12. Modelling of CSF compensation: Mathematical model (Marmarou). Mathematical modelling of pulsatile aqueductal CSF flow

Transcription

1 12. Modelling of CSF compensation: Mathematical model (Marmarou). Mathematical modelling of pulsatile aqueductal CSF flow

2 Hydrocephalus Enlargement of CSF space Shunting? Revision? When?

3 CSF dynamics Prof. A. Marmarou, 2010

4 Electrical model of CSF circulation and pressure- volume compensation PhD Thesis, 1973

5 Original analysis of A.Marmarou: response to boluse injection, withdrawal and constant rate infusion

6 Contemporary version of the model: It has not changed a lot Added elements: a diode and voltage source Po Marmarou A : A theoretical model and experimental evaluation of the cerebrospinal fluid system. Thesis, Drexel University, Philadelphia, PA, 1973

7 Analysis of the model for ICP>Pz and ICP>Pss Thanks to Dr.H.Juniewicz

8 Thanks to Dr.H.Juniewicz

9 Davson s equation p b = p ss + R csf I f ICP ICP Popt is the same as ICPz Cocept of Popt: Sliwka S. A clinical system for the evaluation of selected dynamic propertiesof the intracranial system. PhD Thesis, Polish Academy of Sciences, Warsaw 1980 (in Polish)

10 Thanks to Dr.H.Juniewicz

11 Thanks to Dr.H.Juniewicz

12 Thanks to Dr.H.Juniewicz

13 ICP

14 ICP ICP P - P 0 P - P B (Pz, ΔVz) DV [ml]

15 Pulse amplitude of ICP increases with mean ICP

16 3 AMP [mm Hg] 2 Pz 1 0 P 0 P opt ICP P [mm Hg]

17 P.Smielewski; ICM+; Calculation of CSF compensatory parameters

18 ICP [mm Hg] Example of ICP elevation 1 ICP() t ICP o 1 A ICP ICP A 1 e b E A I t 2 inf o 20 ICP e ICP b D ICP ICP 1 A ICP ICP () b t ICP o E 1 A I t A e 1 inf o where : A ICPb ICP I R time [min] inf CSF o 1. Kasprowicz M, Czosnyka Z, Czosnyka M, Momjian S, Juniewicz H, Pickard JD: Slight elevation of baseline intracranial pressure after fluid infusion into CSF space in patients with hydrocephalus, Neurol Res, 26, 2004,

19 Example of P-V changes during and after infusion 2 D ICP 1 5 I C P - I C P I C P - I C P b o o d u r i n g i n f u s i o n a f t e r i n f u s i o n [ m l ] Kasprowicz M, Czosnyka M, Czosnyka Z, Momjian S, Smielewski P, Juniewicz H, Pickard JD: Hysteresis of the cerebrospinal pressure-volume curve in hydrocephalus, Acta Neurochir Suppl, 86, 2003, E 2 D V C S F E 1

20 Mathematical modelling of aqueductal CSF flow M.Czosnyka, Piechnik SK, Z.Czosnyka, O. Baledent, D.J.Kim, N.Keong, J.D.Pickard Neurosurgical Unit, Department of Clinical Neurosciences, UK and Functional MRI Laboratory, University of Oxford, UK and Biophysic and Image Processing Department, University Hospital of Amiens, France

21 Aqueductal CSF curve flow the slice is in the middle of the aqueduc We know a lot about CSF flow in various cross sectional areas of CSF system... We also know a lot about CSF pressure waveform in NPH Can we marry these two aspects of exploring NPH? Thanks to Dr.O.Baledent

22 Flow through aqueduct is pulsatile because of phase shift of ventricular and subarachnoidal pulse pressure 1. Problems with simultaneous measurement of MRI and Physiological Variables (pressures) 2. As close as we have gone is: simultaneous recording of intraparenchymal pressure and lumbar pressure. Phase shift! 3. If there is phase shift, there is pulsatile pressure gradient

23 Thanks to Dr.S.Piechnik If you cannot measure it, model it! LEFT RIGHT Rrl RRr Rvl Ci Rvr Rsl Rsr CVRl Rac CVRr Ifl Ifr Rfl Ran Rfr MCAl MCAr ACoA ICAl IC Ar Cvo Rvo ABP CSF flow trough aqueduct is modelled as current through Rac

24 Flow through aqueduct: results from pressure gradients. The same phase shift as in clinical recordings +++ and cisternal pressure amplitude is lower than ventricular! Red- ICPventricular, Green- ICP cisternal CSF flow in the aqueduc Cerebral blood flow that represents arterial flow? Time [min] LIMITATION: CSF flow has not been properly calibrated against MRI (pending)!!! Watch only relative changes!!!

25 Increase in PaCO2: amplitude of CBF and CSF flow increase. Also amplitude of ICP increase. ICP ventricular [mm Hg] Arterial blood pressure[mm Hg] CSF flow CBF [ml/min] PaCO2 [mm Hg] LIMITATION: CSF flow has not been properly calibrated against MRI (pending)!!! Watch only relative changes!!!

26 Pulse amplitude of CSF flow is a function of PaCO2 so nice +++ we have to measure it by PCMRI CSF flow pulse amplitude PaCO2 [mm Hg]

27 Stepwise squeezing of Aqueduct Cerebri ICP ventricular [mm Hg] Arterial blood pressure[mm Hg] CSF flow CBF [ml/min] R aqueduct [mmhg/(ml/min)]

28 CSF flow amplitude decreases and ICP pulse amplitude increases when resistance of Aqueduct Cerebri increases CSF flow amplitude ICP pulse amplitude Resistance of aqueduct

29 Infusion test the impact is mainly in CBF than in CSF. I found this result a little bit strange. I expect a bigger increase of CSF without change in CBF ICP ventricular [mm Hg] Arterial blood pressure[mm Hg] CSF flow] CBF [ml/min] Infusion rate [ml/min]

30 Infusion rate [ml/min] CSF flow amplitude ok, I see depends of the scale the graph in the last slide don t show very well the change of CSF Time [minutes]

31 Increase in Rcsf ICP ventricular [mm Hg] Arterial blood pressure[mm Hg] CSF flow] CBF [ml/min] the model is dead? Rcsf [mm Hg/(ml/min]

32 Amplitude of CSF flow depends linearly on amplitude of ventricular CSF pressure CSF flow amplitude Time [minutes] CSF flow amplitude ICP amplitude

33 Stepwise increase in pulsatility of ABP ICP ventricular [mm Hg] Arterial blood pressure[mm Hg] CSF flow] CBF [ml/min]

34 Amplitude of CSF flow seems to be just proportional to amplitude of arterial blood pressure CSF flow amplitude, ABP amplitude

35 Stepwise increase in pulsatility of ABP ICP ventricular [mm Hg] Arterial blood pressure[mm Hg] CSF flow] CBF [ml/min]

36 With increasing amplitude of arterial pulsations, mean ICP increases! Vascular component of ICP? Mean ICP [mm Hg] Time [min]

37 Summary 1. CSF circulation can be described by nonlinear differential equation of 1 st order 2. Analytical solution may be used in analysis of CSF volume-addition tests 3. It explains why pulse amplitude of ICP increases with mean ICP 4. Pressure-volume curve: parameters and its hysteresis 5. Dynamic CSF flow through aqueduct cerebri depends on pulse amplitude of ICP