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June  2011, 15(4): 957-969. doi: 10.3934/dcdsb.2011.15.957

Three-dimensional cerebrospinal fluid flow within the human central nervous system

Leo Howden 1, , Donald Giddings 1, , Henry Power 1, and  Michael Vloeberghs 2,

1. 

Division of Energy and Sustainability, The University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom, United Kingdom, United Kingdom
2. 

Division of Human Development, The University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom

Received  April 2010 Published  March 2011

This work describes a three-dimensional (3D) numerical simulation of the flow field of the complete enclosed Central Nervous System (CNS) including the ventricular system, the spinal cord and spinal sub-arachnoid space (SAS). Previous works on the topic consider only parts of the complete system imposing artificial boundary conditions at internal cross sections. The computational domain was constructed from MRI data using Materialise Software Mimics. In this work pulsatile velocity inlets in the lateral ventricles, due to the cardiac cycle, were used to simulate the dynamic nature of the CSF, whilst pressure outlets were used to model the areas of CSF re-absorption. A porous medium formulation (Darcy flow) was considered in the SAS to account for the effect of the arachnoid trabeculae within these areas. The simulation was run using the commercial CFD code Fluent using the laminar solver and transient simulation. A maximum CSF velocity was found to be in the region 11.8 mm/s, with a peak pressure drop through the aqueduct of the order of 2.8 Pa corresponding to a calculated peak Reynolds number of 12. CSF pressure at the exits of Magendie and Luschke were found to vary over the cardiac cycle, with pressure at the exits of Luschke being higher than Magendie for large periods of the cycle. CSF was seen to enter the SAS as a laminar jet from the exits of Magendie and Luschke. By only considering the cardiac cycle a very slow CSF motion within the spinal SAS was observed with magnitudes significantly reduced after a depth of 50mm down the column from the exit of Magendie. This result suggests that pulsating wall motion in the region of the spinal cord, due to respiratory effects, needs to be considered in order to predict experimentally observed flow recirculation within the spinal sac. 287 words.
Keywords: computational fluid dynamics., CSF, CFD, central nervous system, Cerebrospinal fluid.
Mathematics Subject Classification: Primary: 92C50, 92-08; Secondary: 35G2.
Citation: Leo Howden, Donald Giddings, Henry Power, Michael Vloeberghs. Three-dimensional cerebrospinal fluid flow within the human central nervous system. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 957-969. doi: 10.3934/dcdsb.2011.15.957
References:
[1]

E. E. Jacobson, D. F. Fletcher, M. K. Morgan, and I. H. Johnston, Fluid dynamics of the cerebral aqueduct, Pediatr Neurosurg, 24 (1996), 229-236. doi: doi:10.1159/000121044.

[2]

E. E. Jacobson, D. F. Fletcher, M. K. Morgan and I. H. Johnston, Computer modelling of the cerebrospinal fluid flow dynamics of aqueduct stenosis, Medical and Biological Engineering and Computing, 37 (1999a), 59-63. doi: doi:10.1007/BF02513267.

[3]

L. Fin and R. Grebe, Three dimensional modelling of the cerebrospinal fluid dynamics and brain interactions in the aqueduct of Sylvius, Computer Methods In Biomechanics and Biomedical Engineering, 6 (2003), 163-170. doi: doi:10.1080/1025584031000097933.

[4]

V. Kurtcuoglu, D. Poulikakosa and Y. Ventikos, Computational modelling of the mechanical behaviour of the cerebrospinal fluid system, Journal of Biomechanical Engineering, 127 (2005), 264-269. doi: doi:10.1115/1.1865191.

[5]

V. Kurtcuoglu, M. Soellinger, P. Summers, K. Boomsma, D. Poulikakosa, P. Boesiger and Y. Ventikos, Computational investigation of subject-specific cerebrospinal fluid flow in the third ventricle and aqueduct of Sylvius, J. Biomechanics, 40 (2007), 1235-1245. doi: doi:10.1016/j.jbiomech.2006.05.031.

[6]

S. Cheng, E. Jacobson and L. E. Bilston, Models of the pulsatile hydrodynamics of cerebrospinal fluid flow in the normal and abnormal intracranial system, Computer Methods in Biomechanics and Biomedical Engineering, 10 (2007), 151-157. doi: doi:10.1080/10255840601124753.

[7]

A. A. Linninger, C. Tsakiris, D. C. Zhu, M. Xenos, P. Roycewicz, Z. Danziger and R. Penn, Pulsatile cerebrospinal fluid dynamics in the human brain, IEEE Transactions on Biomedical Engineering, 52 (2005), 557-565. doi: doi:10.1109/TBME.2005.844021.

[8]

A. A. Linninger, M. Xenos, D. C. Zhu, M. B. R. Somayaji, S. Kondapalli and R. D. Penn, Cerebrospinal fluid flow in the normal and hydrocephalic human brain, IEEE Transactions on Biomedical Engineering, 54 (2007), 291-302. doi: doi:10.1109/TBME.2006.886853.

[9]

Leo Howden, "Numerical and Experimental Studies of CSF Fluid Motion and Drug Injections into the Central Nervous System," Ph.D thesis, University of Nottingham, 2007.

[10]

L. Howden, D. Giddings, H. Power, A. Aroussi, M. Vloeberghs, M. Garnett and D. A. Walker, Three dimensional cerebrospinal fluid flow within the human ventricular system, Journal of Computer Methods in Biomechanics and Biomedical Engineering, 11 (2008), 123-133. doi: doi:10.1080/10255840701492118.

[11]

E. A. Bering Jnr, Choroid plexus and arterial pulsation of cerebrospinal fluid; demonstration of the choroid plexuses as a cerebrospinal fluid pump, Arch Neurol Psychiatr, 73 (1955), 165-172.

[12]

H. D. Portnoy and M. Chopp, Cerebrospinal fluid pulse wave form analysis during hypercapnia and hypoxia, Neurosurgery, 9 (1981), 14-27. doi: doi:10.1227/00006123-198107000-00004.

[13]

E. E. Jacobson, D. F. Fletcher, M. K. Morgan and I. H. Johnston, Computer modelling of CSF flow in the subarachnoid space, Journal of Clinical Neroscience, 6 (1999b), 498-500. doi: doi:10.1016/S0967-5868(99)90009-7.

[14]

G. Schroth and U. Klose, Cerebrospinal fluid flow. II. Physiology of respiration-related pulsations, Neuroradiology, 35 (1992), 10-15. doi: doi:10.1007/BF00588271.

[15]

F. Stahlberg, J. Mogelvang, C. Thomsen, B. Nordell, M. Stubgaard, A. Ericsson, G. Sperber, D. Greitz, H. Larsson and O. Henriksen, A method for MR quantification of flow velocities in blood and CSF using interleaved gradient-echo pulse sequences, Magn. Reson. Imaging, 7 (1989), 655-667. doi: doi:10.1016/0730-725X(89)90535-3.

[16]

D. R. Enzmann and N. J. Pelc, Normal flow patterns of intracranial and spinal cerebrospinal fluid defined with phase contrast Cine MR imaging, Radiology, 178 (1991), 467-474.

[17]

D. Greitz, A. Franck and B. Nordell, On the pulsatile nature of intracranial and spinal CSF circulation demonstrated by MR imaging, Acta Radialogica, 34 (1993), 321-328.

[18]

O. Baledent, M. C. Henry-Feugeas and I. Idy-Peretti, Cerebrospinal fluid dynamics and relation with blood flow: A magnetic resonance study with semiautomated cerebrospinal fluid segmentation, Invest Radiol., 37 (2001), 368-377. doi: doi:10.1097/00004424-200107000-00003.

[19]

R. K. Parkkola, M. E. Komu, T. M. Aarimaa, M. S. Alanen and C. Thomsen, Cerebrospinal fluid flow in children with normal and dilated ventricles studied by MR imaging, Acta Radiologica, 42 (2001), 33-38. doi: doi:10.1080/028418501127346431.

show all references

References:
[1]

E. E. Jacobson, D. F. Fletcher, M. K. Morgan, and I. H. Johnston, Fluid dynamics of the cerebral aqueduct, Pediatr Neurosurg, 24 (1996), 229-236. doi: doi:10.1159/000121044.

[2]

E. E. Jacobson, D. F. Fletcher, M. K. Morgan and I. H. Johnston, Computer modelling of the cerebrospinal fluid flow dynamics of aqueduct stenosis, Medical and Biological Engineering and Computing, 37 (1999a), 59-63. doi: doi:10.1007/BF02513267.

[3]

L. Fin and R. Grebe, Three dimensional modelling of the cerebrospinal fluid dynamics and brain interactions in the aqueduct of Sylvius, Computer Methods In Biomechanics and Biomedical Engineering, 6 (2003), 163-170. doi: doi:10.1080/1025584031000097933.

[4]

V. Kurtcuoglu, D. Poulikakosa and Y. Ventikos, Computational modelling of the mechanical behaviour of the cerebrospinal fluid system, Journal of Biomechanical Engineering, 127 (2005), 264-269. doi: doi:10.1115/1.1865191.

[5]

V. Kurtcuoglu, M. Soellinger, P. Summers, K. Boomsma, D. Poulikakosa, P. Boesiger and Y. Ventikos, Computational investigation of subject-specific cerebrospinal fluid flow in the third ventricle and aqueduct of Sylvius, J. Biomechanics, 40 (2007), 1235-1245. doi: doi:10.1016/j.jbiomech.2006.05.031.

[6]

S. Cheng, E. Jacobson and L. E. Bilston, Models of the pulsatile hydrodynamics of cerebrospinal fluid flow in the normal and abnormal intracranial system, Computer Methods in Biomechanics and Biomedical Engineering, 10 (2007), 151-157. doi: doi:10.1080/10255840601124753.

[7]

A. A. Linninger, C. Tsakiris, D. C. Zhu, M. Xenos, P. Roycewicz, Z. Danziger and R. Penn, Pulsatile cerebrospinal fluid dynamics in the human brain, IEEE Transactions on Biomedical Engineering, 52 (2005), 557-565. doi: doi:10.1109/TBME.2005.844021.

[8]

A. A. Linninger, M. Xenos, D. C. Zhu, M. B. R. Somayaji, S. Kondapalli and R. D. Penn, Cerebrospinal fluid flow in the normal and hydrocephalic human brain, IEEE Transactions on Biomedical Engineering, 54 (2007), 291-302. doi: doi:10.1109/TBME.2006.886853.

[9]

Leo Howden, "Numerical and Experimental Studies of CSF Fluid Motion and Drug Injections into the Central Nervous System," Ph.D thesis, University of Nottingham, 2007.

[10]

L. Howden, D. Giddings, H. Power, A. Aroussi, M. Vloeberghs, M. Garnett and D. A. Walker, Three dimensional cerebrospinal fluid flow within the human ventricular system, Journal of Computer Methods in Biomechanics and Biomedical Engineering, 11 (2008), 123-133. doi: doi:10.1080/10255840701492118.

[11]

E. A. Bering Jnr, Choroid plexus and arterial pulsation of cerebrospinal fluid; demonstration of the choroid plexuses as a cerebrospinal fluid pump, Arch Neurol Psychiatr, 73 (1955), 165-172.

[12]

H. D. Portnoy and M. Chopp, Cerebrospinal fluid pulse wave form analysis during hypercapnia and hypoxia, Neurosurgery, 9 (1981), 14-27. doi: doi:10.1227/00006123-198107000-00004.

[13]

E. E. Jacobson, D. F. Fletcher, M. K. Morgan and I. H. Johnston, Computer modelling of CSF flow in the subarachnoid space, Journal of Clinical Neroscience, 6 (1999b), 498-500. doi: doi:10.1016/S0967-5868(99)90009-7.

[14]

G. Schroth and U. Klose, Cerebrospinal fluid flow. II. Physiology of respiration-related pulsations, Neuroradiology, 35 (1992), 10-15. doi: doi:10.1007/BF00588271.

[15]

F. Stahlberg, J. Mogelvang, C. Thomsen, B. Nordell, M. Stubgaard, A. Ericsson, G. Sperber, D. Greitz, H. Larsson and O. Henriksen, A method for MR quantification of flow velocities in blood and CSF using interleaved gradient-echo pulse sequences, Magn. Reson. Imaging, 7 (1989), 655-667. doi: doi:10.1016/0730-725X(89)90535-3.

[16]

D. R. Enzmann and N. J. Pelc, Normal flow patterns of intracranial and spinal cerebrospinal fluid defined with phase contrast Cine MR imaging, Radiology, 178 (1991), 467-474.

[17]

D. Greitz, A. Franck and B. Nordell, On the pulsatile nature of intracranial and spinal CSF circulation demonstrated by MR imaging, Acta Radialogica, 34 (1993), 321-328.

[18]

O. Baledent, M. C. Henry-Feugeas and I. Idy-Peretti, Cerebrospinal fluid dynamics and relation with blood flow: A magnetic resonance study with semiautomated cerebrospinal fluid segmentation, Invest Radiol., 37 (2001), 368-377. doi: doi:10.1097/00004424-200107000-00003.

[19]

R. K. Parkkola, M. E. Komu, T. M. Aarimaa, M. S. Alanen and C. Thomsen, Cerebrospinal fluid flow in children with normal and dilated ventricles studied by MR imaging, Acta Radiologica, 42 (2001), 33-38. doi: doi:10.1080/028418501127346431.

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