Research Papers

Anthropomorphic Model of Intrathecal Cerebrospinal Fluid Dynamics Within the Spinal Subarachnoid Space: Spinal Cord Nerve Roots Increase Steady-Streaming

[+] Author and Article Information
Mohammadreza Khani

Neurophysiological Imaging and Modeling
Department of Biological Engineering,
University of Idaho,
Moscow, ID 83844
e-mail: Khan0242@vandals.uidaho.edu

Lucas R. Sass

Neurophysiological Imaging and Modeling
Department of Biological Engineering,
University of Idaho,
Moscow, ID 83844
e-mail: sass8026@vandals.uidaho.edu

Tao Xing

Department of Mechanical Engineering,
University of Idaho,
Moscow, ID 83844
e-mail: xing@uidaho.edu

M. Keith Sharp

Biofluid Mechanics Laboratory,
University of Louisville,
Louisville, KY 40292
e-mail: keith.sharp@louisville.edu

Olivier Balédent

Bioflow Image,
CHU Nord Amiens-Picardie,
Amiens 80054, France
e-mail: Olivier.Baledent@chu-amiens.fr

Bryn A. Martin

Neurophysiological Imaging and Modeling
Department of Biological Engineering,
University of Idaho,
Moscow, ID 83844
e-mail: brynm@uidaho.edu

Manuscript received February 2, 2018; final manuscript received May 22, 2018; published online June 26, 2018. Assoc. Editor: Rouzbeh Amini.

J Biomech Eng 140(8), 081012 (Jun 26, 2018) (15 pages) Paper No: BIO-18-1065; doi: 10.1115/1.4040401 History: Received February 02, 2018; Revised May 22, 2018

Cerebrospinal fluid (CSF) dynamics are thought to play a vital role in central nervous system (CNS) physiology. The objective of this study was to investigate the impact of spinal cord (SC) nerve roots (NR) on CSF dynamics. A subject-specific computational fluid dynamics (CFD) model of the complete spinal subarachnoid space (SSS) with and without anatomically realistic NR and nonuniform moving dura wall deformation was constructed. This CFD model allowed detailed investigation of the impact of NR on CSF velocities that is not possible in vivo using magnetic resonance imaging (MRI) or other noninvasive imaging methods. Results showed that NR altered CSF dynamics in terms of velocity field, steady-streaming, and vortical structures. Vortices occurred in the cervical spine around NR during CSF flow reversal. The magnitude of steady-streaming CSF flow increased with NR, in particular within the cervical spine. This increase was located axially upstream and downstream of NR due to the interface of adjacent vortices that formed around NR.

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Yildiz, S. , Thyagaraj, S. , Jin, N. , Zhong, X. , Heidari Pahlavian, S. , Martin, B. A. , Loth, F. , Oshinski, J. , and Sabra, K. G. , 2017, “ Quantifying the Influence of Respiration and Cardiac Pulsations on Cerebrospinal Fluid Dynamics Using Real-Time Phase-Contrast MRI,” J. Magn. Reson. Imaging, Press, 46(12), pp. 431–439. [CrossRef]
Chen, L. , Beckett, A. , Verma, A. , and Feinberg, D. A. , 2015, “ Dynamics of Respiratory and Cardiac CSF Motion Revealed With Real-Time Simultaneous Multi-Slice EPI Velocity Phase Contrast Imaging,” Neuroimage, 122, pp. 281–287. [CrossRef] [PubMed]
Baledent, O. , Henry-Feugeas, M. C. , and Idy-Peretti, I. , 2001, “ Cerebrospinal Fluid Dynamics and Relation With Blood Flow: A Magnetic Resonance Study With Semiautomated Cerebrospinal Fluid Segmentation,” Invest. Radiol., 36(7), pp. 368–377. [CrossRef] [PubMed]
Wostyn, P. , Audenaert, K. , and De Deyn, P. P. , 2009, “ More Advanced Alzheimer's Disease May Be Associated With a Decrease in Cerebrospinal Fluid Pressure,” Cerebrospinal Fluid Res., 6(1), p. 14.
Takizawa, K. , Matsumae, M. , Hayashi, N. , Hirayama, A. , Yatsushiro, S. , and Kuroda, K. , 2017, “ Hyperdynamic CSF Motion Profiles Found in Idiopathic Normal Pressure Hydrocephalus and Alzheimer's Disease Assessed by Fluid Mechanics Derived From Magnetic Resonance Images,” Fluids Barriers CNS, 14(1), p. 29.
Martin, B. A. , Labuda, R. , Royston, T. J. , Oshinski, J. N. , Iskandar, B. , and Loth, F. , 2010, “ Spinal Subarachnoid Space Pressure Measurements in an In Vivo Spinal Stenosis Model: Implications on Syringomyelia Theories,” ASME J. Biomech. Eng., 132(11), p. 111007.
Yeo, J. , Cheng, S. , Hemley, S. , Lee, B. B. , Stoodley, M. , and Bilston, L. , 2017, “ Characteristics of CSF Velocity-Time Profile in Posttraumatic Syringomyelia,” Am. J. Neuroradiol., 38(9), pp. 1839–1844. [CrossRef]
Bunck, A. C. , Kroeger, J. R. , Juettner, A. , Brentrup, A. , Fiedler, B. , Crelier, G. R. , Martin, B. A. , Heindel, W. , Maintz, D. , and Schwindt, W. , 2012, “ Magnetic Resonance 4D Flow Analysis of Cerebrospinal Fluid Dynamics in Chiari I Malformation With and Without Syringomyelia,” Eur. Radiol., 22(9), pp. 1860–1870. [CrossRef] [PubMed]
Pahlavian, S. H. , Loth, F. , Luciano, M. , Oshinski, J. , and Martin, B. A. , 2015, “ Neural Tissue Motion Impacts Cerebrospinal Fluid Dynamics at the Cervical Medullary Junction: A Patient-Specific Moving-Boundary Computational Model,” Ann. Biomed. Eng., 43(12), pp. 2911–2923. [CrossRef] [PubMed]
Zhang, L. F. , and Hargens, A. R. , 2014, “ Intraocular/Intracranial Pressure Mismatch Hypothesis for Visual Impairment Syndrome in Space,” Aviat. Space. Environ. Med., 85(1), pp. 78–80.
Bradley , W. G., Jr. , Scalzo, D. , Queralt, J. , Nitz, W. N. , Atkinson, D. J. , and Wong, P. , 1996, “ Normal-Pressure Hydrocephalus: Evaluation With Cerebrospinal Fluid Flow Measurements at MR Imaging,” Radiology, 198(2), pp. 523–529. [CrossRef] [PubMed]
Simpson, K. , Baranidharan, G. , and Gupta, S. , 2012, Spinal Interventions in Pain Management, 1st ed., Oxford University Press, Oxford, UK. [CrossRef]
Papisov, M. I. , Belov, V. V. , and Gannon, K. S. , 2013, “ Physiology of the Intrathecal Bolus: The Leptomeningeal Route for Macromolecule and Particle Delivery to CNS,” Mol. Pharm., 10(5), pp. 1522–1532. [CrossRef] [PubMed]
Rassoli, A. , Nabaei, M. , Fatouraee, N. , and Nabaei, G. , 2017, “ Numerical Modeling of the Brain Hypothermia by Cooling the Cerebrospinal Fluid,” Tehran Univ. Med. J., 75(1), pp. 31–38. http://www.ingentaconnect.com/content/doaj/16831764/2017/00000075/00000001/art00005
Kumar, P. , Srivatsava, M. V. , Singh, S. , and Prasad, H. K. , 2008, “ Filtration of Cerebrospinal Fluid Improves Isolation of Mycobacteria,” J. Clin. Microbiol., 46(8), pp. 2824–2825. [CrossRef] [PubMed]
Urwin, S. C. , and Hunt, P. , 2000, “ Cerebrospinal Fluid Filtration in Guillain-Barre Syndrome,” Anaesthesia, 55(5), pp. 489–518. [CrossRef]
Finsterer, J. , and Mamoli, B. , 1999, “ Cerebrospinal Fluid Filtration in Amyotrophic Lateral Sclerosis,” Eur. J. Neurol., 6(5), pp. 597–600. [CrossRef] [PubMed]
Brizzi, M. , Thoren, A. , and Hindfelt, B. , 1996, “ Cerebrospinal Fluid Filtration in a Case of Severe Pneumococcal Meningitis,” Scand. J. Infect. Dis., 28(5), pp. 455–458. [CrossRef] [PubMed]
Luciano, M. G. , Dombrowski, S. M. , Qvarlander, S. , El-Khoury, S. , Yang, J. , Thyagaraj, S. , and Loth, F. , 2017, “ Novel Method for Dynamic Control of Intracranial Pressure,” J. Neurosurg., 126(5), pp. 1629–1640. [CrossRef] [PubMed]
Stockman, H. W. , 2007, “ Effect of Anatomical Fine Structure on the Dispersion of Solutes in the Spinal Subarachnoid Space,” ASME J. Biomech. Eng., 129(5), pp. 666–675. [CrossRef]
Stockman, H. W. , 2006, “ Effect of Anatomical Fine Structure on the Flow of Cerebrospinal Fluid in the Spinal Subarachnoid Space,” ASME J. Biomech. Eng., 128(1), pp. 106–114. [CrossRef]
Tangen, K. M. , Hsu, Y. , Zhu, D. C. , and Linninger, A. A. , 2015, “ CNS Wide Simulation of Flow Resistance and Drug Transport Due to Spinal Microanatomy,” J. Biomech., 48(10), pp. 2144–2154. [CrossRef] [PubMed]
Tangen, K. , Narasimhan, N. S. , Sierzega, K. , Preden, T. , Alaraj, A. , and Linninger, A. A. , 2016, “ Clearance of Subarachnoid Hemorrhage From the Cerebrospinal Fluid in Computational and In Vivo Models,” Ann Biomed Eng., 44(12), pp. 3478–3494.
Tangen, K. , Linninger, A. , and Narasimhan, N. S. , 2016, “ Clearance of Subarachnoid Hemorrhage from the Cerebrospinal Fluid in Computational and In Vitro Models,” Cerebrovasc. Dis., 44, p. 202.
Khani, M. , Xing, T. , Gibbs, C. , Oshinski, J. N. , Stewart, G. R. , Zeller, J. R. , and Martin, B. A. , 2017, “ Nonuniform Moving Boundary Method for Computational Fluid Dynamics Simulation of Intrathecal Cerebrospinal Flow Distribution in a Cynomolgus Monkey,” ASME J. Biomech. Eng., 139(8), p. 081005.
Hsu, Y. , Harris, T. J. , Hettiarachchi, H. D. M. , Penn, R. , and Linninger, A. A. , 2011, “ Three Dimensional Simulation and Experimental Investigation of Intrathecal Drug Delivery in the Spinal Canal and the Brain,” 21st European Symposium on Computer Aided Process Engineering (ESCAPE), Chalkidiki, Greece, May 29–June 1, pp. 1525–1529.
Hsu, Y. , Hettiarachchi, H. D. , Zhu, D. C. , and Linninger, A. A. , 2012, “ The Frequency and Magnitude of Cerebrospinal Fluid Pulsations Influence Intrathecal Drug Distribution: Key Factors for Interpatient Variability,” Anesth. Analg., 115(2), pp. 386–394. [CrossRef] [PubMed]
Cheng, S. , Fletcher, D. , Hemley, S. , Stoodley, M. , and Bilston, L. , 2014, “ Effects of Fluid Structure Interaction in a Three Dimensional Model of the Spinal Subarachnoid Space,” J. Biomech., 47(11), pp. 2826–2830. [CrossRef] [PubMed]
Tangen, K. M. , Leval, R. , Mehta, A. I. , and Linninger, A. A. , 2017, “ Computational and In Vitro Experimental Investigation of Intrathecal Drug Distribution: Parametric Study of the Effect of Injection Volume, Cerebrospinal Fluid Pulsatility, and Drug Uptake,” Anesth. Analg., 124(5), pp. 1686–1696. [CrossRef] [PubMed]
Kuttler, A. , Dimke, T. , Kern, S. , Helmlinger, G. , Stanski, D. , and Finelli, L. A. , 2010, “ Understanding Pharmacokinetics Using Realistic Computational Models of Fluid Dynamics: Biosimulation of Drug Distribution Within the CSF Space for Intrathecal Drugs,” J. Pharmacokinet. Pharmacodyn., 37(6), pp. 629–644. [CrossRef] [PubMed]
Pizzichelli, G. , Kehlet, G. , Evju, Ø. , Martin, B. A. , Rognes, M. E. , Mardal, K. A. , and Sinibaldi, E. , 2017, “ Numerical Study of Intrathecal Drug Delivery to a Permeable Spinal Cord: Effect of Catheter Position and Angle,” Comput. Methods Biomech. Biomed. Eng., Press., 20(15), pp. 1599–1608.
Haga, P. T. , Pizzichelli, G. , Mortensen, M. , Kuchta, M. , Pahlavian, S. H. , Sinibaldi, E. , Martin, B. A. , and Mardal, K. A. , 2017, “ A Numerical Investigation of Intrathecal Isobaric Drug Dispersion Within the Cervical Subarachnoid Space,” PLoS One, 12(3), p. e0173680. [CrossRef] [PubMed]
Heidari Pahlavian, S. , Bunck, A. C. , Loth, F. , Shane Tubbs, R. , Yiallourou, T. , Kroeger, J. R. , Heindel, W. , and Martin, B. A. , 2015, “ Characterization of the Discrepancies Between Four-Dimensional Phase-Contrast Magnetic Resonance Imaging and In-Silico Simulations of Cerebrospinal Fluid Dynamics,” ASME J. Biomech. Eng., 137(5), p. 051002. [CrossRef]
Heidari Pahlavian, S. , Bunck, A. C. , Thyagaraj, S. , Giese, D. , Loth, F. , Hedderich, D. M. , Kroger, J. R. , and Martin, B. A. , 2016, “ Accuracy of 4D Flow Measurement of Cerebrospinal Fluid Dynamics in the Cervical Spine: An In Vivo Verification against Numerical Simulation,” Ann. Biomed. Eng., 44(11), pp. 3202–3214. [CrossRef] [PubMed]
Heidari Pahlavian, S. , Yiallourou, T. , Tubbs, R. S. , Bunck, A. C. , Loth, F. , Goodin, M. , Raisee, M. , and Martin, B. A. , 2014, “ The Impact of Spinal Cord Nerve Roots and Denticulate Ligaments on Cerebrospinal Fluid Dynamics in the Cervical Spine,” PLoS One, 9(4), p. e91888. [CrossRef] [PubMed]
Bertram, C. D. , Brodbelt, A. R. , and Stoodley, M. A. , 2005, “ The Origins of Syringomyelia: Numerical Models of Fluid/Structure Interactions in the Spinal Cord,” ASME J. Biomech. Eng., 127(7), pp. 1099–1109. [CrossRef]
Bertram, C. , Bilston, L. , and Stoodley, M. , 2008, “ Tensile Radial Stress in the Spinal Cord Related to Arachnoiditis or Tethering: A Numerical Model,” Med. Biol. Eng. Comput., 46(7), pp. 701–707. [CrossRef] [PubMed]
Elliott, N. S. J. , Lucey, A. D. , Lockerby, D. A. , and Brodbelt, A. R. , 2017, “ Fluid-Structure Interactions in a Cylindrical Layered Wave Guide With Application in the Spinal Column to Syringomyelia,” J. Fluids Struct., 70, pp. 464–499. [CrossRef]
Elliott, N. S. , 2012, “ Syrinx Fluid Transport: Modeling Pressure-Wave-Induced Flux Across the Spinal Pial Membrane,” ASME J. Biomech. Eng., 134(3), p. 031006. [CrossRef]
Jain, K. , Ringstad, G. , Eide, P. K. , and Mardal, K. A. , 2017, “ Direct Numerical Simulation of Transitional Hydrodynamics of the Cerebrospinal Fluid in Chiari I Malformation: The Role of Cranio-Vertebral Junction,” Int. J. Numer. Method Biomed. Eng., 33(9), p. e02853.
Cheng, S. , Stoodley, M. A. , Wong, J. , Hemley, S. , Fletcher, D. F. , and Bilston, L. E. , 2012, “ The Presence of Arachnoiditis Affects the Characteristics of CSF Flow in the Spinal Subarachnoid Space: A Modelling Study,” J. Biomech., 45(7), pp. 1186–1191. [CrossRef] [PubMed]
Rutkowska, G. , Haughton, V. , Linge, S. , and Mardal, K. A. , 2012, “ Patient-Specific 3D Simulation of Cyclic CSF Flow at the Craniocervical Region,” AJNR Am. J. Neuroradiol., 33(9), pp. 1756–1762. [CrossRef] [PubMed]
Yiallourou, T. I. , Kröger, J. R. , Stergiopulos, N. , Maintz, D. , Martin, B. A. , and Bunck, A. C. , 2012, “ Comparison of 4D Phase-Contrast MRI Flow Measurements to Computational Fluid Dynamics Simulations of Cerebrospinal Fluid Motion in the Cervical Spine,” PLoS ONE, 7(12), p. e52284. [CrossRef] [PubMed]
Clarke, E. C. , Stoodley, M. A. , and Bilston, L. E. , 2013, “ Changes in Temporal Flow Characteristics of CSF in Chiari Malformation Type I With and Without Syringomyelia: Implications for Theory of Syrinx Development Clinical Article,” J. Neurosurg., 118(5), pp. 1135–1140. [CrossRef] [PubMed]
Shaffer, N. , Martin, B. A. , Rocque, B. , Madura, C. , Wieben, O. , Iskandar, B. , Dombrowski, S. , Luciano, M. , Oshinski, J. , and Loth, F. , 2013, “ Cerebrospinal Fluid Flow Impedance Is Elevated in Type I Chiari Malformation,” ASME J. Biomech. Eng., 136(2), p. 021012.
Martin, B. A. , Kalata, W. , Shaffer, N. , Fischer, P. , Luciano, M. , and Loth, F. , 2013, “ Hydrodynamic and Longitudinal Impedance Analysis of Cerebrospinal Fluid Dynamics at the Craniovertebral Junction in Type I Chiari Malformation,” PLoS One, 8(10), p. e75335. [CrossRef] [PubMed]
Roldan, A. , Wieben, O. , Haughton, V. , Osswald, T. , and Chesler, N. , 2009, “ Characterization of CSF Hydrodynamics in the Presence and Absence of Tonsillar Ectopia by Means of Computational Flow Analysis,” AJNR Am. J. Neuroradiol., 30(5), pp. 941–946. [CrossRef] [PubMed]
Linge, S. O. , Mardal, K.-A. , Helgeland, A. , Heiss, J. D. , and Haughton, V. , 2014, “ Effect of Craniovertebral Decompression on CSF Dynamics in Chiari Malformation Type I Studied With Computational Fluid Dynamics: Laboratory Investigation,” J. Neurosurg. Spine, 21(4), p. 559. [CrossRef] [PubMed]
Linge, S. O. , Haughton, V. , Lovgren, A. E. , Mardal, K. A. , Helgeland, A. , and Langtangen, H. P. , 2011, “ Effect of Tonsillar Herniation on Cyclic CSF Flow Studied With Computational Flow Analysis,” AJNR Am. J. Neuroradiol., 32(8), pp. 1474–1481. [CrossRef] [PubMed]
Linge, S. , Mardal, K.-A. , Haughton, V. , and Helgeland, A. , 2013, “ Simulating CSF Flow Dynamics in the Normal and the Chiari I Subarachnoid Space During Rest and Exertion,” Am. J. Neuroradiol., 34(1), pp. 41–45. [CrossRef]
Bilston, L. E. , Fletcher, D. F. , and Stoodley, M. A. , 2006, “ Focal Spinal Arachnoiditis Increases Subarachnoid Space Pressure: A Computational Study,” Clin. Biomech. (Bristol, Avon), 21(6), pp. 579–584. [CrossRef] [PubMed]
Loth, F. , Yardimci, M. A. , and Alperin, N. , 2001, “ Hydrodynamic Modeling of Cerebrospinal Fluid Motion Within the Spinal Cavity,” ASME J. Biomech. Eng., 123(1), pp. 71–79.
Gupta, S. , Soellinger, M. , Grzybowski, D. M. , Boesiger, P. , Biddiscombe, J. , Poulikakos, D. , and Kurtcuoglu, V. , 2010, “ Cerebrospinal Fluid Dynamics in the Human Cranial Subarachnoid Space: An Overlooked Mediator of Cerebral Disease—I: Computational Model,” J. R. Soc. Interface, 7(49), pp. 1195–1204. [CrossRef] [PubMed]
Sass, L. R. , Khani, M. , Natividad, G. C. , Tubbs, R. S. , Baledent, O. , and Martin, B. A. , 2017, “ A 3D Subject-Specific Model of the Spinal Subarachnoid Space With Anatomically Realistic Ventral and Dorsal Spinal Cord Nerve Rootlets,” Fluids Barriers CNS, 14(1), p. 36. [CrossRef] [PubMed]
Yushkevich, P. A. , Piven, J. , Hazlett, H. C. , Smith, R. G. , Ho, S. , Gee, J. C. , and Gerig, G. , 2006, “ User-Guided 3D Active Contour Segmentation of Anatomical Structures: Significantly Improved Efficiency and Reliability,” Neuroimage, 31(3), pp. 1116–1128. [CrossRef] [PubMed]
Gupta, A. , Church, D. , Barnes, D. , and Hassan, A. , 2009, “ Cut to the Chase: On the Need for Genotype-Specific Soft Tissue Sarcoma Trials,” Ann. Oncol., 20(3), pp. 399–400. [CrossRef] [PubMed]
Honji, H. , 1981, “ Streaked Flow Around an Oscillating Circular-Cylinder,” J Fluid Mech., 107(1), pp. 509–520. [CrossRef]
Hall, P. , 1984, “ On the Stability of the Unsteady Boundary-Layer on a Cylinder Oscillating Transversely in a Viscous-Fluid,” J. Fluid Mech., 146(1), pp. 347–367. [CrossRef]
Hino, M. , Sawamoto, M. , and Takasu, S. , 1976, “ Experiments on Transition to Turbulence in an Oscillatory Pipe-Flow,” J. Fluid Mech., 75(2), pp. 193–207. [CrossRef]
Sanchez, A. L. , Martinez-Bazan, C. , Gutierrez-Montes, C. , Criado-Hidalgo, E. , Pawlak, G. , Bradley, W. , Haughton, V. , and Lasheras, J. C. , 2018, “ On the Bulk Motion of the Cerebrospinal Fluid in the Spinal Canal,” J. Fluid Mech., 841, pp. 203–227. [CrossRef]
Clarke, E. C. , Fletcher, D. F. , Stoodley, M. A. , and Bilston, L. E. , 2013, “ Computational Fluid Dynamics Modelling of Cerebrospinal Fluid Pressure in Chiari Malformation and Syringomyelia,” J. Biomech., 46(11), pp. 1801–1809. [CrossRef] [PubMed]
Linninger, A. A. , Tsakiris, C. , Zhu, D. C. , Xenos, M. , Roycewicz, P. , Danziger, Z. , and Penn, R. , 2005, “ Pulsatile Cerebrospinal Fluid Dynamics in the Human Brain,” IEEE Trans. Biomed. Eng., 52(4), pp. 557–565. [CrossRef] [PubMed]
Greitz, D. , 1993, “ Cerebrospinal Fluid Circulation and Associated Intracranial Dynamics: A Radiologic Investigation Using MR Imaging and Radionuclide Cisternography,”" Acta Radiol. Suppl., 386, pp. 1–23. http://europepmc.org/abstract/med/8517189 [PubMed]
Greitz, D. , Franck, A. , and Nordell, B. , 1993, “ On the Pulsatile Nature of Intracranial and Spinal CSF-Circulation Demonstrated by MR Imaging,” Acta Radiol., 34(4), pp. 321–328. [CrossRef] [PubMed]
Bunck, A. C. , Kroger, J. R. , Juttner, A. , Brentrup, A. , Fiedler, B. , Schaarschmidt, F. , Crelier, G. R. , Schwindt, W. , Heindel, W. , Niederstadt, T. , and Maintz, D. , 2011, “ Magnetic Resonance 4D Flow Characteristics of Cerebrospinal Fluid at the Craniocervical Junction and the Cervical Spinal Canal,” Eur. Radiol., 21(8), pp. 1788–1796. [CrossRef] [PubMed]
Ahmed, S. A. , and Giddens, D. P. , 1984, “ Pulsatile Poststenotic Flow Studies With Laser Doppler Anemometry,” J. Biomech., 17(9) , pp. 695–705. [CrossRef] [PubMed]
Valen-Sendstad, K. , and Steinman, D. A. , 2014, “ Mind the Gap: Impact of Computational Fluid Dynamics Solution Strategy on Prediction of Intracranial Aneurysm Hemodynamics and Rupture Status Indicators,” AJNR Am. J. Neuroradiol., 35(3), pp. 536–543. [CrossRef] [PubMed]
Valen-Sendstad, K. , Mardal, K. A. , Mortensen, M. , Reif, B. A. P. , and Langtangen, H. P. , 2011, “ Direct Numerical Simulation of Transitional Flow in a Patient-Specific Intracranial Aneurysm,” J. Biomech., 44(16), pp. 2826–2832. [CrossRef] [PubMed]
Tagliabue, A. , Dede, L. , and Quarteroni, A. , 2017, “ Complex Blood Flow Patterns in an Idealized Left Ventricle: A Numerical Study,” Chaos, 27(9), p. 093939. [CrossRef] [PubMed]
Jain, K. , and Universität Siegen, 2016, “ Transition to Turbulence in Physiological Flows: Direct Numerical Simulation of Hemodynamics in Intracranial Aneurysms and Cerebrospinal Fluid Hydrodynamics in the Spinal Canal,” universi—Universitätsverlag Siegen, Siegen, Germany.
An, H. W. , Cheng, L. A. , and Zhao, M. , 2011, “ Direct Numerical Simulation of Oscillatory Flow Around a Circular Cylinder at Low Keulegan-Carpenter Number,” J. Fluid Mech., 666, pp. 77–103. [CrossRef]
Kin, E. , and Sakajo, T. , 2005, “ Efficient Topological Chaos Embedded in the Blinking Vortex System,” Chaos, 15(2), p. 23111. [CrossRef] [PubMed]
Aref, H. , 2002, “ The Development of Chaotic Advection,” Phys. Fluids, 14(4), pp. 1315–1325. [CrossRef]
Daitche, A. , and Tel, T. , 2009, “ Dynamics of Blinking Vortices,” Phys. Rev. E, 79(1), p. 016210.
Xing, T. , and Stern, F. , 2010, “ Factors of Safety for Richardson Extrapolation,” ASME J. Fluids Eng., 132(6), p. 061403. [CrossRef]
Xing, T. , and Stern, F. , 2011, “ Closure to Discussion of 'Factors of Safety for Richardson Extrapolation' (2011, ASME J. Fluids Eng., 133, p. 115501),” ASME J. Fluids Eng., 133(11), p. 115502. [CrossRef]
Phillips, T. S. , and Roy, C. J. , 2014, “ Richardson Extrapolation-Based Discretization Uncertainty Estimation for Computational Fluid Dynamics,” ASME J. Fluids Eng., 136(12), p. 121401.
Kurtcuoglu, V. , Soellinger, M. , Summers, P. , Poulikakos, D. , and Boesiger, P. , 2007, “ Mixing and Modes of Mass Transfer in the Third Cerebral Ventricle: A Computational Analysis,” ASME J. Biomech. Eng., 129(5), pp. 695–702. [CrossRef]
Kurtcuoglu, V. , Soellinger, M. , Summers, P. , Boomsma, K. , Poulikakos, D. , Boesiger, P. , and Ventikos, Y. , 2007, “ Computational Investigation of Subject-Specific Cerebrospinal Fluid Flow in the Third Ventricle and Aqueduct of Sylvius,” J. Biomech., 40(6), pp. 1235–1245. [CrossRef] [PubMed]
Wilson, R. V. , Stern, F. , Coleman, H. W. , and Paterson, E. G. , 2001, “ Comprehensive Approach to Verification and Validation of CFD Simulations—Part 2: Application for RANS Simulation of a Cargo/Container Ship,” ASME J. Fluids Eng., 123(4), pp. 803–810.


Grahic Jump Location
Fig. 1

Summary of numerical modeling approach based on subject specific MRI measurements: (a) T2-weighted MR image of the entire spine for the human analyzed (open-source 3D geometry from Ref. [54]). Axial location and slice orientation (lines) of the phase-contrast MRI scans are obtained in this study. Slice axial distance is indicated by dotted lines; (b) The CSF flow rate based on in vivo PCMRI measurement at C2–C3, C7–T1, and T10–T11; (c) three-dimensional CFD model of the SSS; and (d) volumetric and surface mesh visualization with zoom of the upper cervical spine (top).

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Fig. 2

Numerical sensitivity study for velocity and cyclic mean velocity results: (a) 3D geometry of the sensitivity study and axial plane positions, (b) line location along each plane, (c) simulated peak systolic z-velocity component along each line for the four grids (coarse, medium, fine, and X-fine), and (d) simulated cross-sectional mean velocity, Uz-mean, along each line for the four grids

Grahic Jump Location
Fig. 9

Steady-streaming velocity magnitude, Uss, and nondimensional fraction of flow rate amplitude, Qss, increases with NR compared to without NR. Dotted lines indicate that maximum Uss occurs upstream/downstream of NRs in the cervical spine at the interface of adjacent vortices (see vortices in Fig. 6(c)).

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Fig. 5

Thru-plane CSF velocity profiles simulated by CFD at T = 90 ms (peak systole) for three different views: (a) coronal, (b) sagittal, and (c) axial at six slice locations. Note: peak systolic timing was obtained for CSF flow at C2–C3. The axial distribution of peak CSF velocities over the entire cardiac cycle is shown in Fig. 4(a). Also, to help visualize the entire spine, z-scaling of the geometry is set at 0.5 with respect to x- and y-dimensions. Thus, spine curvature appears greater than without scaling.

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Fig. 6

Vortices form around SC NR in the cervical spine at time-points corresponding to CSF flow reversal. (a) CSF flow rate at C2–C3 section, (b) velocity contour for C2–C3 section, and (c) streamlines showing vortices that form around NR pairs (FM-C1, C1–C2, C2–C3, and C3–C4) at four different time steps. The interfaces of these vortices are located upstream and downstream of NR pairs. Note: velocity contours and streamlines are colored with different scales.

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Fig. 7

Presence of SC NR result in a complex distribution of cyclic mean CSF velocities within the SSS. Cyclic mean CSF velocity profiles simulated by CFD for three different views: (a) coronal, (b) sagittal, and (c) axial at six slice locations. Note: Cyclic mean CSF velocity is calculated based on one complete CSF flow cycle.

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Fig. 8

Cyclic mean CSF velocities decrease and change profiles without NR present in the numerical model. CSF cyclic mean velocity profiles, Uz-mean, for the case without SC NRs at three different views: (a) coronal, (b) sagittal, and (c) axial at six slice locations. Compare profiles to Fig. 7 to see impact of NR.

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Fig. 3

Comparison of numerical model axial flow rate distribution with subject specific PCMRI measurements: (a) CSF flow waveforms measured by PCMRI at three axial locations along the spine. Dots indicate experimental data and lines denote CFD results. Note: negative, or peak systolic, CSF flow is in the caudal direction. (b) Spatial–temporal distribution of the average dura radial displacement along the spine.

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Fig. 4

Hydrodynamic parameter distribution computed along the spine in terms of: (a) peak CSF velocity, (b) cross-sectional area, (c) hydraulic diameter and Womersley number, α, (d) Reynolds number, for internal flow within a tube, Re, (e) Stokes–Reynolds number based on Stokes-layer thickness, Reδ, and (f) Reynolds number for external flow over a NR, ReNR



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