Skip to main content
Log in

A mathematical study of human intracranial hydrodynamics part 1—The cerebrospinal fluid pulse pressure

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

An original mathematical model of human intracranial hydrodynamics is proposed. Equations able to mimic the behavior of the intracranial arterial vascular bed, intracranial venous vascular bed, cerebrospinal fluid absorption and production processes, and the constancy of overall intracranial volume are separately presented and discussed. The model parameters were given normal values computed using physiological considerations and recent anatomical data. In this paper the model is used to simulate the genesis and morphology of the intracranial pressure pulse wave. In particular, dependence of the intracranial pressure pulse amplitude on mean intracranial pressure, obtained from the model, shows excellent agreement with recent experimental findings. The model explains the intracranial pressure pulse wave as the result of the pulsating changes in cerebral blood volume (related to cerebrovascular compliance) which occur within a rigid space (i.e., the craniospinal compartment). At low and medium values of intracranial pressure, the intracranial pressure pulse amplitude mainly reflects the cerebral pressure-volume relationship. However, during severe intracranial hypertension, an abrupt increase in the cerebrovascular compliance becomes evident, which is reflected in an abrupt increase in the intracranial pressure pulse wave.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Auer, L.M.; MacKenzie, E.T. Physiology of the cerebral venous system. In: Kapp, J.P.; Schmidek, eds. The cerebral venous system and its disorders. Orlando: Grune & Stratton; 1984: pp. 169–227.

    Google Scholar 

  2. Avezaat, C.J.J.; van Eijndhoven, J.H.M. The conflict between CSF pulse pressure and volume-pressure response during plateau waves. In: Ishii, S.; Nagai, M.; Brock, M., eds. Intracranial pressure V. Berlin, Heidelberg; Springer-Verlag; 1983: pp. 326–332.

    Google Scholar 

  3. Avezaat, C.J.J.; van Eijndhoven, J.H.M. The role of the pulsating pressure variations in intracranial pressure monitoring. Neurosurg. Rev. 9:113–120; 1986.

    Article  CAS  PubMed  Google Scholar 

  4. Avezaat, C.J.J.; van Eijndhoven, J.H.M.; and Wyper, D.J. Cerebrospinal fluid pulse pressure and intracranial volume-pressure relationship. J. Neurol. Neurosurg. and Psych. 42:687–700; 1979.

    CAS  Google Scholar 

  5. Beneken, J.E.W.; DeWit, B. A physical approach to hemodynamic aspects of the human cardiovascular system. In: Reeve, E.B.; Guyton, A.C., eds. Physical bases of circulatory transport: Regulation and exchange. Philadelphia: Saunders Co.: 1967: pp. 1–45.

    Google Scholar 

  6. Bergel, D.H. The static elastic properties of the arterial wall. J. Physiol. 156:458–469; 1961.

    Google Scholar 

  7. Burattini, R.; Sipkema, P.; van Huis, G.A.; Westerhof, N.; Identification of canine coronary resistance and intramyocardial compliance on the basis of the waterfull model. Ann. Biomed. Eng. 13:385–404; 1985.

    CAS  PubMed  Google Scholar 

  8. Chopp, M.; Portnoy, H.D. Starling resistor as a model of the cereborvascular bed. In: Ishii, I.; Nagai, H.; and Brock, M. eds. Intracranial Pressure V. Berlin, Heidelberg: Springer-Verlag; 1983: pp. 174–179.

    Google Scholar 

  9. Cuypers, J.; Matakas, F.; Potolicchio, S.J. Effect of central venous pressure on brain tissue pressure and brain volume. J. Neurosurg. 45:89–94; 1976.

    CAS  PubMed  Google Scholar 

  10. Dereymaker, A.; Stevens, A.; Rombouts, J.J.; Lacheron, J.M.; Pierquin, A. Study on the influence of the arterial pressure upon the morphology of cisternal CSF pulsations. Europ. Neurol. 5:107–114; 1971.

    Google Scholar 

  11. Ekstedt, J. CSF hydrodynamic studies in man. 2: Normal hydrodynamic variables related to CSF pressures and flow. J. Neurol. Neurosurg. and Psych. 41:345–353; 1978.

    CAS  Google Scholar 

  12. Friden, H.; Ekstedt, J. The CSF volume-pressure relationship in man. In: Ishii, S.; Nagai, H.; and Brock, M. eds. Intracranial pressure V. Springer-Verlag; Heidelberg: Berlin, 1983: pp. 252–260.

    Google Scholar 

  13. Gaab, M.R.; Haubitz, I.; Brawanski, A.; Faulstich, J.; Heissler, H.E. Pressure-volume diagram, pulse amplitude and intracranial pulse volume. Analysis and significance. In: Ishii, S.; Nagai, H.; and Brock, M. eds. Intracranial Pressure V. Berlin, Heidelberg: Springer-Verlag; 1983: pp. 261–268.

    Google Scholar 

  14. Gibo, H.; Carver, C.C.; Rhoton, A.L.; Lenkey, C.; Mitchell, R.J. Microsurgical anatomy of the middle cerebral artery: A microsurgical study. J. Neurosurg. 54: 151–169; 1981.

    CAS  PubMed  Google Scholar 

  15. Gibo, H.; Lenkey, C.; Rhoton, A.L. Microsurgical anatomy of the supraclinoid portion of the internal carotid artery. J. Neurosurg. 55: 560–574, 1981.

    CAS  PubMed  Google Scholar 

  16. Guess, H.A.; Charlton, J.D.; Johnson, R.N.; Mann, J.D. A nonlinear least square method for determining cerebrospinal fluid formation and absorption kinetics in pseudotumor cerebri. Comp. & Biomed. Res. 18: 184–192; 1985.

    CAS  Google Scholar 

  17. Hayashi, K.; Handa, H.; Nagasawa, S.; Okumura, A.; Moritake, K. Stiffness and elastic behavior of human intracranial and extracranial arteries. J. Biomech. 13: 175–184; 1980.

    Article  CAS  PubMed  Google Scholar 

  18. Heistad, D.D.; Kontos, H.A. Cerebral circulation. In: Shepard, J.T.; Abboud, F.M. eds. Handbook of physiology: Peripheral circulation and organ blood flow, Sec. 2, Vol. III; American Physiological Society, Bethesda, MD 1983; pp. 137–182.

    Google Scholar 

  19. Higashi, K.; Katano, M.; Ihara, K.; Katayama, S. Cerebral blood flow and production of cerebrospinal fluid. In: Gotoh, F.; Nagai, H.; Tazaki, Y. eds. Cerebral blood flow and metabolism. Acta Neurol. Sca., Suppl. 72; 1979; pp. 598–599.

  20. Hoffman, O. CSF dynamics: Integration of pulsatory components and autoregulation into a mathematical model. In: Ishii, S.; Nagai, H.; and Brock, M. eds. Intracranial Pressure V. Berlin, Heidelberg, Springer-Verlag; 1983; 169–173.

    Google Scholar 

  21. Katzman, R.; Hussey, F. A simple constant infusion manometric test for measurement of CSF absorption. I. Rationale and method. Neurology (Minneapolis) 20: 534–544; 1970.

    CAS  Google Scholar 

  22. Kety, S.S.; Schmidt, C.F. The effect of altered arterial tension of carbon dioxide and oxygen on cerebral blood flow and cerebral oxygen consumption of normal young man. J. Clinic. Invest. 27: 484–492; 1948.

    CAS  Google Scholar 

  23. Kontos, H.A.; Wei, E.P.; Novari, R.M.; Levasseur, J.E.; Rosemblum, W.I.; Patterson, J.L. Responses of cerebral arteries and arterioles to acute hypotension and hypertension, Am. J. Physiol. 234 (4): H371-H383; 1978.

    CAS  PubMed  Google Scholar 

  24. Mann, J.D.; Butler, A.B.; Rosenthal, J.E.; Maffeo, C.J.; Johnson, R.N.; Bass, N.H. Regulation of intracranial pressure in rat, dog and man. Ann. Nerol. 3: 156–165; 1978.

    CAS  Google Scholar 

  25. Marmarou, A.; Schulman, K.; LaMorgese, J. Compartmental analysis of compliance and outflow resistance of the cerebrospinal fluid system. J. Neurosurg. 43: 523–534; 1975.

    CAS  PubMed  Google Scholar 

  26. Marmarou, A.; Schulman, K.; Rosende, R.M. A nonlinear analysis of the cerebrospinal fluid system and intracranial pressure dynamics. J. Neurosurg. 48: 332–344; 1978.

    CAS  PubMed  Google Scholar 

  27. Martins, A.N. Resistance to drainage of cerebrospinal fluid: Clinical measurement and significance. J. Neurol. Neurosurg. Psych. 36: 313–318; 1973.

    CAS  Google Scholar 

  28. Matakas, F. The interrelationship between cerebral microcirculation and intracranial pressure. In: Baan, J.; Noordergraaf, A.; and Raines, J. eds. Cardiovascular system dynamics. Cambridge, MA: MIT press; 1978; pp. 224–230.

    Google Scholar 

  29. Mchedlishvili, G.I. Physiological mechanisms controlling cerebral blood flow. Stroke 11: 240–248; 1980.

    CAS  PubMed  Google Scholar 

  30. Miller, J.D.; Stanek, A.; Langfitt, T.W. Concepts of cerebral perfusion pressure and vascular compression during intracranial hypertension. In: Meyer, J.S.; and Schade, J.P. eds. Progress in brain research: Cerebral blood flow. Amsterdam: Elsevier; 1972; pp. 411–432.

    Google Scholar 

  31. Milnor, W.R. Hemodynamics. Baltimore William & Wilkins; 1982.

    Google Scholar 

  32. Nakagawa, Y.; Tsuru, M.; Yada, K. Site and mechanism for compression of the venous system during experimental intracranial hypertension. J. Neurosurg. 41: 427–434; 1974.

    CAS  PubMed  Google Scholar 

  33. Nornes, H.; Aslid, R.; Lindegaard, K.F. Intracranial pulse pressure dynamics in patients with intracranial hypertension. Acta Neurochirurgica 38: 177–186; 1977.

    CAS  PubMed  Google Scholar 

  34. Nyary, I.; Vajda, J. Relationship of cerebral blood volume changes and estimated intracranial compliance. In: Ishii, S.; Nagai, H.; and Brock, M. eds. Intracranial Pressure V, Berlin, Heidelberg; Springer-Verlag; 1983; pp. 316–319.

    Google Scholar 

  35. Paltsev, E.I.; Sirovsky, E.B. Intracranial physiology and biomechanics. J. Neurosurg. 57: 500–510; 1982.

    CAS  PubMed  Google Scholar 

  36. Pedley, T.J. The fluid mechanics of large blood vessels. London: Cambridge University Press; 1980.

    Google Scholar 

  37. Perlmutter, D.; Rhoton, A.L. Microsurgical anatomy of the anterior cerebral-anterior communicating-recurrent artery complex. J. Neurosurg. 45: 259–272; 1976.

    CAS  PubMed  Google Scholar 

  38. Perlmutter, D.; Rhoton, A.L. Microsurgical anatomy of the distal anterior cerebral artery. J. Neurosurg. 49: 204–208; 1978.

    CAS  PubMed  Google Scholar 

  39. Permutt, S.; Riley, R.L. Hemodynamics of collapsible vessels with tone; The vascular waterfull. J. Appl. Physiol. 18: 924–932; 1963.

    CAS  PubMed  Google Scholar 

  40. Pollay, M. Formation of cerebrospinal fluid. In: Lundberg, N.; Ponten, U.; and Brock, M. eds. Intracranial Pressure II, Berlin Heidelberg: Springer-Verlag; 1975; 42–45.

    Google Scholar 

  41. Portnoy, H.D.; Chopp, M.; Branch, C.; Shannon, M. SCF pulse wave, ICP and autoregulation. In: Ishii, S.; Nagai, H.; and Brock, M. eds. Intracrania Pressure V, Berlin, Heidelberg: Springer-Verlag; 1983; pp. 180–185.

    Google Scholar 

  42. Portnoy, H.D.; Chopp, M.; Branch, C.; Shannon, M. Cerebrospinal fluid pulse waveform as an indicator of cerebral autoregulation. J. Neurosurg. 56: 666–678; 1982.

    CAS  PubMed  Google Scholar 

  43. Saeki, N.; Rhoton, A.L. Microsurgical anatomy of the upper basilar artery and the posterior circle of Willis. J. Neurosurg. 46: 563–578; 1977.

    CAS  PubMed  Google Scholar 

  44. Sahar, A. The effect of pressure on the production of cerebrospinal fluid by the choroid plexus. J. Neurol. Sci. 16: 49–58; 1972.

    Article  CAS  PubMed  Google Scholar 

  45. Shapiro, K.; Marmarou, A.; Shulman, K. Characterization of clinical CSF dynamics and neural axis compliance using the pressure volume index: The normal pressure volume index. Ann. Neurol. 7: 508–514; 1980.

    Article  CAS  PubMed  Google Scholar 

  46. Westerhof, N.; Boosman, F.; DeVries, C.J.; Noordergraff, A. Analog studies of the human systemic arterial tree. J. Biomech. 2: 121–143; 1969.

    Article  CAS  PubMed  Google Scholar 

  47. Yada, K.; Nakagawa, Y.; Tsuru, M. Circulatory disturbances of the venous system during experimental intracranial hypertension. J. Neurosurg. 39: 723–729; 1973.

    CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ursino, M. A mathematical study of human intracranial hydrodynamics part 1—The cerebrospinal fluid pulse pressure. Annals of Biomedical Engineering 16, 379–401 (1988). https://doi.org/10.1007/BF02364625

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02364625

Key words

Navigation