Assessment of intracranial dynamics in hydrocephalus: effects of viscoelasticity on the outcome of infusion tests

Laboratory investigation

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The treatment of hydrocephalus requires insight into the intracranial dynamics in the patient. Resistance to CSF outflow (R0) is a clinically obtainable parameter of intracranial fluid dynamics that quantifies the apparent resistance to CSF absorption. It is used as a criterion for the selection of shunt candidates and serves as an indicator of shunt performance. The R0 is obtained clinically by performing 1 of 3 infusion tests: constant flow, constant pressure, or bolus infusion. Among these, the bolus infusion method has the shortest examination times and provides the shortest time of exposure of patients to artificially increased intracranial pressure (ICP) levels. However, for unknown reasons, the bolus infusion method systematically underestimates the R0. Here, the authors have tested and verified the hypothesis that this underestimation is due to lack of accounting for viscoelasticity of the craniospinal space in the calculation of the R0.


The authors developed a phantom model of the human craniospinal space in order to reproduce in vivo pressure-volume (PV) relationships during infusion testing. The phantom model followed the Marmarou exponential PV equation and also included a viscoelastic response to volume changes. Parameters of intracranial fluid dynamics, such as the R0, could be controlled and set independently. In addition to the phantom model, the authors designed a computational framework for virtual infusion testing in which viscoelasticity can be turned on or off in a controlled manner.

Constant flow, constant pressure, and bolus infusion tests were performed on the phantom model, as well as on the virtual computational platform, using standard clinical protocols. Values for the R0 were derived from each infusion test by using both a standard method based on the Marmarou PV equation and a novel method based on a system identification approach that takes into account viscoelastic behavior.


Experiments with the phantom model confirmed clinical observations that both the constant flow and constant pressure infusion tests, but not the bolus infusion test, yield correct R0 values when they are determined with the standard method according to Marmarou. Equivalent results were obtained using the computational framework. When the novel system identification approach was used to determine the R0, all of the 3 infusion tests yielded correct values for the R0.


The authors' investigations demonstrate that intracranial dynamics have a substantial viscoelastic component. When this viscoelastic component is taken into account in calculations, the R0, is no longer underestimated in the bolus infusion test.

Abbreviations used in this paper:ICP = intercranial pressure; PV = pressure volume; R0 = resistance to CSF outflow.

Article Information

Address correspondence to: Vartan Kurtcuoglu, Ph.D., University of Zurich, Institute of Physiology, Winterthurerstrasse 190, 8057 Zurich, Switzerland. email:

Please include this information when citing this paper: published online September 6, 2013; DOI: 10.3171/2013.8.JNS122497.

© AANS, except where prohibited by US copyright law.



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    Schematic (left) and photograph (right) of the phantom model setup. A silicone brain with mechanical properties similar to those of the human brain is placed inside an open plastic skull within a water-filled Plexiglas container. The subarachnoid space (SAS) is modeled through an external compartment. The production of CSF is represented by steady infusion into the ventricular space using a peristaltic pump. The absorption of the CSF is modeled via drainage through a fine-regulating valve into a reservoir held at superior sagittal sinus pressure (Pss) level. Fluid infusion is modeled via a programmable syringe pump connected to a simplified cisternal space. The PV response is determined via an active compliance device, consisting of a feedback-controlled linear motor and bellow assembly. The PV behavior of the active compliance device alone is equivalent to that predicted by the Marmarou equation of intracranial dynamics1,23 (Equation 1 in Appendix). It is characterized by the physiological parameters P0, P1, and K as reported in Table 1. As depicted in the inset (left), for slow, steady infusion at low flow and blocked CSF absorption, the phantom model closely matched the parameters of the Marmarou model with the same values for the elastance K and resting ICP level prior to infusion, P0 + P1. The silicone brain added a viscoelastic component to the overall PV curve. The ICP was recorded in the ventricular space via a clinical pressure monitor.

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    Infusion tests performed on the phantom model are compared with the ICP response predicted by the Marmarou model (Equation 1 in Appendix). A: Constant flow infusion. B: Constant pressure infusion. C: Bolus infusion. The lower graphs in each panel show the infusion flow curve (green), while the upper graphs indicate the changes in the ICP caused by the infusion as measured in the phantom (blue dashed lines) and predicted by the Marmarou model (red).

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    The mean R0 (± SD) derived from infusion test data on the phantom model using standard methods based on the Marmarou equation (left) and a system-identification approach that accounts for viscoelasticity with Equations 3 and 4 in the Appendix (right). The red dashed horizontal lines indicate the actual value of the R0 (8.57 mm Hg/[ml/min]) that was set via the fine-regulating outflow valve (Fig. 1). Three repetitions were performed for each type of infusion. The standard methods substantially underestimated the R0 in the bolus infusion (BI) tests. In contrast, the system-identification approach yielded correct values of the R0 in all 3 infusion tests. CFI = constant flow infusion; CPI = constant pressure infusion.

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    Time courses of the ICP obtained via virtual infusion testing using the computational framework according to Equations 3 and 4 in the Appendix with (blue and green lines) and without (red lines) considering viscoelastic behavior. The data that do not consider viscoelasticity were generated using the Marmarou equation. Two sets of viscoelastic properties based on experimental data from rat8(green) and bovine20(blue) brain tissue were considered. Viscoelasticity affected the initial phase of the ICP change caused by infusion of the CSF through constant flow (A) or at constant pressure (B). Equilibrium pressures, however, were not markedly influenced in these 2 infusion conditions. During the bolus infusion (C), viscoelasticity affected both the peak ICP and the shape of the ICP curve in the recovery phase.

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    Outflow resistance (R0) calculated with infusion test data from the computational framework with viscoelastic properties of rat8 (green) and bovine brain20 (blue). Left: Using standard methods derived from the Marmarou equation. Right: Using a system-identification approach derived from a viscoelastic model based on Equations 3 and 4 in the Appendix. The red dashed horizontal lines indicate the actual value of the R0 (8.57 mm Hg/[ml/min]). The standard methods substantially underestimated the R0 in the bolus infusion test. In contrast, the system identification approach yielded correct values for the R0 in all 3 infusion types.

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    Time courses of ICP (left) and mean (± SD) of R0(right) based on bolus infusion test data from the virtual computational framework with (green, rat data8) and without (red) taking into account viscoelastic properties. The standard method derived from the Marmarou model according to Equation 2 in the Appendix was used to determine the R0. The dark solid and light dashed lines in the left panel correspond, respectively, to ICP readings in the presence and absence of vascular, respiratory, and slow waves. In the right panel, the red dashed horizontal line indicates the actual value of R0. Data are based on 4 sets of infusion tests between which the phase shifts of the vascular, respiratory, and slow waves were varied with respect to the start of the bolus infusion. Although ICP pulsation introduced variability in the calculation of the R0, this pulsation does not by itself lead to a consistent underestimation of the R0(red bar). The R0 was underestimated only when the Marmarou equation was used in conjunction with the viscoelastic response (green bar).


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