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33. Stoverud, K.H., Langtangen, H.P., Ringstad, G.A., Eide, P.K., Mardal, K.A.: Computational
investigation of cerebrospinal fluid dynamics in the posterior cranial fossa and cervical
subarachnoid space in patients with Chiari I malformation. PLoS One. 11(10), e0162938
(2016)
34. Rutkowska, G., Haughton, V., Linge, S., Mardal, K.A.: Patient-specific 3D simulation of
cyclic CSF flow at the craniocervical region. Am. J. Neuroradiol. 33(9), 1756–1762 (2012)
35. Jain, K., Ringstad, G., Eide, P.K., Mardal, K.A.: 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), (2017)
36. Stockman, H.W.: Effect of anatomical fine structure on the flow of cerebrospinal fluid in the
spinal subarachnoid space. J. Biomech. Eng. 128(1), 106 (2005)
37. Mittal, R., Iaccarino, G.: Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261
(2005)
38. Haslam, M., Zamir, M.: Pulsatile flow in tubes of elliptic gross sections. Ann. Biomed. Eng.
26(5), 780–787 (1998)
39. Gupta, S., Poulikakos, D., Kurtcuoglu, V.: Analytical solution for pulsatile viscous flow in a
straight elliptic annulus and application to the motion of the cerebrospinal fluid. Phys. Fluids.
20(9), (2008)
40. Boutsianis, E., Gupta, S., Boomsma, K., Poulikakos, D.: Boundary conditions by SchwarzChristoffel mapping in anatomically accurate hemodynamics. Ann. Biomed. Eng. 36(12),
2068–2084 (2008)
41. Enzmann, D.R., Pelc, N.J.: Brain motion: measurement with phase-contrast MR imaging.
Radiology. 185(3), 653–660 (1992)
42. Soellinger, M., Rutz, A.K., Kozerke, S., Boesiger, P.: 3D cine displacement-encoded MRI of
pulsatile brain motion. Magn. Reson. Med. 61(1), 153–162 (2009)
43. Pahlavian, S.H., Oshinski, J., Zhong, X., Loth, F., Amini, R.: Regional quantification of
brain tissue strain using displacement-encoding with stimulated echoes magnetic resonance
imaging. J. Biomech. Eng. 140(8), (2018)
44. Shannon, C.E.: Communication in the presence of noise. Proceedings of the Institute of Radio
Engineers. 37(1), 10–21 (1949)
45. Luke, H.D.: The origins of the sampling theorem. IEEE Commun. Mag. 37(4), 106–108
(1999)
46. Terem, I., Ni, W.W., Goubran, M., Rahimi, M.S., Zaharchuk, G., Yeom, K.W., Moseley, M.E.,
Kurt, M., Holdsworth, S.J.: Revealing sub-voxel motions of brain tissue using phase-based
amplified MRI (aMRI). Magn. Reson. Med. 80, 2549 (2018)
47. Ma, Q., Ineichen, B.V., Detmar, M., Proulx, S.T.: Outflow of cerebrospinal fluid is predominantly through lymphatic vessels and is reduced in aged mice. Nat. Commun. 8(1), 1434
(2017)
48. Grzybowski, D.M., Herderick, E.E., Kapoor, K.G., Holman, D.W., Katz, S.E.: Human
arachnoid granulations part I: a technique for quantifying area and distribution on the superior
surface of the cerebral cortex. Cerebrospinal Fluid Res. 4, 6 (2007)
49. Holman, D.W., Kurtcuoglu, V., Grzybowski, D.M.: Cerebrospinal fluid dynamics in the
human cranial subarachnoid space: an overlooked mediator of cerebral disease. II. In vitro
arachnoid outflow model. J. R. Soc. Interface. 7(49), 1205–1218 (2010)
50. Eide, P.K., Vatnehol, S.A.S., Emblem, K.E., Ringstad, G.: Magnetic resonance imaging
provides evidence of glymphatic drainage from human brain to cervical lymph nodes. Sci.
Rep. 8(1), 7194 (2018)
51. Ma, Q., Ries, M., Decker, Y., Muller, A., Riner, C., Bucker, A., Fassbender, K., Detmar,
M., Proulx, S.T.: Rapid lymphatic efflux limits cerebrospinal fluid flow to the brain. Acta
Neuropathol. 137, 151 (2019)
52. Linge, S.O., Haughton, V., Lovgren, A.E., Mardal, K.A., Langtangen, H.P.: CSF flow
dynamics at the craniovertebral junction studied with an idealized model of the subarachnoid
space and computational flow analysis. Am. J. Neuroradiol. 31(1), 185–192 (2010)
V. Kurtcuoglu et al.
33. Stoverud, K.H., Langtangen, H.P., Ringstad, G.A., Eide, P.K., Mardal, K.A.: Computational
investigation of cerebrospinal fluid dynamics in the posterior cranial fossa and cervical
subarachnoid space in patients with Chiari I malformation. PLoS One. 11(10), e0162938
(2016)
34. Rutkowska, G., Haughton, V., Linge, S., Mardal, K.A.: Patient-specific 3D simulation of
cyclic CSF flow at the craniocervical region. Am. J. Neuroradiol. 33(9), 1756–1762 (2012)
35. Jain, K., Ringstad, G., Eide, P.K., Mardal, K.A.: 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), (2017)
36. Stockman, H.W.: Effect of anatomical fine structure on the flow of cerebrospinal fluid in the
spinal subarachnoid space. J. Biomech. Eng. 128(1), 106 (2005)
37. Mittal, R., Iaccarino, G.: Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261
(2005)
38. Haslam, M., Zamir, M.: Pulsatile flow in tubes of elliptic gross sections. Ann. Biomed. Eng.
26(5), 780–787 (1998)
39. Gupta, S., Poulikakos, D., Kurtcuoglu, V.: Analytical solution for pulsatile viscous flow in a
straight elliptic annulus and application to the motion of the cerebrospinal fluid. Phys. Fluids.
20(9), (2008)
40. Boutsianis, E., Gupta, S., Boomsma, K., Poulikakos, D.: Boundary conditions by SchwarzChristoffel mapping in anatomically accurate hemodynamics. Ann. Biomed. Eng. 36(12),
2068–2084 (2008)
41. Enzmann, D.R., Pelc, N.J.: Brain motion: measurement with phase-contrast MR imaging.
Radiology. 185(3), 653–660 (1992)
42. Soellinger, M., Rutz, A.K., Kozerke, S., Boesiger, P.: 3D cine displacement-encoded MRI of
pulsatile brain motion. Magn. Reson. Med. 61(1), 153–162 (2009)
43. Pahlavian, S.H., Oshinski, J., Zhong, X., Loth, F., Amini, R.: Regional quantification of
brain tissue strain using displacement-encoding with stimulated echoes magnetic resonance
imaging. J. Biomech. Eng. 140(8), (2018)
44. Shannon, C.E.: Communication in the presence of noise. Proceedings of the Institute of Radio
Engineers. 37(1), 10–21 (1949)
45. Luke, H.D.: The origins of the sampling theorem. IEEE Commun. Mag. 37(4), 106–108
(1999)
46. Terem, I., Ni, W.W., Goubran, M., Rahimi, M.S., Zaharchuk, G., Yeom, K.W., Moseley, M.E.,
Kurt, M., Holdsworth, S.J.: Revealing sub-voxel motions of brain tissue using phase-based
amplified MRI (aMRI). Magn. Reson. Med. 80, 2549 (2018)
47. Ma, Q., Ineichen, B.V., Detmar, M., Proulx, S.T.: Outflow of cerebrospinal fluid is predominantly through lymphatic vessels and is reduced in aged mice. Nat. Commun. 8(1), 1434
(2017)
48. Grzybowski, D.M., Herderick, E.E., Kapoor, K.G., Holman, D.W., Katz, S.E.: Human
arachnoid granulations part I: a technique for quantifying area and distribution on the superior
surface of the cerebral cortex. Cerebrospinal Fluid Res. 4, 6 (2007)
49. Holman, D.W., Kurtcuoglu, V., Grzybowski, D.M.: Cerebrospinal fluid dynamics in the
human cranial subarachnoid space: an overlooked mediator of cerebral disease. II. In vitro
arachnoid outflow model. J. R. Soc. Interface. 7(49), 1205–1218 (2010)
50. Eide, P.K., Vatnehol, S.A.S., Emblem, K.E., Ringstad, G.: Magnetic resonance imaging
provides evidence of glymphatic drainage from human brain to cervical lymph nodes. Sci.
Rep. 8(1), 7194 (2018)
51. Ma, Q., Ries, M., Decker, Y., Muller, A., Riner, C., Bucker, A., Fassbender, K., Detmar,
M., Proulx, S.T.: Rapid lymphatic efflux limits cerebrospinal fluid flow to the brain. Acta
Neuropathol. 137, 151 (2019)
52. Linge, S.O., Haughton, V., Lovgren, A.E., Mardal, K.A., Langtangen, H.P.: CSF flow
dynamics at the craniovertebral junction studied with an idealized model of the subarachnoid
space and computational flow analysis. Am. J. Neuroradiol. 31(1), 185–192 (2010)