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Research Papers

Nonuniform Moving Boundary Method for Computational Fluid Dynamics Simulation of Intrathecal Cerebrospinal Flow Distribution in a Cynomolgus Monkey

[+] Author and Article Information
Mohammadreza Khani

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

Tao Xing

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

Christina Gibbs

Neurophysiological Imaging and
Modeling Laboratory,
Department of Biological Engineering,
University of Idaho,
Moscow, ID 83844
e-mail: gibb6751@vandals.uidaho.edu

John N. Oshinski

Department of Radiology,
Emory University,
Atlanta, GA 30322
e-mail: jnoshin@emory.edu

Gregory R. Stewart

Alchemy Neuroscience,
Hanover, MA 02340
e-mail: grstewart77@gmail.com

Jillynne R. Zeller

Northern Biomedical Research,
Spring Lake, MI 49456
e-mail: Jill.Zeller@northernbiomedical.com

Bryn A. Martin

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

1Corresponding author.

Manuscript received January 12, 2017; final manuscript received April 24, 2017; published online June 7, 2017. Assoc. Editor: Ching-Long Lin.

J Biomech Eng 139(8), 081005 (Jun 07, 2017) (12 pages) Paper No: BIO-17-1020; doi: 10.1115/1.4036608 History: Received January 12, 2017; Revised April 24, 2017

A detailed quantification and understanding of cerebrospinal fluid (CSF) dynamics may improve detection and treatment of central nervous system (CNS) diseases and help optimize CSF system-based delivery of CNS therapeutics. This study presents a computational fluid dynamics (CFD) model that utilizes a nonuniform moving boundary approach to accurately reproduce the nonuniform distribution of CSF flow along the spinal subarachnoid space (SAS) of a single cynomolgus monkey. A magnetic resonance imaging (MRI) protocol was developed and applied to quantify subject-specific CSF space geometry and flow and define the CFD domain and boundary conditions. An algorithm was implemented to reproduce the axial distribution of unsteady CSF flow by nonuniform deformation of the dura surface. Results showed that maximum difference between the MRI measurements and CFD simulation of CSF flow rates was <3.6%. CSF flow along the entire spine was laminar with a peak Reynolds number of ∼150 and average Womersley number of ∼5.4. Maximum CSF flow rate was present at the C4-C5 vertebral level. Deformation of the dura ranged up to a maximum of 134 μm. Geometric analysis indicated that total spinal CSF space volume was ∼8.7 ml. Average hydraulic diameter, wetted perimeter, and SAS area were 2.9 mm, 37.3 mm and 27.24 mm2, respectively. CSF pulse wave velocity (PWV) along the spine was quantified to be 1.2 m/s.

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References

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 Vitro Spinal Stenosis Model: Implications on Syringomyelia Theories,” ASME J. Biomech. Eng., 132(11), p. 111007. [CrossRef]
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. 1. [CrossRef] [PubMed]
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]
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, Oxford University Press, Oxford, UK.
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. Pharmaceutics, 10(5), pp. 1522–1532. [CrossRef]
Xie, L. , Kang, H. , Xu, Q. , Chen, M. J. , Liao, Y. , Thiyagarajan, M. , O'Donnell, J. , Christensen, D. J. , Nicholson, C. , Iliff, J. J. , Takano, T. , Deane, R. , and Nedergaard, M. , 2013, “ Sleep Drives Metabolite Clearance From the Adult Brain,” Science, 342(6156), pp. 373–377. [CrossRef] [PubMed]
Weller, R. O. , Djuanda, E. , Yow, H. Y. , and Carare, R. O. , 2009, “ Lymphatic Drainage of the Brain and the Pathophysiology of Neurological Disease,” Acta Neuropathol., 117(1), pp. 1–14. [CrossRef] [PubMed]
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]
Martin, B. A. , Kalata, W. , Loth, F. , Royston, T. J. , and Oshinski, J. N. , 2005, “ Syringomyelia Hydrodynamics: An In Vitro Study Based on In Vivo Measurements,” ASME J. Biomech. Eng., 127(7), pp. 1110–1120. [CrossRef]
Martin, B. A. , Yiallourou, T. I. , Pahlavian, S. H. , Thyagaraj, S. , Bunck, A. C. , Loth, F. , Sheffer, D. B. , Kroger, J. R. , and Stergiopulos, N. , 2016, “ Inter-Operator Reliability of Magnetic Resonance Image-Based Computational Fluid Dynamics Prediction of Cerebrospinal Fluid Motion in the Cervical Spine,” Ann. Biomed. Eng., 44(5), pp. 1524–1537. [CrossRef] [PubMed]
Yiallourou, T. , Schmid Daners, M. , Kurtcuoglu, V. , Haba-Rubio, J. , Heinzer, R. , Fornari, E. , Santini, F. , Sheffer, D. B. , Stergiopulos, N. , and Martin, B. A. , 2015, “ Continuous Positive Airway Pressure Alters Cranial Blood Flow and Cerebrospinal Fluid Dynamics at the Craniovertebral Junction,” Interdiscip. Neurosurg., 2(3), pp. 152–159. [CrossRef]
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]
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]
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.
San, O. , and Staples, A. E. , 2012, “ An Improved Model for Reduced-Order Physiological Fluid Flows,” J. Mech. Med. Biol., 12(3), p. 1250052. [CrossRef]
Kalata, W. , Martin, B. A. , Oshinski, J. N. , Jerosch-Herold, M. , Royston, T. J. , and Loth, F. , 2009, “ MR Measurement of Cerebrospinal Fluid Velocity Wave Speed in the Spinal Canal,” IEEE Trans. Biomed. Eng., 56(6), pp. 1765–1768. [CrossRef] [PubMed]
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]
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]
Bertram, C. D. , 2010, “ Evaluation by Fluid/Structure-Interaction Spinal-Cord Simulation of the Effects of Subarachnoid-Space Stenosis on an Adjacent Syrinx,” ASME J. Biomech. Eng., 132(6), p. 061009. [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]
Cirovic, S. , and Kim, M. , 2012, “ A One-Dimensional Model of the Spinal Cerebrospinal-Fluid Compartment,” ASME J. Biomech. Eng., 134(2), p. 021005. [CrossRef]
Lockey, P. , Poots, G. , and Williams, B. , 1975, “ Theoretical Aspects of the Attenuation of Pressure Pulses Within Cerebrospinal-Fluid Pathways,” Med. Biol. Eng., 13(6), pp. 861–869. [CrossRef] [PubMed]
Yiallourou, T. I. , Kroger, 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]
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]
Pahlavian, S. H. , Bunck, A. C. , Thyagaraj, S. , Giese, D. , Loth, F. , Hedderich, D. M. , Kroeger, J. R. , and Martin, B. A. , 2016, “ Accuracy of 4D Flow Measurement of Cerebrospinal Fluid Dynamics in the Cervical Spine: An In Vitro Verification Against Numerical Simulation,” Ann. Biomed. Eng., 44(11), pp. 3202–3214. [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]
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]
Sigmund, E. E. , Suero, G. A. , Hu, C. , McGorty, K. , Sodickson, D. K. , Wiggins, G. C. , and Helpern, J. A. , 2012, “ High-Resolution Human Cervical Spinal Cord Imaging at 7 T,” NMR Biomed., 25(7), pp. 891–899. [CrossRef] [PubMed]
Helgeland, A. , Mardal, K. A. , Haughton, V. , and Reif, B. A. , 2014, “ Numerical Simulations of the Pulsating Flow of Cerebrospinal Fluid Flow in the Cervical Spinal Canal of a Chiari Patient,” J. Biomech., 47(5), pp. 1082–1090. [CrossRef] [PubMed]
Sweetman, B. , and Linninger, A. A. , 2011, “ Cerebrospinal Fluid Flow Dynamics in the Central Nervous System,” Ann. Biomed. Eng., 39(1), pp. 484–496. [CrossRef] [PubMed]
Martin, B. A. , Reymond, P. , Novy, J. , Baledent, O. , and Stergiopulos, N. , 2012, “ A Coupled Hydrodynamic Model of the Cardiovascular and Cerebrospinal Fluid System,” Am. J. Physiol. Heart Circ. Physiol., 302(7), pp. H1492–H1509. [CrossRef] [PubMed]
Elliott, N. S. J. , Bertram, C. D. , Martin, B. A. , and Brodbelt, A. R. , 2013, “ Syringomyelia: A Review of the Biomechanics,” J. Fluids Struct., 40, pp. 1–24. [CrossRef]

Figures

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Fig. 1

(a) T2-weighted MR image of the entire spine for the cynomolgus monkey analyzed. Axial location and slice orientation (solid lines) of the phase-contrast MRI scans obtained in the study. Slice axial distance from foramen magnum indicated by dotted lines. (b) The CSF flow rate based on in vivo PCMRI measurement at FM, C2-C3, T4-T5, T10-T11, and L2-L3. (c) Sagittal view of the SAS segmentation based on T2-weighted MRI.

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Fig. 2

(a) Three-dimensional CFD model of the SAS, (b) zoom of the upper cervical spine mesh showing the model inlet (top), and (c) volumetric mesh visualization in the axial and sagittal planes within the cervical SAS

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Fig. 3

(a) Dynamic mesh motion flow chart used for the CFD simulation. Recursive arrows indicate repetition of steps. (b) A 2D axial cross section with relevant variables and key equation used to compute radial deformation of the dura.

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Fig. 4

(a) Three-dimensional geometry of the independence study and axial plane positions, (b) line location along each plane, and (c) peak systolic w-velocity component visualized along each line for the three grids (coarse, medium, and fine)

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Fig. 5

Hydrodynamic parameter distribution for the dura, spinal cord, and subarachnoid space computed along the spine for a cynomolgus monkey in terms of: (a) perimeter, (b) cross-sectional area, (c) hydraulic diameter, (d) Reynolds number, Re, and Womersley number, α. Comparison of CFD simulation (continuous line) and PCMRI measurements (dots) in terms of: (e) peak systolic and diastolic CSF velocity and (f) mean CSF velocity at peak systolic and diastolic flow.

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Fig. 6

(a) CSF flow waveforms measured by PCMRI at five 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 interpolated CSF flow rate along the spine. Dotted line indicates peak CSF flow rate at each axial level used to compute CSF PWV. (c) Radial displacement of the dura surface at 100 ms intervals over the CSF flow cycle. (d) Spatial-temporal distribution of the dura radial displacement along the spine. Dotted line indicates the three locations along the spine with zero radial motion of the dura.

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Fig. 7

Peak-systolic thru-plane CSF velocity profiles simulated by CFD and measured by PCMRI for a cynomolgus monkey. (a) Overall view of the CFD model and slice locations. Note: different velocity scales are used at each slice location. (b) CSF velocity profiles at each slice location. (c) PCMRI visualization of CSF velocity profiles. + symbols indicate locations where spinal cord nerve roots appear to impact CSF flow profiles. (d) PCMRI gray scale images used to compute CSF flow waveforms. ↑ symbols highlight nearby regions with PCMRI signal that are not within the CSF space ROI (epidural venous flow at L2-L3, and vertebral artery flow at the FM).

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