Background
Infusion testing is a standard procedure to assess whether patients with normal pressure hydrocephalus (a type of dementia) would benefit from shunt surgery. During infusion of artificial cerebrospinal fluid (CSF), intracranial pressure (ICP) is monitored, and a CSF outflow resistance (
\(R_{\text {out}}\)) is calculated. Typically, a constant infusion rate of 1.5 mL/min results in an ICP increase by around 10–25 mmHg, and the calculated
\(R_{\text {out}}\) parameter is commonly used as a supplementary parameter in the selection of patients for shunt surgery [
1]. The procedure has a well developed theoretical foundation as well as corresponding mathematical models (see [
2] for an overview). The main outflow route is assumed to be the arachnoid granulations (AG) [
3] in accordance with the traditional view of the third circulation where CSF is produced in the choroid plexus and absorbed through AG as described by Cushing in 1925 [
4].
More recently, an alternative CSF circulation has been proposed—the glymphatic circulation. Here, paravascular spaces (PVS), extensions of the Virchow–Robin spaces, play an active role in a brain-wide CSF circulation in conduits that run in parallel with the vasculature. The purpose of this circulation is to clear solutes from deep inside the brain, thus taking the role of the lymphatic system within the central nervous system which is absence of lymphatic vessels. Therefore, this waste clearance system has been named the glymphatic system [
5], where the “g” indicates that glial cells play an important role. Glymphatic dysfunction has been hypothesized to contribute to development in neurodegenerative disorders, traumatic brain injury and stroke [
5]. In the glymphatic circulation, CSF moves through the subarachnoid space (SAS) along arteries and dives into the brain along arterial PVS. The glymphatic pathway enters the extracellular space (ECS) through AQP-4 channels or inter-endfeet gaps, and from there eventually reaches the venous PVS.
Most of the evidence for the glymphatic pathway has been established via in-vivo rodent experiments. In these experiments, tracers are typically infused in the CSF in rodents at a rate of
\(0.34{-}2 \, \upmu \text {L/min}\), with a resulting pressure increase of 0.1–2.5 mmHg [
6‐
8]. Even though CSF turnover time differs between mice and men [
9], an infusion rate of 1.5 mL/min and a total CSF volume up to 350 mL in humans [
10], and in some cases possibly as low as 100 mL [
9] is comparable to an infusion rate of
\(\approx 0.15 \, \upmu \text {L/min}\) and a total CSF volume of
\(35 \, \upmu \text {L}\) in mice [
9]. Thus, such tracer experiments may in fact be viewed as infusion tests. This potential link, between infusion tests and the glymphatic system, has not yet been explored.
Recently, the resistance of the glymphatic system under normal conditions was estimated by Faghih and Sharp [
11]. They concluded that the glymphatic circulation was unlikely, as the high resistance of the pathway would prevent sufficient flow. In their model, the resistance of the paraarterial tree was relatively low before reaching the precapillary level where the gap size of the PVS was set to 100 nm in accordance with a study of Bedussi et al. [
7]. The narrow PVS at the capillary level effectively blocked the circulation. However, other studies suggest flow within the paravascular spaces at the level of capillaries [
12,
13]. Furthermore, it has been argued that fixation, which was used by Bedussi et al. [
7], shrinks the PVS [
8]. As such, the resistance of the PVS at the capillary level should be further investigated and compared to the low permeability in the ECS of the brain parenchyma [
14‐
16].
There is also compelling evidence of flow directly from the SAS to the lymphatic system. In earlier works, Bradbury et al. [
17] reported that at least 30% of CSF drains to cervical lymphatics. More recently, Ma et al. suggest that lymphatic outflow is responsible for the main portion of CSF leaving the SAS [
18], and that flow through the cribriform plate dominates the paravascular flow route when total CSF efflux is large [
19]. In sheep it has been reported that outflow through the cribriform plate plays a major role in CSF absorption, whereas the importance of the AG is unclear [
20].
Within the brain parenchyma, the Bulat-Klarica-Orešković hypothesis states that production and absorption of CSF mainly occurs over the capillary wall due to its large surface area [
21]. Other CSF outflow routes have also been proposed [
22,
23], however, a quantification of the fluid distribution and interplay between each outflow pathway is yet to be properly addressed. In particular, resistance of flow from the paraarterial space through the ECS and/or along capillaries in the setting of infusion tests (i.e. under temporarily elevated pressure) has not yet been investigated. We note that lumbar intrathecal contrast delivery during infusion to assess glymphatic function in humans was proposed in Yang et al. [
24]. Further, as suggested by Ma et al. [
19] increased flow, and a possible change in ICP, may alter the distribution of CSF to different outflow pathways. In addition, if the glymphatic circulation is a main outflow route for CSF, the outflow resistance
\(R_{\text {out}}\) is a direct measure of glymphatic dysfunction, which in turn has been linked to neurodegenerative disorders [
5].
On this background, the aim of this work was to quantify different CSF outflow routes in the setting of an infusion test in supine position. To do so, we first gathered and summarized available resistances of the more probable outflow pathways including the AG, the cribriform plate, the arterial and venous PVS, and CSF drainage/filtration over the capillary wall. We next estimated resistances in the missing segments, i.e. the capillary gaps, the inter-endfeet (IEG) and the ECS. With these resistances, we extended a well-established mathematical infusion model to include additional pathways and then assessed the relative importance of the different outflow routes at baseline ICP and during infusion of fluid into the CSF system. We modeled an infusion test to explore potential changes in CSF outflow routes with the rising pressure. The relative importance of each outflow route was found to change with increasing ICP, although clearance through AG was dominant both at baseline and (elevated) plateau ICP. At baseline, flow in PVS was slow, with an average velocity of \(0.18 \, \upmu \text {m/s}\) from the PVS into the SAS due to capillary filtration. During the infusion, PVS velocities decreased, and eventually stagnated.
Discussion
In this work, we computed CSF resistance, pressure and outflow both during resting state and during infusion. The mathematical model extended the traditional infusion modeling with pathways related to the glymphatic system. In addition, we calculated PVS pressure, flow and average velocity in both states. Model 1, 3, 4, and 6 all gave reasonable ICP both at rest and during constant infusion of fluid at a rate of 1.5 mL/min. Model 2 and 7, which involved significant flow in the PVS, did not result in the expected ICP increase during infusion. On the other hand, model 5 eliminated AG flow and caused unphysiologically high pressures. The best match between the traditional reference model and the proposed model was achieved with the full model (model 1), but the model with constant capillary filtration (model 3) also showed good agreement in ICP for both baseline and plateau levels.
Our estimate of resistance along the capillary gaps was on the same order of magnitude as resistances to other outflow routes such as the cribriform plate and arachnoid granulations as measured by others [
55,
56,
64]. However, the resistance in the capillary gaps was about 30 times greater than the resistance in the paraarterial tree used in our model, the latter based on estimations by Faghih and Sharp [
11]. In particular, such an increase in resistance on the capillary level renders flow along capillary PVS unlikely. In our case, a reasonable flow rate would require a pressure drop of 4.19 mmHg. Such flow must rely on local ICP differences in the SAS, and would be expected to induce flow directly along the SAS rather than through the possibly high-resistant glymphatic system. In addition, pressure gradients in the SAS are likely less than 3 mmHg/m [
81,
82], and the transmantle pressure difference has been estimated to be no more than 0.03 mmHg [
80]. Glymphatic circulation driven by local differences in pulsatile pressure of several mmHg also seems implausible, as the ICP wave is almost synchronous throughout the brain [
83]. Maximal estimated pulsatile pressure differences in the brain have been reported at no more than 0.2 mmHg [
84], and a net driving force would be expected to be even lower.
In contrast to flow along the capillary gaps, resistance in the ECS was found to be surprisingly low at 0.57 mmHg/(mL/min), approximately half the resistance of that reported in arterial PVS by Faghih and Sharp [
11]. The inclusion of IEG increased resistance with a factor 3 to yield a resistance of only 1.78 mmHg. Including PVS, the resistance increase to nearly 3 mmHg/(mL/min), and a pressure difference of 1 mmHg would thus have the potential to drive flow comparable to CSF production through the glymphatic circulation. To this end, we found a direct communication between the glymphatic circulation and cervical lymphatics unlikely. If the counter pressure at the level of cervical lymphatics stays relatively stable during infusion, an ICP increase of several mmHg is not possible as all infused CSF will exit with low resistance through the glymphatic circulation to cervical lymphatics.
Ma et al. [
19] suggest that outflow through the cribriform plate dominate, but only when the total outflow from the SAS is large. We also found the relative distribution of flow to the different outflow pathways to be affected by infusion, but there are important differences. In contrast to Ma et al. [
19], we found the AG to become even more important at high outflow rates (i.e. at higher infusion rates and high ICP). With the full model, at baseline ICP, AG flow was 50% greater than flow through the cribriform plate, and fourfold greater at plateau ICP. AG flow was greater than or equal to flow through the cribriform plate in all cases in all models except for models 2, 5 and 7, which were all models not able to predict the expected increase in ICP during the infusion test. Flow in PVS has been assessed under both awake and anaesthetized conditions. While we did not address this question, there is conflicting evidence whether PVS flow increases or decreases during sleep or anesthesia [
19,
85,
86]. To what extent pressure, outflow resistances, or CSF production cause changes between different states is not well understood.
Net capillary flow in our model was always directed from the capillaries to the PVS. Thus, under normal conditions, the capillaries functioned as a site of CSF production. This suggests net fluid movement from the PVS into the SAS in the framework of a circular glymphatic system. In models we tested where pressure exceeded 20 mmHg, the capillaries ceased net filtration. It is interesting to note that this pressure threshold of above 20 mmHg is close to the value for which
\(R_{\text {out}}\) becomes pressure dependent as measured experimentally [
39]. Capillary flow rates were relatively small, up to 0.16 mL/min when a constant flow was assumed (model 3), and less than 0.1 mL/min when the flow was modelled. Capillaries functioning as a route of absorption and filtration of CSF is in line with the Bulat-Klarica-Orešković hypothesis [
21]. However, it should be noted that passage of substances such as proteins and electrolytes is difficult across the blood–brain barrier as compared to water [
87]. The routes of CSF/water clearance (CSF is 99% water [
21]) do not necessarily align perfectly with the routes of clearance of other substances from the brain. We finally note that our estimation of capillary resistance is one order of magnitude lower than what has been estimated by Koch [
88].
The average PVS velocity in the full model was
\(0.18 \, \upmu \text {m/s}\) out from the PVS into the SAS at baseline and no flow occurred at plateau ICP. The maximal recorded PVS velocity was computed to be
\(7.46 \, \upmu \text {m/s}\), during infusion in model 7, in which almost all infused and produced CSF went through PVS. In the experimental studies, several investigators used an infusion rate of
\(2 \, \upmu \text {L/min}\) in rodents [
6,
8,
29], which was shown to increase ICP by 2.5 mmHg [
6], a substantial increase, but less than in our model of a human with an infusion rate of 1.5 mL/min. In addition, Bedussi et al. [
7], used a much lower infusion rate of
\(0.34 \, \upmu \text {L/min}\), only resulting in a pressure rise of 0.1 mmHg. Still, the net PVS velocity of
\(17 \, \upmu \text {m/s}\) found with this low increase in ICP is almost identical to the typical flow speed of
\(18.7 \, \upmu \text {m/s}\) found by Mestre et al. [
8] at the infusion rate of
\(2 \, \upmu \text {L/min}\), suggesting elevated ICP is not the sole reason for PVS flow. It should be noted that both Bedussi et al. [
7], and Mestre et al. [
8] consider PVS at the brain surface. All observed CSF flowing in these spaces does not necessarily need to follow PVS into the brain, but could also be drained to other outflow pathways. Thus, increased AG or cribriform plate flow during infusion in our model could very well be in accordance with increased velocities around arteries on the brain surface.
Our findings suggest that average velocities up to
\(20 \, \upmu \text {m/s}\) are unlikely around penetrating arteries in the parenchyma of the human brain as the corresponding flow rate in all PVS combined would be threefold greater than the CSF production rate and the infusion rate combined. It should be noted that our model applies to humans, while the experimental findings [
7,
8] concern rodents. Even if the infusion rate is scaled with CSF volume of the species, the mouse ICP could be expected to change less because CSF turnover time is
\(\approx 3\) times shorter in mice than in humans [
9]. In addition, a shorter turnover time may also suggest higher velocities related to drainage of CSF in mice.
The current study gives new insight to the relation between ICP and CSF clearance. This is not only highly relevant to the glymphatic theory, but also to understand pathological conditions related to increased ICP. Patients with increased ICP often exhibit clinical visual symptoms, which are also typical in idiopathic intracranial hypertension (IIH) and in astronauts suffering from Spaceflight Associated Neuro-ocular Syndrome (SANS) [
89].
Limitations
Resistance parameters in our model were taken from many different species and types of experiments. Ideally, resistance in each outflow pathway could be measured experimentally by blocking one outflow pathway, and measuring the resulting increase in pressure. To our knowledge, this has not been done in humans and it is likely challenging both from a technical and ethical perspective. Specifically, the exact size of capillary and inter-endfeet gaps for CSF/ISF flow would provide answers to whether a circular glymphatic system is plausible. The current data suggest a resistance of 32.24 mmHg/(mL/min) to flow along the capillary gaps, while increasing the gap radius reduces this resistance with several orders of magnitude. In addition, more data on what happens at the venous side of the glymphatic system (e.g. whether PVS form a route directly to cervical lymphatics or a return to the SAS, the magnitude of the potential counter pressure at cervical lymphatics etc.) would increase the robustness of the model presented. Thus, the finding of a low resistance pathway through from PVSa-ECS-PVSv was crucial for disproving a glymphatic pathway with drainage through pial sleeves to cervical lymphatics. An approximately fifteen times increase in resistance would render a PVSa-ECS-PVSv flow in balance with AG flow and accordingly both give a relevant glymphatic pathway and a total outflow resistance that are in agreement with pressure increases seen in typical infusion tests. This emphasizes the importance of additional experimental research to investigate these critical resistances. Although our model well describes the time-evolution of the CSF pressure in the SAS during infusion test, additional experimental data may further allow for detailed dynamic response of pressure in the other compartments shown in Fig.
1, such as e.g. the ECS.
Our model did not include the effect of cardiac or respiratory pulsatility. Pulsations in the arterial, venous and CSF compartments have all been proposed to drive glymphatic clearance [
6‐
8]. Indeed, the cardiac pulsation on the arterial side seems related to the PVS pulsatile movement as shown in Mestre et al. [
8], but modeling attempts deem it unlikely that arterial wall movements alone drive a net flow of sufficient magnitude for clearance of fluid [
16,
54]. In addition, when ignoring pulsatility, the large inflow of blood on the arterial side during systole will not affect the compliance of the system. Adding pulsatility to the presented linear compartment model would not change the average distribution of flow rates to the different compartments. A valve-like mechanism could be modeled by assuming the PVS resistance to be different in the two directions. However, at present no such valves have been identified [
90].
According to Tithof et al. [
91], PVS are not concentric cylinders, but rather form ellipses around vessels to minimize resistance. This geometrical change along all vessels may decrease resistance by a factor of 2–3 [
91], and thus likely increase PVS velocities by a similar factor in some of our models. In addition, peak velocity in a concentric cylinder is double that of the mean velocity, which possibly may increase our velocity estimates in some of the models by another factor of approximately two.
In the current study we only consider supine position and thereby we neglect hydrostatic effects [
61,
92]. This simplification justifies the representation of a single compliance for the craniospinal space and allows us to lump spinal absorption into the AGs [
28]. Spinal absorption is believed to increase in upright posture due to hydrostatic effects [
60,
92]. Including spinal arachnoid villi in the AG resistance would reduce the magnitude of this parameter approximately by 20% [
58‐
60]. This will not change our conclusions from the model, and if anything it will make AG even more important in terms of total outflow.
A single craniospinal compliance assigns all compliance to the SAS. However, for transient analysis, a compliance distributed between the physiological units including the SAS and adjacent compartments could be more appropriate. In this latter case, quantification of the separate compartment compliances would be needed. Further, in this study, we have not accounted for spatial variations, but rather assumed a compartment model in which the pressures are functions of time only. We note that ICP has been shown to be nearly constant in space [
83], whilst the blood flow pulse propagation has been reported to show spatial directionality [
93,
94].
Capillary filtration is regulated by osmotic gradients [
21,
23] and cotransporting proteins [
76], which were not considered in our study. The effective capillary pressure was assumed constant in time for
\(p_1 < p_{\mathrm{cap}}\), for higher PVS pressure the capillary filtration ceased and
\(p_{\mathrm{cap}}\) was set equal to
\(p_1\). Whether the capillary pressure always stays above ICP regardless of ICP increase is not well known. In model 3, we ensured that a pressure independent constant filtration model (and also alterations in the magnitude of filtration) yielded reasonable results. A constant filtration over the blood–brain barrier is only possible if we allow a flux of solutes, while in the current study we have not computed ion permeabilities and solute fluxes across the blood–brain barrier.
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