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Effect of resting pressure on the estimate of cerebrospinal fluid outflow conductance
Fluids and Barriers of the CNS volume 8, Article number: 15 (2011)
Abstract
Background
A lumbar infusion test is commonly used as a predictive test for patients with normal pressure hydrocephalus and for evaluation of cerebrospinal fluid (CSF) shunt function. Different infusion protocols can be used to estimate the outflow conductance (C_{out}) or its reciprocal the outflow resistance (R_{out}), with or without using the baseline resting pressure, P_{r}. Both from a basic physiological research and a clinical perspective, it is important to understand the limitations of the model on which infusion tests are based. By estimating C_{out} using two different analyses, with or without P_{r}, the limitations could be explored. The aim of this study was to compare the C_{out} estimates, and investigate what effect P_{r}had on the results.
Methods
Sixtythree patients that underwent a constant pressure infusion protocol as part of their preoperative evaluation for normal pressure hydrocephalus, were included (age 70.3 ± 10.8 years (mean ± SD)). The analysis was performed without (C_{excl Pr}) and with (C_{incl Pr}) P_{r}. The estimates were compared using BlandAltman plots and paired sample ttests (p < 0.05 considered significant).
Results
Mean C_{out} for the 63 patients was: C_{excl Pr} = 7.0 ± 4.0 (mean ± SD) μl/(s kPa) and C_{incl Pr} = 9.1 ± 4.3 μl/(s kPa) and R_{out} was 19.0 ± 9.2 and 17.7 ± 11.3 mmHg/ml/min, respectively. There was a positive correlation between methods (r = 0.79, n = 63, p < 0.01). The difference, ΔC_{out}= 2.1 ± 2.7 μl/(s kPa) between methods was significant (p < 0.01) and ΔR_{out} was 1.2 ± 8.8 mmHg/ml/min). The BlandAltman plot visualized that the variation around the mean difference was similar all through the range of measured values and there was no correlation between ΔC_{out} and C_{out}.
Conclusions
The difference between C_{out} estimates, obtained from analyses with or without P_{r}, needs to be taken into consideration when comparing results from studies using different infusion test protocols. The study suggests variation in CSF formation rate, variation in venous pressure or a pressure dependent C_{out} as possible causes for the deviation from the CSF absorption model seen in some patients.
Background
Patients with normal pressure hydrocephalus (NPH) are treated with and often improved by a cerebrospinal fluid (CSF) shunt that changes the dynamics of the CSF system [1–4]. In order to assist in the selection of patients likely to benefit from shunt surgery, predictive tests are performed [5]. One such test is the infusion test. It measures changes in intracranial pressure due to infusion or withdrawal of Ringer solution. For clinical interpretation, the relation between pressure and flow obtained during an infusion test must be quantified into accessible parameters, i.e. a model of the CSF system is needed.
In the early seventies, Davson presented a model of the CSF absorption [6, 7]. This has since been widely accepted and is used as one part of the model describing the dynamics of the CSF system:
Thus, it states that the rate of absorption (I_{a}) is proportional to the difference between the pressure in the subarachnoid space (P_{ic}) and venous pressure in dural sinus (P_{d}). The proportionality coefficient is the outflow conductance (C_{out}), or its reciprocal, the outflow resistance (R_{out}). C_{out} describes the ease of flow across the CSF outflow pathways. In addition to being used as a prognostic parameter for selecting patients responding to CSF shunt surgery, infusion measurement of C_{out} is also used for evaluation of CSF shunt function [5, 8–11].
To use equation (1) in the analysis of an infusion test, P_{d}, which is difficult to measure, can be replaced by the measureable baseline resting pressure P_{r}. To replace P_{d} with P_{r}, three assumptions are needed, that C_{out} is a physical property independent of pressure and that the variations in P_{d} and CSF formation rate, I_{f}, during the infusion test are sufficiently small for P_{d} and I_{f} to be approximated as constants. If the variations in P_{d}, I_{f} and C_{out} are negligible, the relationship between steady state pressure and net infusion flow should be linear. Since a model is never better than the validity of its assumptions, it is important to understand the effects on estimated C_{out} caused by unfulfilled assumptions.
There are different infusion protocols, one such is the constant pressure infusion (CPI) protocol. It measures P_{r} and six elevated pressure levels together with corresponding net flow [12]. With this particular protocol, as opposed to the commonly used constant infusion protocol [13], a more detailed pressure/flow relationship can be plotted. As mentioned, data is expected to form a straight line throughout the pressure range with a trajectory through P_{r} and with the slope corresponding to C_{out} (Figure 1). However, from clinical experience it is suspected that the regression line does not always pass through P_{r}.
To understand the limitations of the current model used in infusion tests is important, both for basic physiological research and for clinical purposes. These limitations could be explored by comparing C_{out} estimates calculated using two different analyses, one that included P_{r} and one that did not. The aim of this study was to investigate how the use of baseline resting pressure influences the estimate of C_{out}.
Methods
Patient population
The study population consisted of patients that underwent preoperative evaluation for NPH. All patients had an MRI that revealed ventriculomegaly (Evans ratio > 0.3) and they were without any visual obstruction to CSF flow. Sixtythree patients (age 70.3 ± 10.8 years (mean ± SD), 18 women) underwent a CPI protocol. The study has been reviewed by the Regional Ethical Review Board in Umeå who concluded that there were no ethical problems with the project.
Infusion apparatus and investigation
The highly standardized infusion apparatus has been thoroughly described previously [12]. Two needles were inserted in the spinal canal while the patient was in the sitting position, one needle was used for pressure measurement and the other for infusion or withdrawal of Ringer solution. The patient was placed in the supine position and the zeropressure reference level was placed at the level of the auditory meatus. The investigation is illustrated in Figure 1. First, P_{ic} was measured during 1520 minutes of rest, and P_{r} was calculated as the mean P_{ic} over the last five minutes. To ensure a stable measurement of P_{r}, the patient was lying comfortably in supine position during the investigation, the importance of minimizing leakage during lumbar puncture was accentuated to the physician and the routine sample of CSF was taken after the measurement of P_{r}. Following the P_{r} measurement, the CPI protocol was initiated. P_{ic} was increased to six, consecutive, predetermined pressure levels lasting seven minutes each (Figure 1) followed by a spontaneous relaxation phase.
Estimation of C_{out}
The CSF absorption is estimated from Davson's equation (1). The two estimation methods used in this study are described below and illustrated in Figure 1 and Figure 2. They are derived from the model of CSF absorption and a CSF system in steady state. The assumption of conservation of fluid in the CSF system can be stated as
where I_{f} is the formation rate, I_{ext} is the infusion rate of a possible external infusion, I_{a} is the rate of absorption and I_{s} is the rate of change of fluid stored in the system. The normal unperturbed baseline resting pressure, P_{r}, (I_{s} and I_{ext} equal to zero) of the patient is defined as
When in steady state during an infusion test, I_{a} = I_{ext} + I_{f}, see equation (2). Combining this with equations (1) and (3), the relation between I_{ext} and P_{ic} is
Method 1, analysis without P_{r}
On each of the six elevated pressure levels, mean P_{ic} as well as the net inflow (I_{ext}) needed to maintain a constant P_{ic} was measured. The relation between I_{ext} and P_{ic} was
C_{excl Pr} was estimated as the slope of the linear regression between I_{ext} and P_{ic} using the six elevated pressure levels [12, 14] (Figure 1).
Method 2, analysis with P_{r}
Pressure and flow from all six elevated levels, but without using the P_{r}, were averaged into one pressure and flow point (${\overline{P}}_{\text{ic}}$ and ${I}_{\text{ext}}$respectively). C_{incl Pr} was calculated as
i.e. a line was drawn between P_{r} and ${\overline{P}}_{\text{ic}}$ and the slope corresponded to C_{incl Pr} (Figure 1). The classic Katzman method of estimating C_{out} during a constant infusion is achieved by dividing the mean flow with the difference between resting pressure and a pressure plateau [13]. The method for C_{incl Pr} simulates that approach and uses the same formula.
Statistics
Pearson's correlation coefficient was used for correlation analysis. The two estimates of C_{out} were compared using BlandAltman plots and paired sample ttests, p < 0.05 was considered significant.
Results
A typical infusion investigation is shown in Figure 1 with corresponding C_{out} from the two methods. The mean outflow conductance for the 63 patients was C_{excl Pr} = 7.0 ± 4.0 (mean ± SD) μl/(s kPa) (R_{excl Pr} = 19.0 ± 9.2 mmHg/ml/min) and C_{incl Pr} = 9.1 ± 4.3 μl/(s kPa) (R_{incl Pr} = 17.7 ± 11.3 mmHg/ml/min) respectively. There was a positive correlation between the two methods (r = 0.79, n = 63, p < 0.01). The paired difference between estimation methods (ΔC_{out} = C_{excl Pr}  C_{incl Pr}) was significant, ΔC_{out} = 2.1 ± 2.7 μl/(s kPa), n = 63, p < 0.01 (ΔR_{out} = 1.2 ± 8.8 mmHg/ml/min). The SD of ΔC_{out} was 13% of the measurement range. Figure 2 illustrates a case where the difference between methods was large, ΔC_{out} = 4.1 μl/(s kPa), is shown. Two phases were identified: 1. a net flow needed to raise the pressure from P_{r} to the first level, 2. a pattern following a straight line from the first level to the sixth level.
The BlandAltman plot in Figure 3 shows ΔC_{out} plotted against the mean of the two analysis methods. The variation around the mean difference in C_{out} was similar all through the range of measured pressures and there was no correlation between ΔC_{out} and C_{out}. A corresponding plot for R_{out} is given in Figure 4.
Discussion
This study investigated two analysis methods for estimating C_{out}, with or without P_{r}. The significant difference between the two methods (Figure 3) should be considered when comparing C_{out} in studies using different methods and when setting threshold values for shunting. The correlation between methods was in the same range as between C_{excl Pr} and C_{out} from a previous study [15]. It should be noted that the difference between the two methods was small and similar to what has been found for repeated infusion protocols [12, 15, 16], therefore one has to be careful with regard to any clinical implications. Most analysis methods for infusion tests are based on the model and basic assumptions described in this paper, and current development of new analysis methods for pressurecontrolled infusion will, as opposed to the CPI method used today, rely on P_{r}[17]. It is therefore important to investigate the limitations of these assumptions and the effects they have on calculated C_{out}.
The difference that was found depending on whether or not P_{r} was used in the estimation of C_{out}, (Figure 3), could be explained by several underlying causes. The infusion test analysis based on equation (1) assumes that P_{d} and I_{f}[18] are constant, but if they varied during the investigation, both P_{r} and the estimation of C_{out} would be affected. A potential explanation could be that the infusion of Ringer solution caused a physiological response with a reduction in P_{d} and/or I_{f} which would result in an increase of needed inflow as observed in this study (Figure 2), giving rise to the systematic difference in estimated C_{out} depending on whether or not P_{r} was used. Another assumption was that C_{out} is constant and pressure independent. This assumption has been based on visual inspection or correlation coefficients of the pressure/flow relationship [19–24]. Specifically, a linear relationship was shown for a pressure interval of 0.71.6 kPa above P_{r}[25], but that study focused on the use of C_{excl Pr} and did not analyse the relationship down to P_{r}. Other studies have proposed a nonlinear relationship between pressure and flow [26–28]. These studies suggested a continuously pressure dependent C_{out} while in the present study, the results suggest that for certain patients (Figure 2), there was a higher C_{out} in the vicinity of P_{r} followed by a pressure independent C_{out}. This could be explained by an active CSF outflow transport that starts when the system is perturbed by infusion, but with an absorption rate that is independent of further increases in pressure. This would indicate that the CSF outflow in the vicinity of P_{r} in some cases may differ from the Davson equation.
It was not possible to deduce from this study which of I_{f}, P_{d} and a pressure independent C_{out} was the major contributor to the systematic difference in results. The authors believe that the Davson equation is valid and that the deviation came from variations in P_{d} and/or I_{f} during the infusion. Monitoring of variation in central venous pressure during infusion tests could be a possible way forward. In addition to the systematic difference between methods, there was also a variation around the mean. This variation was probably mainly caused by the vascular effects on the CSF system (Figure 3). Vasomotion can cause large volume variations on the arterial side which in turn induce large pressure variations, e.g. Bwaves [29]. The relatively small flows involved during an infusion test in comparison with these effects, will make the estimation of C_{out} challenging. The steadystate analysis approach assumes that the dynamics of the system will be sufficiently suppressed by averaging over the 7 minutes of measurement time. However, the system dynamics for many patients can include components with potential to violate this assumption, e.g. Bwaves or plateau waves, that can cause a reduction in accuracy of the estimated pressures and flows for the elevated levels [29, 30]. These comparatively large physiological variations will also influence measured P_{r}. Visual inspection of the P_{r} measurements showed that four patients had marked Bwaves. One of which was the subject with the highest difference between methods while the other three were method independent (Figure 3). Furthermore, pressure that had not stabilised enough during its 1520 min baseline measurement, would also affect P_{r}. This could be caused by apprehension of the patient. Another possibility was a slow formation rate unable to compensate for the loss of CSF during lumbar puncture. To avoid this, a routine was followed in order to obtain as reliable estimates as possible (see Methods section). Results of repeated measurements in the same patient with consecutive CPI and constant infusion protocols suggest that the vascular effects limit the expected precision for measurements with current infusion tests to approximately 2 μl/(s kPa) (SD) [12, 15, 16]. We interpret this as an inherent characteristic of the vascular and CSF system that limits the expected repeatability independently of which infusion method that is used.
Since C_{incl Pr} uses an average value it will be less sensitive to physiological variations at the lowest or highest pressure levels. On the other hand it is dependent on P_{r}, and an error in this parameter will have a major impact on the estimated C_{out}, equation (6). Thus, the accuracy of estimated P_{r} becomes essential. Furthermore, if results are compared with results from the constant infusion protocol with either static analysis according to Katzman [13] or dynamic analysis [31], C_{incl Pr} should be used. Until future clinical studies have investigated the pressure/flow relationship in the vicinity of P_{r} in more detail and its pathophysiological importance have been established, both methods are still relevant. An erroneous flow measurement could produce the shift upwards in flow (Figure 2). However, careful calibration and testing of the equipment on experimental setup was performed [12, 17], and these types of errors have not been observed.
Conclusions
Using P_{r} for estimating C_{out} produced a higher estimated C_{out}. Possible causes for a deviation from the model of CSF absorption in some patients were a variation in formation rate or venous pressure or a pressure dependent C_{out}. The observed difference needs to be taken into consideration when setting threshold values for shunting and when comparing results from studies using different infusion test protocols.
Abbreviations
 NPH:

Normal pressure hydrocephalus
 CSF:

Cerebrospinal fluid
 P _{ic} :

Intracranial pressure
 P _{r} :

Resting pressure
 P _{d} :

Venous pressure in dural sinus
 I _{a} :

Absorption rate of CSF
 I _{f} :

Formation rate of CSF
 I _{ext} :

Rate of external infusion
 I _{s} :

CSF stored in system
 ${\overline{P}}_{\text{ic}}$ :

Average pressure
 ${\overline{I}}_{\text{ic}}$ :

Average pressure
 AF:

Average flow
 C _{excl Pr} :

Outflow conductance estimated by method 1, without P_{r}
 C _{incl Pr} :

Outflow conductance estimated by method 2, with P_{r}
 ΔC_{out}:

Difference in conductance between methods
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Acknowledgements
The study was funded by the Objective 2 Norra NorrlandEU Structural Fund, the Swedish research council, Vinnova, and the Foundation for Strategic Research through their joint initiative Biomedical Engineering for Better Health.
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Drs. Sundström, Malm, and Eklund have a patent interest in the inhousedeveloped infusion apparatus used in the study. Likvor AB has acquired the patent rights for commercialization.
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All authors participated in the conception and design of the study, collection of data, statistical analysis and critically revised the article, reviewed the final version of the manuscript and approved it for submission.
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Andersson, K., Sundström, N., Malm, J. et al. Effect of resting pressure on the estimate of cerebrospinal fluid outflow conductance. Fluids Barriers CNS 8, 15 (2011). https://doi.org/10.1186/20458118815
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Keywords
 Infusion Test
 Normal Pressure Hydrocephalus
 Normal Pressure Hydrocephalus
 Outflow Resistance
 Plateau Wave