianwen Luo 1 , Elisa E. Konofagou 1,2 1 Department of Biomedical Engineering, 2 Department of Radiology, Columbia University, New York, NY Introduction Theoretical MK PWV model: Modified Moens-Korteweg (MK) relation was used as the theoretical reference model to relate E and PWV in an elastic cylindrical tube [6,7]: E : Young’s modulus; ν: Poisson’s ratio; ρ: density; r: lumen radius; PWV: pulse wave velocity; t: wall thickness Simulated PWI: Simulated PWI was implemented on Coupled Eulerian-Lagrangian solver of Abaqus 6.10-1 3D Model geometry was generated identical to patient-specific aortic phantoms obtained from CT scan (r=12mm; t=2.2mm) Model material parameters were taken from mechanical testing on the phantoms • Cyclic tensile and stress relaxation tests using Instron to determine Young's modulus, E; and 2D strain fields using digital image correlation (DIC) system to determine Poisson’s ratio). Frictionless interaction of fluid and phantom wall Linear fit of wave peaks versus arrival times was calculated as PWV Additional simulations were perfomed with input Young’s moduli of double and triple the true modulus Silicone Phantom PWI: Custom laboratory set up was used to implement PWI on same silicone phantoms of L=78mm (Fig. 6) Linear-array ultrasound transducer; 38mm imaging width; 16 beams; 915 fps; 35mm depth 1-D cross correlation method was performed on radio-frequency (RF) data to estimate the wall displacement [11] Linear fit of wave locations versus arrival times was calculated as PWV Materials and Methods Simulated PWI • Negligible viscosity and hysteresis at small-strain regime (not shown here) • Isotropic • Elastic material constants Silicone phantoms PWI Results Difference between simulated/experimental PWV estimates and theoretical PWV could be due to deviations from MK model assumptions such as: • Phantom’s finite length and thin-walled approximation • Boundary effects such as wave development initially as well as reflection at the end • Fluid-solid interaction properties, e.g. friction, meshing match • Difference in material properties, e.g. non-homogeneity, viscoelasticity • Deviation from circular cross section and cylindrical shape • Flow profile and turbulence as well as velocity magnitude • Identifying the most robust and reliable wave characteristic point to measure PWV Challenges in simulated PWI: • Determining the most realistic physical parameters for material modeling, boundary conditions and fluid-solid interaction • Compromising between accuracy/robustness of the results and computational cost, e.g. mesh configuration, spatio-temporal resolution on requested outputs Challenges in silicone phantoms PWI: • Compromise between transducer beam density versus imaging frame rate • Maintaining accurate in-plane imaging across phantom’s axial cross section Discussion Simulated PWI was found to be an effective method to capture the changes in the material properties, i.e. higher PWV on phantoms of higher stiffness Higher correlation of wave propagation data to the linear fit was observed on simulated models versus experimental silicone phantoms Very similar PWV measures were found for wave peak and foot points, both in simulation and experiment, which show linear wave propagation • Selection of characteristic point on the wave was found not to be critical for PWV estimates Finite element simulation models of PWI could be a powerful tool to investigate pulse wave propagation mechanisms and to measure local PWV for stiffness estimation Simulated PWI can be used on cardiovascular systems in health as well as in diseases where local changes in geometry, stiffness and composition are of interest Conclusion Acknowledgements Figure 2. Stress-strain curve under cyclic tensile testing of silicone phantom specimens used to determine Young’s modulus Figure 1. 3D finite element model of aortic phantom under pulsatile flow Figure 4. 3D visualization of upper wall displacement versus axial location on the tube versus time Figure 5. Spatio-temporal plot of upper wall displacement: (Left)E=2.56MPa; (Middle)E=5.12MPa; (Right)E=7.68MPa. At each time point, points that correspond to wave peak and 50% of the wave peak are identified and used to calculate PWV. Input E (MPa) Theoretical M-K PWV (m/s) Simulation PWV (m/s) Silicone Phantom PWV (m/s) Estimated E (MPa) Wave Peak Wave Foot Wave Peak Wave Foot Simulation Silicone Phantom 2.56 17.04 12.22 (r²=0.996) error=-28.28% 12.97 (r²=0.998) error=-23.88% 17.55 (r²=0.856) error=2.99% 17.22 (r²=0.971) error=1.06% 1.48 2.56 5.12 24.10 17.16 (r²=0.997) error=-28.80% 17.15 (r²=0.999) error=-28.84% N/A N/A 2.60 N/A 7.68 29.52 20.49 (r²=0.998) error=-30.59% 20.67 (r²=0.999) error=-29.98% N/A N/A 3.76 N/A Table 1. Theoretical PWV and stiffness as well as simulation and silicone phantom estimates. PWV errors on silicone and simulated phantoms were measured based on theoretical PWV. In each case, the PWV value, that was used for estimation of E, is underlined. Figure 3. Consecutive frames of the phantom wall motion obtained from simulated PWI Figure 6. Schematic of phantom PWI laboratory set up Figure 7. Consecutive frames of the wall motion in silicone phantom obtained from PWI Figure 8. Spatio-temporal plot of upper wall displacement References [1] Laurent, S, et al. 2001. Hypertension 37(5): 1236-41. [2] Sutton-Tyrrell, K, et al. 2005. Circulation 111: 3384–3390. [3] Nichols, WW, et al. 1987. Vascular/ventricular coupling NY. Springer-Verlag: 79-114.\ [4] Vappou J, et al.2010. AM J Hyper 23(4): 393-98. [5] Hirai, T, et al. 1989. Circulation 80: 78-86 [6] MacSweeney, STR, et al. 1992. Br J Surg 79: 1281-1284 [7] Di Martino, ES, et al. 2006. J Vasc Surg 43(3): 576. [8] Segers, P, et al. 2005. Am J Physiol-Heart Circul Physiol 288: H1157-H1164. [9] O'Rourke, M, et al. 2002. Am J Hypertens 15: 426–444. [10] Pannier, B, 2002. Am J Hypertens 15: 743–753. [11] Luo, J, et al. 2009. IEEE Trans Med Imaging 28(4): 477-86. [12] Avolio, AP. 1980. Medical Biological Engineering Computing 18: 709-718. [13] Reuderink, PJ, et al. 1989. Biomech 22: 819-27. [14] Stergiopulos,N, et al. 1992.Biomech 25: 1477-88. [15] Schaaf, BW, 1974. Biomechanics 5(4): 345-364 [16] Berger, D, et al. 1994. Am J Physiol 266(4): H1626-42 [17] Mookerjee, A, et al. 2010 Biomech Model Mechanobiol 9(6): 773-81 [18] Zervantonakis, IK, et al. 2007. Ultrasonic Measurement Imag . NM, Nov. 2–5. [19] Vappou J, et al. 2008. Computational Biomechanics Medicine III : 118-127 [20] Cooper, DB, et al. 2009. Joint ASCE‐ASME‐SES Conf Mechanics and Materials, VA, June 24-27. ( ) t rPWV E / 1 2 2 2 ρ ν − = 48 . 0 ; 56 . 2 = = ν MPa E
Transcript of Theoretical and Experimental Assessment of Aortic Stiffness … · 2013. 9. 6. · propagation...
-
The lab member, Dr. S. Nandlall, for providing helpful discussions.
Dr. K. Myers and M. Fernandez, Department of Mechanical Engineering, Columbia University, for helping with mechanical testing design and facilities.
Drs. T. McGloughlin and B. Doyle, Dept of Mechanical and Aeronautical Engineering, Univ of Limerick, Limerick, Ireland, for providing the patient-specific silicone phantoms.
Arterial stiffness has been shown as a reliable indicator of cardiovascular diseases such as hypertension and aneurysms [1-2]
Large variability in existing measurements of aortic stiffness:• Human healthy abdominal aorta: Young’s modulus: 120-1150kPa [3,4,5]• Human aneurysmal abdominal aorta: Pressure-diameter modulus:100-800kPa [6], Ultimate tensile strength: 480-910kPa [7]
Available methods for aortic stiffness estimation:• Based on central pressure vs. diameter data; either via catheterization [8] (invasive), or via tonometry along with empirical pressure transfer functions [9] (inaccurate)• Based on pulse pressure profiles usually between carotid-femoral arteries to obtain average pulse wave velocity (PWV) for stiffness estimate [10] (nonlocal)
Pulse wave imaging (PWI) has been developed as an effective method for noninvasive, accurate and local estimation of PWV, and its reliability has been shown on experimental aortic phantoms as well as on human and mouse healthy and aneurysmal aortas in vivo [4,11].
Various numerical methods have been used to solve one-dimensional pulse wave propagation [12,13,14] and to simulate wave propagation in cardiovascular system [15,16,17]. Just recently, finite element simulation models have been proposed as an effective method to study pulse wave propagation [18,19,20].
The objective of this study is to implement PWI on finite element simulated models of aorta and to measure PWV under different material stiffness
Theoretical and Experimental Assessment of Aortic Stiffness using Pulse Wave ImagingDanial Shahmirzadi1, Ronny X. Li1, Jianwen Luo1, Elisa E. Konofagou1,2
1Department of Biomedical Engineering, 2Department of Radiology, Columbia University, New York, NY
Introduction
Theoretical MK PWV model: Modified Moens-Korteweg (MK) relation was used as the theoretical reference model to relate E and PWV in an elastic cylindrical tube [6,7]:
E : Young’s modulus; ν: Poisson’s ratio; ρ: density; r: lumen radius; PWV: pulse wave velocity; t: wall thickness
Simulated PWI: Simulated PWI was implemented on Coupled Eulerian-Lagrangian solver of Abaqus6.10-1
3D Model geometry was generated identical to patient-specific aortic phantoms obtained from CT scan (r=12mm; t=2.2mm)
Model material parameters were taken from mechanical testing on the phantoms• Cyclic tensile and stress relaxation tests using Instron to determine Young's modulus, E; and 2D strain fields using digital image correlation (DIC) system to determine Poisson’s ratio). Frictionless interaction of fluid and phantom wall
Linear fit of wave peaks versus arrival times was calculated as PWV
Additional simulations were perfomed with input Young’s moduli of double and triple the true modulus
Silicone Phantom PWI: Custom laboratory set up was used to implement PWI on same silicone phantoms of L=78mm (Fig. 6)
Linear-array ultrasound transducer; 38mm imaging width; 16 beams; 915 fps; 35mm depth
1-D cross correlation method was performed on radio-frequency (RF) data to estimate the wall displacement [11]
Linear fit of wave locations versus arrival times was calculated as PWV
Materials and Methods
Simulated PWI• Negligible viscosity and hysteresis at small-strain regime (not shown here)
• Isotropic• Elastic material constants
Silicone phantoms PWI
Results Difference between simulated/experimental PWV estimates and theoretical PWV could be due to deviations from MK model assumptions such as:
• Phantom’s finite length and thin-walled approximation• Boundary effects such as wave development initially as well as reflection at the end• Fluid-solid interaction properties, e.g. friction, meshing match• Difference in material properties, e.g. non-homogeneity, viscoelasticity• Deviation from circular cross section and cylindrical shape• Flow profile and turbulence as well as velocity magnitude• Identifying the most robust and reliable wave characteristic point to measure PWV
Challenges in simulated PWI:• Determining the most realistic physical parameters for material modeling, boundary conditions and fluid-solid interaction• Compromising between accuracy/robustness of the results and computational cost, e.g. mesh configuration, spatio-temporal resolution on requested outputs
Challenges in silicone phantoms PWI:• Compromise between transducer beam density versus imaging frame rate• Maintaining accurate in-plane imaging across phantom’s axial cross section
Discussion
Simulated PWI was found to be an effective method to capture the changes in the material properties, i.e. higher PWV on phantoms of higher stiffness
Higher correlation of wave propagation data to the linear fit was observed on simulated models versus experimental silicone phantoms
Very similar PWV measures were found for wave peak and foot points, both in simulation and experiment, which show linear wave propagation
• Selection of characteristic point on the wave was found not to be critical for PWV estimates
Finite element simulation models of PWI could be a powerful tool to investigate pulse wave propagation mechanisms and to measure local PWV for stiffness estimation
Simulated PWI can be used on cardiovascular systems in health as well as in diseases where local changes in geometry, stiffness and composition are of interest
Conclusion
Acknowledgements
Figure 2. Stress-strain curve under cyclic tensile testing of silicone phantom specimens used to determine Young’s modulus
Figure 1. 3D finite element model of aortic phantom under pulsatile flow
Figure 4. 3D visualization of upper wall displacement versus axial location on the tube versus time
Figure 5. Spatio-temporal plot of upper wall displacement: (Left)E=2.56MPa; (Middle)E=5.12MPa; (Right)E=7.68MPa.At each time point, points that correspond to wave peak and 50% of the wave peak are identified and used to calculate PWV.
Input E (MPa) Theoretical M-K PWV (m/s) Simulation PWV (m/s) Silicone Phantom PWV (m/s) Estimated E (MPa)Wave Peak Wave Foot Wave Peak Wave Foot Simulation Silicone Phantom
2.56 17.04 12.22 (r²=0.996)
error=-28.28%
12.97 (r²=0.998)
error=-23.88%
17.55 (r²=0.856)
error=2.99%
17.22 (r²=0.971)
error=1.06%
1.48 2.56
5.12 24.10 17.16 (r²=0.997)
error=-28.80%
17.15 (r²=0.999)
error=-28.84%
N/A N/A 2.60 N/A
7.68 29.52 20.49 (r²=0.998)
error=-30.59%
20.67 (r²=0.999)
error=-29.98%
N/A N/A 3.76 N/A
Table 1. Theoretical PWV and stiffness as well as simulation and silicone phantom estimates. PWV errors on silicone and simulated phantoms were measured based on theoretical PWV. In each case, the PWV value, that was used for estimation of E, is underlined.
Figure 3. Consecutive frames of the phantom wall motion obtained from simulated PWI
Figure 6. Schematic of phantom PWI laboratory set up
Figure 7. Consecutive frames of the wall motion in silicone phantom obtained from PWI
Figure 8. Spatio-temporal plot of upper wall displacement
References[1] Laurent, S, et al. 2001. Hypertension 37(5): 1236-41.[2] Sutton-Tyrrell, K, et al. 2005. Circulation 111: 3384–3390.[3] Nichols, WW, et al. 1987. Vascular/ventricular coupling NY. Springer-Verlag: 79-114.\[4] Vappou J, et al.2010. AM J Hyper 23(4): 393-98.[5] Hirai, T, et al. 1989. Circulation 80: 78-86[6] MacSweeney, STR, et al. 1992. Br J Surg 79: 1281-1284[7] Di Martino, ES, et al. 2006. J Vasc Surg 43(3): 576.[8] Segers, P, et al. 2005. Am J Physiol-Heart Circul Physiol 288: H1157-H1164.[9] O'Rourke, M, et al. 2002. Am J Hypertens 15: 426–444.[10] Pannier, B, 2002. Am J Hypertens 15: 743–753.[11] Luo, J, et al. 2009. IEEE Trans Med Imaging 28(4): 477-86.[12] Avolio, AP. 1980. Medical Biological Engineering Computing 18: 709-718.[13] Reuderink, PJ, et al. 1989. Biomech 22: 819-27.[14] Stergiopulos,N, et al. 1992.Biomech 25: 1477-88.[15] Schaaf, BW, 1974. Biomechanics 5(4): 345-364[16] Berger, D, et al. 1994. Am J Physiol 266(4): H1626-42 [17] Mookerjee, A, et al. 2010 Biomech Model Mechanobiol 9(6): 773-81[18] Zervantonakis, IK, et al. 2007. Ultrasonic Measurement Imag. NM, Nov. 2–5.[19] Vappou J, et al. 2008. Computational Biomechanics Medicine III: 118-127[20] Cooper, DB, et al. 2009. Joint ASCE‐ASME‐SES Conf Mechanics and Materials, VA, June 24-27.
( ) trPWVE /12 22 ρν−=
48.0;56.2 == νMPaE
Slide Number 1
![A comparison of four software programs for implementing ...paceomics.org/wp-content/uploads/2016/05/PACEOMICS... · Table 2: Prices (US $) for Microsoft Excel – March 2016[15,16,17]](https://static.fdocuments.in/doc/165x107/5f22ab8eb1a1e96fe2111e74/a-comparison-of-four-software-programs-for-implementing-table-2-prices-us.jpg)
