Introduction
Severe ocular conditions such as glaucoma and papilledema have been related to abnormal flows and pressures in the cerebrospinal fluid (CSF) within the optic nerve subarachnoid space (ONSAS) [
1‐
5]. The CSF dynamics of the ONSAS are not fully understood, but the CSF communicates between the ONSAS and the intracranial subarachnoid space (SAS), and evidence suggest that CSF is absorbed along the ONSAS through the optic nerve sheath (ONS) to reach the lymphatic system [
6‐
8], providing a CSF absorption route and a possible outlet for waste products [
8]. Thus, disturbances in the local flow and pressure dynamics of the ONSAS may contribute to disorders related to both the eye and the brain. Due to the small size and sensitive anatomical location of the ONSAS, it is difficult to perform in vivo pressure and flow measurements in this compartment. Therefore, mathematical models provide an attractive tool for investigating the ONSAS dynamics by predicting the flow and pressure numerically, based on available in vivo data.
Most mathematical models and clinical fluid dynamic investigations of the ONSAS mainly reflect horizontal body positions and in special cases head-down tilt [
1,
2,
9‐
14], not including upright postures. As craniospinal CSF pressures and volumes change between different postures due to gravity [
15‐
17], the pressure and flow in the ONSAS are altered in upright postures compared to horizontal postures. Based on MRI data of the ONSAS, we previously predicted a potential compartmentalization of the ONSAS in the upright posture, hindering flow and pressure transmittance between the eye and brain [
18], possibly protecting the eye from low CSF pressures. However, the predictive model used in this previous study did not include the effects of the complex system of microstructures occupying the ONSAS [
19]. The ONSAS is traversed by trabeculae, pillars, and septae, which connect the pia around the optic nerve to the arachnoid membrane [
20,
21] and may therefore affect flow and pressure in the ONSAS. Kaskar et al. modelled the CSF circulation in the cranial SAS and ONSAS in the supine position and found that the resistance to flow through the ONSAS was heavily dependent on the density of these microstructures [
9]. Moreover, they concluded that the ONSAS pressure was highly sensitive to the ONSAS resistance. To fully investigate the ONSAS dynamics, these effects should be included in the predictive modelling.
Furthermore, the findings of a possible glymphatic system for the eye, with CSF entering the ONSAS from the intraocular side and then passing through the optic nerve sheath [
8,
22], provide an additional fluid dynamic component that may affect the ONSAS pressure and flows. Investigating the effects of such a pathway in both horizontal and upright postures could contribute valuable insight into ocular glymphatic function and its driving pressure gradients.
Thus, the aim of the current study was to apply mathematical modelling to investigate how ONSAS microstructures affect ONSAS pressure and flow during a change from supine to an upright body posture, thereby further evaluating the previously suggested postural compartmentalization of the ONSAS. A secondary aim was to investigate how these flows and pressures would align with an ocular glymphatic flow pathway. This manuscript will describe the model implementation and showcase results of predicted flows and pressures for the ONSAS, including both temporal changes and steady state levels.
Discussion
To date, the ONSAS pressure and flow alterations between horizontal and upright body postures remain essentially unexplored. Based on existing mathematical models, we developed a new model that allows for prediction of the ONSAS dynamics as a function of body posture including the effects of the microstructures occupying the ONSAS. As the ONSAS is part of the CSF system, a crucial aspect of the model is the interaction between the ONSAS and the craniospinal SAS. This interaction was affected by the content of the ONSAS, possibly allowing for a compartmentalization of the ONSAS in upright postures that introduces significant alterations in steady state ONSAS pressures. The intraocular glymphatic flow increased in upright compared to the supine position, but the flow was redirected from the ONS towards the cranial SAS. Sustaining the glymphatic flow did not require any larger changes in ONSAS pressure even for relatively large intraocular-CSF flows in any body posture.
In clinical studies, the ICP is often used as a surrogate for the ONSAS pressure (
\({p}_{ONSAS}\)) when estimating potential pressure disturbances between the eye and brain [
59‐
61]. Furthermore, the size of the ONSAS posterior to the globe has for some years been investigated as a potential non-invasive indicator of ICP made accessible by ultrasound or MRI [
62,
63]. These investigations are based on the assumption of a fully communicating ONSAS and a negligible flow resistance along this pathway. While these assumptions may hold under certain circumstances, e.g., in horizontal body postures (in healthy subjects) or for elevated pressures, they may not hold for all situations. Furthermore, the postural dependency of ICP is often completely overlooked, as the ICP is seldom assessed in upright body postures [
51,
58]. Our results open for the possibility that
\({p}_{{c}_{LC}}\) and
\({p}_{ONSAS}\) are not always the same in upright postures, as even the prediction using Poiseuille flow estimated a small (1 mmHg) difference between the two pressures (Fig.
3). The dependency on ONSAS porosity could mean that differences in porosity, e.g., between different persons or groups of people, could lead to different pressures and flows in the ONSAS (Fig.
5). The model results indicate that a baseline porosity of 0.9 is needed for the
\({p}_{ONSAS}\) to mimic midbrain ICP (the common reference for CSF pressure), although the temporal behavior of these pressures differ somewhat (Fig.
5). Thus, if the baseline porosity lies somewhere close to 0.9, midbrain ICP may be a reasonable surrogate for the ONSAS pressure even in upright postures.
One main assumption in our default model [
18] is that we extrapolate the distensibility results from 13 to 90 degrees. Imposing a lower limit on the calculated porosity is a way to remedy this, and to investigate the effects of this assumption (Fig.
7). The results show that the limit must be low (roughly 0.1) to uphold a pressure above
\({p}_{{c}_{LC}}\) indefinitely, while a limit in between 0.3 and 0.1 may keep the pressure elevated in between one to several hours. Both these options would require a high flow resistance and a low flow in the ONSAS. CT contrast infusions [
64] in porcine models has indicated a limited and posture (or gravity) dependent filling of the ONSAS, and could support a limited flow rate in upright postures. If the minimum porosity is higher than 0.3, we can expect relatively quick changes in ONSAS pressure (roughly less than 30 min–1 h to reach
\({p}_{{c}_{LC}}\)). Another result of imposing a lower limit on the porosity is that the size of the ONSAS keeps decreasing closer to the bulbar region all the way to the 90-degree upright posture, something that is prevented if “complete” compartmentalization occurs. Thus, a larger change in the bulbar ONSAS size may indicate a lack of compartmentalization and a transfer of lower pressures to the back of the eye, or, alternatively, an increased distensibility of the optic nerve sheath.
In the supine position, our simulations predicted a
\({p}_{ONSAS}\) equal to the ICP at the level of the
\(LC\) (that is,
\({p}_{{c}_{LC}}\)) or slightly lower (Fig.
5). While data are sparse, measurements in animals have shown horizontal
\({p}_{ONSAS}\) values similar to
\({p}_{{c}_{LC}}\) [
65] or values a few mmHg lower [
66], and measurements in cadavers yielded a
\({p}_{ONSAS}\) in the range of 0–6 mmHg [
67]. While the latter may not represent the physiological situation, the animal studies support that non-fluid content within the ONSAS may contribute to a non-negligible resistance already in horizontal positions. Thus, a decreased ONSAS porosity leads to a decreased ONSAS pressure in supine position, but also to an increased ONSAS pressure in upright postures, diminishing the postural effect on the ONSAS pressure in two different ways (Fig.
5).
Our model can be compared to the work by Kaskar et al. who modeled the CSF system in the supine position. Based on the pressure measurements in the cadavers [
67], their model predicted an ONSAS resistance of 200–241 mmHg/(mL/min) and an ONS absorption of 5–10% of the total CSF outflow [
9]. Their outflow rates are high compared to ours (roughly 5–10% vs. 0.5–0.6%), which may indicate that our
\({R}_{ou{t}_{ONS}}\) was overestimated. Decreasing our
\({R}_{ou{t}_{ONS}}\) by a factor of 10 would yield a lowered supine
\({p}_{ONSAS}\) since the flow rate would then increase, but only for a porosity of 0.75 would the change be larger than 1 mmHg (1.2 mmHg for 0.75, 0.36 mmHg for 0.85, and < 0.15 mmHg for the rest). Since
\({p}_{ONSAS}\) quickly dropped below the intra-orbital pressure during the posture change, stopping any ONS absorption, any error in
\({R}_{ou{t}_{ONS}}\) will have a limited effect on the dynamic changes during the alteration in posture (Fig.
5). A limitation of the Kaskar model is that the ONS absorption is set as a constant and is not pressure-driven, i.e., it is independent of factors such as the intra-orbital pressure and does not explicitly include any resistance to absorption across the ONS. Because
\({p}_{ONSAS}\) is affected by both
\({R}_{ONSAS}\) and
\({R}_{ou{t}_{ONS}}\), our model does allow for analyses of these contributions separately (in addition to their postural dependency).
Clinical applications
The ONSAS dynamics are believed to relate to ocular disorders through the trans-lamina cribrosa pressure difference, i.e., the difference between intraocular pressure and ONSAS pressure. A relevant example is normal tension glaucoma where a low ICP has been suspected as a contributing factor to the development of the disorder [
5,
59,
68,
69]. Understanding the link between ICP and the pressure within the ONSAS is crucial to accurately interpret findings related to this pressure difference, especially since the trans-LC pressure difference is often just calculated as IOP-ICP, which likely does not hold for all postures (Figs.
3,
5). For example, a lack of compartmentalization could allow for lower pressures to reach the posterior eye in upright postures, thus increasing the pressure difference despite normal IOP and ICP [
70]. The ONSAS dynamics may also be disturbed in other ways. For example, there is evidence of a hindered ONSAS flow both in patients with normal-tension glaucoma [
1,
71] and those with papilledema [
2] in horizontal positions, which could mean that the ONSAS resistance is instead increased in these patients.
Posture, and thus gravitational effects, is also of importance for understanding the spaceflight associated neuro-ocular syndrome, a syndrome where astronauts lose their visual acuity after extended visits in microgravity [
72]. An abnormal ICP (and by extension an abnormal ONSAS pressure) is one suggested hypothesis [
51,
73,
74] and compartmentalization of the ONSAS another [
72,
73]. The pressure behaviour as studied with our model may contribute valuable reference data for comparison to the microgravity state. While ICP measurements during long-duration spaceflight are non-existent, measurements in acute microgravity suggest a decrease in both ICP and CVP by roughly 3–4 mmHg [
74]. By removing gravitational effects and lowering the CVP accordingly (3.5 mmHg), our model predicts an ONSAS pressure of 7.7 mmHg in microgravity. This is slightly larger than the supine baseline value of 7.35 mmHg. This happens because the hydrostatic difference between the LC and the auditory meatus disappears in microgravity, and this hydrostatic effect is slightly larger than the microgravity-induced change in CVP/ICP. Furthermore, microgravity removes the normal lowering of ICP that occurs in upright postures on earth, resulting in an, on average, higher ICP in microgravity (assuming 16 h per day are spent upright). The difference in this average will depend on the porosity of the microstructures, where a denser (low porosity) ONSAS will lead to a smaller postural effect on the ONSAS pressure on earth.
The extended model could potentially be used for understanding the clearance of eye metabolites, through the ocular glymphatic system [
75] of the ONSAS pathway [
8]. Assessing local pressure gradients that drive the fluid flow will be essential for increasing our understanding of this clearance system. The sensitivity analysis of the LC flow resistance (Table
4) revealed that flow from the intraocular system could be quite substantial (even up to 24%) without requiring any larger (< 1 mmHg) changes in the ONSAS pressure, despite the high resistance pathway of the ONSAS in the upright posture. As shown by Wang et al. [
8], the flow through the posterior of the eye to the ONSAS depends on the
\(IOP-{p}_{ONSAS}\) pressure difference (by design in our model). This suggests that flow from the intraocular system increases in upright postures. This is in contrast to glymphatic function in general, which has been shown to be increased during sleep (when we are horizontal) [
76]. Our model does predict that clearance across the ONS mainly occurs in supine (horizontal) positions however, while in upright positions the flow is directed to the rest of the SAS, suggesting different pathways for the two postures. Thus, intraocular fluid is absorbed in supine while it contributes to CSF production in upright. If absorption across the ONS still occurs in upright postures, it would likely indicate that the counter pressure to this absorption, i.e., the intraorbital pressure, must change in a similar fashion as
\({p}_{ONSAS}\). However, we consider this unlikely as the intraorbital pressure can be suspected to remain fairly constant. An alternative is that some other pressure constitutes the counter pressure to this absorption.
Finally, additional CSF compartments can subsequently be added to the current model, moving towards a more complete description of the CSF dynamics and glymphatic functions. As CSF dynamics do vary with body position, including the effects of posture in such models are likely essential. Additional outflow/absorption routes related to the glymphatic system could be included. However, this should not affect the dynamics investigated in this study as absorption in our model is based on the total outflow resistance \({R}_{out}\).
Limitations
We extrapolated the distensibility values from 13 degrees head-up tilt (maximum achievable in our scanner) to 90 degrees head-up tilt. Imaging in sitting MRIs could contribute important data here, however, in this study, this limitation was instead addressed by the porosity limitation analysis. We did not include any pulsations in this study, including general CSF pulsations as well as local arterial pulsations in the optic nerve and ONS, which may contribute to the mixing and distribution of CSF between the ONSAS and cranial SAS. The relative contribution from the spinal and cranial compartments to CSF compliance has been debated, where some estimations indicate a larger spinal contribution compared to the cranial contribution [
17,
77]. Changing this parameter in this way will lower ICP slightly, exacerbating the effect of the compartmentalization. However, this will increase the postural shift in volume to values much higher than that measured in vivo, as opposed to the current setup, suggesting that our choice recreates the in vivo situation satisfactorily. Only CSF absorption to venous blood was included for the craniospinal CSF compartments despite lymphatic outflow existing for these compartments as well [
78,
79]. Since accurate postural craniospinal CSF pressures and volume changes were achieved with the current model, they were deemed sufficient for the specific application of the current study (where we focus on the ONSAS), but these other flow pathways need to be added to study for example general glymphatic flow throughout the brain. There is a lack of studies of ocular glymphatics in the upright posture to validate our glymphatics flow predictions. While our model can predict the outcome of different scenarios, more work in this area is needed to validate these predictions and for further improving the model.
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