Skip to main content

Advertisement

SpringerLink
Log in

Model-based Indices Describing Cerebrovascular Dynamics

  • Review Article
  • Published:
Neurocritical Care Aims and scope Submit manuscript

Abstract

Understanding the dynamic relationship between cerebral blood flow (CBF) and the circulation of cerebrospinal fluid (CSF) can facilitate management of cerebral pathologies. For this reason, various hydrodynamic models have been introduced in order to simulate the phenomena governing the interaction between CBF and CSF. The identification of hydrodynamic models requires an array of signals as input, with the most common of them being arterial blood pressure, intracranial pressure, and cerebral blood flow velocity; monitoring all of them is considered as a standard practice in neurointensive care. Based on these signals, physiological parameters like cerebrovascular resistance, compliances of cerebrovascular bed, and CSF space could then be estimated. Various secondary model-based indices describing cerebrovascular dynamics have been introduced, like the cerebral arterial time constant or critical closing pressure. This review presents model-derived indices that describe cerebrovascular phenomena, the nature of which is both physiological (carbon dioxide reactivity and arterial hypotension) and pathological (cerebral artery stenosis, intracranial hypertension, and cerebral vasospasm). In a neurointensive environment, real-time monitoring of a patient with these indices may be able to provide a detection of the onset of a cerebrovascular phenomenon, which could have otherwise been missed. This potentially “early warning” indicator may then prove to be important for the therapeutic management of the patient.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Krammer SP. On the function of the circle of Willis. J Exp Med. 1912;15:348–54.

    Article  Google Scholar 

  2. Rogers L. A dynamic model of the circle of Willis. J Biomech. 1947;4:141–7.

    Google Scholar 

  3. Avman N, Bering EA. A plastic model for the study of pressure changes in the circle of Willis and major cerebral arteries following arterial occlusion. J Neurosurg. 1961;21:361–5.

    Article  Google Scholar 

  4. Himwich WA, Knapp FM, Wenglarz RA, et al. The circle of Willis as simulated by an engineering model. Arch Neurol. 1965;13:164–72.

    Article  CAS  PubMed  Google Scholar 

  5. Agarwal G, Berman B, Stark L. A lumped parameter model of the cerebrospinal system. IEEE Trans Biomed Eng BME. 1969;16:45–53.

    Article  CAS  Google Scholar 

  6. Murray KD. Dimensions of the circle of Willis and dynamic studies using electrical analogy. J Neurosurg. 1964;21:26–34.

    Article  CAS  PubMed  Google Scholar 

  7. Sorek S, Bear J, Karni Z. Resistances and compliances of a compartmental model of the cerebrovascular system. Ann Biomed Eng. 1989;17:1–12.

    Article  CAS  PubMed  Google Scholar 

  8. Takemae T, Kosugi Y, Ikebe J, et al. A simulation study of intracranial-pressure increment using an electrical circuit model of cerebral-circulation. IEEE Trans Biomed Eng. 1987;34:958–62.

    Article  CAS  PubMed  Google Scholar 

  9. Bekker A, Wolk S, Turndorf H, et al. Computer simulation of cerebrovascular circulation: assessment of intracranial hemodynamics during induction of anesthesia. J Clin Monit. 1996;12:433–44.

    Article  CAS  PubMed  Google Scholar 

  10. Czosnyka M, Harris NG, Pickard JD, et al. CO2 cerebrovascular reactivity as a function of perfusion pressure—a modeling study. Acta Neurochir Wien. 1993;121:159–65.

    Article  CAS  PubMed  Google Scholar 

  11. Czosnyka M, Pickard J, Whitehouse H, et al. The hyperemic response to a transient reduction in cerebral perfusion-pressure—a modelling study. Acta Neurochir Wien. 1992;115:90–7.

    Article  CAS  PubMed  Google Scholar 

  12. Hoffmann O. Biomathematics of intracranial CSF and haemodynamics. Simulation and analysis with the aid of a mathematical model. Acta Neurochir Suppl Wien. 1987;40:117–30.

    CAS  PubMed  Google Scholar 

  13. Piechnik S, Czosnyka M, Richards H, et al. Effects of decreasing cerebral perfusion pressure on pulsatility of cerebral blood flow velocity—a modelling study. In: Nagai H, Kamiya K, Ishii S, editors. Intracranial pressure IX. Berlin: Springer; 1994. p. 496–7.

    Google Scholar 

  14. Ursino M. A mathematical study of human intracranial hydrodynamics. Part 1—the cerebrospinal fluid pulse pressure. Ann Biomed Eng. 1988;16:379–401.

    Article  CAS  PubMed  Google Scholar 

  15. Ursino M. Computer analysis of the main parameters extrapolated from the human intracranial basal artery blood flow. Comput Biomed Res. 1990;23:542–59.

    Article  CAS  PubMed  Google Scholar 

  16. Ursino M. A mathematical model of overall cerebral blood flow regulation in the rat. IEEE Trans Biomed Eng. 1991;38:795–807.

    Article  CAS  PubMed  Google Scholar 

  17. Ursino M, Cristalli C. Mathematical modeling of noninvasive blood pressure estimation techniques—part I: pressure transmission across the arm tissue. J Biomech Eng. 1995;117:107–16.

    Article  CAS  PubMed  Google Scholar 

  18. Ursino M, Di Giammarco P. A mathematical model of the relationship between cerebral blood volume and intracranial pressure changes: the generation of plateau waves. Ann Biomed Eng. 1991;19:15–42.

    Article  CAS  PubMed  Google Scholar 

  19. Ursino M, Lodi CA. A simple mathematical model of the interaction between intracranial pressure and cerebral hemodynamics. J Appl Physiol. 1997;82:1256–69.

    CAS  PubMed  Google Scholar 

  20. Ursino M, Lodi CA, Rossi S, et al. Intracranial pressure dynamics in patients with acute brain damage. J Appl Physiol. 1997;82:1270–82.

    CAS  PubMed  Google Scholar 

  21. Tym R, Lichtenstein S, Leutheusser J. The Munro-Kellie doctrine and the intracranial venous space at the ‘limit’ of raised intracranial pressure—an hydrodynamic experimental approach. In: Brock M, Dietz H, editors. Intracranial pressure—experimental and clinical aspects. Berlin: Springer; 1972. p. 139–43.

    Google Scholar 

  22. Hoffmann O, Zierski JT. Analysis of the ICP pulse-pressure relationship as a function of arterial blood pressure. Clinical validation of a mathematical model. Acta Neurochir Wien. 1982;66:1–21.

    Article  CAS  PubMed  Google Scholar 

  23. Nishimura H, Yasui N. A simulation study of wave transformation using a nonlinear model of artery and a physical model of intracranial vascular bed. Berlin: Springer; 1993. p. 390–393.

    Google Scholar 

  24. Chopp M, Portnoy HD, Branch C. Hydraulic model of the cerebrovascular bed: an aid to understanding the volume–pressure test. J Neurosurg. 1983;13:5–11.

    Article  CAS  Google Scholar 

  25. Giulioni M, Ursino M. Impact of cerebral perfusion pressure and autoregulation on intracranial dynamics: a modeling study. J Neurosurg. 1996;39:1005–14.

    CAS  Google Scholar 

  26. Ursino M, Di Giammarco P, Belardinelli E. A mathematical model of cerebral blood flow chemical regulation—part II: reactivity of cerebral vascular bed. IEEE Trans Biomed Eng. 1989;36:192–201.

    Article  CAS  PubMed  Google Scholar 

  27. Czosnyka M, Piechnik S, Richards HK, et al. Contribution of mathematical modelling to the interpretation of bedside tests of cerebrovascular autoregulation. J Neurol Neurosurg Psychiatry. 1997;63:721–31.

    Article  CAS  PubMed  Google Scholar 

  28. Czosnyka M, Smielewski P, Timofeev I, et al. Intracranial pressure: more than a number. Neurosurg Focus. 2007;22(5):E10.

    Article  PubMed  Google Scholar 

  29. Sorrentino E, Budohoski KP, Kasprowicz M, et al. Critical thresholds for Transcranial Doppler indices of cerebral autoregulation in traumatic brain injury. Neurocrit Care. 2010;14(2):188–93.

    Article  Google Scholar 

  30. Zweifel C, Lavinio A, Steiner LA, et al. Continuous monitoring of cerebrovascular pressure reactivity in patients with head injury. Neurosurg Focus. 2008;25(4):E2.

    Article  PubMed  Google Scholar 

  31. Balestreri M, Czosnyka M, Hutchinson P, et al. Impact of intracranial pressure and cerebral perfusion pressure on severe disability and mortality after head injury. Neurocrit Care. 2006;04:8–13.

    Article  Google Scholar 

  32. Gopinath SP, Robertson CS, Narayan RG, et al. Evaluation of a microsensor intracranial pressure transducer. In: Nagai H, Kamiya K, Ishii S, editors. Intracranial pressure IX. Berlin: Springer; 1994. p. 2–5.

    Google Scholar 

  33. Czosnyka M, Czosnyka Z, Pickard JD. Laboratory testing of three intracranial pressure microtransducers: technical report. J Neurosurg. 1996;38(1):219–24.

    Article  CAS  Google Scholar 

  34. Kirkpatrick PJ, Czosnyka M, Pickard JD. Multimodal monitoring in neurointensive care. J Neurol Neurosurg Psychiatry. 1996;60:131–9.

    Article  CAS  PubMed  Google Scholar 

  35. Carrera E, Kim DJ, Castellani G, et al. Effect of hyper- and hypocapnia on cerebral arterial compliance in normal subjects. J Neuroimaging. 2009;21(2):121–5.

    Article  Google Scholar 

  36. Sloan MA, Alexandrov AV, Tegeler CH, et al. Transcranial Doppler ultrasonography in 2004: a comprehensive evidence-based update. Report of the American Academy of Neurology Therapeutics and Technology Assessment Subcommittee: Transcranial Doppler. J Neurol. 1990;40:680–1.

    Article  Google Scholar 

  37. Aaslid R, Markwalder TM, Nornes H. Noninvasive transcranial Doppler recording of flow velocity in basal cerebral arteries. J Neurosurg. 1982;57:769–74 Class II–III.

    Article  CAS  PubMed  Google Scholar 

  38. Matta B, Czosnyka M. Transcranial Doppler ultrasonography in anesthesia and neurosurgery. Cottrell and Young’s Neuroanesthesia, Chapter 8. Philadelphia: Elsevier; 2010.

    Google Scholar 

  39. Aaslid R. Transcranial Doppler examination techniques. In: Aaslid R, editor. Transcranial Doppler sonography. New York: Springer; 1986. p. 39.

    Chapter  Google Scholar 

  40. Nelson RJ, Czosnyka M, Pickard JD, et al. Experimental aspects of cerebrospinal haemodynamics: the relationship between blood flow velocity waveform and cerebral autoregulation. J Neurosurg. 1992;31:705–10.

    Article  CAS  Google Scholar 

  41. Czosnyka M, Richards HK, Reinhard M, et al. Cerebrovascular time constant: dependence on cerebral perfusion pressure and end-tidal carbon dioxide concentration. Neurol Res. 2012;34(1):17–24.

    Article  CAS  PubMed  Google Scholar 

  42. Kasprowicz M, Diedler J, Reinhard M, et al. Time constant of the cerebral arterial bed. Acta Neurochir Suppl. 2012;114:17–21.

    Article  PubMed  Google Scholar 

  43. Czosnyka M, Richards H, Pickard JD, Harris N, Iyer V. Frequency-dependent properties of cerebral blood transport-an experimental study in anaesthetized rabbits. Ultrasound Med Biol. 1994;20:391–9.

    Article  CAS  PubMed  Google Scholar 

  44. Kim DJ, Kasprowicz M, Carrera E, et al. The monitoring of relative changes in compartmental compliances of brain. Physiol Meas. 2009;30(7):647–59.

    Article  CAS  PubMed  Google Scholar 

  45. Kasprowicz M, Diedler J, Reinhard M, et al. Time constant of the cerebral arterial bed in normal subjects. Ultrasound Med Biol. 2012;38(7):1129–37.

    Article  PubMed  Google Scholar 

  46. Kasprowicz M, Czosnyka M, Soehle M, et al. Vasospasm shortens cerebral arterial time constant. Neurocrit Care. 2011;16(2):213–8.

    Article  Google Scholar 

  47. Czosnyka M, Smielewski P, Piechnik S, et al. Hemodynamic characterization of intracranial pressure plateau waves in head-injury patients. J Neurosurg. 1999;91(1):11–9.

    Article  CAS  PubMed  Google Scholar 

  48. Avezaat CJJ, van Eijndhoven JHM. Cerebrospinal fluid pulse pressure and craniospinal dynamics. A theoretical clinical and experimental study. Thesis. The Hague: A Jongbloed, 1984

  49. Toth M, Nadasy GL, Nyar I, Kerenyi T, Monos E. Are there systemic changes in the arterial biomechanics of intracranial aneurysm patients? Pflugers Arch. 2000;439:573–8.

    Article  CAS  PubMed  Google Scholar 

  50. Alperin N, Lee SH, Sivaramakrishnan A, Hushek SG. Quantifying the effect of posture on intracranial physiology in humans by MRI flow studies. J Magn Reson Imaging. 2005;22:591–6.

    Article  PubMed  Google Scholar 

  51. Carrera E, Kim DJ, Castellani G, et al. What shapes pulse amplitude of intracranial pressure? J Neurotrauma. 2010;27:317–24.

    Article  PubMed  Google Scholar 

  52. Eide PK, Sorteberg A, Bentsen G, Marthinsen PB, Stubhaug A, Sorteberg W. Pressure-derived versus pressure wave amplitude-derived indices of cerebrovascular pressure reactivity in relation to early clinical state and 12-month outcome following aneurysmal subarachnoid hemorrhage. J Neurosurg. 2012;116(5):961–71.

    Article  PubMed  Google Scholar 

  53. Eide PK. Assessment of childhood intracranial pressure recordings using a new method of processing intracranial pressure signals. Pediatr Neurosurg. 2005;41(3):122–30.

    Article  PubMed  Google Scholar 

  54. Radolovich DK, Aries MJ, Castellani G, et al. Pulsatile intracranial pressure and cerebral autoregulation after traumatic brain injury. Neurocrit Care. 2011;15(3):379–86.

    Article  CAS  PubMed  Google Scholar 

  55. Czosnyka M, Richards HK, Whitehouse HE, Pickard JD. Relationship between transcranial Doppler-determined pulsatility index and cerebrovascular resistance: an experimental study. J Neurosurg. 1996;84(1):79–84.

    Article  CAS  PubMed  Google Scholar 

  56. Gosling RG, King DH. Arterial assessment by Doppler-shift ultrasound. Proc R Soc Med. 1974;67(6 Pt 1):447–9.

    CAS  PubMed  PubMed Central  Google Scholar 

  57. Michel E, Zernikow B. Goslig’s Doppler pulsatility index revisited. Ultrasound Med Biol. 1998;24(4):597–9.

    Article  CAS  PubMed  Google Scholar 

  58. de Riva N, Budohoski KP, Smielewski P, et al. Transcranial Doppler pulsatility index: what it is and what it isn’t. Neurocrit Care. 2012;17(1):58–66.

    Article  PubMed  Google Scholar 

  59. O’Rourke MF, Taylor MG. Input impedance of the systemic circulation. Circ Res. 1967;20(4):365–80.

    Article  PubMed  Google Scholar 

  60. Giller CA, Hodges K, Batjer HH. Transcranial Doppler pulsatility in vasodilation and stenosis. J Neurosurg. 1990;72(6):901–6.

    Article  CAS  PubMed  Google Scholar 

  61. Behrens A, Lenfeldt N, Ambarki K, Malm J, Eklund A, Koskinen LO. Transcranial Doppler pulsatility index: not an accurate method to assess intracranial pressure. J Neurosurg. 2010;66(6):1050–7.

    Article  Google Scholar 

  62. Bellner J, Romner B, Reinstrup P, Kristiansson KA, Ryding E, Brandt L. Transcranial Doppler sonography pulsatility index (PI) reflects intracranial pressure (ICP). Surg Neurol. 2004;62(1):45–51.

    Article  PubMed  Google Scholar 

  63. Burton AC. Fundamental instability of the small blood vessels and critical closing pressure in vascular beds. Am J Physiol. 1951;164:330–1.

    PubMed  Google Scholar 

  64. Brunner MJ, Greene AS, Sagawa K, Shoukas AA. Determinants of systemic zero-flow arterial pressure. Am J Physiol. 1983;245:H453–9.

    CAS  PubMed  Google Scholar 

  65. Czosnyka M, Smielewski P, Piechnik S, et al. Critical closing pressure in cerebrovascular circulation. J Neurol Neurosurg Psychiatry. 1999;66:606–11.

    Article  CAS  PubMed  Google Scholar 

  66. Panerai RB. The critical closing pressure of the cerebral circulation. Med Eng Phys. 2003;25:621–32.

    Article  CAS  PubMed  Google Scholar 

  67. Dewey RC, Pierer HP, Hunt WE. Experimental cerebral hemodynamics. Vasomotor tone, critical closing pressure, and vascular bed resistance. J Neurosurg. 1974;41:597–606.

    Article  CAS  PubMed  Google Scholar 

  68. Panerai RB, Moody M, Eames PJ, Potter JF. Cerebral blood flow velocity during mental activation: interpretation with different models of the passive pressure–velocity relationship. J Appl Physiol. 2005;99:2352–62.

    Article  PubMed  Google Scholar 

  69. Aaslid R, Lash SR, Bardy GH, Gild WH, Newell DW. Dynamic pressure-flow velocity relationships in the human cerebral circulation. Stroke. 2003;34(7):1645–9.

    Article  PubMed  Google Scholar 

  70. Newell DW, Aaslid R. Transcranial Doppler: clinical and experimental uses. Cerebrovasc Brain Metab Rev. 1992;4(2):122–43.

    CAS  PubMed  Google Scholar 

  71. López-Magaña JA, Richards HK, Radolovich DK, et al. Critical closing pressure: comparison of three methods. J Cereb Blood Flow Metab. 2009;29:987–93.

    Article  PubMed  Google Scholar 

  72. Panerai RB, et al. Influence of calculation method on estimates of cerebral critical closing pressure. Physiol Meas. 2011;32:1–16.

    Article  Google Scholar 

  73. Michel E, Hillebrand S, von Twickel J, et al. Frequency dependence of cerebrovascular impedance in preterm neonates: a different view on critical closing pressure. J Cereb Blood Flow Metab. 1997;17:1127–31.

    Article  CAS  PubMed  Google Scholar 

  74. Puppo C, Camacho J, Yelicich B, Moraes L, Biestro A, Gomez H. Bedside study of cerebral critical closing pressure in patients with severe traumatic brain injury: a Transcranial Doppler study. Acta Neurosurg Suppl. 2012;114:283–8.

    Article  Google Scholar 

  75. Soehle M, Czosnyka M, Pickard JD, Kirkpatrick PJ. Critical closing pressure in subarachnoid hemorrhage: effect of cerebral vasospasm and limitations of a transcranial Doppler-derived estimation. Stroke. 2004;35(6):1393–8.

    Article  PubMed  Google Scholar 

  76. Varsos GV, Richards H, Kasprowicz M, et al. Critical closing pressure determined with a model of cerebrovascular impedance. J Cereb Blood Flow Metab. 2012;33(2):235–43.

    Article  PubMed  Google Scholar 

  77. Richards HK, Czosnyka M, Pickard JD. Assessment of critical closing pressure in the cerebral circulation as a measure of cerebrovascular tone. Acta Neurochir Wien. 1999;141(11):1221–7.

    Article  CAS  PubMed  Google Scholar 

  78. Kontos HA, Wei EP, Navari RM, Levasseur JE, Rosenblum WI, Patterson JL Jr. Responses of cerebral arteries and arterioles to acute hypotension and hypertension. Am J Physiol. 1978;234(4):H371–83.

    CAS  PubMed  Google Scholar 

  79. Serrador JM, Picot PA, Rutt BK, Shoemaker JK, Bondar RL. MRI measures of middle cerebral artery diameter in conscious humans during simulated orthostasis. Stroke. 2000;31(7):1672–8.

    Article  CAS  PubMed  Google Scholar 

  80. Giller CA, Bowman G, Dyer H, Mootz L, Krippner W. Cerebral arterial diameters during changes in blood pressure and carbon dioxide during craniotomy. J Neurosurg. 1993;32(5):737–42.

    Article  CAS  Google Scholar 

  81. Newell DW, Aaslid R, Lam A, Mayberg TS, Winn HR. Comparison of flow and velocity during dynamic autoregulation testing in humans. Stroke. 1994;25(4):793–7.

    Article  CAS  PubMed  Google Scholar 

  82. Müller HR, Brunhölzl C, Radü EW, Buser M. Sex and side differences of cerebral arterial caliber. Neuroradiology. 1991;33(3):212–6.

    Article  PubMed  Google Scholar 

  83. Caekebeke JF, Ferrari MD, Zwetsloot CP, Jansen J, Saxena PR. Antimigraine drug sumatriptan increases blood flow velocity in large cerebral arteries during migraine attacks. J Neurology. 1992;42(8):1522–6.

    Article  CAS  Google Scholar 

  84. Giller CA, Giller AM, Cooper CR, Hatab MR. Evaluation of the cerebral hemodynamic response to rhythmic handgrip. J Appl Physiol. 2000;88(6):2205–13.

    CAS  PubMed  Google Scholar 

  85. Giller CA, Mueller M. Linearity and non-linearity in cerebral hemodynamics. Med Eng Phys. 2003;25(8):633–46.

    Article  PubMed  Google Scholar 

  86. Mitsis GD, Zhang R, Levine BD, Marmarelis VZ. Cerebral hemodynamics during orthostatic stress assessed by nonlinear modeling. J Appl Physiol. 2006;101(1):354–66.

    Article  PubMed  Google Scholar 

Download references

Conflict of interests

ICM+ software is licensed by Cambridge Enterprise Ltd (www.neurosurg.cam.ac.uk/icmplus). PS and MC have a share in a fraction of licensing fee. There is no other conflict of interest regarding equipment used for monitoring of clinical and experimental signals.

Author information

Authors and Affiliations

  1. Neurosurgical Unit, Department of Clinical Neurosciences, Addenbrooke’s Hospital, University of Cambridge, Cambridge, UK

    Georgios V. Varsos, Peter Smielewski & Marek Czosnyka

  2. Institute of Biomedical Engineering and Instrumentation, Wroclaw University of Technology, Wroclaw, Poland

    Magdalena Kasprowicz

  3. Institute of Electronic Systems, Warsaw University of Technology, Warsaw, Poland

    Marek Czosnyka

  4. Division of Neurosurgery, Department of Clinical Neurosciences, Addenbrooke’s Hospital, Hills Road, Cambridge, CB2 0QQ, UK

    Georgios V. Varsos

Authors
  1. Georgios V. Varsos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Magdalena Kasprowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Smielewski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marek Czosnyka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Georgios V. Varsos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Varsos, G.V., Kasprowicz, M., Smielewski, P. et al. Model-based Indices Describing Cerebrovascular Dynamics. Neurocrit Care 20, 142–157 (2014). https://doi.org/10.1007/s12028-013-9868-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12028-013-9868-4

Keywords

Search

Navigation