Introduction

Normal pressure hydrocephalus (NPH) is a pathopsychological condition that has potentially reversible symptoms of gait apraxia, dementia, and urinary incontinence [1,2]. Therefore, proper diagnosis is extremely crucial for the timely treatment and subsequent quality of a patient’s life. Since NPH is defined as excessive accumulation of cerebrospinal fluid (CSF) in and around the ventricles with no signs of significant pressure elevation, the hydrodynamics of CSF is one of the key phenomena in diagnosis and management of NPH. The treatment is usually shunting the patients who are responsive to the diagnostic tests such as external lumbar drainage (ELD) and transient monitoring of CSF dynamics [3]. CSF pressure is considered as the main variable monitored from an invasively conducted test and conceptually can be defined as the pressure that must be exerted against a needle placed in the CSF space to just prevent the escape of fluid. It is also proposed that the outflow resistance (R) of CSF and the pulsing characteristics of CSF pressure may be a good candidate to analyze and derive diagnostic conclusions through the same test; however, there is still so much that is unknown. In this chapter, we will briefly describe the CSF dynamics and how fluid inside the central nervous system (CNS) is generated, stored, and absorbed within the context of a mathematical model developed by Marmarou [4,5]. Then, we proceed to explain the main infusion techniques in theory and their practical applications by various clinics. Finally, we will present a comparative analysis of clinically accepted methods followed by a brief discussion and conclusion.

CSF dynamics

The CSF is secreted through the choroid plexus in the ventricles [6]. The rate of formation was reported to be on average constant and about 0.35 ml/min [7]. After being secreted mainly in the lateral and third ventricles, the CSF follows a path to the fourth ventricle through the aqueduct of Sylvius. Then, it flows into the subarachnoid space through the foramina of Luschka and the foramen of Magendie, where most of it is absorbed by the superior sagittal sinus through the arachnoid villi. Some absorption of CSF also takes place in the spinal subarachnoid space [8].

Marmarou [4] developed a model analogous to an electric circuit with some key parameters which are beneficial in diagnosis of NPH. According to Marmarou’s theory [4], the CSF formation is balanced by its storage and absorption in equilibrium condition:

(13.1)

where I_f, I_s, and I_a are formation, storage, and absorption rates, respectively, in the units of ml/min. A general equation governing time-dependent pressure dynamics was derived in terms of the following parameters: The quantized intracranial compliance, i.e. pressure–volume index (PVI), dural sinus pressure (P_d), resistance to absorption (R), and an external input rate of fluid summed up with the intrinsic CSF formation rate.

Compliance means the elasticity or compensatory mechanism of brain parenchyma in response to non-equilibrium conditions such as an external volume addition to CSF space and/or internal pressure fluctuations. It is formulated as volume change per unit pressure difference, ΔV/ΔP. However, Figure 13.1a shows that the compliance curve has an exponential trend and it varies moving along the curve. Thus, plotting the same data on a semilog scale exhibits a linear behavior and yields a unique constant value as obtained from the slope of the line (Figure 13.1b). The inverse slope is called PVI (measured in ml), which is defined as the extra fluid volume necessary to increase the CSF pressure 10-fold.

Figure 13.1 (a) A representative simulation of pressure–volume (P-V) curve, which is a characteristic property for each brain. The P-V relationship was shown to be exponential [4]. (b) PVI is the inverse slope obtained from a semilog plot of the P-V curve.

Figure 13.2 The CSF system was modeled by analogy to an electrical circuit and the equations were derived using the rules of circuit operation. Formation and storage are represented by a current source and a nonlinear capacitance, respectively. In addition, absorption branch is represented by a potential difference and a resistance element, which are for dural sinus pressure, P_d and resistance to outflow, R, respectively.

Absorption rate (I_a) is defined as the gradient of pressure between CSF space (P) and the venous system of the dural sinus (P_d) divided by the resistance to absorption (R):

(13.2)

Storage rate is by definition the rate of change of CSF volume stored:

(13.3)

In addition, compliance (C) can be expressed differentially as:

(13.4)

Due to the exponential feature of the compliance curve, C can be expressed as follows:

(13.5)

where K is a constant determining the steepness of compliance curve. Combining equations (13.4) and (13.5) and differentiating with respect to time yields the form:

(13.6a)

and

(13.6b)

Thus, a first order nonlinear differential equation can be obtained by substituting the new terms for I_s (13.6b) and I_a (13.2) in (13.1):

(13.7)

A simplification by rearranging the terms yields the standard differential equation form below:

(13.8)

The general analytical time-dependent solution of (13.8) for pressure is achieved by a specific mathematical transformation and the result is as follows:

(13.9)

where is the integration factor. Details may be found in the appendix of reference 4.

In addition, the model invokes two physiological constraints: the venous drainage is linear, i.e., drainage is linearly proportional to the pressure gradient between CSF pressure on the granulation side (P) and pressure on the dural sinus side (P_d) as verified for adult cats by Marmarou et al. [4]. In addition, CSF pressure must be greater than dural sinus pressure, i.e., P > P_d, to have actual drainage. It is also assumed that the dural sinus pressure is constant under normal physiological circumstances.

Once the governing CSF model has been developed, it can be solved for both steady-state and transient conditions. At steady-state condition as imposed by the model, CSF pressure is governed by the dural sinus pressure and the product of constant formation rate and resistance to absorption:

(13.10)

Note that there is no storage term involving the compliance component at equilibrium condition. This is analogous to the capacitor model acting as open circuit under direct current operating conditions in an electrical circuit. In fact, Marmarou [4] proposed his model using an electrical circuit analogy to the CSF circulation as seen schematically in Figure 13.2. Meanwhile, Eq. (13.10) suggests that the slope gives the outflow resistance and an increase in formation rate will reflect as an increase in the CSF pressure under the assumption of R and P_d held constant. In addition, at zero formation rate, CSF pressure is pinned to the dural sinus pressure for which there is no absorption expected.

Lumbar infusion techniques

The infusion of fluid to the CSF space was clinically introduced by Katzman and Hussey [9,10] and since then it has been effectively implemented as a useful diagnostic tool for hydrocephalus and in vivo patency tests of malfunctioning shunts as well as for research conducted on animals [4,8]. In principle, the infusion test is done by introducing a sufficient amount of fluid (saline or artificial CSF) to the CSF space. Marmarou used the above-mentioned mathematical model (Eq. 13.9) for three different types of external inputs which are for bolus injection, volume removal, and constant infusion methods. Current clinical applications are mainly based on those with slight modifications comprising the specifics for a particular method. The solution depicts the transient effects as a response to the specific input types summed up with the constant formation rate. The mathematical equivalent of a selected physical external input, i.e., I(τ), must be inserted in Eq. (13.9) for the corresponding desired solution (Table 13.1, columns B and C). Ideally a positive/negative square-pulse function represents a rapid injection/removal as in the case of the bolus method. For example, the external input rate for bolus injection is 1 ml/s for a few seconds. In contrast, constant infusion is simply a summation of two constant-rate inputs, which are the intrinsic formation rate and constant infusion rate. The ideal mathematical representation for this type of physical input is a step function, for which the starting moment for the infusion process corresponds to the location of the step-like feature (Table 13.1, bottom row, column B).

Table 13.1 Three different infusion methods (rows) were evaluated using the Marmarou model for CSF dynamics [4]. Column (A) is the volume added to the CSF system as a function of time; (B) external input rate summed up with constant intrinsic production rate; (C) the mathematical equivalent of the added/removed volume; (D) the solution of the model for pressure as a function of time with respect to the given inputs; (E) the output response of the respective solutions for each infusion method

The solutions and output responses for time-dependent pressure, P(t), have specific results with respect to the constraints imposed as well as the infusion type, as summarized in Table 13.1. After collecting the output response data, one can subsequently solve for desired quantities (R, I_f, C, PVI, etc.) by using the expression for P(t) at any time. The main parameters of interest are resistance to outflow and the pressure–volume index.

Bolus injection

The bolus injection method is defined as a small amount of volume (≈4 ml) introduced to the CSF system in a short amount of time, usually within about 4–5 s. The amount of liquid must be small but significant enough to create an observable transient as invasively monitored from the CSF pressure. The injected amount is mathematically formulated using a delta function keeping the formation rate as a constant background. The pressure profile exhibits an abrupt increase from its equilibrium state reaching a maximum value immediately after introduction of the injected amount. Then, pressure starts to decrease as a function of the compliance parameter, K, and resistance to outflow, R. Finally, the CSF system is expected to restore itself ideally at opening pressure, P_o.

The general solution for R is shown below as derived from the time-dependent pressure result (Table 13.1, top row, column D):

(13.11)

where t is time, P_o is the resting (base) pressure, P_p is peak pressure immediately after injection, and P_t is the pressure value recorded at a selected time after injection.

Similarly, PVI is calculated using the data obtained from bolus method through the following expression:

(13.12)

where ΔV is the total volume injected. Equation (13.12) can be derived from the definition of PVI and using Figure 13.1b.

Bolus infusion measurement can be performed in an outpatient clinic. The procedure conducted at the Medical College of Virginia (Virginia Commonwealth University, Richmond, USA) can be described as follows. After surgical preparation of the site and application of a local analgesic, a 25-gauge needle is used to access percutaneously into the lumbar intrathecal space. After reaching CSF space, the needle, sterile saline syringe, and strain-gauge type pressure transducer are interconnected through a tube and three-way stopcock. An auxiliary setup consisting of a tube and stopcock is also used to get air-free tubing filled with saline. Then, the output of the transducer is connected to a bedside monitor (Philips Intellivue MP5), which provides a pressure waveform on the screen. Similarly, the output of the bedside monitor is connected to a computer to store and analyze the pressure data. Finally, the transducer reading must be zeroed to atmosphere, and a careful check of the fluid lines is needed to ensure that they are continuously filled with fluid with no air bubbles. Following these steps, the operator may inject 4 ml of fluid at a rate of 1 ml/s and monitor and record the time course of pressure for data analyses. The number of necessary bolus injections is three or four for each patient and the total test duration is approximately 20 to 30 minutes including preparation.

Figure 13.3 shows an example of bolus injection data obtained from a patient. The outflow resistance can be calculated by picking the values of relevant parameters and plugging in Eq. 13.11. The normal range for R lies within 4–6 mmHg/(ml/min) from the clinical studies conducted at the Medical College of Virginia NPH clinic [3]. Below this range is considered to be still normal yielding even better conductance (G), where conductance is defined as the reciprocal of resistance (G = 1/R). In contrast, values above 6 mmHg/(ml/min) are regarded as a diagnostic indication of possible NPH, i.e. positive shunt responder. Additionally, an approximate value of 25 ml is considered to be a normal PVI value for a healthy person, whereas a PVI below 15 ml is an indication of low compliance, which implies a “tight brain.” PVI values higher than 25 ml may be caused by some anomalies such as an atrophic brain.

Figure 13.3 An example of bolus injection data obtained from a patient. PVI and R can be calculated by picking the values of the relevant parameter from the patient data collected. Data were processed to smooth the ripples.

Volume removal

Volume removal is defined as the opposite of bolus injection and is also called bolus withdrawal. In this scenario one must take into account that another condition emerges by removal of CSF as follows: The model suggests that absorption of CSF is only possible when the gradient between the CSF pressure and dural sinus pressure is positive, i.e., P > P_d. However, CSF pressure may drop below the dural venous sinus pressure immediately after bolus removal. Thus the time evolution after bolus removal must be separated into two regimes where the resistance to absorption is effectively infinite for the first part. The second regime starts at the threshold point where CSF pressure becomes greater than or equal to the dural venous pressure, which builds up by constant formation of CSF. The time-dependent CSF pressure can be formulated by considering these two pre- and post-threshold regions. Before the threshold point, CSF pressure recovers as a function of formation rate and compliance coefficient, whereas when absorption starts to take place after threshold, CSF pressure evolves as a function of absorption resistance and compliance coefficient until it reaches the equilibrium pressure as in the case of bolus injection.

Volume removal technique also enables calculation of PVI. In addition, the formation rate can be calculated using the region right after volume removal until the threshold point through the equation below:

(13.13)

where P and t must be picked at a point before the threshold level, i.e., t < t_c (Table 13.1, center row, column D).

In 1934, Masserman [11] reported an average CSF formation rate of 0.32 ml/min by relatively rapid removal of 20–35 ml of CSF and observing spontaneous recovery of pressure up to its resting value. Although Masserman’s prediction turned out to be pretty close to the recently accepted rate of 0.35 ml/min, his method has been criticized due to the assumption of constant absorption rate during the pressure restoration and not allowing for the vascular compensation of the initial pressure drop. In addition, Ekstedt [12] measured formation rate through a modified method by continuous lumbar drainage of CSF. The value reported was 0.4 ml/min, which is also within range of the commonly accepted rate. The bolus removal method also relies on the assumption that no absorption takes place before the CSF pressure surpasses the dural sinus pressure following a rapid withdrawal of fluid, for which pressure drops below the threshold value.

Gradual infusion methods

The bolus technique introduces a relatively sudden perturbation to the CSF system. Monitoring of the subsequent relaxation to the equilibrium state allows acquisition of the data necessary to calculate R and PVI. In contrast, gradual infusion methods suggest adding fluid in a controlled manner and simultaneously monitoring the time course of CSF pressure. Here we cover two main types of gradual infusion techniques, which are constant flow infusion and constant pressure infusion methods.

Constant flow infusion

As a third method, the constant flow infusion technique comprises a continuous infusion of fluid at a constant rate on top of the intrinsic formation rate [9,10,13]. The model suggested a solution for time-dependent pressure P(t) which results in a rapid increase in time and then slowly levels off. Finally, it forms a plateau, where the CSF system attains its new equilibrium with a steady-state pressure of caused by spontaneous balancing of external infusion through an increased absorption rate. The outflow resistance R can be calculated from the dynamic pressure expression given in Table 13.1 (bottom row, column D) as a response to an applied external input. Other relevant parameters such as the resting pressure (P_o), compliance constant (K), and pressure (P) must be determined from a curve fitting to experimental data. It is also possible to solve for R using the static approach by simply dividing the difference between steady-state pressure (P_ss) and resting pressure (P_o) by the infusion rate (ΔI) as follows:

(13.14)

After Katzman and Hussey [9,10] clinically introduced the constant rate infusion technique in 1970, it was adopted and modified by several others [14–20]. In particular, Marmarou tested his model on adult cats by comparing the data monitored during an infusion into the cisterna magna at a constant rate of 0.35 ml/min. His original work published in 1978 exhibited a good agreement between theory and experiment, confirming that the model successfully governs the time course of CSF pressure for constant and bolus infusion methods. Figure 13.4 shows a selected dataset comparing the model with the data obtained from the constant infusion method. However, he picked the transient method (bolus infusion) to assess outflow resistance for clinical practice mainly due to the fact that the bolus method is faster than other methods, which is especially beneficial for patient comfort and low complication rates. Also, the transient method was expected to yield more novel data due to the impulsive nature of the technique compared with the constant flow rate method.

Figure 13.4 Model compared with experimental CSF pressure responses. Fluid was infused into the cisterna magna at a constant rate of 0.35 ml/min [4].

In contrast, Børgesen et al. [21] applied a modified version of lumbo-ventricular constant flow method called the “constant pressure constant infusion rate technique.” They used the software developed by Czosnyka et al. [22] to capture the time course of pressure and faster assessment of outflow resistance using the Davson equation [23]. In particular, Juniewicz et al. [24] measured an elevation in resting pressure of about 3 mmHg following a constant infusion test. Figure 13.5 displays a typical recording of constant flow infusion at a rate of 1 ml/min [24]. The time evolution of pressure response exhibited an expected increase and plateau formation during the infusion and subsequent exponential pressure decay, resting at a higher value than the opening pressure. The possible suggestions to explain this hysteresis effect were either through transient volume change caused by excessive CSF diffusion into parenchyma [25] or by increase in the vascular component of intracranial pressure after infusion [26].

Figure 13.5 Typical clinical data monitored using constant infusion method at a rate of 1 ml/min [24].

Constant pressure infusion

The constant pressure method was suggested by Ekstedt in 1977 [27]. Principally, the technique is based on keeping the pressure at a constant level during the flow of sustaining artificial CSF. A peristaltic infusion pump and a computer-based regulating feedback system are utilized to achieve this for several pressure steps. For each level, flow rate and CSF pressure must be recorded. Then, R can be calculated based on steady-state solution for the model using Eq. (13.14).

In this method, two needles must be used, one assigned for infusion and the other for pressure measurement. The patient needs to rest in the supine position for about 20 min followed by about 5 min of resting pressure (P_o) monitoring. The step height for each consecutive pressure level is kept about 4 mmHg and each step is sustained at a stable level for 5–8 min. The overall procedure may take 1–1.5 h [28].

Figure 13.6a displays typical data collected for constant pressure infusion [28]. Six different pressure steps are clearly achieved by regulating the flow rate. In addition, the pressure level goes back to the resting pressure after the infusion process has halted. In principle, the constant pressure method is based on the dynamics of constant flow infusion. The basic modification is as follows: instead of monitoring the data several times under the same pressure–flow conditions and averaging them all, the constant pressure method suggests monitoring CSF pressure with the increments of small offset values. This would allow plotting flow as a function of pressure or vice versa. The linear relationship between pressure and flow is shown in Figure 13.6b as Marmarou assumed in his circuit model and confirmed experimentally on cats [4]. The linearity also implies that resistance to outflow is constant as long as one does not exceed the compensatory system of the brain, i.e., by staying within a reasonable compliance range.

Figure 13.6 (a) Clear observation of pressure levels by regulating the flow rate [28]. (b) Linear fit on the data collected by recording flow rate corresponding to each pressure level. The inverse slope yields outflow resistance [28].

External lumbar drainage and tap test

External lumbar drainage (ELD) is an excellent prognostic tool for which the accuracy of prediction rate can be more than 90% [3]. The test is based on the idea of simulating the shunt operation in real life by withdrawing CSF for relatively long time durations at drainage rates roughly comparable to regular shunt drainage. The standard application of the method usually requires 48–72 hours at an inpatient setting. The drainage rate may change depending on the patient’s condition such as age and brain atrophy. For the patients below 75 years and having a relatively “tight” brain, the rate is kept at around 10 ml/h. However, for patients older than 75 years or having an atrophic brain, the rate must be reduced and watched carefully. ELD yields the most accurate prognostic indications since it simulates the shunt for an extended time duration, which also helps to exclude some placebo effects. However, the long-term hospitalization may cause high complication rates and very uncomfortable conditions for elderly patients. Therefore, the possible elimination of ELD by replacing it with a combination of other tools is favored.

The tap test can be considered as a method for partial replacement of ELD; it involves the removal of one-shot large-volume CSF, i.e. withdrawal of about 40–50 ml within 15–30 min. It is possible to conduct the tap test in an outpatient clinic usually following an infusion test. Patients may leave the clinic after resting for an hour. The outcome can be evaluated by comparing the symptoms of gait impairment and cognitive findings before and after the CSF removal, supported by imaging and infusion test results. The symptoms may also alleviate after the patient goes home and rests overnight. Therefore good patient communication and follow-up is necessary.

Discussion

Infusion tests are mainly used as an auxiliary diagnostic tool for patients with NPH symptoms along with other clinical diagnostic methods such as the tap test or ELD [3,29–32]. In addition, outflow resistance is beneficial for testing in vivo shunt patency, which is effectively utilized to determine suspected malfunctioning shunt valves and antisiphon devices [33–36]. Moreover, coupling between vascular pulsing effect and CSF pressure also draws attention and is still being extensively studied after the advent of continuous computerized monitoring of intracranial pressures. Hence, monitoring of CSF pulse pressure amplitude during the lumbar infusion test was proposed for further understanding of CSF dynamics as well as for predicting outcome after NPH treatment [37–39]. The parameters of CSF dynamics extracted from an infusion test may also be beneficial for differential diagnostics such as distinguishing atrophic brain from hydrocephalus [40].

Technically, clinical prognostic applications of infusion methods can be classified into two groups: transient and steady-state. The bolus method is a means of monitoring transient behavior of CSF pressure after a rapid injection, whereas gradual infusion methods simply use the steady-state conditions by regulating the infusion process. The underlying basic principle of both methods is the linearity of the pressure–flow relationship within safe compensatory limits of the central nervous system. The pressure–flow linearity intrinsically holds the concept of constant R. However, clinical studies designed for shunt outcome prediction showed that there is no consensus on the magnitude of R calculated from the data collected using both methods. The threshold of resistance to outflow for the bolus method was determined as 4 mmHg/(ml/min) from a clinical study on 151 patients [3]. In contrast, centers using steady-state methods suggest significantly higher threshold values scattered in the range of 8–18 mmHg/(ml/min) [29,41–46]. Both methods offer positive predictive values (PPV) above 70%. However, negative predictive values (NPV) are not as high as PPVs, especially for constant infusion methods [29]. Thus, the use of other complementary diagnostic tools such as imaging, evaluation of the triad of symptoms, and CSF removal via tap test or ELD is imperative for the purpose of accurate outcome prediction. The gold standard process for predicting shunt responders is ELD, for which the accuracy rate is 92% [3]. However, the procedure requires an inpatient setting, and patients undergoing the ELD test may suffer from various complications. Moreover, 48- to 72-hour hospitalization may not be suitable for many elderly patients. Therefore, an infusion test with the aforementioned complementary diagnostic tools may increase outcome prediction accuracy comparable to the ELD prediction level and possibly eliminate hospitalization.

Clinically, there is no clear evidence to judge that the transient method is superior to the steady-state method or vice versa in terms of prognostic impact. The two methods are based on different physical standpoints yielding two different threshold outflow resistances for steady-state and transient solutions, even though the model suggests unique outflow resistance for both. The underlying cause of the difference is not known yet, possibly due to a missing parameter or a scaling factor which may unify the results. Therefore, each method should be treated separately and self consistently. For comparison in terms of application, the bolus method takes much less time, requiring a maximum of 30 min for each patient. In addition, it does not require complex equipment such as infusion pumps and regulatory systems and only one needle is necessary for lumbar puncture. The total amount of injected fluid is also much less than the amount necessary for constant pressure infusion, which is about 12 ml for three consecutive injections. In contrast, it demands more experience and better understanding of CSF dynamics while handling the process.

Since NPH is considered to occur at a late age, generally over 60, a large number of patients have atrophic brains of varying severities. The response of atrophic brain to bolus injection may skew the results for the first infusion. Hence, a second injection is necessary to compensate for the “pseudo-compliance” induced by atrophic brain. Injections that are applied following the first one exhibit similar R and PVI values, confirming the reliability of data. Imaging may be highly beneficial to assess dilation of sylvian fissures, which was reported as an indication of NPH [47,48]. Assessment of PVI together with imaging may also be useful to evaluate any atrophic brain and observations can be incorporated for interpretation of outflow resistance.

CSF pulse pressure is another aspect of CSF dynamics. CNS consists of three major components: brain parenchyma, CSF, and cerebral blood. Pressures exerted by the active compartments (CSF and cerebral blood) are in communication with each other and arterial/venous pressure components are scaled with a lever arm factor, i.e. the compensatory reserve of the aforementioned three components. The arterial blood pressure is roughly scaled down by more than an order of magnitude, where peak-to-peak CSF pulse amplitudes may vary in a range of 3–10 mmHg. The infusion technique is an integral part of probing the pulsed feature of CSF pressure for which the compliance response can be deduced and used for prediction of prognosis in NPH [39]. However, there are no theoretical and practical certainties and well-established clinical thresholds to date. Nevertheless, periodic pulse amplitude measurements should continue to support and enrich the interpretation of findings obtained from an infusion test. The periodic pulse feature superimposed on top of CSF pressure acts like an AC signal (with some distortion factor) straddled on a DC signal. Addition of this concept to the Marmarou circuit model and solving it quantitatively may lead to a better understanding of CSF dynamics, filling the gaps between theory and acquired data and in turn improving the overall results obtained from an infusion test.