Abstract
A method for the construction of both rigid and compliant (flexible) transparent flow phantoms of biological flow structures, suitable for PIV and other optical flow methods with refractive-index-matched working fluid is described in detail. Methods for matching the in vivo compliance and elastic wave propagation wavelength are presented. The manipulation of MRI and CT scan data through an investment casting mould is described. A method for the casting of bubble-free phantoms in silicone elastomer is given. The method is applied to fabricate flexible phantoms of the carotid artery (with and without stenosis), the carotid artery bifurcation (idealised and patient-specific) and the human upper airway (nasal cavity). The fidelity of the phantoms to the original scan data is measured, and it is shown that the cross-sectional error is less than 5% for phantoms of simple shape but up to 16% for complex cross-sectional shapes such as the nasal cavity. This error is mainly due to the application of a PVA coating to the inner mould and can be reduced by shrinking the digital model. Sixteen per cent variation in area is less than the natural patient to patient variation of the physiological geometries. The compliance of the phantom walls is controlled within physiologically realistic ranges, by choice of the wall thickness, transmural pressure and Young’s modulus of the elastomer. Data for the dependence of Young’s modulus on curing temperature are given for Sylgard 184. Data for the temperature dependence of density, viscosity and refractive index of the refractive-index-matched working liquid (i.e. water–glycerol mixtures) are also presented.
Similar content being viewed by others
Notes
The viscosity of water/glycerol is obtained using a HAAKE Viscometers Rotovisco© RV20 concentric cylinder viscometer.
STL is a widely used file format for rapid prototyping and computer-aided design. It describes the unstructured triangulated surface by the unit normal and vertices of the triangles.
Dow Corning SYLGARD® 184 Silicone Elastomer data sheet.
Temperatures obtained with a Maxim DS19121G Thermochron® iButton® that has an accuracy of ±1°C and a resolution of 0.5°C.
Abbreviations
- α:
-
Womersley number
- ε:
-
Uniaxial strain
- εθ :
-
Hoop strain
- λ:
-
Propagation wavelength
- ρ:
-
Density
- σ:
-
Uniaxial stress
- ν:
-
Kinematic viscosity
- ω:
-
Angular frequency of the oscillation
- A :
-
Cross-sectional area
- B :
-
Dispersion coefficient
- CAD:
-
Computer-aided design
- CA:
-
Carotid artery
- CCA:
-
Common carotid artery
- CFD:
-
Computational fluid dynamics
- CT:
-
X-ray computed tomography
- c 0 :
-
Propagation wave speed
- d :
-
Distensibility
- D :
-
Diameter
- E :
-
Young’s modulus
- ECA:
-
External carotid artery
- F :
-
Force
- FSI:
-
Fluid–structure interaction
- h :
-
Wall thickness
- ICA:
-
Internal carotid artery
- L, L 0 :
-
Vessel length
- LDA:
-
Laser doppler anemometry
- LDV:
-
Laser doppler velocimetry
- MRI:
-
Magnetic resonance imaging
- PIV:
-
Particle image velocimetry
- N :
-
Index of refraction
- P :
-
Pressure
- PVA:
-
Polyvinyl acetate
- Q :
-
Inlet flow rate
- R :
-
Radius
- Re :
-
Reynolds Number
- SD:
-
Standard deviation
- St :
-
Strouhal number
- STL:
-
Stereolithography
- T :
-
Time period
- TOF:
-
Time of flight
- U m :
-
Time-averaged mean inlet velocity
- WSS:
-
Wall shear stress
References
Adler K, Brücker C (2007) Dynamic flow in a realistic model of the upper human lung airways. Exp Fluids 43(2):411–423. doi:10.1007/s00348-007-0296-0
Aspert N, Santa-Cruz D, Ebrahimi T (2002) MESH: measuring errors between surfaces using the Hausdorff distance. In: Proceedings of the IEEE international conference on multimedia, pp 705–708
Bailie N, Hanna B, Watterson J, Gallagher G (2006) An overview of numerical modelling of nasal airflow. Rhinology 44(1):53–57
Bale-Glickman J, Selby K, Saloner D, Savas O (2003) Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady input conditions. J Biomech Eng 125(1):38–48
Bertram CD, Elliott NSJ (2003) Flow-rate limitation in a uniform thin-walled collapsible tube, with comparison to a uniform thick-walled tube and a tube of tapering thickness. J Fluids Struct 17(4):541–559
Boutsianis E, Guala M, Olgac U, Wildermuth S, Hoyer K, Ventikos Y, Poulikakos D (2009) CFD and PTV steady flow investigation in an anatomically accurate abdominal aortic aneurysm. J Biomech Eng 131(1):011008–011015. doi:10.1115/1.3002886
Buchmann NA, Jermy MC, Nguyen CV (2009) Experimental investigation of carotid artery haemodynamics in an anatomically realistic model. Int J Exp Comput Methods Biomech 1(2):172–192
Buchmann NA, Yamamoto M, Jermy M, David T (2010) Particle image velocimetry (PIV) and computational fluid dynamics (CFD) modelling of carotid artery haemodynamics under steady flow: a validation study. J Biomech Sci Eng 5(4):421–436
Buchmann N, Atkinson C, Jeremy M, Soria J (2011) Tomographic particle image velocimetry investigation of the flow in a modeled human carotid artery bifurcation. Exp Fluids 50(4):1131–1151. doi:10.1007/s00348-011-1042-1
Burgmann S, Große S, Schröder W, Roggenkamp J, Jansen S, Gräf F, Büsen M (2009) A refractive index-matched facility for fluid–structure interaction studies of pulsatile and oscillating flow in elastic vessels of adjustable compliance. Exp Fluids 47(4):865–881. doi:10.1007/s00348-009-0681-y
Bushberg JT, Seibert JA, Leidholdt EM Jr, Boone JM (2002) The essential physics of medical imaging. Lippincott Williams & Wilkins, Philadelphia
Çakmak O, Coskun M, Celik H, Buyuklu F, Ozluoglu LN (2003) Value of acoustic rhinometry for measuring nasal valve area. Laryngoscope 113(2):295–302
Caro CG, Pedley TJ, Schroter RC, Seed WA (1978) THe mechanics of circulation. Oxford University Press, Oxford
Churchill SE, Shackelford LL, Georgi JN, Black MT (2004) Morphological variation and airflow dynamics in the human nose. Am J Hum Biol 16(6):625–638. doi:10.1002/ajhb.20074
Deplano V, Knapp Y, Bertrand E, Gaillard E (2007) Flow behaviour in an asymmetric compliant experimental model for abdominal aortic aneurysm. J Biomech 40(11):2406–2413
Ding Z, Wang K, Li J, Cong X (2001) Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation. J Biomech 34(12):1555–1562
Doorly DJ, Taylor DJ, Schroter RC (2008) Mechanics of airflow in the human nasal airways. Respir Physiol Neurobiol 163(1–3):100–110
Doyle BJ, Morris LG, Callanan A, Kelly P, Vorp DA, McGloughlin TM (2008) 3D reconstruction and manufacture of real abdominal aortic aneurysms: from CT scan to silicone model. J Biomech Eng 130(3):034501–034505
Elkins C, Alley M (2007) Magnetic resonance velocimetry: applications of magnetic resonance imaging in the measurement of fluid motion. Exp Fluids 43(6):823–858. doi:10.1007/s00348-007-0383-2
Galdi GP, Rannacher R, Robertson AM, Turek S (2008) Hemodynamical flows modelling, analysis and simulation, vol 37. Oberwolfach seminars, vol 37. Birkhäuser, Basel
Geoghegan PH, Jermy MC, Buchmann NA, Spence CJ, Freitag T (2009) Experimental investigation of flow in a compliant tube using particle image velocimetry. Paper presented at the 8th international symposium on particle image velocimetry, Melbourne Australia
Gijsen FJH, Palmen DEM, van der Beek MHE, van de Vosse FN, van Dongen MEH, Janssen JD (1996) Analysis of the axial flow field in stenosed carotid artery bifurcation models–LDA experiments. J Biomech 29(11):1483–1489
Gijsen FJH, van de Vosse FN, Janssen JD (1999) The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. J Biomech 32(6):601–608
Girardin M, Bilgen E, Arbour P (1983) Experimental study of velocity fields in a human nasal fossa by laser anemometry. Ann Otol Rhinol Laryngol 92:231–236
Goubergrits L, Kertzscher U, Schöneberg B, Wellnhofer E, Petz C, Hege H-C (2008) CFD analysis in an anatomically realistic coronary artery model based on non-invasive 3D imaging: comparison of magnetic resonance imaging with computed tomography. Int J Cardiovasc Imaging (formerly Cardiac Imaging) 24(4):411–421. doi:10.1007/s10554-007-9275-z
Goubergrits L, Wellnhofer E, Kertzscher U, Affeld K, Petz C, Hege H-C (2009) Coronary artery WSS profiling using a geometry reconstruction based on biplane angiography. Ann Biomed Eng 37(4):682–691. doi:10.1007/s10439-009-9656-7
Gray J, Owen I, Escudier M (2007) Dynamic scaling of unsteady shear-thinning non-Newtonian fluid flows in a large-scale model of a distal anastomosis. Exp Fluids 43(4):535–546. doi:10.1007/s00348-007-0317-z
Hahn I, Scherer PW, Mozell MM (1993) Velocity profiles measured for airflow through a large-scale model of the human nasal cavity. J Appl Physiol 75(5):2273–2287
Hopkins LM, Kelly JT, Wexler AS, Prasad AK (2000) Particle image velocimetry measurements in complex geometries. Exp Fluids 29(1):91–95. doi:10.1007/s003480050430
Isnard RN, Pannier BM, Laurent S, London GM, Diebold B, Safar ME (1989) Pulsatile diameter and elastic modulus of the aortic arch in essential hypertension: a noninvasive study. J Am Coll Cardiol 13(2):399–405. doi:10.1016/0735-1097(89)90518-4
Kelly JT, Prasad AK, Wexler AS (2000) Detailed flow patterns in the nasal cavity. J Appl Physiol 89(1):323–337
Kobayashi S, Tang D, Ku DN (2004) Collapse in high-grade stenosis during pulsatile flow experiments. JSME Int J Ser C Mech Syst Mach Elements Manuf 47(4):1010–1018
Kook Kim J, Yoon J-H, Hoon Kim C, Wook Nam T, Bo Shim D, Ae Shin H (2006) Particle image velocimetry measurements for the study of nasal airflow. Acta Oto-laryngologica 126(3):282–287. doi:10.1080/00016480500361320
Ku D, Giddens D, Zarins C, Glagov S (1985) Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arterioscler Thromb Vasc Biol 5(3):293–302
Lee S-W, Antiga L, Steinman DA (2009) Correlations among indicators of disturbed flow at the normal carotid bifurcation. J Biomech Eng 131(6):061013–061017
Liepsch D (2002) An introduction to biofluid mechanics–basic models and applications. J Biomech 35(4):415–435
Liepsch D, Pflugbeil G, Matsuo T, Lesniak B (1998) Flow visualization and 1- and 3-D laser-Doppler-anemometer measurements in models of human carotid arteries. Clin Hemorheol Microcirc 18(1):1–30
Lowe ML, Kutt PH (1992) Refraction through cylindrical tubes. Exp Fluids 13(5):315–320. doi:10.1007/bf00209503
Marshall I, Zhao S, Papathanasopoulou P, Hoskins P, Xu XY (2004) MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models. J Biomech 37(5):679–687
Moore S (2007) Computational 3D modelling of hemodynamics in the circle of willis. University of Canterbury, Christchurch
Motomiya M, Karino T (1984) Flow patterns in the human carotid artery bifurcation. Stroke 15(1):50–56. doi:10.1161/01.str.15.1.50
Nguyen TT, Biadillah Y, Mongrain R, Brunette J, Tardif JC, Bertrand OF (2004) A method for matching the refractive index and kinematic viscosity of a blood analog for flow visualization in hydraulic cardiovascular models. J Biomech Eng 126(4):529–535
Palmen DEM, Gijsen FJH, van de Vosse FN, Janssen JD, van Dongen MEH (1993) LDA measurements in a non-stenosed and a stenosed model of the carotid artery bifurcation. In: The international society for optical engineering, pp 219–226
Perktold K, Rappitsch G (1995) Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J Biomech 28(7):845–856
Perry JH (1950) Chemical engineers’ handbook. J Chem Educ 27(9):533. doi:10.1021/ed027p533.1
Potter MC, Wiggert DC (2002) Mechanics of fluids, 3rd edn. Brooks/Cole, USA
Proetz A (1951) Air currents in the upper respiratory tract and their clinical importance. Ann Otol Rhinol Laryngol 60:439–467
Riley W, Barnes R, Evans G, Burke G (1992) Ultrasonic measurement of the elastic modulus of the common carotid artery. The Atherosclerosis Risk in Communities (ARIC) Study. Stroke 23(7):952–956
Shelby JE (2005) Introduction to glass science and technology, 2nd edn. Royal Society of Chemistry, Cambridge
Soloff SM et al (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8(12):1441
Spence C, Buchmann N, Jermy M (2011a) Unsteady flow in the nasal cavity with high flow therapy measured by stereoscopic PIV. Exp Fluids 1–11. doi:10.1007/s00348-011-1044-z
Spence C, Buchmann N, Jermy M, Moore S (2011b) Stereoscopic PIV measurements of flow in the nasal cavity with high flow therapy. Exp Fluids 50(4):1005–1017. doi:10.1007/s00348-010-0984-z
Steiger HJ, Aaslid R, Keller S, Reulen H-J (1989) Strength, elasticity and viscoelastic properties of cerebral aneurysms. Heart Vessels 5(1):41–46. doi:10.1007/bf02058357
Swift DL, Proctor DF (1977) Access of air to the respiratory tract. Respiratory Defense Mechanisms, pp 63–90
Tateshima S, Murayama Y, Villablanca JP, Morino T, Takahashi H, Yamauchi T, Tanishita K, Vinuela F (2001) Intraaneurysmal flow dynamics study featuring an acrylic aneurysm model manufactured using a computerized tomography angiogram as a mold. J Neurosurg 95:1020–1027
Vennemann P, Lindken R, Westerweel J (2007) In vivo whole-field blood velocity measurement techniques. Exp Fluids 42(4):495–511. doi:10.1007/s00348-007-0276-4
Womersley JR (1955) Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol 127:553
Yagi T, Kamoda A, Sato A, Yang W, Umezu M (2009) 3D volume flow visualization for vascular flow modelling using stereo PIV with fluorescent tracer particles. Paper presented at the 8th international symposium on particle image velocimetry (PIV 09), Melbourne, Australia
Zamir M (2000) The physics of pulsatile flow. Springer, New York
Zarins C, Giddens D, Bharadvaj B, Sottiurai V, Mabon R, Glagov S (1983) Carotid bifurcation atherosclerosis. Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress. Circ Res 53(4):502–514
Zhao SZ, Xu XY, Hughes AD, Thom SA, Stanton AV, Ariff B, Long Q (2000) Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation. J Biomech 33(8):975–984
Acknowledgments
We are grateful to Prof. Olaf Diegel of AUT for his advice and assistance in producing the 3D-printed cores, and to Mr Graeme Harris and the staff of the Department Of Mechanical Engineering workshop for technical support. NB and PHG carried out their parts of the work under UC Doctoral Scholarships, and CJS under an Enterprise scholarship supported by Fisher and Paykel Healthcare.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Geoghegan, P.H., Buchmann, N.A., Spence, C.J.T. et al. Fabrication of rigid and flexible refractive-index-matched flow phantoms for flow visualisation and optical flow measurements. Exp Fluids 52, 1331–1347 (2012). https://doi.org/10.1007/s00348-011-1258-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00348-011-1258-0