Design, Development and Temporal Evaluation of an MRI-compatible In-vitro

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(1)Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 1. Design, Development and Temporal Evaluation of an MRI-compatible In-vitro. 2. Circulation Model using a Compliant AAA Phantom. 3. Mirunalini Thirugnanasambandam,1 Tejas Canchi,2 Senol Piskin,3,4 Christof Karmonik,5. 4. Ethan Kung,6 Prahlad G. Menon,7 Stephane Avril,8 Ender A. Finol1,3*. ed ite d. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. University of Texas at San Antonio, UTSA/UTHSCSA Joint Graduate Program in Biomedical Engineering, San Antonio, TX, U.S.A. 1. Technological University, Department of Mechanical and Aerospace Engineering, Singapore. Co. py. 2 Nanyang. University of Texas at San Antonio, Department of Mechanical Engineering, San Antonio, TX, U.S.A.. Houston Methodist Research Institute, MRI Core, Houston, TX, U.S.A.. 6 Clemson. sc rip. 5. University, Department of Mechanical Engineering, Istanbul, Turkey. tN. 4 Istinye. ot. 3. University, Department of Mechanical Engineering, Clemson, SC, U.S.A.. Carlow University, Department of Mathematics and Data Analytics, Pittsburgh, PA, U.S.A.. Ma nu. 7. 8 Ecole. Nationale Supérieure des Mines, Center for Biomedical and Healthcare Engineering, St-Etienne, France. ce. pt. ed. *Corresponding author University of Texas at San Antonio Department of Mechanical Engineering Room EB 3.04.08 One UTSA Circle San Antonio, TX 78249 Tel: (210) 458-8058 Fax: (210) 458-6504 [email protected]. Ac. 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35. JBME BIO-20-1288 (Thirugnanasambandam et al). 1.

(2) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 37. Biomechanical characterization of abdominal aortic aneurysms (AAA) has become. 38. commonplace in rupture risk assessment studies. However, its translation to the clinic. 39. has been greatly limited due to the complexity associated with its tools and their. 40. implementation. The unattainability of patient-specific tissue properties leads to the use. 41. of generalized population-averaged material models in finite element analyses, which. 42. adds a degree of uncertainty to the wall mechanics quantification. In addition,. 43. computational fluid dynamics modeling of AAA typically lacks the patient-specific inflow. 44. and outflow boundary conditions that should be obtained by non-standard of care clinical. 45. imaging. An alternative approach for analyzing AAA flow and sac volume changes is to. 46. conduct in vitro experiments in a controlled laboratory environment. In this study, we. 47. designed, built, and characterized quantitatively a benchtop flow-loop using a deformable. 48. AAA silicone phantom representative of a patient-specific geometry. The impedance. 49. modules, which are essential components of the flow-loop, were fine-tuned to ensure. 50. typical intraluminal pressure conditions within the AAA sac. The phantom was imaged. 51. with a magnetic resonance imaging (MRI) scanner to acquire time-resolved images of the. 52. moving wall and the velocity field inside the sac. Temporal AAA sac volume changes lead. 53. to a corresponding variation in compliance throughout the cardiac cycle. The primary. 54. outcome of this work was the design optimization of the impedance elements, the. 55. quantitative characterization of the resistive and capacitive attributes of a compliant AAA. 56. phantom, and the exemplary use of MRI for flow visualization and quantification of the. 57. deformed AAA geometry.. 58. Key terms: aneurysm; biomechanics; Windkessel; optimization; magnetic resonance. Ac. ce. pt. ed. Ma nu. sc rip. tN. ot. Co. py. ed ite d. ABSTRACT. JBME BIO-20-1288 (Thirugnanasambandam et al). 2. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 36.

(3) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. INTRODUCTION. 60. Abdominal aortic aneurysms (AAA) are a vascular pathology of the abdominal aorta,. 61. which, upon rupture, have a mortality rate of up to 90% [1]. It is the 13th leading cause of. 62. death in the United States, resulting in approximately 11,000 deaths per year [2, 3]. The. 63. pathogenesis of AAA is multi-factorial and often combinatorial, ranging from mechanical. 64. weakening of the aortic wall to loss of smooth muscle cells and elastin [4]. Treatment. 65. options for AAA are limited to either a minimally invasive endovascular repair or an open. 66. surgical repair, unless the patient is recommended to a surveillance program and followed. 67. every 6-12 months [5, 6]. To improve the clinical management of AAA and make an. 68. informed decision on their rupture risk, extensive work has been done in the past two. 69. decades to identify a more scientifically sound rupture risk marker.. tN. ot. Co. py. ed ite d. 1.. From a biomechanical perspective, peak wall stress (PWS) was found to be a. 71. better indicator of rupture risk compared to maximum diameter [7-9]. However, for the. 72. evaluation of PWS, simplifications are made to model the mechanical characteristics of. 73. the AAA wall [10], as these are never known on a patient-specific basis. To improve the. 74. accuracy of material models, structural parameters were used to characterize the. 75. underlying mechanobiology of AAA [11-15]. However, it was observed that PWS. 76. evaluated using finite element analysis (FEA) is sensitive to differences in the material. 77. model formulation [16, 17]. Hence, there is need for an alternate method that can quantify. 78. patient-specific constitutive material models non-invasively or, conversely, minimize the. 79. use of constitutive material models as part of the AAA biomechanical evaluation. One. 80. way to implement this is by directly measuring volumetric changes of the AAA sac over a. Ac. ce. pt. ed. Ma nu. sc rip. 70. JBME BIO-20-1288 (Thirugnanasambandam et al). 3. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 59.

(4) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 81. cardiac cycle, since these implicitly bear information on the mechanical characteristics of. 82. the wall.. 84. with corresponding changes in AAA geometry. Thus, knowledge of both pressure and. 85. geometry at specific time points can provide a pathway to evaluate the material properties. 86. of AAA wall. van Disseldorpet et al. [18] calibrated a patient-specific finite element AAA. 87. model using an iterative matching of the model output to the displacement data measured. 88. by 4D ultrasound. Wall motion evaluated using 4D image acquisition methods has also. 89. gained attention due to its importance in estimating vessel wall strain [19]. To validate. 90. these algorithms, it is important to develop robust in vitro circulation models, which can. 91. be imaged using the same 4D sequences used for patients in the clinic.. tN. ot. Co. py. ed ite d. The temporal variation of intraluminal pressure over a cardiac cycle is associated. The objective of the current study was to design, build, and characterize a fully. 93. functional magnetic resonance imaging (MRI)-compatible benchtop flow-loop using a. 94. deformable AAA phantom. Such a flow-loop can be used to measure temporal changes. 95. of intraluminal pressure and AAA sac volume as a means to acquire the experimental. 96. data needed to validate a constitutive material model. While postulating a new AAA wall. 97. constitutive material model is not within the scope of this work, we describe the. 98. development of the flow-loop, which mimics pathological pressure and flow conditions.. 99. Impedance modules were designed as a pair of Windkessel models, which play the. 100. central role in achieving the desired pressure waveform at a specific location within the. 101. AAA phantom. Different variations of Windkessel models have been used previously to. 102. characterize and represent the load endured by the heart and the systemic circulatory. 103. system [20-23]. The components of the Windkessel model are lumped parameter. Ac. ce. pt. ed. Ma nu. sc rip. 92. JBME BIO-20-1288 (Thirugnanasambandam et al). 4. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 83.

(5) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 105. Manual adjustment of these components is time consuming and might not always provide. 106. the most accurate and unique solution. An optimization algorithm that automates the. 107. design of impedance module components could improve the construction and. 108. implementation of in vitro flow-loops. Such an algorithm was used to determine the values. 109. of the components in each Windkessel model. In addition, we used contrast-enhanced. 110. time-resolved MRI during a cardiac cycle to generate a series of images used to build the. 111. deformed configuration of the AAA phantom at each cardiac phase.. Co. py. ed ite d. representations of arterial compliance, peripheral resistance, and the inertia of blood [24].. 112. 2.. MATERIALS AND METHODS. 114. 2.1. Benchtop AAA flow-loop. 115. 2.1.1 Schematic and components of the flow-loop. 116. The flow-loop was used to recreate a realistic pathological pressure waveform at the. 117. center of the AAA phantom. The silicone phantom was manufactured based on a patient-. 118. specific AAA (Vascular Simulations, LLC, Stony Brook, NY) using a proprietary injection. 119. molding technique. The length of the phantom, measured along the longitudinal (z) axis,. 120. was 14.5 cm from the neck to the bifurcation and 21 cm from the proximal to the distal. 121. end. The maximum AAA diameter was 6 cm measured along the plane perpendicular to. 122. the z axis. The non-uniform wall thickness of the phantom ranged from 2.4 mm to 7.1 mm. 123. (mean of 4.7 ± 0.4 mm). The reference pressure waveform, shown in Fig. S1 of the. 124. Supplementary Material, was derived from [25] where a fluid-filled pig-tail catheter was. 125. used to measure pressure invasively within a human infrarenal AAA.. Ac. ce. pt. ed. Ma nu. sc rip. tN. ot. 113. JBME BIO-20-1288 (Thirugnanasambandam et al). 5. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 104.

(6) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 127. CardioFlow 5000 MR programmable pump (Shelley Medical Systems, London, ON),. 128. which operates with a contrast-enhanced blood mimicking fluid (BMF - 40% glycerin, 60%. 129. deionized water). The viscosity of the BMF was measured using a Brookfield LVD-I. 130. PRIME viscometer (Brookfield Engineering Laboratories, Inc., Middleboro, MA) at 25.4°C,. 131. resulting in a mean dynamic viscosity of 4.24 cP. The density of the BMF was measured. 132. at 1.2 g/cm3 and, hence, the kinematic viscosity was calculated as 3.53 cSt. The flow rate. 133. was specified by a flow waveform measured at the entrance of the abdominal aorta under. 134. resting conditions [26].. Co. py. ed ite d. The schematic of the flow-loop is presented in Fig. 1. We used the MRI-compatible. The phantom has one inlet representing this entrance and two outlets representing. 136. the combined flow of the renal arteries and common iliac arteries, respectively. The ends. 137. of the phantom were secured within a custom-built housing (Regal Plastics, San Antonio,. 138. TX) and submerged entirely in contrast-enhanced BMF. The rationale for this is to provide. 139. the necessary contrast required to identify the lumen and outer wall boundaries of the. 140. phantom in the acquired MR images. While the physiological input flow rate is maintained. 141. by the pump, the target pressure waveform is achieved by placing an impedance module. 142. at each of the outlets. Each impedance module is represented by a 4-element Windkessel. 143. model consisting of inductance, capacitance and resistance [23, 24]. The output from the. 144. iliac and renal impedance modules drain into a custom-built reservoir (Regal Plastics,. 145. San Antonio, TX) which feeds back into the pump inlet.. 147. tN. sc rip. Ma nu. ed. pt. ce. Ac. 146. ot. 135. 2.1.2 The Windkessel model. JBME BIO-20-1288 (Thirugnanasambandam et al). 6. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 126.

(7) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 149. representing the structural characteristics of the vasculature. The impedance module. 150. serves as the physical equivalent of the impedance offered by the systemic arterial. 151. system and blood motion to the heart. While inductance and resistance represent the. 152. geometric properties of the vessels, the capacitance represents the elasticity of the. 153 154. conduit arteries. In the frequency domain, 𝑃𝑃(𝜔𝜔) represents the pressure, 𝑄𝑄(𝜔𝜔) represents. 155. circuit [27], and their functional relationship is given by Eqs. (1) and (2),. ed ite d. The electrical components of the Windkessel model translate to specific functions. 𝑃𝑃(𝜔𝜔) = 𝑄𝑄(𝜔𝜔)𝑍𝑍(𝜔𝜔). 𝑍𝑍(𝜔𝜔) = 𝑗𝑗𝑗𝑗𝑗𝑗 + 𝑅𝑅𝑝𝑝 +. 𝑅𝑅𝑑𝑑 , 1 + 𝑗𝑗𝑗𝑗𝑗𝑗𝑅𝑅𝑑𝑑. tN. 157. ot. 156. Co. py. the volumetric flow rate, 𝑍𝑍(𝜔𝜔) represents the impedance of the 4-element Windkessel (1). (2). 160. arteries, an optimization script was written in MATLAB (The MathWorks, Inc., Natick, MA). 161. based on the combination of a genetic algorithm and the Levenberg-Macquardt algorithm.. 162. Such was used to derive the corresponding impedance module parameters. The sum of. 163. 𝑅𝑅𝑝𝑝 and 𝑅𝑅𝑑𝑑 , calculated as the ratio between mean pressure and mean flow rate, was held. ed. Ma nu. the capacitance. Using in vivo pressure and flow waveforms at the common iliac and renal. constant and used as a constraint. The two parameters optimized were the capacitance. pt. 164. sc rip. 159. where 𝑅𝑅𝑝𝑝 is the proximal resistance, 𝑅𝑅𝑑𝑑 the distal resistance, 𝐿𝐿 the inductance, and 𝐶𝐶 is. 158. 167. whereas changes in 𝐶𝐶 and 𝐿𝐿 yield a phase shift in the pressure waveform. To achieve a combination of the independent flow waveform and the target pressure waveform shown. 168. in Fig. 2, the impedance module parameters were derived using the optimization. 169. algorithms. To verify the accuracy of these parameters, they were substituted back into. 170. Eq. (2) to derive the predicted pressure waveform corresponding to the same input flow. Ac. ce. 166. 𝐶𝐶 and the ratio 𝑅𝑅𝑝𝑝 /𝑅𝑅𝑑𝑑 . The pressure pulse amplitude is controlled by both 𝑅𝑅𝑝𝑝 /𝑅𝑅𝑑𝑑 and 𝐶𝐶,. 165. JBME BIO-20-1288 (Thirugnanasambandam et al). 7. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 148.

(8) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 172. waveforms was 1.97%. The optimization procedure, shown graphically in Fig. S2 of the. 173. Supplementary Material, was repeated for different combinations of flow and pressure. 174. waveforms, e.g. the flow waveform at the iliac arteries and the pressure waveform within. 175. the AAA, and flow waveform at the renal arteries and the pressure waveform within the. 176. AAA. This resulted in the optimized impedance module parameters for the iliac and renal. 177. impedance modules, respectively. Table 1 shows the values of the optimized parameters. 178. used in the construction of the module components.. Co. py. ed ite d. waveform. The L2 norm of the relative error between the target and predicted pressure. For a fully developed, laminar flow of a Newtonian fluid through a horizontal tube. 180 181. of constant circular cross section under steady flow conditions, the resistance [8𝜇𝜇𝜇𝜇/(𝜋𝜋𝑟𝑟 4 )]. 182. module is dependent on the dynamic viscosity of the working fluid (𝜇𝜇), the length of the. 183. tube (𝑙𝑙), and the inner radius of the tube (𝑟𝑟), in addition to maintaining a Reynolds number. 184. adequate to achieve laminar flow. A practical method to increase the resistance while. 185. maintaining laminar flow is to replace a single thin tube by a larger one that houses a set. 186. of capillary tubes. The mathematical validation of this method is presented in the work of. 187. Kung and Taylor [24].. ot. 179. ed. Ma nu. sc rip. tN. is calculated from the Hagen-Poiseuille formula. Therefore, the design of the resistance. pt. 188. 2.1.3 Construction of the module components. 190. The basic design for the construction of the components of the impedance modules was. 191. adapted from [24]. The calculation of the design parameters for an exemplary resistance. 192. component is described as follows. From Table 1, the value of the optimized proximal. 193. resistance offered by the iliac impedance module is 0.463 mmHg⋅s/cm3. The functional. Ac. ce. 189. JBME BIO-20-1288 (Thirugnanasambandam et al). 8. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 171.

(9) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 195. nylon tube. The module is enclosed by a 3D printed encasing (MakerBot Replicator,. 196. MakerBot Industries LLC, Brooklyn, NY), with the conduits at the inlet and outlet designed. 197. to ensure laminar flow during the transition across the resistance module and the flow-. 198. loop tubing. The total resistance offered by ‘𝑁𝑁’ capillary tubes of inner radius ‘𝑟𝑟𝑐𝑐 ’ is given. ed ite d. portion of the resistance module consists of a set of capillary tubes tightly held inside a. 200. by 8𝜇𝜇𝜇𝜇/(𝜋𝜋𝜋𝜋𝑟𝑟𝑐𝑐 4 ). Given the proximal iliac resistance 𝑅𝑅𝑝𝑝 from Table 1 and for a standard. 201. for this impedance module: 𝑁𝑁 =. 202. 8𝜇𝜇𝜇𝜇 . 𝜋𝜋𝑅𝑅𝑝𝑝 𝑟𝑟𝑐𝑐 4. Co. py. capillary tube length of 0.1 m, Eq. (3) yields the optimum number of capillary tubes needed. ot. 199. (3). 205. Instrument, Novato, CA), 𝑁𝑁 is calculated and rounded to the nearest integer. The outer radius of the capillary tubes was used in a circle packing algorithm to estimate the inner. 206. diameter of the nylon tube (Product No. 8628K59, McMaster-Carr, Elmhurst, IL). The. 207. conduit diameter, which corresponds to the outer diameter of the nylon tube, was used to. 208. verify that laminar flow conditions were satisfied at the connections between the. 209. resistance module and the flow-loop tubing. This protocol was repeated to fabricate the. 210. other three resistance modules used in the flow-loop. An exemplary resistance module is. 211. shown in Fig. 3(a).. ce. pt. ed. Ma nu. sc rip. tN. 204. For different values of 𝑟𝑟𝑐𝑐 that are characteristic of capillary tubes B200-156-10 (Sutter. 203. The capacitance component of the impedance module was built using Plexiglas. 213. sheets (Plastic Supply of San Antonio, San Antonio, TX), as shown in Fig. 3(b). The. 214. module consisted of a cuboid chamber with an inlet and an outlet on each side, along. 215. with two ports for adjusting the volume of air in the chamber and measuring pressure.. Ac. 212. JBME BIO-20-1288 (Thirugnanasambandam et al). 9. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 194.

(10) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 216. The required capacitance was provided by trapping a calculated volume of air inside the. 217. capacitance module. The capacitance of a pocket of air is calculated using Eq. (4):. 218. (𝑉𝑉 − ∆𝑉𝑉) , 𝑃𝑃. (4). 221. using Eq. (5) with the geometry of the fluid system (ℓ being the representative length of. py. the fluid system and 𝐴𝐴 being the representative cross-sectional area of the fluid system). 224. 𝐿𝐿 =. 225. (5). 2.2. 227. The performance of the module components was tested individually and in combination. 228. with other components to validate the analytical calculations and design predictions.. sc rip. 226. Ma nu. Experimental design. 𝜌𝜌ℓ . 𝐴𝐴. Co. and the BMF density (𝜌𝜌):. ot. 223. 𝑃𝑃 is the reference pressure. The inductance (𝐿𝐿) is a property of the fluid and is calculated. tN. 222. ed ite d. 220. where 𝑉𝑉 is the reference volume, ∆𝑉𝑉 is the change in volume due to incoming fluid, and. 219. 229. 2.2.1 Experimental setup 1: testing the resistance modules. 231. Four resistance modules were built: two proximal and two distal, one pair for each outlet.. 232. The resistance modules were isolated and tested individually in a loop at different flow. 233. rates. Steady flow rates were prescribed at the inlet of the resistance module, while the. 234. outlet of the resistance module was connected to the reservoir. The schematic of this. 235. setup is shown in Fig. 4(a). The pressure drop across the resistance module was. 236. calculated from the pressures measured at two locations immediately proximal and distal. Ac. ce. pt. ed. 230. JBME BIO-20-1288 (Thirugnanasambandam et al). 10. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 𝐶𝐶𝑎𝑎 =.

(11) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 237. to the resistance module. The pressure was measured using a Mikro-tip SPR524 3.5F. 238. pressure catheter (Millar Inc., Houston, TX).. 239. 241. The iliac and renal impedance modules were tested individually in this setup. The. 242. proximal resistance, capacitance, and distal resistance modules were combined into a. 243. single impedance unit with short rigid connections between them. The flow waveform at. 244. the entrance of the iliac/renal impedance module was prescribed at the inlet. The volume. 245. of air trapped in the capacitance module at atmospheric pressure was adjusted to achieve. 246. the desired capacitance. The output from the distal resistance module was directed to the. 247. reservoir, which was then recirculated back through the pump. The schematic of this. 248. setup is presented in Fig. 4(b).. sc rip. 249. tN. ot. Co. py. ed ite d. 2.2.2 Experimental setup 2: testing the Windkessel model. 2.2.3 Experimental setups 3-5: testing the effect of the phantom. 251. The Windkessel model shows the effect of the downstream module components on the. 252. upstream pressure waveform for a specific flow waveform. Since the impedance module. 253. does not include components that take into account the properties of the phantom, the. 254. pressure waveform at the center of the AAA sac may vary according to the mechanical. 255. characteristics of the AAA wall.. 256. 2.2.3.1 Experimental setup 3. 257. A rigid phantom [24] should provide a baseline for characterizing the values of the. 258. impedance module components using the optimization algorithms. Hence, initially, a rigid. 259. wall tube whose diameter matched the equivalent diameter of the compliant AAA. Ac. ce. pt. ed. Ma nu. 250. JBME BIO-20-1288 (Thirugnanasambandam et al). 11. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 240.

(12) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 261. Pressure was measured proximal to the impedance modules (i.e., distal to the rigid tube).. 262. 2.2.3.2 Experimental setup 4. 263. The effect of a deformable phantom was studied by replacing the rigid tube with the. 264. compliant silicone AAA phantom as shown in the schematic of Fig. 4(d). The pressure. 265. waveform at the entrance to the impedance modules was compared to that obtained in. 266. experimental setup 3. Experimental setup 4 was later used with the MRI scanner to detect. 267. AAA wall motion and measured fluid velocity.. 268. 2.2.3.3 Experimental setup 5. 269. To detect the true impedance properties of the phantom, the pump was connected directly. 270. to the phantom. The outlets of the phantom were drained into the reservoir bypassing all. 271. impedance modules along the flow-loop path, as shown in Fig. 4(e). Pressure. 272. measurements were taken at the entrance and exit of the phantom at varying steady flow. 273. rates. The resistance of the phantom was calculated for each flow rate. The measurement. 274. of compliance of the phantom in one cardiac cycle cannot be computed in a similar. 275. straightforward manner; this was addressed in section 2.3.2.. Ma nu. sc rip. tN. ot. Co. py. ed ite d. phantom at zero intraluminal pressure was used in the setup as illustrated in Fig. 4(c).. ed. 276. 2.3. MR imaging and reconstruction. 278. 2.3.1 Imaging the phantom in the flow-loop. 279. The entire flow-loop using experimental setup 4 was placed inside the bore of a 70 cm. 280. wide-bore 3.0 Tesla whole body MRI scanner (Phillips Ingenia 3.0T, Philips, Amsterdam,. 281. Netherlands). Magnevist (Bayer Healthcare LLC, Whippany NJ; chemical name:. 282. gadopentetate dimeglumine; 469.01 mg/mL), a gadolinium-based contrast agent, was. Ac. ce. pt. 277. JBME BIO-20-1288 (Thirugnanasambandam et al). 12. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 260.

(13) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 284. signal to noise ratio. A human torso coil was placed on the housing containing the AAA. 285. phantom. Padding was used to eliminate any potential movement together with straps. 286. secured on either side of the scanner table. After acquiring a set of orthogonal scout. 287. images, static imaging was performed at zero pressure (with no fluid flow through the. 288. phantom) along the axial direction using the following pulse sequence: T1 3D (Echo time. 289. (TE): 4.05 ms, Repetition time (TR): 8.72 ms, Flip Angle: 8°, Number of signals averaged. 290. (NSA): 1, Echo Train Length 200, slice thickness: 1 mm, Field of view (FOV): 180 mm).. 291. A 4D phase contrast MRI (PC-MRI) sequence was then utilized to acquire three-. 292. dimensional image sets with high contrast between the fluid and the wall at different time. 293. points (20 phases) in one cardiac cycle. Only the magnitude images of the 4D PC-MRI. 294. sequence were used; phase difference images were discarded. In addition, contrast-. 295. enhanced ECG gated time resolved imaging was performed in the axial orientation using. 296. the following pulse sequence: TE: 2.61 ms, TR: 4.65 ms, Flip Angle: 15°, NSA: 2, Echo. 297. Train Length 1, slice thickness: 3 mm, FOV: 275 mm.. Ma nu. sc rip. tN. ot. Co. py. ed ite d. mixed with 12 liters of BMF to reduce the relaxation time of the liquid and increase the. 298. 2.3.2 Image processing and reconstruction. 300. Static images were used to obtain the zero-pressure configuration of the phantom. This. 301. is particularly useful since it is impossible to obtain the true zero-pressure geometry of. 302. human AAA. The contrast-enhanced images were segmented using AAAVASC (v.1.0.3,. 303. University of Texas at San Antonio, San Antonio, TX), which is an in-house segmentation. 304. and geometry quantification code written in MATLAB, to identify the lumen and outer wall. 305. surfaces of the phantom. The spatial distribution of wall thickness was evaluated from. Ac. ce. pt. ed. 299. JBME BIO-20-1288 (Thirugnanasambandam et al). 13. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 283.

(14) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 307. 20 phases) were reconstructed into 3D image volumes. These were subsequently. 308. segmented using a 3D marching cubes approach and reconstructed to fit a smooth,. 309. closed, manifold surface to the endoluminal surface. The volume contained in each of. 310. these luminal geometries and their corresponding pressures were evaluated from the. 311. AAA pressure waveform at time points matching each cardiac phase. Changes in. 312. pressure (∆𝑃𝑃) and volume (∆𝑉𝑉) were calculated between each pair of consecutive. 313. phases. Using these values, the corresponding variation of phase-to-phase compliance. 314. (𝐶𝐶𝑛𝑛 ) was estimated using Eq. (6),. 316. ot. (∆𝑉𝑉)𝑛𝑛 . (∆𝑃𝑃)𝑛𝑛. (6). sc rip. 𝐶𝐶𝑛𝑛 =. tN. 315. Co. py. ed ite d. these images using AAAVASC. The image stacks obtained at each cardiac phase (viz.. 3.. RESULTS. 318. 3.1. Module testing. 319. 3.1.1 Iliac and renal resistances. 320. The resistances (mean ± SD) calculated from experimental setup 1 for all resistance. 321. modules are presented in Table 2 alongside the theoretical resistances based on which. 322. they were built. The resistances measured across different flow rates varying from 50. 323. cm3/s to 150 cm3/s for the renal proximal resistance module is presented in Fig. S3 of the. 324. Supplementary Material. As expected, the resistance does not vary as a function of the. 325. flow rate since laminar flow conditions were met for the operational flow rates. The. 326. maximum percentage variation between minimum and maximum resistances across. 327. these flow rates was 7.2%. The experiment was repeated for all resistance modules with. 328. similar results (not shown).. Ac. ce. pt. ed. Ma nu. 317. JBME BIO-20-1288 (Thirugnanasambandam et al). 14. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 306.

(15) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 329. 331. In experimental setup 2, the pressure measured at the entrance of the iliac impedance. 332. module under iliac flow conditions was compared to the theoretical prediction of pressure. 333. evaluated using Eqs. (1) and (2), and is presented in Fig. S4(a) of the Supplementary. 334. Material. A similar validation was performed for the renal impedance module using the. 335. renal flow waveform input at the entrance to the renal module. The comparison of. 336. theoretically and experimentally measured renal pressure waveforms is shown in Fig.. 337. S4(b) of the Supplementary Material.. ot. 338. Co. py. ed ite d. 3.1.2 Iliac and renal impedance modules. 3.1.3 The rigid tube and the AAA phantom. 340. We studied the effect of the phantom mechanics on altering the pressure waveform. 341. proximal to the impedance modules. Using experimental setup 3, the pressure was. 342. measured at the entrance of the modules under normal abdominal aortic flow conditions.. 343. This waveform was then compared to the theoretical pressure waveform derived using. 344. Eq. (1) and shown in Fig. 5(a). The theoretical pressure waveform was calculated using. 345. the impedance module parameters, which were identified with the optimization. 346. algorithms. The key input to the algorithms was the “target” waveform adapted from [25].. 347. Thus, the theoretical pressure waveform follows the target waveform closely. Using. 348. experimental setup 4, the pressure waveform at the entrance of the impedance module. 349. was compared to that obtained with experimental setup 3, as shown in Fig. 5(b). The. 350. difference between these pressure waveforms represents the combined effects of the. 351. differences in geometry and compliance of the phantom, relative to the rigid tube, on the. Ac. ce. pt. ed. Ma nu. sc rip. tN. 339. JBME BIO-20-1288 (Thirugnanasambandam et al). 15. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 330.

(16) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 352. AAA sac pressure. The impedance pertaining to the difference in pressure represents the. 353. total impedance offered by the compliant phantom. This can be obtained by deconvolution. 354. in the time domain using Eq. (1).. 3.2. Impedance properties of the phantom. 357. We calculated the resistance across the phantom at each flow rate ranging from 20 cm3/s. 358. to 150 cm3/s, as illustrated in Fig. 6(a). It can be seen that this resistance is not constant. 359. but rather has a linear relationship with volume flow rate. The volume of the phantom and. 360. its corresponding intraluminal pressure as a function of time in one cardiac cycle are. 361. shown in Fig. 6(b). The combination of the resistive and capacitive attributes of the. 362. phantom has a greater effect on the pressure measured within the AAA sac compared to. 363. the individual contributions of phantom resistance and capacitance.. sc rip. tN. ot. Co. py. 356. In experimental setup 5, a catheter placed at the entrance of the phantom. 365. measured the pressure waveform. This pressure and the flow waveforms were input to. 366. the optimization algorithm to calculate optimized resistance and capacitance values (Req. 367. = 0.49 mmHg⋅s/cm3; Ceq = 5.67 cm3/mmHg). Since this calculation assumes a constant. 368. resistance across the phantom over a cardiac cycle, they should be considered as the. 369. equivalent resistance and capacitance of the phantom, and thus cannot be used for. 370. impedance measurements.. 371. Ac. ce. pt. ed. Ma nu. 364. 372. 3.3. AAA hemodynamics. 373. The temporal evolution of the velocity field for a cardiac cycle was calculated using the. 374. PC-MR images, as illustrated in Figure 7 for distinct phases of one period. The pulsating. JBME BIO-20-1288 (Thirugnanasambandam et al). 16. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. 355.

(17) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 376. from one phase to the next. Phases P0 through P18 form one period (1.2 s). Systolic. 377. acceleration spans P0 to P4, systolic deceleration is represented by P6 and P8, and. 378. diastole spans P10 to P18. During systole, the flow is approximately unidirectional with. 379. minimal recirculation. However, in late systole, vortex formation can be observed within. 380. the AAA sac. During diastole, secondary flow patterns become more prominent and the. 381. primary vortex breaks down into smaller vortices, causing a disturbed low-velocity flow. 382. pattern. In addition, during the transition from systole to diastole (phase P8), retrograde. 383. flow can be seen throughout the phantom.. ot. 384. Co. py. ed ite d. behavior of the flow can be observed by the change in magnitude of the velocity vectors. 4.. DISCUSSION. 386. 4.1. Benchtop flow-loop design and characterization. 387. The main contribution of this work is the development of a fully functional MRI-compatible. 388. benchtop flow-loop using a patient-specific deformable AAA phantom under. 389. physiologically realistic pulsatile flow conditions. The potential applications for this flow-. 390. loop span across different areas of cardiovascular research, ranging from non-invasive. 391. material property identification to measurement of realistic in-vitro boundary conditions. 392. required for computational fluid dynamics [27, 28] and fluid-structure interaction models.. 393. The addition of flow-dependent changes of the phantom’s impedance properties in the. 394. Windkessel module, when studied in combination with pulse wave reflections, can. 395. potentially help understand in-vivo mechanisms representing the overall causal and. 396. responsive mechanical behavior of AAA.. Ac. ce. pt. ed. Ma nu. sc rip. tN. 385. JBME BIO-20-1288 (Thirugnanasambandam et al). 17. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 375.

(18) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 398. constructing the module components, we substituted the exhaustive process of. 399. experimental trials with an optimization script written in MATLAB. The script replaces the. 400. process of trial and error in determining the values of impedance module components.. 401. The algorithms can be easily modified for any future variation of the Windkessel circuit,. 402. underscoring its potential for a variety of flow-loop experiments. Key data derived from. 403. the two sets of MR images correspond to the visualization of aortic wall motion and AAA. 404. hemodynamics, respectively. The use of the compliant phantom in the flow-loop furthers. 405. our understanding of the effect of AAA wall mechanical characteristics on the aneurysmal. 406. hemodynamics by subsequent intraluminal pressure changes.. ot. Co. py. ed ite d. Using the design models proposed by Kung and Taylor [24] as the basis for. The differences between the theoretical and experimental pressure waveforms. 408. observed during testing of the impedance modules (Fig. S4) are likely due to an. 409. accumulation of minor variations in the experimental values of resistances and. 410. capacitances. For example, wave reflections at the connections between module. 411. components can dampen the waveforms and cause deviation from the analytical. 412. calculations. It should also be noted that the differences between the theoretical and. 413. experimental pressure waveforms are higher for low flow rates where the measurements. 414. are not as sensitive as for the high flow rates due to low signal to noise ratio. Impedance. 415. module testing was performed using different flow waveforms to investigate their. 416. consistency under different flow conditions. As seen from Fig. S4, the close agreement. 417. between the analytical and experimental pressure waveforms for different flow conditions. 418. shows the stability of the modules.. Ac. ce. pt. ed. Ma nu. sc rip. tN. 407. 419. JBME BIO-20-1288 (Thirugnanasambandam et al). 18. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 397.

(19) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. AAA structural and flow characteristics. 421. The study of the structural and functional mechanisms underlying AAA mechanics has. 422. been addressed using in-vitro flow loops [29-34]. The temporal variation of AAA wall strain. 423. was investigated in a few of these setups with compliant AAA phantoms [33, 34]. In these. 424. studies, strain was evaluated with area/radius based compliance changes, diametral. 425. strain, and pressure-diameter curves using idealized symmetric AAA phantoms. Wang et. 426. al. [34] performed cine-MRI of a symmetric AAA phantom and compared the. 427. circumferential strains derived from this imaging method to those evaluated using. 428. stereovision techniques. To the best of our knowledge, the present work represents the. 429. first attempt to address the temporal variation of AAA compliance while using a patient-. 430. specific deformable phantom.. tN. ot. Co. py. ed ite d. 4.2. In addition to the assessment of wall motion, we also quantified the fluid flow. 432. velocity within the AAA phantom. Earlier studies used laser Doppler velocimetry (LDV) to. 433. quantify the velocity of the flow field in rigid AAA phantoms [30, 32]. With the use of. 434. compliant AAA phantoms with AP (anterior-posterior) asymmetry and imbalanced flow. 435. rates in the iliac branches, 3D flow visualization was accomplished using 2D particle. 436. image velocimetry (PIV) measurements. An evaluation of vortex formation, vortex. 437. trajectory, vortex ring dynamics, and transition to turbulent flow was possible using this. 438. technique [31]. Basciano et al. [35] used a numerical model to demonstrate the combined. 439. effect of patient-specific geometry and particle hemodynamics (by means of particle. 440. residence times) on the onset of ILT. Activation of platelets in the vortex ring is followed. 441. by their subsequent deposition in the low wall shear stress regions inside the AAA sac.. 442. Therefore, assessing the patient-specific vortex ring propagation is important in AAA. Ac. ce. pt. ed. Ma nu. sc rip. 431. JBME BIO-20-1288 (Thirugnanasambandam et al). 19. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 420.

(20) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 444. and compliant AAA models. The viscoelastic dissipation seen in compliant AAAs. 445. contribute to the cycle of converting kinetic energy to potential energy and vice versa.. 446. Kinetic energy is stored as potential energy by the expanding AAA during flow. 447. acceleration, whereas when the flow decelerates, the potential energy stored in the AAA. 448. walls contract the AAAs back again during reconversion into kinetic energy. This process. 449. leads to progression of vortices towards the distal end during the flow deceleration phase.. 450. Similarly, Yu et al. [37] explain the contribution of pulsatile flow towards non-localization. 451. of the vortex ring in AAAs. Unlike in steady flow conditions where the vortex ring is. 452. typically localized at the distal end of the AAA sac, under pulsatile flow conditions, it. 453. appears at the proximal site during early systolic phase, and then progresses towards the. 454. distal end through the cardiac cycle. Similar to the above observations in compliant AAAs. 455. subjected to pulsatile flow conditions, we observed that vortex formation at the proximal. 456. site in the AAA phantom during systole is followed by its progression towards the distal. 457. end during diastole. Collision of these vortices with the AAA wall at the distal end leads. 458. to high pressures and increased wall stresses. This has been attributed to higher. 459. compliance values of the AAAs in literature [36].. ed. Ma nu. sc rip. tN. ot. Co. py. ed ite d. hemodynamics. Deplano et al. [36] evaluated the difference in flow fields while using rigid. In this study, the spatio-temporal variation of 3D velocity vectors within the sac of. 461. a compliant patient-specific AAA phantom was quantified for the first time using 4D flow. 462. MRI. The quantitative characterization of the AAA phantom hemodynamics revealed that. 463. flow at the inlet and outlet typically exhibit higher velocities compared to the AAA sac (Fig.. 464. 7). High curvature and expansion of the aorta leading to the aneurysm sac yields flow. Ac. ce. pt. 460. JBME BIO-20-1288 (Thirugnanasambandam et al). 20. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 443.

(21) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 465. separation, which in turn generates decreased convective transport compared to the. 466. proximal and distal ends of the phantom.. 467. 469. There are several important limitations to the research work described herein. The. 470. variable impedance offered by the deformable phantom was not included in the. 471. optimization algorithms. This may explain, in part, the differences between the. 472. experimental and theoretical intraluminal pressure waveforms measured within the AAA. 473. sac. Connections between different components of the flow-loop can lead to minor. 474. pressure losses, which also affect the measured pressure waveform. Differences in the. 475. material properties of neighboring components may also contribute to these losses.. 476. Reflection of pulsatile waves from the connections and transitions were not taken into. 477. consideration to model the impedance module components. These reflections may. 478. dampen or amplify the wave by interference depending on the frequency of the wave and. 479. the distance from the reflection zones. The use of an elastomer to build the AAA phantom. 480. is an inherent limitation on the ability of this flow-loop design to represent actual AAA wall. 481. material properties. In addition, the phantom was devoid of a synthetic material. 482. representing the presence of intraluminal thrombus (ILT). It is expected that ILT may have. 483. further dampened the amplitude of the intraluminal pressure waveform measured within. 484. the AAA sac and added additional capacitance to the overall impedance of the phantom.. py. Co. ot. tN. sc rip. Ma nu. ed. pt. ce. Ac. 485 486. Limitations. ed ite d. 4.3. 5.. ACKNOWLEDGMENTS. JBME BIO-20-1288 (Thirugnanasambandam et al). 21. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 468.

(22) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 488. part by American Heart Association award 15PRE25700288 and National Institutes of. 489. Health award R01HL121293. The content is solely the responsibility of the authors and. 490. does not necessarily represent the official views of the American Heart Association or the. 491. National Institutes of Health.. ed ite d. The authors have no conflicts of interest to disclose. Research funding was provided in. 493. REFERENCES. 494. [1]. Co. Solomon C. G. and Kent K. C., 2014, "Abdominal aortic aneurysms," The New England Journal of Medicine, 371, pp. 2101-2108.. [2]. Jordan W. D., Alcocer F., Wirthlin D. J., Westfall A. O., and Whitley D., 2003,. ot. 495 496. py. 492. "Abdominal aortic aneurysms in “high-risk” surgical patients: comparison of open. 498. and endovascular repair," Annals of Surgery, 237, pp. 623-630. Patel M. I., 1995, "Current views on the pathogenesis of abdominal aortic aneurysms," Journal of the American College of Surgeons, 181, pp. 371-382.. 500 501. sc rip. [3]. [4]. Ma nu. 499. tN. 497. Kuivaniemi H., Ryer E. J., Elmore J. R., and Tromp G., 2015, "Understanding the pathogenesis of abdominal aortic aneurysms," Expert Review of Cardiovascular. 503. Therapy, 13, pp. 975-987. [5]. Valentine R. J., DeCaprio J. D., Castillo J. M., Modrall J. G., Jackson M. R., and. pt. 504. ed. 502. Clagett G. P., 2000, "Watchful waiting in cases of small abdominal aortic. 506. aneurysms‒appropriate for all patients?" Journal of Vascular Surgery, 32, pp. 441-. 507. 450.. Ac. ce. 505. JBME BIO-20-1288 (Thirugnanasambandam et al). 22. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 487.

(23) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 508. [6]. Wilt T. J., Lederle F. A., MacDonald R., Jonk Y. C., Rector T. S., and Kane R. L.,. 509. 2006, "Comparison of endovascular and open surgical repairs for abdominal aortic. 510. aneurysm," Evidence Report/Technology Assessment, 1(144), pp. 1-113. [7]. Fillinger M. F., Raghavan M. L., Marra S. P., Cronenwett J. L., and Kennedy F. E.,. 512. 2002, "In vivo analysis of mechanical wall stress and abdominal aortic aneurysm. 513. rupture risk," Journal of Vascular Surgery, 36, pp. 589-597. [8]. Venkatasubramaniam A., Fagan M., Mehta T., Mylankal K., Ray B., Kuhan G.,. py. 514. Chetter I., and McCollum P., 2004, "A comparative study of aortic wall stress using. 516. finite element analysis for ruptured and non-ruptured abdominal aortic. 517. aneurysms," European Journal of Vascular and Endovascular Surgery, 28, pp.. 518. 168-176.. ot. tN. [9]. Vorp D. A. and VandeGeest J. P., 2005, "Biomechanical determinants of. sc rip. 519. Co. 515. abdominal aortic aneurysm rupture," Arteriosclerosis, Thrombosis, and Vascular. 521. Biology, 25, pp. 1558-1566.. 522. [10]. Ma nu. 520. Raghavan M. L. and Vorp D. A., 2000, "Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain. 524. constitutive model and evaluation of its applicability," Journal of Biomechanics, 33,. 525. pp. 475-482.. pt. [11]. Badel P., Avril S., Lessner S., and Sutton M., 2012, "Mechanical identification of. ce. 526. ed. 523. layer-specific properties of mouse carotid arteries using 3D-DIC and a hyperelastic. 528. anisotropic constitutive model," Computer Methods in Biomechanics and. 529. Biomedical Engineering, 15, pp. 37-48.. Ac. 527. JBME BIO-20-1288 (Thirugnanasambandam et al). 23. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. 511.

(24) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 530. [12]. arteries," Journal of Biomechanical Engineering, 138, p. 124503.. 531 532. Fatemifar F. and Han H.-C., 2016, "Effect of axial stretch on lumen collapse of. [13]. Holzapfel G. A., Gasser T. C., and Ogden R. W., 2000, "A new constitutive. 534. Journal of Elasticity and the Physical Science of Solids, 61, pp. 1-48.. 535. [14]. ed ite d. framework for arterial wall mechanics and a comparative study of material models,". Mottahedi M. and Han H.-C., 2016, "Artery buckling analysis using a two-layered wall model with collagen dispersion," Journal of the Mechanical Behavior of. 537. Biomedical Materials, 60, pp. 515-524. [15]. Co. 538. py. 536. Holzapfel G. A., Gasser T. C., and Ogden R. W., 2004, "Comparison of a multilayer structural model for arterial walls with a Fung-type model, and issues of. 540. material stability," Journal of Biomechanical Engineering, 126(2), pp. 264-275.. tN. [16]. Maier A., Gee M., Reeps C., Pongratz J., Eckstein H.-H., and Wall W., 2010, "A. sc rip. 541. ot. 539. comparison of diameter, wall stress, and rupture potential index for abdominal. 543. aortic aneurysm rupture risk prediction," Annals of Biomedical Engineering, 38, pp.. 544. 3124-3134.. 545. [17]. Ma nu. 542. Rodríguez J. F., Martufi G., Doblaré M., and Finol E. A., 2009, "The effect of material model formulation in the stress analysis of abdominal aortic aneurysms,". 547. Annals of Biomedical Engineering, 37, pp. 2218-2221.. pt. [18]. van Disseldorp E. M. J., Petterson N. J., Rutten M. C. M., van de Vosse F. N., van. ce. 548. ed. 546. Sambeek M. R. H. M., and Lopata R. G. P., 2016, "Patient specific wall stress. 550. analysis and mechanical characterization of abdominal aortic aneurysms using 4D. 551. ultrasound," European Journal of Vascular and Endovascular Surgery, 52(5), pp.. 552. 635-642.. Ac. 549. JBME BIO-20-1288 (Thirugnanasambandam et al). 24. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 533.

(25) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 553. [19]. Golemati S., Patelaki E., and Konstantina S. N., 2019, "Image-based motion and strain estimation of the vessel wall," In: Golemati S., Nikita K. (eds) Cardiovascular. 555. Computing—Methodologies and Clinical Applications. Series in BioEngineering.. 556. Springer, Singapore. [20]. vitro benchtop modeling," HIM 1990-2015, p. 1854. [21]. Cappello A., Gnudi G., and Lamberti C., 1995, "Identification of the three-element. py. 558 559. Beggs K. W., 2015, "Design of a physical Windkessel model for use in LVAD in-. windkessel model incorporating a pressure-dependent compliance," Annals of. 561. Biomedical Engineering, 23, pp. 164-177. [22]. Stergiopulos N., Westerhof B. E., and Westerhof N., 1999, "Total arterial inertance. ot. 562. Co. 560. as the fourth element of the Windkessel model," American Journal of Physiology-. 564. Heart and Circulatory Physiology, 276, pp. H81-H88. Westerhof N., Elzinga G., and Sipkema P., 1971, "An artificial arterial system for pumping hearts," Journal of Applied Physiology, 31, pp. 776-781.. 566 567. sc rip. [23]. [24]. Ma nu. 565. tN. 563. Kung E. O. and Taylor C. A., 2011, "Development of a physical Windkessel module to recreate in vivo vascular flow impedance for in vitro experiments,". 569. Cardiovascular Engineering and Technology, 2, pp. 2-14. [25]. van‘t Veer M., Buth J., Merkx M., Tonino P., van den Bosch H., Pijls N., and van. pt. 570. ed. 568. de Vosse F., 2008, "Biomechanical properties of abdominal aortic aneurysms. 572. assessed by simultaneously measured pressure and volume changes in humans,". 573. Journal of Vascular Surgery, 48, pp. 1401-1407.. Ac. ce. 571. JBME BIO-20-1288 (Thirugnanasambandam et al). 25. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. 557. ed ite d. 554.

(26) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 574. [26]. Maier S., Meier D., Boesiger P., Moser U., and Vieli A., 1989, "Human abdominal. 575. aorta: comparative measurements of blood flow with MR imaging and multigated. 576. Doppler US," Radiology, 171, pp. 487-492. [27]. Kung E. O., Les A. S., Medina F., Wicker R. B., McConnell M. V., and Taylor C. A., 2011, "In vitro validation of finite-element model of AAA hemodynamics. 579. incorporating realistic outlet boundary conditions," Journal of Biomechanical. 580. Engineering, 133, p. 041003. [28]. Kung E. O., Les A. S., Figueroa C. A., Medina F., Arcaute K., Wicker R. B.,. Co. 581. py. 578. McConnell M. V., and Taylor C. A., 2011, "In vitro validation of finite element. 583. analysis of blood flow in deformable models," Annals of Biomedical Engineering,. 584. 39, pp. 1947-1960.. tN. [29]. Ahamed T., Peattie R. A., Dorfmann L., and Cherry Kemmerling E. M., 2018,. sc rip. 585. ot. 582. "Pulsatile flow measurements and wall stress distribution in a patient specific. 587. abdominal aortic aneurysm phantom," ZAMM‐Journal of Applied Mathematics and. 588. Mechanics, 98(12), pp. 2258-2274.. 589. [30]. Ma nu. 586. Asbury C. L., Ruberti J. W., Bluth E. I., and Peattie R. A., 1995, "Experimental investigation of steady flow in rigid models of abdominal aortic aneurysms," Annals. 591. of Biomedical Engineering, 23(1), pp. 29-39.. pt. [31]. Deplano V., Meyer C., Guivier-Curien C., and Bertrand E., 2013, "New insights into. ce. 592. ed. 590. the understanding of flow dynamics in an in vitro model for abdominal aortic. 594. aneurysms," Medical Engineering & Physics, 35(6), pp. 800-809.. Ac. 593. JBME BIO-20-1288 (Thirugnanasambandam et al). 26. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. 577.

(27) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. 595. [32]. Egelhoff C. J., Budwig R. S., Elger D. F., Khraishi T. A., and Johansen K. H., 1999,. 596. "Model studies of the flow in abdominal aortic aneurysms during resting and. 597. exercise conditions," Journal of Biomechanics, 32(12), pp. 1319-1329. [33]. Ene F., Gachon C., Delassus P., Carroll R., Stefanov F., O’Flynn P., and Morris L., 2011, "In vitro evaluation of the effects of intraluminal thrombus on abdominal. 600. aortic aneurysm wall dynamics," Medical Engineering & Physics, 33(8), pp. 957-. 601. 966. [34]. Wang Y., D. Joannic, P. Juillion, A. Monnet, P. Delassus, A. Lalande, and.. Co. 602. py. 599. Fontaine J.-F, 2018, "Validation of the strain assessment of a phantom of. 604. abdominal aortic aneurysm: comparison of results obtained from magnetic. 605. resonance imaging and stereovision measurements," Journal of Biomechanical. 606. Engineering, 140, p. 031001. [35]. tN. sc rip. 607. ot. 603. Basciano C., Kleinstreuer C., Hyun S., and Finol E. A., 2011, "A relation between near-wall particle-hemodynamics and onset of thrombus formation in abdominal. 609. aortic aneurysms," Annals of Biomedical Engineering, 39(7), pp. 2010-2026.. 610. [36]. Ma nu. 608. Deplano V., Guivier-Curien C., and Bertrand E., 2016, “3D analysis of vortical structures in an abdominal aortic aneurysm by stereoscopic PIV,” Experiments in. 612. Fluids, 57(11), pp. 167.. pt. [37]. Yu, S. C. M., 2000, “Steady and pulsatile flow characteristics in abdominal aortic. ce. 613. ed. 611. aneurysm models using particle image velocimetry,” International Journal of Heat. 615. and Fluid Flow, 21, pp. 74–83.. Ac. 614. JBME BIO-20-1288 (Thirugnanasambandam et al). 27. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. 598.

(28) op y ot C tN sc rip Ma nu. d. Figure 1: Schematic representing the benchtop flow-loop built using the deformable silicone AAA phantom. The. te. programmable pump supplies a physiological flow waveform to the AAA phantom, while the renal and iliac impedance. ce p. modules recreate physiological impedance provided by the peripheral arterial system. This is experimental setup 4. Ac. described in section 4.2.3.2. The inset illustrates basic dimensions of the phantom.. JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(29) py Co ot. tN. Figure 2: The in-house optimization algorithm outputs unique values of resistances and. sc rip. capacitance for the flow rate and target pressure waveforms. The predicted pressure waveform represents the resultant pressure calculated using these optimized values. The. Ac. ce. pt. ed. Ma nu. relative error between the target and predicted pressure waveforms was 1.97%.. JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(30) py Co ce. pt. ed. Ma nu. sc rip. tN. ot. (a). (b). Ac. Figure 3: (a) A representative resistance module built as part of the Windkessel model. A set of capillary tubes inside a nylon tube housed in a custom 3D printed casing provides a constant resistance. (b) A capacitance module used in the flow-loop; the volume of air trapped in the module determines its capacitance. The two ports on the top are used for pressure and volume control.. JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(31) (b). Ac. ce. pt. ed. Ma nu. py. sc rip. tN. ot. Co. (a). (c). JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(32) Ma nu. py. sc rip. tN. ot. Co. (d). (e). Figure 4: Schematic representing (a) experimental setup 1, which was used for characterizing the resistance modules; these provide constant resistance nearly identical. ed. to the value for which they were designed. (b) Experimental setup 2, which was used to. pt. characterize the impedance modules; these provide a proximal pressure waveform. ce. similar to the analytical solution for both iliac and renal modules. (c) Experimental setup 3, which shows a rigid tube instead of a (d) compliant phantom in the flow-loop, as in. Ac. Experimental setup 4. (e) Experimental setup 5, which was used to evaluate the impedance offered by the compliant AAA phantom. The circles with P and F indicate the location of the pressure probe and the flow rate sensor in the benchtop model.. JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(33) Co. py (b). ce. pt. ed. Ma nu. sc rip. tN. ot. (a). Figure 5: (a) Comparison between the target pressure waveform and the pressure. Ac. waveform measured at the entrance of the impedance module in a rigid tube flow-loop following experimental setup 3. (b) Pressure waveforms at the entrance of the impedance modules in flow-loops with the rigid tube or the compliant phantom, following experimental setups 3 and 4, respectively. The difference in pressure waveforms represents the net impedance offered by the phantom.. JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(34) py Co ot ce. pt. ed. Ma nu. sc rip. tN. (a). (b). Ac. Figure 6: (a) Variation of resistance measured across the phantom for a range of constant flow rates. (b) Pressure and volume of the phantom over one cardiac cycle in the flowloop.. JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(35) py Co ot tN sc rip Ma nu ed pt ce Ac JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(36) py Co ot tN sc rip Ma nu ed pt ce Ac. Figure 7: Temporal variation of the velocity field within the AAA phantom measured by phase-contrast MRI. Phases P0 through P18 correspond to ten of the twenty phases of the pulsatile cycle acquired during MR imaging.. JBME BIO-20-1288 Figures (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(37) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. Table 1: Optimized values of impedance module components obtained from the optimization protocol. Renal module. 𝐿𝐿 (𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∙ 𝑠𝑠 2 /𝑐𝑐𝑐𝑐3). 0.032. 0.032. 𝐶𝐶 (𝑐𝑐𝑐𝑐3 /𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚). 0.144 5.786. py. 𝑅𝑅𝑑𝑑 (𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∙ 𝑠𝑠/𝑐𝑐𝑐𝑐3). 0.484. Co. 0.463. Ac. ce. pt. ed. Ma nu. sc rip. tN. ot. 𝑅𝑅𝑝𝑝 (𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∙ 𝑠𝑠/𝑐𝑐𝑐𝑐3 ). ed ite d. Iliac module. JBME BIO-20-1288 Tables (Thirugnanasambandam et al). 0.048. 12.097. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. Impedance component.

(38) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. Table 2: Comparison of experimental and theoretical values of resistance offered by the resistance modules. Experimental (𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 ∙ 𝒔𝒔/𝒄𝒄𝒄𝒄𝟑𝟑 ). Mean Relative Difference (%). 0.512 ± 0.019. 10.5. Iliac distal resistance. 5.786. 5.835 ± 0.134. 0.8. Renal proximal resistance. 0.484. 0.497 ± 0.007. 2.6. Renal distal resistance. 12.097. 11.530 ± 0.381. 4.7. Iliac proximal resistance. Ac. ce. pt. ed. Ma nu. sc rip. tN. ot. Co. py. ed ite d. 0.463. JBME BIO-20-1288 Tables (Thirugnanasambandam et al). Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. Theoretical (𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 ∙ 𝒔𝒔/𝒄𝒄𝒄𝒄𝟑𝟑 ). Module.

(39) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. py Co ot tN sc rip Ma nu. Figure S1: Reference pressure waveform representing an invasively measured pressure. ed. over a cardiac cycle in the human infrarenal AAA. This was used as the target pressure. pt. waveform in the optimization algorithm to evaluate the optimal Windkessel model. Ac. ce. component values. Adapted from [25].. JBME BIO-20-1288 Supplementary Material (Thirugnanasambandam et al). i. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. SUPPLEMENTARY MATERIAL.

(40) Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME. Pressure waveform measured at the center of AAA. compare. Inlet flow waveform to pump. Adjust , and. ed ite d. Figure S2: Schematic of the optimization routine used to derive the impedance module parameters based on a combination of a genetic algorithm and the Levenberg-Macquardt. Ac. ce. pt. ed. Ma nu. sc rip. tN. ot. Co. py. algorithm.. JBME BIO-20-1288 Supplementary Material (Thirugnanasambandam et al). ii. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. Literature-derived AAA pressure waveform [25].

(41) py Co ot tN. Figure S3: Results from experimental setup 1 showing constant resistance provided by. sc rip. an exemplary resistance module across different volumetric flow rates under steady flow. Ac. ce. pt. ed. Ma nu. conditions.. JBME BIO-20-1288 Supplementary Material (Thirugnanasambandam et al). iii. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

(42) Co. py (b). ce. pt. ed. Ma nu. sc rip. tN. ot. (a). Ac. Figure S4: Comparison of theoretical and experimental pressure waveforms (a) at the entrance of the iliac impedance module while supplying an iliac flow waveform in experimental setup 2, and (b) at the entrance of the renal impedance module while supplying a renal flow waveform in experimental setup 2.. JBME BIO-20-1288 Supplementary Material (Thirugnanasambandam et al). iv. Downloaded from http://asmedigitalcollection.asme.org/biomechanical/article-pdf/doi/10.1115/1.4049894/6625070/bio-20-1288.pdf by TU Wien user on 01 February 2021. ed ite d. Journal of Biomechanical Engineering. Received June 23, 2020; Accepted manuscript posted January 25, 2021. doi:10.1115/1.4049894 Copyright (c) 2021 by ASME.

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