The cerebrospinal fluid is a complex flow system likely involved in many brain-related tasks such as neuronal communication, waste clearance and immune surveillance of the brain (Abbott, 2004; Veening and Barendregt, 2010; Ransohoff and Engelhardt, 2012; Rodan et al., 2015). Its close proximity to the brain parenchyma and its delineation from the systemic circulation makes CSF a valuable source of information about brain-related changes. The CSF system is located in the ventricles (inner cavities of the brain), the central canal of the spinal cord and the area surrounding the brain and spinal parenchyma, the cranial and spinal subarachnoid space (SAS). The total fluid volume is around 150 ml at a production rate of ~0.3–0.5 ml/min. The CSF cushions the brain parenchyma and reduces the net weight of the human brain from ~1,500 to ~50 g (Cserr, 1971). In addition the fluid system acts as an important passive modulator of intracranial pressure (ICP) by equalizing cardiac cycle-driven blood volume changes inside the unyielding skull. During systole, the arterial blood inflow into the cranium exceeds the venous outflow, the compliant CSF fluid is pushed down the vertebrae and the lumbar sac dilates. The process is reversed during diastole (Wagshul et al., 2011). This leads to the bi-directional flow characteristics of CSF. The characteristics of pulsatile movement of CSF, depending on a variety of other physiological aspects such as breathing (Klose et al., 2000), or compliance, are more elaborately reviewed in Wagshul et al. (2011) and Linninger et al. (2016). Besides the generally accepted pulsatile flow characteristics; there is more controversial discussion on the bulk flow concept of CSF. The majority of scientists assume that the CSF is predominantly produced inside the ventricular system at the site of the choroid plexuses (CP) and absorbed into the lymph system and into the blood circulation in the subarachnoid space (SAS). In the cranial SAS CSF may partly flow from the SAS into the brain parenchyma via paravascular pathways and is then absorbed via the glymphatic system (Nedergaard, 2013). An excellent review focusing on the mechanisms of interstitial and CSF fluid movement is given in Hladky and Barrand (2014). For the purpose of this study it is sufficient to state that these assumptions presume a directed flow (bulk flow) from the ventricular space into the SAS. However, other researchers believe that CSF fluid is mainly generated and absorbed by the blood brain barrier (Brinker et al., 2014) and CSF movement is only a blood flow-dependent to-and-fro movement (Ore and Klarica, 2014). Although the majority of experimental results indicate a directed CSF flow, as reviewed in Abbott (2004), Damkier et al. (2013) and Spector et al. (2015), these experiments can be criticized based on their inherent invasiveness (Orešković and Klarica, 2010; Brinker et al., 2014).

The concentration of blood-derived proteins increases along the rostrocaudal axis whereas brain- or leptomeningeal-derived proteins remain relatively constant or possess a reverse gradient (Weisner and Bernhardt, 1978; Mollenhauer et al., 2012; Brandner et al., 2013, 2014; Aasebø et al., 2014; Sections The Rostrocaudal Gradient and Brain-Derived Proteins in CSF, Table 3). This is well explainable with the bulk-flow concept; blood-derived proteins enter the CSF system along the whole flow path of CSF, whereas brain-derived proteins predominantly enter the CSF system in the cranial area. Therefore, the concentration of blood-derived proteins rise with increasing distance from the ventricular system but the concentration of brain-derived proteins remains fairly constant along the spinal flow path (Table 3). With a pulsatile-only CSF flow concept, these subproteomic gradient characteristics are hard to explain. Further, although the pulsatile flow exceeds the bulk flow of CSF up to tenfold (Hladky and Barrand, 2014) and more (Gupta et al., 2009), the CSF flow remains laminar (Loth et al., 2001; Gupta et al., 2010) which is also indicated by the rostrocaudal gradient of blood-derived proteins, which would not exist in an CSF flow with predominantly turbulent flow characteristics. Therefore, evaluation of the source-related protein gradient values can be understood as intrinsic tracers for CSF flow characteristics.

Evaluating source-dependent protein characteristics can contribute to the understanding of the CSF system, but the consideration of the characteristics of the CSF system is of key importance for CSF proteomics.

For routine diagnostics CSF is withdrawn by lumbar puncture at the lumbar vertebrae. This gives rise to the questions as to how the brain-derived proteins are transported to the lumbar space (point of readout) and how their concentration is influenced by CSF dynamics (Section Brain-Derived Proteins in CSF).

Another key question is how blood-derived proteins are able to pass the barriers delineating blood from CSF (Section Discussion about the Diffusion Barriers). In the following sections we provide evidence that the passage of blood-borne proteins into CSF is at least predominantly based on diffusion (Section Blood-Derived Proteins in CSF), critically review a preceding diffusion-based model, the molecular flux model (Section The Molecular Flux Theory), and show that the diffusion-based protein exchange between blood and CSF can be precisely modeled with a system of steady states connected by bulk flow (Section The Connected Steady State Model).

How precisely blood-borne proteins overcome the blood brain barrier (BBB) and/or the blood-cerebrospinal fluid barrier (BCSFB) remains to be shown on the physiological level, see (de Vries et al., 1997; Damkier et al., 2013) and Section Discussion about the Diffusion Barriers. However, it has been shown that the concentration quotient (Q) of blood-derived proteins in CSF (concentration CSF/concentration serum) is dependent on the hydrodynamic radius R_H of the protein and is lower for proteins with a higher hydrodynamic radius (Felgenhauer, 1974).

This is best studied with immunoglobulins in reference to albumin. Felgenhauer and Reiber showed that the relation of CSF to serum quotients of albumin to immunoglobulins (IgX = IgG/-A/-M) can be fitted with a hyperbolic function with the general formula: (1)QIgX = abQAlb + b2−c Equation (1) is derived from Reiber and Felgenhauer (1987) and claims that the Q-value (cCSFcblood) of immunoglobulins can be expressed by the Q-value of albumin if the parameters a, b, and c are fitted correctly. Typically, the highly abundant protein albumin is chosen as the reference protein, but in principle all exclusively blood-derived proteins should be comparable by this method (Reiber and Felgenhauer, 1987). The hyperbolic function works well in the defined physiological range, but differently than stated by Reiber (1994a) this cannot have general validity since no combination of a, b, and c exists that can fulfill the Equation if one sets Q_IgX = Q_Alb (see also Appendix in Figure 5A).

The Reibergrams (Figure 1) with albumin as the reference protein are used to elucidate whether the occurrence of immunoglobulins in CSF is exclusively blood-derived or if there is additional contribution such as intrathecal immunoglobulin synthesis (Reiber and Felgenhauer, 1987). Values above the population-based determined upper hyperbolic function indicate inflammatory processes in the brain (Reiber and Peter, 2001).

In a follow-up study Reiber repeated the approach but with a considerably higher number of patients (4254 patients) (Reiber, 1994a). The high number of data points over a huge range of Q_Alb values allowed him to draw general conclusions. In short, with increasing Q_Alb the Q values of the considered immunoglobulins—IgG/-A/-M—also increase. Further, with increasing Q_Alb the absolute deviation of the mean hyperbolic function to the upper and lower discrimination line increases but the relative variation decreases or remains almost constant (see Table 1). Based on the high number of patient data this variation of Q_IgX to Q_Alb was termed population variation coefficient (Table 1).

At the same Q_Alb the specific Q_IgG/A/M/Q_Alb ratio is dependent on the difference in R_H of the bigger immunoglobulins to the smaller albumin (see Table 2). IgG has the least difference in size to albumin and IgM the highest; therefore, at the same Q_Alb, Q_IgG/Q_Alb > Q_IgA/Q_Alb > Q_IgM/Q_Alb (values listed in Figure 1). Reiber concluded that this R_H dependency and the relative constancy of the population variation coefficients support the concept of a diffusion-driven process.

For instance, if the variation of Q_IgX to Q_Alb were based on individual variance of non-diffusional immunoglobulin transport from blood to CSF, then the population variation coefficient would decrease considerably with higher Q_Alb values. This is because the total variation would remain unchanged and not the variation coefficient (Reiber, 1994a). So far we follow his assumptions but in contrast to him we want to emphasize that the Q_IgX/Q_Alb values increase with increasing Q_Alb (values in Figure 1). We further observed that the population variation coefficients of Q_IgA and Q_IgM decrease with increasing Q_Alb and that the extent of decrease seems to be dependent on the difference in R_H of IgX to albumin (Tables 1, 2).

Based on his observations, Reiber proposed a diffusion-based concept, the “molecular flux theory.” Although the basic ideas are intriguing and are fundamental for this work, the implementation contains several misconceptions leading to erroneous conclusions. He stated: “The steady state between molecular flux into CSF and CSF flow rate determines the CSF concentration of a single protein” and that the blood CSF system has the following boundary conditions “[…] diffusion in a semi-infinite media with constant concentration at one surface […]” (Reiber, 1994a). We concur with these assumptions, but surprisingly, he selected a nonlinear diffusion model without keeping the concentration constant at one boundary. The selected diffusion model with constant concentration c₀ at the blood facing boundary yields: (2)Q = c(x,t)c0 = erfc x2(Dt) In Equation (2) (Equation 2.45 in Crank, 1975), the constant concentration c₀ equates to the concentration in blood, c(x,t) equates to the respective concentration in CSF, −∞ < x ≤ 0 equates to the semi-infinite media (blood), the boundary is at x = 0 and CSF has values of x > 0, t = time and D is the diffusion constant. Erfc, the error function complement is a standard mathematical function described in Equation 2.11 by Crank (1975). The conditions selected by Reiber (1994a) and Equation 2.14 in Crank (1975) yield: (3)Q = c(x,t)c0 = 12 erfc x2Dt This has the consequence that the concentration at the boundary c(x = 0) = 12 C₀ for all t > 0. These boundary conditions do not meet the required conditions at the blood surface and this means that the concentration of a blood-derived molecule in CSF can never reach the blood concentration of this molecule. This in turn violates Fick's first law that postulates that a net diffusional flux exists as long as a concentration gradient exists. (4)J = −D∂c∂x Equation (4) is Fick's first law of diffusion; it postulates that the “diffusion flux” J is proportional to the concentration gradient (∂c∂x), where D is the diffusion coefficient, c the concentration of the diffusing substance and x the position. Another consequence of the selected model is that the molecular flux from blood into CSF increases with increasing c(CSF) as long as c(CSF) <0.5 c(blood). Reiber explained this increase in molecular flux with increased tissue concentration because of increased concentration in CSF (Reiber, 1994a). However, under the assumption of diffusional exchange between blood and CSF, the molecule concentration between both systems is a consequence of diffusion from blood to CSF and diffusion from CSF to blood.

The CSF system is separated from the blood by the cerebrospinal fluid barrier (BCSFB) at the site of the CP, the blood brain barrier (BBB) which makes up 99% of all brain capillaries (de Vries et al., 1997) and the blood-meningeal barrier (BMB, alternatively referred to as outer BCSFB) which separates the SAS from the perfused dura, the outermost meningeal layer. The brain capillaries and the blood vessels in the SAS are enclosed by endothelial cells closely tied by tight junctions with pore sizes of only up to 1 nm, therefore attributing main barrier functions closely to the vasculature (Nabeshima et al., 1975; Sarin, 2010). In contrast, the capillaries of the CP and partly in the dura are fenestrated, providing pore sizes of up to 12 nm; which is also the approximate diameter of the 800 kDa protein ferritin, and therefore allowing passage of proteins (Strazielle and Ghersi-Egea, 2013). The main barrier function is attributed to the CSF-facing side, by the arachnoid barrier cell layer in the BMB and the epithelial cells of the CP (CPE) in the BCSFB, both barriers are tightly sealed by tight junctions, revealing no obvious space for diffusional fluxes for molecules in the size range of proteins (Vandenabeele et al., 1996; Barshes et al., 2005; Damkier et al., 2013). In contrast to the other barrier structures, a transcellular passage is commonly observed at the CPE and is therefore seemingly the main exchange route between CP and CSF (Becker et al., 1967; Damkier et al., 2013). This questions the observed size dependency of blood-borne protein entry at this barrier site but possibly size differentiation occurs via a staggered mechanism of preceding barrier structures (see Figure 4). At the other barriers transcellular passage is commonly not observed which questions how proteins are able to diffuse from blood to CSF at all at these sites. More elaborate descriptions of the morphology and function of the barriers are given for instance in de Vries et al. (1997), Barshes et al. (2005), Redzic (2011), Damkier et al. (2013) and Strazielle and Ghersi-Egea (2013). For this work, it is sufficient to conclude that the physiological mechanism allowing diffusional exchange remains to be clarified.

Regarding the influence of the barriers the following physiological aspects have to be considered. The total volume of CSF ~150 ml divides into ventricle CSF ~25 ml and SAS ~125 ml (Sakka et al., 2011). At a CSF synthesis rate of 0.4 ml/min, this results in a mean residence time in the ventricle CSF of ~1 h and ~5 h in the SAS. Since beyond the ventricles, the CSF flow divides into the cranial and the spinal SAS flow and the volume flow in the spinal SAS is further reduced continuously by CSF outflow along spinal nerve roots (Pollay, 2010) reducing the bulk flow velocity to almost zero at the lumbar area (Greitz and Hannerz, 1996), the flow time in the SAS might be considerably longer than indicated by this calculation. Even so, the concentration of blood-derived proteins in ventricle CSF is almost half the concentration of lumbar CSF (Weisner and Bernhardt, 1978; Reiber, 2001; Table 3). A possible explanation might be that the barriers delineating CSF from blood have different properties (Figure 4). Intriguingly, the population variation coefficients (Table 1) first increase up to Q_Alb ~ 5 [10⁻³] and then decrease continuously. Potentially the impact of the presumably lower restrictive barrier of the BCSFB inside the ventricles is higher at lower Q_Alb-values because of shorter spinal flow time of CSF. However, at lower Q_Alb-values, the Q_IgG to Q_Alb values are lowest (Figure 1). This supports the general assumption that the barrier is more restrictive at low Q_Alb values. There might be a break-even point between the influence of the BCSFB and the other barriers. However, since we used the fitted hyperbolic functions (Table 1, Figure 1) as the representation of the experimental data, we are not aware how well the fit worked in the lower physiological Q_Alb range (see Appendix in Figures 5A,B).

It is noteworthy that different barrier permeabilities and/or bulk flow velocities of CSF along its course do not influence the outcome of the connected steady state model, since ͽ refers to the resulting mean barrier permeability in one individual and t to the resulting total flow time (see Equation 10).

Another possibility is that ventricle CSF is not only “young” CSF produced by the CP but also interstitial fluid from the highly perfused brain parenchyma, which already contains blood-derived proteins, see for instance Section 4.1 in Hladky and Barrand (2014) for a more detailed discussion.

The third possibility, an up-mixing of CSF from SAS back into the ventricles, is rather unlikely in normal physiological conditions and the diffusional fluxes are too low. However, most ventricle CSF samples described in the literature (summarized in Table 3) are derived from patients suffering from normal pressure hydrocephalus (NPH). In these patients retrograde flow has been observed (Penn et al., 2011). Possibly, the rostrocaudal gradient of blood-derived proteins tends to be less steep in NPH patients than in healthy individuals but this was not conclusive from the existing experimental data (see Table 3). Clearly, the discussed aspects need further experimental elucidation.

The rostrocaudal gradient of blood-derived proteins suggests that the CSF bulk flow is the dominant process in explaining protein abundancies in CSF. However, as the bidirectional pulsatile flow velocity of CSF is considerably greater than bulk flow of CSF, and the geometry of the spinal SAS does not precisely resemble a straight cylinder and contains obstacles to flow such as at nerve roots (Pahlavian et al., 2014), it is plausible to assume that the pulsatile flow has an impact on the rostrocaudal gradient although the flow is predominantly laminar. Further, it was shown previously that pulsatile flow characteristics of CSF in the spinal canal influence the dispersion of intrathecally delivered drugs (Hettiarachchi et al., 2011) and change with activity (Edsbagge et al., 2004). In a study comparing the rostrocaudal gradient of total protein concentrations between young adults and elderly people, a roughly twofold higher CSF production rate and a ~25% (non-significant) higher protein rostrocaudal gradient were found in the younger group. In contrast, the total protein concentration in the older group was significantly higher than in the younger group (~59 mg^*dl⁻¹ compared to ~46.8 mg^*dl⁻¹) (May et al., 1990). A possible explanation for this discrepancy—a higher total protein concentration in the older group but a higher rostrocaudal gradient in the younger group—is the pulsatile flow of CSF. The lower turnover in the older group increased the mixing rate concomitantly with a decreased rostrocaudal gradient. Possibly, the compliant reaction to cranial blood flow was also diminished in the older cohort and therefore the peak flow amplitude of the pulsating CSF was higher, enhancing the mixing of spinal CSF as well. In conclusion, the total protein concentration is influenced by CSF bulk flow but the spinal rostrocaudal gradient of blood-derived proteins is also influenced by pulsatile flow characteristics of CSF.

It would be interesting to see experiments investigating the rostrocaudal gradient of blood-derived proteins in diseases such as Chiari malformation in which the flow path is hindered and CSF pulsatility is increased (Haughton et al., 2003; Wagshul et al., 2011). It was further shown that in patients suffering from Chiari malformation, turbulent flow pattern occurs (Helgeland et al., 2014). These altered CSF flow characteristics should be detectable by a decreased or breakdown of the rostrocaudal gradient of blood-derived proteins. However, spatial distances between altered flow patterns and lumbar puncture must be taken into account.

The barrier between brain and CSF is considered to be leaky (Cserr, 1971), therefore uptake of brain proteins from the brain parenchyma into the CSF system might be dependent on diffusion and/or bulk flow; reviewed in Cserr (1971). This is also supported by various proteomic studies performed with lumbar CSF, showing that the lumbar proteome contains a CNS-derived fraction, for instance (Guldbrandsen et al., 2014; Zhang et al., 2015).

Further, the few clinically established brain-derived biomarkers measured in lumbar CSF such as S100B, amyloid-beta 42 or tau (Michetti et al., 1980; Blennow et al., 2001) indicate that brain-derived cranial protein uptake into CSF is reflected in lumbar CSF. Tracer studies suggest that the extent to which ISF is drained into the Cisterna magna (upstream of lumbar CSF) is different for different brain regions (Cserr et al., 1981; Szentistványi et al., 1984; Yamada et al., 1991). However, the intriguing question as to how well suited different brain areas are for readouts in lumbar CSF is beyond the scope of this work.

Here we simply state that the uptake of brain-derived substances in CSF is dependent on the exchange rate multiplied by the exchange time and therefore assume a dependency on CSF flow characteristics. Surprisingly, Reiber showed that brain-derived proteins do not correlate to Q_Alb in lumbar CSF which is used in CSF proteomics as an indicator of CSF flow characteristics. He suggested that the spatial limited uptake of brain-derived proteins into the CSF system is compensated by diffusional loss, as indicated by the distinctly higher ventricular than lumbar concentration of brain proteins (Reiber, 2001).

However, if increased uptake of brain-derived information is counterbalanced by diffusional loss, lumbar CSF-based diagnosis must be highly inaccurate. The extent of diffusion-out for brain proteins can be estimated by observing the diffusion rates of blood-derived proteins. The physiological normal Q_Alb in lumbar CSF is around 2–8 [10⁻³] meaning that only 0.2–0.8% of total albumin diffuses from serum into CSF. In conclusion, diffusional loss of brain proteins in the size range of albumin can be neglected but might be an aspect for small proteins or in CSF samples with very high Q_Alb values. Intriguingly the brain proteins Reiber presented, S100-B, Tau, NSE (gamma enolase), are all intracellular proteins (Reiber, 2001). Therefore, using Q_Alb as a reference protein might be biased since Q_Alb represents a different source (blood) and the uptake is dependent on cranial and spinal flow characteristics, whereas the uptake of brain-derived proteins predominantly takes place in the cranial space. Further, the reasons why these intracellular proteins are abundant in extracellular fluids is most likely independent of CSF flow characteristics.

These aspects and the fact that the Q_Alb represents not only CSF flow characteristics but also blood to CSF barrier characteristics might explain the lacking correlation of Q_Alb to the lumbar CSF concentrations of the investigated intracellular brain-derived proteins. Nevertheless, based on the expected common dependency to CSF flow characteristics we expect a certain degree of correlation between Q_Alb and brain-derived proteins if the sample size is sufficiently large.

Another important aspect is that under the assumption of bulk-flow (ventricular CSF mostly upstream and lumbar CSF mostly downstream) and diffusional loss being a very minor factor, the stoichiometry of the lateral ventricular to lumbar CSF protein concentration ratios for the investigated brain-derived proteins presented by Reiber (Table 3, 2nd column) and the general conclusion that brain-derived proteins are higher in ventricular than lumbar CSF is hard to explain (Reiber, 2001).

Net fluid introduction into the CSF system past the lateral ventricle CSF and therefore dilution to such an extent that brain-derived proteins are several times higher in lateral ventricle CSF than in lumbar CSF is unlikely considering the gross anatomic relations of the ventricular system; lateral ventricles make up ~80–90% of the ventricular system (Akdogan et al., 2010), and the corresponding ratio of blood-derived proteins (Table 3).

With an intelligent experimental design Brandner et al. showed that the high levels of brain-derived proteins in ventricular CSF compared to lumbar CSF is an effect of surgical interference (Brandner et al., 2013, 2014) releasing intracellular proteins in ventricular CSF and that the ventricular to lumbar CSF ratio is around 1 when the ventricular CSF withdrawal is performed sufficiently long after the traumatic surgery procedure (Table 3, 1st column).

These findings concur well with the assumption of bulk flow and the relative stable spinal protein concentration of brain-derived proteins along the rostrocaudal axis (Table 3).

Again, based on the limited sample and study numbers, the discussed aspects need further experimental elucidation.

In our view, the assumed dependency of brain-derived proteins on CSF flow characteristics introducing non-pathological individual variances questions the dominating biomarker discovery strategy based on the comparison of absolute concentration differences. We claim that the diagnostic accuracy can be improved by evaluating relative concentration values with suitable reference proteins similar to the approach used for blood-derived proteins. This aspect is presumed to be of special importance for early diagnosis purposes when subtle concentration changes of diseased to non-diseased individuals can be expected.

The connected steady state model offers a solution for barrier-restricted diffusion between a continuous regenerating fluid system such as blood, and a river-like start/end system such as CSF. The model might have the potential to be a general solution concept for diffusional exchange of blood to other body fluids such as blood to the urine or lymph. The model fits perfectly to the available experimental data and is able to explain all the experimental findings. For our considerations we used experimental data already interpreted with the hyperbolic function (Reiber, 1994a). This might be an issue when interpreting the contradictory results at low Q_Alb values (see Section Discussion about the diffusion barriers and Appendix Figure 5A). So far we have described the diffusion through the barrier with a hydrodynamic radius-dependent factor and ignored other aspects such as biochemical properties of the proteins. This might be sufficient for soluble blood proteins but not for lipophilic substances. The availability of more experimental data and a more precise physiological understanding of how diffusion occurs will help to clarify these issues.

The source-related rostrocaudal gradient of proteins in CSF and the possibility to link the rostrocaudal gradient of blood-derived proteins to pulsatile flow characteristics are highly intriguing and so far underestimated aspects in CSF physiology but worthy of being investigated in more detail in the near future.

In spite of the enormous diagnostic potential of brain-derived proteins in CSF, their dependency on CSF flow characteristics is not sufficiently clarified. We assume that a better understanding and a better implementation of CSF dynamics in biomarker discovery approaches is the way toward the development of optimized analyzing strategies of the CSF-Proteome consequently leading to the identification of more sensitive and reliable brain-derived biomarkers.

FM designed the study, was involved in all tasks and wrote the paper. DM contributed to the physical aspects of the study and to the discussion of the mathematical aspects of the study (Appendix A1). FS carried out the mathematical implementation of the model (Appendix A1) and contributed to the discussion of the physical aspects of the study.