This indicates that there is a constant production of a "new" ISF in the brain which contributes to total volume of the CSF. This process is essential for maintaining correct fluid balance in the brain. As in other tissues, the activity of this enzyme is tightly associated with cell volume regulation [ ]. In addition, rat brain endothelial cells express Kv1 and Kir2 potassium channels; these are probably located on both the luminal and abluminal sides of the BECs [ ] Figure 5A.
However, the CSF recovered from the brain, contains 2. It has been shown that following in vitro loading of BECs with small acid load, HCO 3 - influx was mainly responsible for the acid extrusion and it was mediated partially by Cl - dependent HCO 3 - transporters.
Ion transporters in the CPs have been studied intensively because ion transport across the CPE drives CSF secretion, which could be considered as the most apparent and the most important function of CPs. CSF has a number of important roles in brain homeostasis, including reduction of the effective weight of the brain by being submerged in CSF, removal of waste products of metabolism, removing excess neurotransmitters and debris from the surface lining epithelium and delivering signalling molecules for a review of CSF functions see [ ].
Bicarbonate transport by the CPE directly affects the pH of CSF, which in turn affects neuronal activity in the respiratory centre in the medulla oblongata. Overall, two main processes are driven by ion transporters in the CP. First, the transepithelial basolateral-to-CSF movement of sodium, bicarbonate and chloride creates a small osmotic force driving net movement of water in the same direction.
Water movement across the CPE is via aquaporin 1, the waater channel which is abundantly expressed in the apical membrane and less so in the basolateral membrane Figure 5B. This water channel is typical for epithelia that have a high rate of water transfer generated by a small osmotic gradient. Second, CSF to basolateral movement of potassium takes place [ , ]. Two major anions, Cl - and HCO 3 - also pass the CPE layer via a transcellular route; the CSF concentrations of both Cl - and HCO 3 - are less than predicted for simple diffusion, which suggests that the paracellular route contributes negligibly to the overall transfer.
Mice that had this transporter genetically removed had severe reduction in brain ventricle size, which suggested that the rate of CSF secretion was decreased [ ]. Transport of these ions through the apical membrane to the CSF involves several proteins. This channel Clir plays some role in apical HCO 3 - extrusion in mammals, but permeability of this channel for HCO 3 - appears to be small.
Studies of the past two decades have provided insight into the molecular biology which underlines function of the two most important blood-brain fluid interfaces, the BBB and the BCSFB.
Efficient homeostatic mechanisms established by those two barriers control composition of brain extracellular fluids, the ISF and CSF. These are vital to normal neuronal function and signal processing in the CNS. Two obvious functions that are common to the BBB and the BCSFB are the restriction of free diffusion and the transport of nutrients, waste products, signalling molecules and ions between blood and brain extracellular fluids.
However, those two structures show important differences in their respective roles that are underlined by differences in expression of cell junction proteins, transport proteins and ion channels.
An important similarity between the two barriers is that they are both dynamic systems and are able to respond rapidly to changes in brain requirements. The molecular basis of this feature is that the BBB and the BCSFB could be regulated via a number of molecular mechanisms under normal physiological or pathological conditions. Crone C, Christensen O: Electrical resistance of a capillary endothelium.
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A possible transepithelial pathway via endoplasmic reticulum in foetal sheep choroid plexus. Monuki, E. Patterning of the dorsal telencephalon and cerebral cortex by a roof plate-Lhx2 pathway. Morgan, E. Figure 2. We assumed that sodium exchange between blood and CSF does not change blood concentration of sodium significantly, due to the large volume of blood compared to CSF. Figures 2C,F show that the elevated levels of sodium in the ventricular CSF lead to diffusion of sodium from CSF to brain tissue and distribution of sodium into the brain tissue over time Smith and Rapoport, ; Murphy and Johanson, Sodium moves by bulk flow of CSF from the ventricular system to the subarachnoid space, where it can be exchanged between CSF and brain tissue.
These behaviors can be explained by the observation that steady state loss of ventricular CSF sodium is largely due to bulk flow of CSF from the ventricular system into the subarachnoid space rather than to sodium uptake by blood across the BCSFB Equation 1 and physiological data in Table 1.
However, the only source for sodium in the ventricular system is the choroid plexus epithelial cells, a. Figure 3. The elevated levels of sodium in the brain tissue increase sodium transport from brain tissue to the ventricular system and subarachnoid space Figures 3A,B,D,E.
Our results indicate that sodium flux from the ventricular system to the brain tissue is larger than sodium flux from the subarachnoid space to the brain tissue. Figure 4. The positive sign of the flux indicates that sodium is diffusing from the CSF to the brain tissue, while the negative sign indicates that sodium is diffusing from the brain tissue to the CSF.
Figures 2 , 3 compare the variations in C v , C s , and C br when a single parameter i. However, in the case of migraines, all influx and efflux permeability coefficients can potentially vary. Additionally, Table 1 shows the average values of the physiological model's parameters.
These values can change across a population of rats of the same type. Thus, we used GSA Pianosi et al. This is due to considering the impacts of intrinsic variations between a population of rats of the same type, and the effects of measurement errors in the estimations of physiological model parameters on our simulations.
Following a uniform distribution, we sampled 10 5 sets of parameters within their ranges of variability. We then calculated the dependent parameters, i. Each of these 10 5 sets of parameters characterizes one healthy rat with different physiological parameters.
It is important to note that each permeability coefficient is defined at two states: physiological and pathophysiological. A given permeability coefficient e. This implies that migraine triggers can change physiological permeability coefficients. This is mainly because the model output was defined as the percent change of total ventricular CSF sodium concentration between the pathophysiological and physiological states. It is important to note that total-effect sensitivity indices, which account for total contribution of the inputs to variations in the model response, should be used to compare the significance of the model inputs in controlling the model output.
Figure 5. Sensitivity ranking of the model parameters. The model output was set to the time integral of C v within 2 h after perturbation of the model's parameters.
The blue bars represent first-order sensitivity indices, while the green bars show the total-effect sensitivity indices. Total-effect sensitivity indices of some of the parameters are smaller than 0.
This means that the variations of these parameters do not influence the variance of the model output significantly; thus these parameters can be fixed at arbitrary values within their ranges Tang et al.
Figure 6. This result implies that sodium exchange between CSF and brain tissue at the contact surface of the ventricular system and brain tissue, as well as at the contact surface of the subarachnoid space and brain tissue can significantly influence brain sodium levels during migraine. Figure 7. Table 2. Total-effect sensitivity indices of the permeability coefficients at different total experiment times.
Our results demonstrate that the ventricular CSF sodium concentration is highly sensitive to pathophysiological variations in P BCSFB , independent of experiment duration time.
This implies that the BCSFB becomes more important in controlling brain tissue sodium homeostasis as time passes. This change in the significance of BCSFB and BBB in the regulation of brain tissue and subarachnoid CSF sodium levels over time is mainly due to the model structure, physiological model parameters and the model output expression. This trend is due also in part to the fact that the ventricular CSF, whose sodium content is largely regulated by the BCSFB, would have enough time to influence sodium levels of its downstream compartments, including the brain tissue and the subarachnoid space.
To investigate the dynamics of sodium exchange between the CSF and brain tissue at the interface of brain tissue and the ventricular system, and at the contact surface of brain tissue and subarachnoid space during an episode of migraine, we randomly sampled 10 5 sets of parameters, following a uniform distribution over a dimensional parameter space and compared the average absolute sodium flux q v between brain tissue and ventricular CSF, with the average absolute sodium flux q s between the brain tissue and subarachnoid CSF.
The average absolute fluxes q v and q s are defined by. Figure 8 shows the ratio of q v to q s for the 10 5 randomly sampled parameters. Figure 8. The ratio of absolute sodium flux at the interface of the ventricular system and the brain tissue q v to absolute sodium flux at the interface of the subarachnoid space and the brain tissue q s.
Previous studies Harrington et al. However, blood levels of sodium remain unchanged during migraine Harrington et al. In this regard, first we developed a computational model for sodium exchange between different brain compartments, i. The model presented in this paper is similar in some respects to that of Smith and Rapoport However, there are two major differences between our model and theirs.
First, our model includes the ventricular system and subarachnoid space as separate compartments. Thus, our model can distinguish between the ventricular and subarachnoid CSF, as well as provide insight into the dynamics of sodium exchange between the CSF and brain tissue at the interface of brain tissue and the ventricular system, and at the contact surface of brain tissue and the subarachnoid space. Second, we have proposed a more realistic model of brain tissue compared to previous studies Davson and Welch, ; Collins and Dedrick, ; Smith and Rapoport, Unlike previous studies that modeled brain tissue as a rectangular sheet bathed on two opposite sides by CSF, we modeled brain tissue as the area between two concentric spheres.
Concentric spheres are more similar to the real shape of a rat brain, which resembles an ellipsoid. As a result, the contact surface area of the brain tissue and the subarachnoid space is larger than that of the brain tissue and the ventricular system in our model. Thus, sodium exchange between the CSF and brain tissue at the two contact surfaces, as well as sodium diffusion in the brain tissue have been modeled more accurately in this work than in previous studies.
This hypothesis needs to be tested experimentally for different migraine triggers. Overall, sodium transport from blood to CSF across the BCSFB is regulated by a variety of transporters, channels and proteins, whose interactions with each other are not well-understood. It has been suggested that sodium transport from the brain ISF into the BBB endothelial cells is mainly mediated by sodium-linked transporters of organic solutes, including those for amino acids Hladky and Barrand, NHE 1,2 can also potentially contribute to sodium entry across the ISF-facing abluminal membrane of endothelial cells.
However, the impacts of migraine triggers on the activity and expression levels of these sodium transporters are yet to be understood. Our results suggest that alterations of BBB sodium transporters homeostasis have more significant effects than variations of BCSFB sodium transporters homeostasis on brain tissue sodium levels within 30 min of the perturbation onset.
It should be noted that our results were obtained using GSA, which gives us some insight into the importance of influx and efflux permeability of the BCSFB and the BBB to sodium in controlling CSF and brain tissue sodium by covering the entire parameter space, where all model parameters can vary within the specified ranges. Thus, in a rat model, the intrinsic variations between a population of rats of the same type were considered in this work. This study has some limitations. First, for simplicity, we modeled the rat brain with three spheres.
However, the real geometry of a rat brain is more complicated. A more realistic model of the brain and ventricles can provide a better understanding of the phenomenon under study. Second, we modeled the CSF with two well-mixed compartments, i. However, CSF flows through the lateral ventricles, the third ventricle, the cerebral aqueduct, the fourth ventricle, the cisterns and the subarachnoid space.
Sodium concentration can vary slightly to significantly from one ventricle to another one and to the subarachnoid space. Thus, the current model can be improved to include all of the ventricles and subarachnoid space as separate compartments. CSF flow can be modeled using various numerical methods Howden et al.
However, further information regarding the dynamics of sodium transport between different ventricles and adjacent brain tissues is needed. Furthermore, we assumed that there is no rate-limiting diffusion between the CSF and brain tissue at the two contact surfaces of the CSF and brain tissue. This assumption may not be true for some ependymal regions, such as those in the third ventricle as it has been shown that benzamil, an ENaC blocker can prevent sodium movement from the third ventricle CSF into brain tissue across the ependyma Wang et al.
Third, for simplicity we assumed that the value of the sodium distribution factor f d remains constant after perturbations of the BCSFB and the BBB permeability coefficients to sodium. This assumption implies that the ratio of extracellular sodium concentration to intracellular sodium concentration remains unchanged at any time after perturbations of the permeability coefficients. In other words, sodium is always distributed between the ISF and the brain cells in the ratio of their physiological sodium contents.
Previous studies made a somewhat similar assumption to estimate the ISF sodium concentration from brain tissue sodium levels, using the cerebral distribution volume of sodium Smith and Rapoport, The physiological value of f d was found to be 0. The obtained value of 0. The dynamics of sodium exchange between the brain cells and the ISF can be better understood by adding the brain cells as a new compartment to the current model.
Our model can be expanded to include brain cells once more information becomes available regarding the permeability coefficients of different types of brain cell to sodium. One approach to modeling of dynamic sodium exchange between the brain cells and the ISF is to use neuron models which are based on Hodgkin-Huxley type dynamics and extended to include time-dependent intracellular and extracellular sodium concentration Dahlem et al.
These dynamic models include differential equations for concentration of sodium, potassium and chloride. However, coupling these models with the current model may require modeling of further mechanisms that regulate potassium and chloride in the CSF and ISF. Fifth, we assumed that diffusion is the major mechanism of sodium movement in the brain tissue.
Although there are several lines of evidence supporting the existence of a convective transport mechanism called the glymphatic system in the brain Iliff et al. Furthermore, it is not well-understood how the proposed transport mechanisms are affected during migraine and how these mechanisms interact with the BBB to regulate ionic homeostasis in the brain.
In this work, we ignored sodium transport between the CSF and brain ISF via convection, as it has been shown that diffusion without convection in the brain tissue is enough to account for many experimental transport studies in the brain parenchyma Jin et al.
Intuitively, we think that adding the convective CSF transport from the subarachnoid space to the brain ISF, based on the proposed glymphatic circulation, will increase the effects of subarachnoid CSF in general CSF on the brain tissue sodium levels, as the convective transport mechanism allows more sodium to be transported in a shorter amount of time compared to diffusive transport. However, the exact extent of the contribution of the glymphatic system to the regulation of brain sodium homeostasis depends on not only the dynamical properties of the glymphatic system, such as the rate of glymphatic flow, the glymphatic efflux pathways and the ISF bulk flow driving force, but also the dynamic interactions between the glymphatic flow, the BBB and brain diffusive transport mechanisms.
The current model can be expanded to include the convective CSF flow from the subarachnoid space to brain ISF once more information regarding the contribution of the glymphatic flow to the regulation of brain sodium homeostasis becomes available.
Finally, we ignored water fluxes between the model compartments. Any barrier theory, however plausible, must be able to be measured against these data on protein dynamics in the CSF. Generations of neurophysiologists and neuropathologists 3 3. Davson H. Physiology of the ocular and cerebrospinal fluids. London: Churchill; The development of the human blood-brain and Blood-CSF barriers. Neuropathol Appl Neurobiol. Weller RO. Microscopic morphology and histology of the human meninges.
Wolburg H, Lippoldt A. Tight junctions of the blood-brain barrier: development, composition and regulation. Vascul Pharmacol. Wolburg H, Paulus W. Choroid plexus: biology and pathology. Acta Neuropathol. However, this illustrative work on the morphology of the normal barriers has completely obscured the view of CSF flow as the main modulating parameter for the barrier function for proteins in pathological processes 3 3.
This steady state idea can be regarded as a consensus in the scientific community for the normal CSF. The dissent came, however, with the question about the cause of a pathological shift of the steady state in the case of blood CSF barrier dysfunctions 8 8.
Non-linear ventriculo-lumbar protein gradients validate the diffusion-flow model for the blood-CSF barrier. Figure 1. Idealized cross-section through the subarachnoid space with adjacent blood vessels and interstitial fluid between individual cells hexagon. Open arrows are for bulk volume flow, F, and double arrows refer to the bidirectional molecular diffusion. The descriptive terms like blood-brain barrier leakage, impairment, disruption or breakdown dominate the scientific literature with together about Since in most studies the cause of the increased blood-derived protein concentrations in CSF was not explicitly investigated, the term leakage in these publications is more a metaphor than a scientific finding.
It is the aim of this review to show the data that will help to resolve this hindrance in the development of new diagnostic approaches and therapies in neurology. Interest in the flow of CSF is very old 22 J Comp Neurol. The former experiments and observations need to be reviewed on the basis of current knowledge. With the two components, diffusion and fluid flow, all data on protein measured in CSF could be interpreted with a common biophysical model 7 7.
Under these two critical aspects the former data may have to be reinterpreted:. Proteins diffuse from the blood through the tissue into the brain extracellular fluid, ISF and CSF depending on their molecular size Table 1. Diffusion is an undirected process with non-linear concentration gradients through the tissue 7 7.
For proteins there is no active or facilitated transfer mechanism as is the case for glucose and vitamin C 23 Intrathecal Accumulation and CSF flow rate. Amino acid transport across the human blood-CSF barrier. An evaluation graph for amino acid concentrations in cerebrospinal fluid.
The transport of molecules in a fluid solvent takes place in the dissolved state solute and the transport speed of this bulk flow is not dependent on the size of the molecule 25 Diagnostic relevance of free light chains in cerebrospinal fluid - the hyperbolic reference range for reliable data interpretation in quotient diagrams.
The change in the albumin quotient, QAlb, is the reciprocal measure for the change in flow rate. For example, a model that associates QAlb with a molecular size-dependent exponent 13 The use of insoluble crystals cinnabar, mercurysulfide in the oldest CSF flow experiment of Quincke 22 The recent use of these experiments as an argument for a reverse direction of the cerebrospinal fluid flow 22 CSF flow research has received a new upswing with imaging techniques.
But images of CSF pulsations 26 Interactions between flow oscillations and biochemical parameters in the cerebrospinal fluid. Front Aging Neurosci.
Relation between tag position and degree of visualized cerebrospinal fluid reflux into the lateral ventricles in time-spatial labeling inversion pulse magnetic resonance imaging at the foramen of Monro. MR imaging and quantification of the movement of the lamina terminalis depending on the CSF dynamics. J Neurosci. Cerebrospinal fluid volumetric net flow rate and direction in idiopathic normal pressure hydrocephalus. Neuroimage Clin. The use of experimental barrier models such as cell cultures and mechanical chips 4 4.
A perfused human blood-brain barrier on a chip for high throughput assessment of barrier function and antibody transport. These models focus on the lipophilicity of molecules for the transcellular passage, different from the intercellular passage of proteins. Analogies to animal models 32 Koh l, Zakharov A, Johnston M. Integration of the subarachnoid space and lymphatics: Is it time to embrace a new concept of cerebrospinal fluid absorption?
Cerebrospinal Fluid Res. Lymphatic drainage of the brain and the pathophysiology of neurological disease. Spinal CSF absorption in healthy individuals.
Mathematical models, which ignore biological contexts 14 Front Neurosci. Recent findings on the bulk flow of the interstitial extracellular fluid 36 Abbott NJ. Evidence for bulk flow of brain interstitial fluid: Significance for physiology and pathology. Neurochem Int. Int J Mol Med. Analysis of convective and diffusive transport in the brain interstitium. Mechanisms of fluid movement into, through and out of the brain: evaluation of the evidence. Comparison of inflammation-dependent and mechanically blocked CSF flow or restricted CSF outflow in different neurological diseases.
Thompson EJ. The CSF proteins: a biochemical approach. Amsterdam: Elsevier; Only a small fraction of brain-derived proteins in CSF is exclusively brain-cell derived 40 Most of the brain-derived proteins in CSF are only predominantly brain-derived, i.
Figure 2. Data base from control patients without an intrathecal immunoglobulin synthesis 8 8. The larger the molecule, the slower the diffusion is to reach the steady state concentration in CSF.
A change of albumin concentration in blood is equilibrated with its CSF concentration in about 1 day, IgG in two and IgM much later 41
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