A Lumped Parameter Modelling Study of Idiopathic Intracranial Hypertension: Does the CSF Formation Rate vary with the Capillary Transmural Pressure?

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Grant Alexander Bateman, Alexander Robert Bateman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4626772/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Studies simultaneously measuring the intracranial pressure (ICP) and sagittal sinus pressures in idiopathic intracranial hypertension (IIH), suggest either a reduction in the CSF outflow resistance or the CSF formation rate. A study maintaining the ICP at zero showed a significantly elevated CSF formation rate. The purpose of this study is to define the most feasible explanation for these findings. A lumped parameter model originally developed to study normal pressure hydrocephalus was extended to investigate IIH. The model was used to estimate the CSF formation rate and the capillary transmural pressure (TMP), utilizing the data from 4 experiments published within the literature. When the CSF formation rates of these 4 studies were plotted against the estimated capillary transmural pressures, a straight line with an R 2 of 0.999 was returned. The model suggests the CSF formation rate in IIH varies with the capillary TMP. A reduced capillary TMP secondary to a reduced blood flow in IIH moderates the ICP. The variation in formation rate is most likely a function of the blood brain barrier (BBB) breakdown known to occur in this disease. Drugs which stabilize the BBB may trigger IIH. Health sciences/Diseases Health sciences/Neurology Health sciences/Pathogenesis cerebral blood flow idiopathic intracranial hypertension CSF formation rate blood brain barrier tetracycline retinoic acid Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The clinical syndrome of idiopathic intracranial hypertension (IIH), also known as pseudotumor cerebri, occurs in patients who present with high pressure type headaches and/or papilledema and visual obscuration. At lumbar puncture, the cerebrospinal fluid (CSF) pressures are elevated but the CSF composition is normal [ 1 ]. The diagnosis is made by lumbar puncture, with the accepted cut-off for the diagnosis of IIH being a CSF pressure elevation above 25 cm H 2 O in adults [ 2 ]. Using Davson’s Eq. ( 2 ), it has been argued the elevated intracranial pressure (ICP) could come about by an increase in the CSF formation rate, a CSF outflow obstruction or an increased venous sinus pressure [ 3 ]. However, it has been suggested that, on the basis of a reduced pressure gradient between the CSF and sagittal sinus in IIH, the venous pressure, rather than an increase in CSF formation rate or increase in CSF outflow resistance, is the underlying cause of IIH [ 4 ]. There are two recent studies where the pressure gradient between the CSF and venous sinuses were measured at baseline and found to be 2.7 mmHg [ 5 ] and 1.8 mmHg [ 6 ] compared to a normal value of 4 mmHg [ 7 ]. Davson’s equation would suggest these results indicate either a significant reduction in the CSF formation rate or the CSF outflow resistance. Indeed, in the later study [ 6 ], the CSF formation rate was assumed to be normal by the authors and the outflow resistance was calculated to be 5.2 mmHg/ml/min compared to a normal figure for age of approximately 13 mmHg/ml/min [ 8 ]. Paradoxically, either a reduced formation rate or outflow resistance are the reverse of what would be expected to induce a raised CSF pressure. When mock CSF was infused in IIH [ 6 ], the ICP to sinus pressure gradient increased above normal to 4.9 mmHg. In a study where the ICP was maintained at 0 mmHg using a liquoGuard7 pump, the CSF formation rate in IIH was found to be 86 ml/h or 1.43 ml/min [ 9 ] compared to the normal value of 0.35 ml/min [ 10 ]. This later study suggests the CSF formation rate is increased by over 300% in IIH and would indicate that the CSF formation rate is the variable of interest in IIH rather than the outflow resistance. This raises an apparent paradox, the CSF formation rate is normal, increased or decreased in IIH depending on the circumstances. The purpose of this study is to extend a lumped parameter modelling study, initially performed to look at blood flow and pressure in normal pressure hydrocephalus [ 11 ], to incorporate the CSF formation rate and capillary transmural pressure (TMP), to try to provide the most feasible explanation for this apparent paradox. Results The modelling findings are summarized in Figure 1. The five vascular segments modelled are shown in Fig 1a, with the arterial segment shown in red, the capillaries in orange, the veins in yellow, the outflow cuff in green and the sinus in blue. The pressures obtained from the literature have been appended to the beginning and end of each vascular segment within the vessels in Fig 1a. Given the arterial inflow volume passes through each segment sequentially, the resistance of each segment can be calculated using equation (3). These resistances are appended below the vessels in fig 1. The normal cerebral blood volume (CBV) values for each segment and the total CBV has been obtained from the literature and is shown below the resistances. The blue numbers represent the transmural pressure gradients between the pressure at the beginning and end of each capacitance vessel segment and the ICP, and are obtained by subtraction. The red figure is the average capillary TMP obtained by averaging the TMP before and after the capillaries. Figures 1b-d represent the effects of the differing alterations in perfusion pressure from the differing studies modelled. In these figures, the red segments represent the areas of increased resistance compared to the normal findings and the green represent reduced resistance. Idiopathic intracranial hypertension In figure 1b, the baseline findings in IIH found in the study by Lalou et al. [6] (i.e., an ICP of 27 mmHg and superior sagittal sinus pressure of 25.2 mmHg.) have been modelled. The arterial inflow has been reduced by 13% compared to normal in keeping with the majority of IIH patients who are oligemic. The pressure drop across the entire system is known from the data as supplied and the total blood flow is specified so the total resistance is calculated using equation (3). The TMP across the outflow cuff is obtained by subtracting the ICP from the sinus pressure and is reduced below normal. The cuff outflow resistance can be calculated from equation (14) and is also reduced. Knowing the cuff resistance and blood flow will set the blood pressure at the end of the veins by using equation (3). The reduction in TMP across the veins reduces their volume using equation (12). The change in venous resistance can be calculated using the change in vein volume using equation (10). This allows the post capillary pressure to be calculated using equation (3). As the capillary outflow pressures and the blood flow are reduced, the capillary TMP will also likely be reduced. Using the capillary tube law as defined, the volume and resistance of this segment will be unchanged from normal. Knowing the total resistance and the other resistances, the arterial inflow resistance can be calculated using equation (4). Note there is a reduction in both the arterial and the outflow cuff resistance with a reduction in resistance overall. The calculated average capillary TMP is reduced by 18.3% compared to the normal value. Using the same technique the capillary TMP can be calculated using the simultaneously obtained data from a similar study from Liu et al. where the baseline ICP and sagittal sinus pressures were 42.2 mmHg and 39.5 mmHg in IIH respectively. The calculated capillary TMP from this study is 10.4 mmHg (not illustrated). Infusion study in IIH Figure 1c models the findings in the study by Lalou et al. following their infusion study [6]. The ICP was found to be 38 mmHg and the sinus pressure 33.1 mmHg. Using the same technique as for Fig 1b, the total resistance is reduced despite the cuff resistance being increased due to the effect of the arterial resistance dropping. The capillary TMP has returned to the normal range at 11.9 mmHg. CSF drainage in IIH Figure 1d models the effect of draining the CSF using the LiquoGuard7 device as used in the study by Tariq et al. [9]. The effect of dropping the ICP to zero is to effectively treat the IIH. A transcranial Doppler study showed the elevation in arterial resistance in IIH will rapidly normalize following CSF withdrawal by lumbar puncture [12], suggesting the CBF should be returned to the normal range with the CSF drainage. Therefore, the flow been set to 750 ml/min in the model. In IIH patients the venous transverse sinuses show narrowing (a stenosis), which shows a rapid return to normal following lumbar puncture [13]. This is the equivalent to the dilatation of the transverse sinuses which occurs in successful stenting procedures in IIH i.e. the pressure gradient along the transverse sinuses returns to normal. The superior sagittal sinus pressure following a successful sinus stenosis stent remains higher than normal at 15.4 mmHg [14]. This appears to be due to the stent failing to treat the raised venous pressure secondary to the obesity induced central venous pressure elevation. Therefore, a normal CBF of 750 ml/min and an outflow pressure of 15.4 mmHg have been modelled in Fig 1d. The model indicates that the outflow cuff is maximally dilated and the resistance of this short segment is reduced to zero. The vastly increased venous TMP maximally dilates the veins by 70% and reduces their resistance. The capillary TMP is increased and the capillary volume will increase. The capillary volume and resistance have been adjusted to allow for this effect. The overall result is to increase the capillary TMP by 86% above normal. Discussion As discussed in the introduction, there seems to be some variability in either the CSF outflow resistance (R out ), or the CSF formation rate (CSF fr ) in IIH. Lalou et al. directly measured the background ICP and venous sinus pressure in IIH, finding mean values of 42.2 mmHg and 39.5 mmHg respectively. They assumed a normal CSF formation rate of 0.35 ml/min and using Davson’s Eq. ( 2 ), obtained a Rout of 5.2 mmHg/ml/min which is 60% less than the normal figure of 13 mmHg/ml/min. Similarly, Liu et al. using a similar technique found an average ICP in IIH of 42.2 mmHg and sinus pressure of 39.5 mmHg, which would give a Rout of 7.7 mmHg/ml/min or 41% less than normal. Finally, Lalou et al. performed an infusion test on their cohort. According to their methodology, the average rate of mock CSF infusion was 1 ml/min, giving an apparent total CSF formation rate of 1.35 ml/min. During the infusion, the average ICP was 38 mmHg and the ICP 33.1 mmHg. Placing these data into Eq. ( 1 ) gives a Rout of 3.6 mmHg/ml/min or 72% below normal. It is difficult to conceive of a mechanism whereby a very low resistance could fall even further over the space of 10 minutes during the infusion study and then bounce back to normal when finished. If rather than the CSF formation rate being a constant, the R out was made a constant, then the CSF formation rate would vary. If the underlying R out were normal, then the baseline data from Lalou et al. would give a CSF fr of 0.14ml/min, the data from Liu et al. a CSF fr of 0.21 ml/min and the post infusion study data a CSF fr of 0.38 ml/min. As already discussed, in the study by Tariq et al. [ 9 ], the CSF was drained to maintain an ICP of 0 mmHg. The effect of this is to place an additional outflow resistance (with an effective resistance of zero) in the system in parallel to all the others. Thus, all of the other normal outflow resistances are effectively excluded from the measurement. The CSF fr was found to be 1.43 ml/min in IIH or an increase of over 300%. Given the large change in CSF fr in the final study, and the exclusion of a change in R out by this technique, it would seem more likely that the CSF fr is varying in IIH rather than the R out . Therefore, the purpose of the current study is to model the blood flow and pressure of the intracranial system in IIH, to try to find a feasible solution to account for these findings. It is generally thought that the CSF fr does not change with the ICP and remains a constant [ 15 ]. CSF is produced from differing regions within the brain. Seventy percent of CSF production comes from the choroid plexus, 18% from the capillaries and 12% from glucose metabolism [ 16 ]. The only possible variable component of the CSF production could come from the capillaries but this is excluded if the blood brain barrier (BBB) is intact. Net capillary CSF production or absorption is expected to follow the Starling forces relationship. This is modelled using the following equation: $$\:{J}_{cap}={L}_{cap}[\left\{{P}_{cap}-{P}_{CSF}\right\}-{\sigma\:}_{cap}\left\{{\pi\:}_{cap}-{\pi\:}_{CSF}\right\}]$$ 1 Where J cap is the capillary fluid flow rate, L cap is the capillary hydraulic conductivity, P cap -P csf is the hydraulic pressure gradient across the capillary wall (i.e. the TMP), σ cap is the osmotic reflection coefficient and π cap -π csf is the osmotic pressure gradient across the capillary wall [ 17 ]. Note, that at steady state, there is no significant difference in hydrostatic pressure between the CSF and the brain parenchyma [ 18 ]. With an intact BBB, the cerebral capillaries have hydraulic conductivities 2–3 orders of magnitude less than systemic capillaries [ 19 ], the osmotic reflection coefficient is 1 [ 17 ] and the osmotic pressure gradient is close to zero [ 20 ]. Therefore, any increase in capillary fluid flow occurring secondary to an increase in capillary TMP would rapidly increase the osmotic pressure difference between the plasma and the interstitium, because the salt does not follow the water due to the high osmotic reflection coefficient. Thus, the capillary plasma would increase in osmotic pressure and the interstitium decrease effectively opposing the hydrostatic pressure difference [ 17 ]. However, this feedback control of water flow into the brain fails as the BBB breaks down and the net result is an increase in brain water and ICP [ 17 ]. This is because the hydraulic conductivity would increase and the osmotic reflection coefficient decrease. In IIH there is evidence of a significant disruption of the BBB in IIH with protein leakage [ 21 ]. The barrier breakdown probably occurs secondary to the elevated venous pressure because there is also a BBB disruption in a mouse model of raised cerebral venous pressure [ 22 ]. If the osmotic reflection coefficient is low, then the salt will follow the water, and the capillary osmotic pressure gradient will not increase. From the Starling forces equation is can be predicted that the capillary flow (i.e. the CSF fr ) will be a linear function of the capillary TMP, with the hydraulic conductivity being the slope of the line. Figure 2 is a plot of the 4 experiments from the literature where we estimated the CSFfr (from their data by using a normal R out) vs our estimates for the capillary TMP from the modelling (see Fig. 1 for the TMP results). Note this graph returns a straight blue line with an R 2 of 0.99 indicating an almost perfect correlation. This adds weight to the suggestion that the CSF fr varies with the capillary TMP in IIH. The red line is the expected constant CSF fr if the BBB is intact. Cerebral perfusion depends on the pressure across the vasculature. The cerebral perfusion pressure is dependent on the mean arterial pressure minus the ICP [ 23 ]. The brain does not tolerate hypo- or hyper-perfusion, therefore, the maintenance of a constant flow over a range of pressures is achieved by autoregulation [ 23 ]. Dynamic cerebral autoregulation is impaired in IIH and improves after venous sinus stenting [ 24 ], suggesting a reduced blood flow pre-stent. It can be seen in Fig. 2 that the baseline CSF formation rate for two of the published studies is well below normal. It is apparent this is because the capillary TMP is below normal. This occurs because the cerebral blood flow is lower than normal and the arterial resistances are higher than what would be expected if autoregulation were to maintain a normal flow rate. As discussed in the methods section, the reduction in blood flow rate of 13% was selected because it corresponds to the lower mode of the bimodal distribution of blood flow in IIH patients, in the largest published study [ 25 ]. This correlates with the literature where 71% of IIH patients are obese [ 26 ] and obesity reduces the CBF by approximately 12% [ 27 ], suggesting the majority of IIH patients will have a low blood flow. This reduction in blood flow is not trivial, there is an elevated lactate/ pyruvate ratio in the CSF of IIH patients suggesting anerobic metabolism [ 28 ]. Thus, the majority of IIH patients have a low blood flow despite evidence of anerobic metabolism. Previous modelling suggests that the arterial supply to the brain can dilate and reduce its resistance down to 24 mmHg/ml/min [ 11 ], which is never approached in this current study. This suggests the brain in IIH is electing to be oligemic rather than being forced to be oligemic. Raichle et al. came to a similar conclusion stating “the cerebral perfusion pressure does not appear to approach the limit of autoregulation in IIH” [ 29 ]. When we attempted to increase the blood flow in the model (in Fig. 1 b) back to normal at 750 ml/min, a positive feedback loop ensued whereby the arterial segment was required to dilate. This increased the capillary TMP (and CSF fr ), which increased the ICP, which compressed the venous sinus and outflow cuff, increasing the capillary TMP further and also initiating a further dilatation of the artery to maintain blood flow. This feedback loop could continue until the artery was fully dilated and a very high ICP resulted. This suggests a reduced blood flow is a harm minimisation strategy of the brain to reduce the ICP to a minimum. Thus paradoxically, the reduction in CBF and the opening of the blood brain barrier are partially beneficial in IIH, in that they allow the ICP to be moderated. The modelling would predict that the stabilisation of this blood brain barrier disruption would increase the ICP by not allowing for some net absorption of CSF via the capillaries. There are two classes of drugs known to stabilise the blood brain barrier, tetracycline based antibiotics [ 30 , 31 ] and retinoic acid compounds [ 32 ]. These compounds are both known to trigger IIH in those predisposed to the disease [ 33 , 34 ]. Suggesting blood brain barrier stabilisation is not an ideal strategy in IIH. There are many assumptions inherent in the lumped parameter modelling. We can test the modelling we have performed by comparing the outcomes predicted by the model with the literature. The oligemic IIH model incorporates the majority of IIH patients, and the model suggests the total blood volume is not significantly different at 50.4 ml, to normal at 51 ml. Two studies have found a normal cerebral blood volume in IIH [ 35 , 36 ]. One study found a 33% increase in CBV in IIH [ 29 ]. However, the methodology in this paper was flawed. They measured the CBV with one technique (carbon monoxide red cell labelling) but compared the findings to controls using another method (fluorescence) [ 29 ]. Comparing their results to the normal red cell findings in an earlier paper by the same group [ 37 ] showed no significant difference in the CBV in IIH. Thus, our modelling appears to be accurate enough for the current purposes. Poiseuille’s equation requires flow through a thin, rigid, circular tube of a Newtonian fluid, without turbulence. To the degree that these assumptions hold, the findings would be accurate. However, despite its limitations, this equation is commonly used in modelling the vasculature in the literature. Methods Equations The study begins with Davson’s equation which relates the intracranial pressure (ICP) to the CSF formation rate, the CSF outflow resistance and the venous sinus pressure [ 38 ]. $$\:ICP={CSF}_{fr}\times\:{R}_{out}+{P}_{sss}$$ 2 Where ICP is the intracranial pressure, CSF fr is the CSF formation rate, R out is the CSF outflow resistance and P sss is the pressure in the superior sagittal sinus. Next Ohms law for hydraulic circuits is required: $$\:\varDelta\:P=Q\:\times\:\:R$$ 3 Where ΔP is the pressure drop across a vascular segment, Q is the flow rate through the segment and R is the resistance. As resistances in series are directly additive the following can be derived: $$\:{R}_{art}+{R}_{cap}+{R}_{ven}+{R}_{cuf}={R}_{tot}$$ 4 Where R art is the arterial segment resistance, R cap is the resistance of the capillaries, R ven is the venous resistance, R cuf is the resistance of the venous outflow cuff and R tot is the total resistance for the entire vascular system. Poiseuille’s equation calculates the pressure drop across each of these segments: $$\:\varDelta\:P=\raisebox{1ex}{$8\mu\:LQ$}\!\left/\:\!\raisebox{-1ex}{$\pi\:{r}^{4}$}\right.$$ 5 Where ΔP is the pressure drop, µ is the viscosity, L is the vessel length, Q is the fluid flow rate, π is the circle proportionality constant and r is the radius. Substituting Eq. ( 3 ) into (5) and eliminating Q from both sides gives an equation for the resistance in each segment: $$\:R=\raisebox{1ex}{$8\mu\:L$}\!\left/\:\!\raisebox{-1ex}{$\pi\:{r}^{4}$}\right.$$ 6 In this modeling study the viscosity, the length of each vessel segment, and π are constants, so it can be shown that a change in resistance for any segment depends only on a change in the vessel radius i.e. $$\:\varDelta\:R=\varDelta\:{r}^{-4}$$ 7 The volume of a vessel is given by the equation for a cylinder i.e. $$\:V=L\pi\:{r}^{2}$$ 8 Where V is the volume, L is the vessel length and r is the radius of the vessel. Given L and π are constants for any given segment, the change in volume is dependent on the change in radius i.e. $$\:\varDelta\:V=\varDelta\:{r}^{2}$$ 9 Substituting Eq. ( 9 ) into Eq. ( 7 ) gives $$\:\varDelta\:R=\varDelta\:{V}^{-2}$$ 10 The next equation relates the transmural pressure across a vessel to the vessel cross-sectional area [ 39 ]: $$\:{P}_{tm}=\frac{4Eh}{{3R}_{o}}(1-\sqrt{\frac{{A}_{o}}{A}})$$ 11 Where P tm is the transmural pressure across the vessel wall (lumen pressure- CSF pressure), E is the circumferential Young’s modulus of the vessel wall, h is the wall thickness, R o is the radius in the stress free state, A o is the area in the stress free state and A is the area following the applied transmural pressure. This equation was previously used to show that the volume of the venous outflow varies with the transmural pressure by the equation [ 11 ]: $$\:{\varDelta\:TMP}_{ven\:\:}=-0.033{{\varDelta\:V}_{ven}}^{2}+7.49\times\:{\varDelta\:V}_{ven}-3.44$$ 12 Where ΔTMP ven is the normalized increase in venous transmural pressure and ΔV ven is the change in venous volume. Model input parameters The input parameters are unchanged from the previous study [ 11 ] and will only be briefly described as the details can be obtained from the original study. This study is based on a middle aged individual with a brain size of 1500g. A normal global CBF is 50 ml/100g/min [ 40 ], giving a normal cerebral blood arterial inflow of 750 ml/min. The normal mean arterial inflow pressure is 100 mmHg [ 41 ]. The normal precapillary bed pressure is 32 mmHg [ 42 ]. The end capillary pressure is estimated to be 15 mmHg [ 43 ]. The normal CSF pressure in middle age is 11.5 mmHg [ 44 ] and the normal pressure gradient from the CSF to the superior sinus lumen is 4 mmHg, [ 7 ] giving a normal sinus pressure by subtraction of 7.5 mmHg [ 45 ]. The normal transmural pressure of the subarachnoid cortical veins in primates is 2.5 mmHg [ 46 ]. Using this figure for the model, it can be seen that the pre-venous outflow cuff pressure is 14 mmHg by addition of the TMP to the ICP. In a 1500g brain, the total CBV would be 51 ml [ 11 ]. Hua et al. found the arterial component of the CBV to be 25% [ 47 ] or 12.8 ml in total. This leaves the remaining 75% for the capacitance vessels, including the veins and capillaries or 38.2 ml. The estimated percentage of this latter figure for the capillaries is 53% [ 48 ], giving a total capillary blood volume of 20.3 ml and a total venous blood volume of 17.9 ml. The normal CSF outflow resistance (R out ) has been found to depend linearly with age, with the regression line being: [ 8 ]. $$\:{R}_{out}=0.075\times\:Age+9.88$$ 13 This gives a normal R out for a 40 year old of 13 mmHg/ml/min. The normal CSF formation rate is 0.35 ml/min [ 10 ]. Vessel responses to transmural pressure variations It is assumed that variations in the arterial resistance and volume in this model depend entirely on the arterial autoregulation and muscle tone and not the vessel transmural pressure. As the arterial pressure is always much higher than the ICP, the arterial transmural pressure will have no effect on the outcome of the current modelling study. In the capillary bed, the vessels do not actively alter their diameter [ 49 ], indicating they react purely to their transmural pressure. In a rat model, extreme hyperventilation decreased the PCO 2 from 40 to 21.6 mmHg without affecting PO 2 , the capillary size was not significantly different to controls despite the expected arteriolar constriction [ 50 ]. However, in the opposite case, in rats made extremely hypercapnic secondary to hypoventilation, the PCO 2 increased to 95.6 mmHg but PO 2 was normal, the capillary diameter increased by 20% consistent with a 44% increase in volume compared to known control values [ 50 ]. Thus, a moderate reduction in capillary TMP does not change the capillary size but a maximal increase in TMP increases their volume by 44%. To simplify the current study, it is assumed the volume of the capillaries vary between normal and maximally dilated as a linear function of their transmural pressure. A previous study indicated an increase in capillary TMP from 12 to 37.9 mmHg would increase the capillary volume by 44% or a 1.7% increase in volume for each 1 mmHg pressure rise. Below a TMP of 12 mmHg the volume is unchanged at 20.3 ml and above a TMP of 37.9 the elastic limit is reached and the volume is set to 29.2 ml. Similar to the capillaries, the veins alter their size purely depending on their transmural pressures. In a previous modelling study [ 11 ] the function for the outflow vein dilatation was found to be summarized by Eq. ( 12 ). At the distal end of the cortical veins, as they join the sinus wall, the outflow cuff segment resides. The collapse of this segment occurs physiologically and is passively modulated by the transmural pressure between the ICP and the sinus pressure, which is usually negative [ 51 ]. The segment is very short, and as it is mostly under a state of collapse with physiological ICPs, the change in volume from this segment will be ignored in this model. However, its resistance will be taken into consideration. In the previous study four differing cuff transmural pressures resulted in 4 differing resistances [ 11 ]. When these points were plotted, a line with R 2 of 0.998 resulted, suggesting the cuff resistance varies as a linear function of the cuff TMP (see Fig. 3 ). Thus giving Eq. 14: \(\:{R}_{cuf}=-2.71\times\:{TMP}_{cuf}\) +0.008 (14) Where R cuf is the cuff resistance and TMP cuf is the cuff transmural pressure. The sagittal sinus pressure will be varied as per the literature being modelled. The arterial inflow in IIH It has been argued that there are actually two populations within most studies where cerebral blood flow has been measured in IIH [ 52 ]. Capel et al. measured CBF in 13 patients with IIH [ 53 ]. Their data were consistent with two populations, a larger one with reduced CBF, and two outliers with a larger CBF [ 52 ]. Bicakci et al. found an overall normal CBF in IIH [ 36 ]. However, of the 16 patients they studied, there were 6 with a blood flow two standard deviations below the mean compared to the controls, 8 with flow in the normal range and two with flow greater than 8 standard deviations above the mean compared to the controls [ 36 ]. The largest study quantifying the arterial inflow in IIH patients was performed by one of the current authors describing 40 patients [ 25 ]. The pooled data from this study is depicted in Fig. 4 . A Shapiro- Wilk test confirms the control data in Fig. 4 to be a normal distribution, with the CBF averaging 920 ± 108 ml/min and the ages averaging 33.1 ± 12 years. A Tukey test indicated the IIH data had a single outlier at 2000 ml/min which will be removed from further evaluation. The remaining data showed a bimodal distribution with the first mode at 800 ml/min and the second at 1300 ml/min. There was a gap with no IIH patient at 950 ml/min. A Shapiro-Wilk test confirmed the patients with a CBF below 950 ml/min (the oligemic group) conformed to a normal distribution with the CBF 13% below the controls (p = 0.0006), their age was 30.6 ± 10.3 years. The average ICP for the oligemic group was 33.3 ± 24.5 mmHg. The patients with a CBF above 950 ml/min also conformed to a normal distribution with the CBF averaging 35% above the controls (p < 0.0001), their age averaged 31 ± 12.4 years and the ICP 31 ± 22.8 mmHg. Given that most studies seem to indicate that the oligemic patients predominate, a CBF 13% below normal will be utilized in this study. Abbreviations BBB, blood brain barrier; CBF, cerebral blood flow; CBV, cerebral blood volume; CSF, cerebrospinal fluid; CSF fr , cerebrospinal fluid formation rate; ICP, intracranial pressure; IIH, idiopathic intracranial hypertension; min, minute; ml, milliliter; mm, millimeters; mmHg, millimeters of mercury; R out , CSF outflow resistance; TMP, transmural pressure. Declarations Availability of data and materials All data generated or analysed during this study are available within the original paper or on reasonable request to the corresponding author GAB. Author’s contributions Conceptualisation and design GAB, ARB. Modelling GAB, ARB. Writing original draft GAB. Review and editing all authors. All authors read and approved the final manuscript. Ethics approval and consent to participate Not applicable. Consent for publication N/A Competing interests The authors declare no competing interests. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Johnston, I., Hawke, S., Halmagyi, M. & Teo, C. The pseudotumor syndrome. Disorders of cerebrospinal fluid circulation causing intracranial hypertension without ventriculomegaly. Arch Neurol 48 , 740-747, doi:10.1001/archneur.1991.00530190088020 (1991). Friedman, D. I., Liu, G. T. & Digre, K. B. 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Sci Rep 12 , 5415, doi:10.1038/s41598-022-09394-4 (2022). Kong, L. et al. Retinoic acid ameliorates blood-brain barrier disruption following ischemic stroke in rats. Pharmacol Res 99 , 125-136, doi:10.1016/j.phrs.2015.05.014 (2015). Digre, K. B. & Corbett, J. J. IDIOPATHIC INTRACRANIAL HYPERTENSION (PSEUDOTUMOR CEREBRI): A REAPPRAISAL. The Neurologist 7 , 2-68 (2001). Friedman, D. I. et al. Doxycycline and intracranial hypertension. Neurology 62 , 2297-2299, doi:10.1212/wnl.62.12.2297 (2004). Brooks, D. J. et al. Regional cerebral oxygen utilization, blood flow, and blood volume in benign intracranial hypertension studied by positron emission tomography. Neurology 35 , 1030-1034, doi:10.1212/wnl.35.7.1030 (1985). Bicakci, K., Bicakci, S. & Aksungur, E. Perfusion and diffusion magnetic resonance imaging in idiopathic intracranial hypertension. Acta Neurol Scand 114 , 193-197, doi:10.1111/j.1600-0404.2006.00702.x (2006). Grubb, R. L., Jr., Raichle, M. E., Higgins, C. S. & Eichling, J. O. Measurement of regional cerebral blood volume by emission tomography. Ann Neurol 4 , 322-328, doi:10.1002/ana.410040407 (1978). Davson, H., Welch, K. & Segal, M. B. Physiology and Pathophysiology of the Cerebrospinal Fluid . (Churchill Livingstone, 1987). Zislin, V. & Rosenfeld, M. Impedance Pumping and Resonance in a Multi-Vessel System. Bioengineering (Basel) 5 , doi:10.3390/bioengineering5030063 (2018). del Zoppo, G. J., Sharp, F. R., Heiss, W. D. & Albers, G. W. Heterogeneity in the penumbra. J Cereb Blood Flow Metab 31 , 1836-1851, doi:10.1038/jcbfm.2011.93 (2011). Ursino, M. A mathematical study of human intracranial hydrodynamics. Part 1--The cerebrospinal fluid pulse pressure. Ann Biomed Eng 16 , 379-401, doi:10.1007/BF02364625 (1988). Salmon, J. H. & Timperman, A. L. Effect of intracranial hypotension on cerebral blood flow. J Neurol Neurosurg Psychiatry 34 , 687-692, doi:10.1136/jnnp.34.6.687 (1971). Cirovic, S., Walsh, C. & Fraser, W. D. Mathematical study of the role of non-linear venous compliance in the cranial volume-pressure test. Med Biol Eng Comput 41 , 579-588, doi:10.1007/BF02345321 (2003). Fleischman, D. et al. Cerebrospinal fluid pressure decreases with older age. PLoS One 7 , e52664, doi:10.1371/journal.pone.0052664 (2012). Bateman, G. A. & Siddique, S. H. Cerebrospinal fluid absorption block at the vertex in chronic hydrocephalus: obstructed arachnoid granulations or elevated venous pressure? Fluids Barriers CNS 11 , 11, doi:10.1186/2045-8118-11-11 (2014). Johnston, I. H. & Rowan, J. O. Raised intracranial pressure and cerebral blood flow. 3. Venous outflow tract pressures and vascular resistances in experimental intracranial hypertension. J Neurol Neurosurg Psychiatry 37 , 392-402, doi:10.1136/jnnp.37.4.392 (1974). Hua, J. et al. MRI techniques to measure arterial and venous cerebral blood volume. Neuroimage 187 , 17-31, doi:10.1016/j.neuroimage.2018.02.027 (2019). Menéndez González, M. in Liquorpheresis: Cerebrospinal Fluid Filtration to Treat CNS Conditions (ed Manuel Menéndez González) 1-19 (Springer Nature Switzerland, 2023). Claassen, J., Thijssen, D. H. J., Panerai, R. B. & Faraci, F. M. Regulation of cerebral blood flow in humans: physiology and clinical implications of autoregulation. Physiol Rev 101 , 1487-1559, doi:10.1152/physrev.00022.2020 (2021). Duelli, R. & Kuschinsky, W. Changes in brain capillary diameter during hypocapnia and hypercapnia. J Cereb Blood Flow Metab 13 , 1025-1028, doi:10.1038/jcbfm.1993.129 (1993). R, D. E. S., Ranieri, A. & Bonavita, V. Starling resistors, autoregulation of cerebral perfusion and the pathogenesis of idiopathic intracranial hypertension. Panminerva Med 59 , 76-89, doi:10.23736/S0031-0808.16.03248-1 (2017). Bateman, G. A. A scoping review of the discrepancies in the measurement of cerebral blood flow in idiopathic intracranial hypertension: oligemia, euvolemia or hyperemia? Fluids Barriers CNS 20 , 63, doi:10.1186/s12987-023-00465-w (2023). Capel, C. et al. Cerebrospinal Fluid and Cerebral Blood Flows in Idiopathic Intracranial Hypertension. Acta Neurochir Suppl 126 , 237-241, doi:10.1007/978-3-319-65798-1_48 (2018). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4626772","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":338215444,"identity":"6bf2d586-ee51-4a2a-bc83-a3dc2cddae1f","order_by":0,"name":"Grant Alexander Bateman","email":"data:image/png;base64,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","orcid":"","institution":"John Hunter Hospital","correspondingAuthor":true,"prefix":"","firstName":"Grant","middleName":"Alexander","lastName":"Bateman","suffix":""},{"id":338215445,"identity":"b9eb057a-5dee-45b2-a451-139ea241d2e6","order_by":1,"name":"Alexander Robert Bateman","email":"","orcid":"","institution":"University of New South Wales","correspondingAuthor":false,"prefix":"","firstName":"Alexander","middleName":"Robert","lastName":"Bateman","suffix":""}],"badges":[],"createdAt":"2024-06-24 01:08:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4626772/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4626772/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":62556624,"identity":"c09f56c2-c031-430d-92aa-8fee1dc7c001","added_by":"auto","created_at":"2024-08-15 19:39:40","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":634059,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eResults of modelling\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. 1a depicts the normal findings. The red segment is the arterial, orange the capillary, yellow the veins, green the outflow cuff and blue the venous sinus. The vascular pressures are shown within the vessels. The blue numbers are the transmural pressures at each site. The red numbers are the average capillary transmural pressure. The resistances and volumes for each segment are shown below the vessel.\u003c/p\u003e\n\u003cp\u003eFig. 1b shows the findings in oligemic IIH with the red area indicating an increase in resistance in the veins and the green decreased resistance compared to normal.\u003c/p\u003e\n\u003cp\u003eFig. 1c shows the findings in IIH following an infusion study with the green area highlighting a reduction in resistance in the arteries and veins and the red an increase in the outflow cuff.\u003c/p\u003e\n\u003cp\u003eFig. 1d shows the findings in IIH following CSF drainage with increased resistance in the arteries and reduced elsewhere.\u003c/p\u003e","description":"","filename":"IIHfig1300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-4626772/v1/2f10456ceaf873186f8745b6.png"},{"id":62556890,"identity":"b2efd732-957f-44d8-9b56-2c5cd05ee6cd","added_by":"auto","created_at":"2024-08-15 19:47:40","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":157954,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCSF formation rate vs capillary transmural pressure\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. 2 A graph of the four calculated CSF formation rates vs the transmural pressures for the 4 studies obtained from the literature in blue. The red line is the expected unchanged CSF formation rate if the blood brain barrier were intact i.e. 0.35 ml/min. Note, two studies show a formation rate below normal.\u003c/p\u003e","description":"","filename":"IIHfig2300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-4626772/v1/d56e70af0497a294b6f014a5.png"},{"id":62556626,"identity":"f98637bc-965b-4027-b79d-22ee08635339","added_by":"auto","created_at":"2024-08-15 19:39:40","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":174748,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRelationship between the change in transmural pressure and volume of cortical veins\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. 3 A graph of the change in the cuff resistance vs the cuff transmural pressure with data obtained from [11].\u003c/p\u003e","description":"","filename":"IIHfig3300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-4626772/v1/27b5e3add7ba6f06085fcf58.png"},{"id":62556891,"identity":"d7fbf05d-75a3-4ea1-9a12-e6a4c8febd2a","added_by":"auto","created_at":"2024-08-15 19:47:40","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":542896,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe distribution of the cerebral blood flow from 40 patients with IIH\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. 4 A graph of the blood flow distribution obtained from the data from a published study from one of the authors [25]. Note the IIH data shows a bimodal distribution with peaks at 800 and 1300 ml/min.\u003c/p\u003e","description":"","filename":"IIHfig4300dpi.png","url":"https://assets-eu.researchsquare.com/files/rs-4626772/v1/9ea971af8fb8ab2343fdb2fd.png"},{"id":66388165,"identity":"1f94376e-7eaa-464a-b929-586f2366834d","added_by":"auto","created_at":"2024-10-11 08:31:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2318739,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4626772/v1/6fd94736-834f-49b9-bd3e-c4ffb107ca87.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Lumped Parameter Modelling Study of Idiopathic Intracranial Hypertension: Does the CSF Formation Rate vary with the Capillary Transmural Pressure?","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe clinical syndrome of idiopathic intracranial hypertension (IIH), also known as pseudotumor cerebri, occurs in patients who present with high pressure type headaches and/or papilledema and visual obscuration. At lumbar puncture, the cerebrospinal fluid (CSF) pressures are elevated but the CSF composition is normal [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The diagnosis is made by lumbar puncture, with the accepted cut-off for the diagnosis of IIH being a CSF pressure elevation above 25 cm H\u003csub\u003e2\u003c/sub\u003eO in adults [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Using Davson\u0026rsquo;s Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), it has been argued the elevated intracranial pressure (ICP) could come about by an increase in the CSF formation rate, a CSF outflow obstruction or an increased venous sinus pressure [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. However, it has been suggested that, on the basis of a reduced pressure gradient between the CSF and sagittal sinus in IIH, the venous pressure, rather than an increase in CSF formation rate or increase in CSF outflow resistance, is the underlying cause of IIH [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. There are two recent studies where the pressure gradient between the CSF and venous sinuses were measured at baseline and found to be 2.7 mmHg [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] and 1.8 mmHg [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] compared to a normal value of 4 mmHg [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Davson\u0026rsquo;s equation would suggest these results indicate either a significant reduction in the CSF formation rate or the CSF outflow resistance. Indeed, in the later study [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], the CSF formation rate was assumed to be normal by the authors and the outflow resistance was calculated to be 5.2 mmHg/ml/min compared to a normal figure for age of approximately 13 mmHg/ml/min [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Paradoxically, either a reduced formation rate or outflow resistance are the reverse of what would be expected to induce a raised CSF pressure. When mock CSF was infused in IIH [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], the ICP to sinus pressure gradient increased above normal to 4.9 mmHg. In a study where the ICP was maintained at 0 mmHg using a liquoGuard7 pump, the CSF formation rate in IIH was found to be 86 ml/h or 1.43 ml/min [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] compared to the normal value of 0.35 ml/min [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. This later study suggests the CSF formation rate is increased by over 300% in IIH and would indicate that the CSF formation rate is the variable of interest in IIH rather than the outflow resistance.\u003c/p\u003e \u003cp\u003eThis raises an apparent paradox, the CSF formation rate is normal, increased or decreased in IIH depending on the circumstances. The purpose of this study is to extend a lumped parameter modelling study, initially performed to look at blood flow and pressure in normal pressure hydrocephalus [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], to incorporate the CSF formation rate and capillary transmural pressure (TMP), to try to provide the most feasible explanation for this apparent paradox.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe modelling findings are summarized in Figure 1. \u0026nbsp;The five vascular segments modelled are shown in Fig 1a, with the arterial segment shown in red, the capillaries in orange, the veins in yellow, the outflow cuff in green and the sinus in blue. The pressures obtained from the literature have been appended to the beginning and end of each vascular segment within the vessels in Fig 1a. Given the arterial inflow volume passes through each segment sequentially, the resistance of each segment can be calculated using equation (3). These resistances are appended below the vessels in fig 1. The normal cerebral blood volume (CBV) values for each segment and the total CBV has been obtained from the literature and is shown below the resistances. The blue numbers represent the transmural pressure gradients between the pressure at the beginning and end of each capacitance vessel segment and the ICP, and are obtained by subtraction. The red figure is the average capillary TMP obtained by averaging the TMP before and after the capillaries. \u0026nbsp;Figures 1b-d represent the effects of the differing alterations in perfusion pressure from the differing studies modelled. In these figures, the red segments represent the areas of increased resistance compared to the normal findings and the green represent reduced resistance.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eIdiopathic intracranial hypertension\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn figure 1b, the baseline findings in IIH found in the study by Lalou et al.\u0026nbsp;[6]\u0026nbsp;(i.e., an ICP of 27 mmHg and superior sagittal sinus pressure of 25.2 mmHg.) have been modelled. The arterial inflow has been reduced by 13% compared to normal in keeping with the majority of IIH patients who are oligemic. The pressure drop across the entire system is known from the data as supplied and the total blood flow is specified so the total resistance is calculated using equation (3). The TMP across the outflow cuff is obtained by subtracting the ICP from the sinus pressure and is reduced below normal. The cuff outflow resistance can be calculated from equation (14) and is also reduced. Knowing the cuff resistance and blood flow will set the blood pressure at the end of the veins by using equation (3). The reduction in TMP across the veins reduces their volume using equation (12). The change in venous resistance can be calculated using the change in vein volume using equation (10). This allows the post capillary pressure to be calculated using equation (3). As the capillary outflow pressures and the blood flow are reduced, the capillary TMP will also likely be reduced. Using the capillary tube law as defined, the volume and resistance of this segment will be unchanged from normal. Knowing the total resistance and the other resistances, the arterial inflow resistance can be calculated using equation (4). Note there is a reduction in both the arterial and the outflow cuff resistance with a reduction in resistance overall. The calculated average capillary TMP is reduced by 18.3% compared to the normal value. Using the same technique the capillary TMP can be calculated using the simultaneously obtained data from a similar study from Liu et al. where the baseline ICP and sagittal sinus pressures were 42.2 mmHg and 39.5 mmHg in IIH respectively. The calculated capillary TMP from this study is 10.4 mmHg (not illustrated).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInfusion study in IIH\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFigure 1c models the findings in the study by Lalou et al. following their infusion study\u0026nbsp;[6]. The ICP was found to be 38 mmHg and the sinus pressure 33.1 mmHg. Using the same technique as for Fig 1b, the total resistance is reduced despite the cuff resistance being increased due to the effect of the arterial resistance dropping. The capillary TMP has returned to the normal range at 11.9 mmHg.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCSF drainage in IIH\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFigure 1d models the effect of draining the CSF using the LiquoGuard7 device as used in the study by Tariq et al. [9]. The effect of dropping the ICP to zero is to effectively treat the IIH. A transcranial Doppler study showed the elevation in arterial resistance in IIH will rapidly normalize following CSF withdrawal by lumbar puncture [12], suggesting the CBF should be returned to the normal range with the CSF drainage. Therefore, the flow been set to 750 ml/min in the model. In IIH patients the venous transverse sinuses show narrowing (a stenosis), which shows a rapid return to normal following lumbar puncture [13]. This is the equivalent to the dilatation of the transverse sinuses which occurs in successful stenting procedures in IIH i.e. the pressure gradient along the transverse sinuses returns to normal. The superior sagittal sinus pressure following a successful sinus stenosis stent remains higher than normal at 15.4 mmHg [14]. This appears to be due to the stent failing to treat the raised venous pressure secondary to the obesity induced central venous pressure elevation. Therefore, a normal CBF of 750 ml/min and an outflow pressure of 15.4 mmHg have been modelled in Fig 1d. The model indicates that the outflow cuff is maximally dilated and the resistance of this short segment is reduced to zero. The vastly increased venous TMP maximally dilates the veins by 70% and reduces their resistance. The capillary TMP is increased and the capillary volume will increase. The capillary volume and resistance have been adjusted to allow for this effect. The overall result is to increase the capillary TMP by 86% above normal.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eAs discussed in the introduction, there seems to be some variability in either the CSF outflow resistance (R\u003csub\u003eout\u003c/sub\u003e), or the CSF formation rate (CSF\u003csub\u003efr\u003c/sub\u003e) in IIH. Lalou et al. directly measured the background ICP and venous sinus pressure in IIH, finding mean values of 42.2 mmHg and 39.5 mmHg respectively. They assumed a normal CSF formation rate of 0.35 ml/min and using Davson\u0026rsquo;s Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), obtained a Rout of 5.2 mmHg/ml/min which is 60% less than the normal figure of 13 mmHg/ml/min. Similarly, Liu et al. using a similar technique found an average ICP in IIH of 42.2 mmHg and sinus pressure of 39.5 mmHg, which would give a Rout of 7.7 mmHg/ml/min or 41% less than normal. Finally, Lalou et al. performed an infusion test on their cohort. According to their methodology, the average rate of mock CSF infusion was 1 ml/min, giving an apparent total CSF formation rate of 1.35 ml/min. During the infusion, the average ICP was 38 mmHg and the ICP 33.1 mmHg. Placing these data into Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) gives a Rout of 3.6 mmHg/ml/min or 72% below normal. It is difficult to conceive of a mechanism whereby a very low resistance could fall even further over the space of 10 minutes during the infusion study and then bounce back to normal when finished. If rather than the CSF formation rate being a constant, the R\u003csub\u003eout\u003c/sub\u003e was made a constant, then the CSF formation rate would vary. If the underlying R\u003csub\u003eout\u003c/sub\u003e were normal, then the baseline data from Lalou et al. would give a CSF\u003csub\u003efr\u003c/sub\u003e of 0.14ml/min, the data from Liu et al. a CSF\u003csub\u003efr\u003c/sub\u003e of 0.21 ml/min and the post infusion study data a CSF\u003csub\u003efr\u003c/sub\u003e of 0.38 ml/min. As already discussed, in the study by Tariq et al. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], the CSF was drained to maintain an ICP of 0 mmHg. The effect of this is to place an additional outflow resistance (with an effective resistance of zero) in the system in parallel to all the others. Thus, all of the other normal outflow resistances are effectively excluded from the measurement. The CSF\u003csub\u003efr\u003c/sub\u003e was found to be 1.43 ml/min in IIH or an increase of over 300%. Given the large change in CSF\u003csub\u003efr\u003c/sub\u003e in the final study, and the exclusion of a change in R\u003csub\u003eout\u003c/sub\u003e by this technique, it would seem more likely that the CSF\u003csub\u003efr\u003c/sub\u003e is varying in IIH rather than the R\u003csub\u003eout\u003c/sub\u003e. Therefore, the purpose of the current study is to model the blood flow and pressure of the intracranial system in IIH, to try to find a feasible solution to account for these findings.\u003c/p\u003e \u003cp\u003eIt is generally thought that the CSF\u003csub\u003efr\u003c/sub\u003e does not change with the ICP and remains a constant [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. CSF is produced from differing regions within the brain. Seventy percent of CSF production comes from the choroid plexus, 18% from the capillaries and 12% from glucose metabolism [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The only possible variable component of the CSF production could come from the capillaries but this is excluded if the blood brain barrier (BBB) is intact. Net capillary CSF production or absorption is expected to follow the Starling forces relationship. This is modelled using the following equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{J}_{cap}={L}_{cap}[\\left\\{{P}_{cap}-{P}_{CSF}\\right\\}-{\\sigma\\:}_{cap}\\left\\{{\\pi\\:}_{cap}-{\\pi\\:}_{CSF}\\right\\}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere J\u003csub\u003ecap\u003c/sub\u003e is the capillary fluid flow rate, L\u003csub\u003ecap\u003c/sub\u003e is the capillary hydraulic conductivity,\u003c/p\u003e \u003cp\u003eP\u003csub\u003ecap\u003c/sub\u003e-P\u003csub\u003ecsf\u003c/sub\u003e is the hydraulic pressure gradient across the capillary wall (i.e. the TMP), σ\u003csub\u003ecap\u003c/sub\u003e is the osmotic reflection coefficient and π\u003csub\u003ecap\u003c/sub\u003e-π\u003csub\u003ecsf\u003c/sub\u003e is the osmotic pressure gradient across the capillary wall [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Note, that at steady state, there is no significant difference in hydrostatic pressure between the CSF and the brain parenchyma [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. With an intact BBB, the cerebral capillaries have hydraulic conductivities 2\u0026ndash;3 orders of magnitude less than systemic capillaries [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], the osmotic reflection coefficient is 1 [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] and the osmotic pressure gradient is close to zero [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Therefore, any increase in capillary fluid flow occurring secondary to an increase in capillary TMP would rapidly increase the osmotic pressure difference between the plasma and the interstitium, because the salt does not follow the water due to the high osmotic reflection coefficient. Thus, the capillary plasma would increase in osmotic pressure and the interstitium decrease effectively opposing the hydrostatic pressure difference [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. However, this feedback control of water flow into the brain fails as the BBB breaks down and the net result is an increase in brain water and ICP [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. This is because the hydraulic conductivity would increase and the osmotic reflection coefficient decrease. In IIH there is evidence of a significant disruption of the BBB in IIH with protein leakage [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The barrier breakdown probably occurs secondary to the elevated venous pressure because there is also a BBB disruption in a mouse model of raised cerebral venous pressure [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. If the osmotic reflection coefficient is low, then the salt will follow the water, and the capillary osmotic pressure gradient will not increase. From the Starling forces equation is can be predicted that the capillary flow (i.e. the CSF\u003csub\u003efr\u003c/sub\u003e) will be a linear function of the capillary TMP, with the hydraulic conductivity being the slope of the line. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e is a plot of the 4 experiments from the literature where we estimated the CSFfr (from their data by using a normal R\u003csub\u003eout)\u003c/sub\u003e vs our estimates for the capillary TMP from the modelling (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003e for the TMP results). Note this graph returns a straight blue line with an R\u003csup\u003e2\u003c/sup\u003e of 0.99 indicating an almost perfect correlation. This adds weight to the suggestion that the CSF\u003csub\u003efr\u003c/sub\u003e varies with the capillary TMP in IIH. The red line is the expected constant CSF\u003csub\u003efr\u003c/sub\u003e if the BBB is intact.\u003c/p\u003e \u003cp\u003eCerebral perfusion depends on the pressure across the vasculature. The cerebral perfusion pressure is dependent on the mean arterial pressure minus the ICP [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The brain does not tolerate hypo- or hyper-perfusion, therefore, the maintenance of a constant flow over a range of pressures is achieved by autoregulation [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Dynamic cerebral autoregulation is impaired in IIH and improves after venous sinus stenting [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], suggesting a reduced blood flow pre-stent. It can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e2\u003c/span\u003e that the baseline CSF formation rate for two of the published studies is well below normal. It is apparent this is because the capillary TMP is below normal. This occurs because the cerebral blood flow is lower than normal and the arterial resistances are higher than what would be expected if autoregulation were to maintain a normal flow rate. As discussed in the \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003emethods\u003c/span\u003e section, the reduction in blood flow rate of 13% was selected because it corresponds to the lower mode of the bimodal distribution of blood flow in IIH patients, in the largest published study [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. This correlates with the literature where 71% of IIH patients are obese [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] and obesity reduces the CBF by approximately 12% [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], suggesting the majority of IIH patients will have a low blood flow. This reduction in blood flow is not trivial, there is an elevated lactate/ pyruvate ratio in the CSF of IIH patients suggesting anerobic metabolism [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Thus, the majority of IIH patients have a low blood flow despite evidence of anerobic metabolism. Previous modelling suggests that the arterial supply to the brain can dilate and reduce its resistance down to 24 mmHg/ml/min [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], which is never approached in this current study. This suggests the brain in IIH is electing to be oligemic rather than being forced to be oligemic. Raichle et al. came to a similar conclusion stating \u0026ldquo;the cerebral perfusion pressure does not appear to approach the limit of autoregulation in IIH\u0026rdquo; [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. When we attempted to increase the blood flow in the model (in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e1\u003c/span\u003eb) back to normal at 750 ml/min, a positive feedback loop ensued whereby the arterial segment was required to dilate. This increased the capillary TMP (and CSF\u003csub\u003efr\u003c/sub\u003e), which increased the ICP, which compressed the venous sinus and outflow cuff, increasing the capillary TMP further and also initiating a further dilatation of the artery to maintain blood flow. This feedback loop could continue until the artery was fully dilated and a very high ICP resulted. This suggests a reduced blood flow is a harm minimisation strategy of the brain to reduce the ICP to a minimum.\u003c/p\u003e \u003cp\u003eThus paradoxically, the reduction in CBF and the opening of the blood brain barrier are partially beneficial in IIH, in that they allow the ICP to be moderated. The modelling would predict that the stabilisation of this blood brain barrier disruption would increase the ICP by not allowing for some net absorption of CSF via the capillaries. There are two classes of drugs known to stabilise the blood brain barrier, tetracycline based antibiotics [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] and retinoic acid compounds [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. These compounds are both known to trigger IIH in those predisposed to the disease [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Suggesting blood brain barrier stabilisation is not an ideal strategy in IIH.\u003c/p\u003e \u003cp\u003eThere are many assumptions inherent in the lumped parameter modelling. We can test the modelling we have performed by comparing the outcomes predicted by the model with the literature. The oligemic IIH model incorporates the majority of IIH patients, and the model suggests the total blood volume is not significantly different at 50.4 ml, to normal at 51 ml. Two studies have found a normal cerebral blood volume in IIH [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. One study found a 33% increase in CBV in IIH [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. However, the methodology in this paper was flawed. They measured the CBV with one technique (carbon monoxide red cell labelling) but compared the findings to controls using another method (fluorescence) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Comparing their results to the normal red cell findings in an earlier paper by the same group [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] showed no significant difference in the CBV in IIH. Thus, our modelling appears to be accurate enough for the current purposes. Poiseuille\u0026rsquo;s equation requires flow through a thin, rigid, circular tube of a Newtonian fluid, without turbulence. To the degree that these assumptions hold, the findings would be accurate. However, despite its limitations, this equation is commonly used in modelling the vasculature in the literature.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eEquations\u003c/h2\u003e \u003cp\u003eThe study begins with Davson\u0026rsquo;s equation which relates the intracranial pressure (ICP) to the CSF formation rate, the CSF outflow resistance and the venous sinus pressure [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:ICP={CSF}_{fr}\\times\\:{R}_{out}+{P}_{sss}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere ICP is the intracranial pressure, CSF\u003csub\u003efr\u003c/sub\u003e is the CSF formation rate, R\u003csub\u003eout\u003c/sub\u003e is the CSF outflow resistance and P\u003csub\u003esss\u003c/sub\u003e is the pressure in the superior sagittal sinus. Next Ohms law for hydraulic circuits is required:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:P=Q\\:\\times\\:\\:R$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere ΔP is the pressure drop across a vascular segment, Q is the flow rate through the segment and R is the resistance. As resistances in series are directly additive the following can be derived:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{R}_{art}+{R}_{cap}+{R}_{ven}+{R}_{cuf}={R}_{tot}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere R\u003csub\u003eart\u003c/sub\u003e is the arterial segment resistance, R\u003csub\u003ecap\u003c/sub\u003e is the resistance of the capillaries, R\u003csub\u003even\u003c/sub\u003e is the venous resistance, R\u003csub\u003ecuf\u003c/sub\u003e is the resistance of the venous outflow cuff and R\u003csub\u003etot\u003c/sub\u003e is the total resistance for the entire vascular system. Poiseuille\u0026rsquo;s equation calculates the pressure drop across each of these segments:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:P=\\raisebox{1ex}{$8\\mu\\:LQ$}\\!\\left/\\:\\!\\raisebox{-1ex}{$\\pi\\:{r}^{4}$}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere ΔP is the pressure drop, \u0026micro; is the viscosity, L is the vessel length, Q is the fluid flow rate, π is the circle proportionality constant and r is the radius. Substituting Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) into (5) and eliminating Q from both sides gives an equation for the resistance in each segment:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:R=\\raisebox{1ex}{$8\\mu\\:L$}\\!\\left/\\:\\!\\raisebox{-1ex}{$\\pi\\:{r}^{4}$}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this modeling study the viscosity, the length of each vessel segment, and π are constants, so it can be shown that a change in resistance for any segment depends only on a change in the vessel radius i.e.\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:R=\\varDelta\\:{r}^{-4}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe volume of a vessel is given by the equation for a cylinder i.e.\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:V=L\\pi\\:{r}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere V is the volume, L is the vessel length and r is the radius of the vessel. Given L and π are constants for any given segment, the change in volume is dependent on the change in radius i.e.\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:V=\\varDelta\\:{r}^{2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eSubstituting Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e9\u003c/span\u003e) into Eq.\u0026nbsp;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) gives\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:\\varDelta\\:R=\\varDelta\\:{V}^{-2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe next equation relates the transmural pressure across a vessel to the vessel cross-sectional area [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]:\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:{P}_{tm}=\\frac{4Eh}{{3R}_{o}}(1-\\sqrt{\\frac{{A}_{o}}{A}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere P\u003csub\u003etm\u003c/sub\u003e is the transmural pressure across the vessel wall (lumen pressure- CSF pressure), E is the circumferential Young\u0026rsquo;s modulus of the vessel wall, h is the wall thickness, R\u003csub\u003eo\u003c/sub\u003e is the radius in the stress free state, A\u003csub\u003eo\u003c/sub\u003e is the area in the stress free state and A is the area following the applied transmural pressure. This equation was previously used to show that the volume of the venous outflow varies with the transmural pressure by the equation [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]:\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\:{\\varDelta\\:TMP}_{ven\\:\\:}=-0.033{{\\varDelta\\:V}_{ven}}^{2}+7.49\\times\\:{\\varDelta\\:V}_{ven}-3.44$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere ΔTMP\u003csub\u003even\u003c/sub\u003e is the normalized increase in venous transmural pressure and ΔV\u003csub\u003even\u003c/sub\u003e is the change in venous volume.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e\u003cb\u003eModel input parameters\u003c/b\u003e\u003c/h2\u003e \u003cp\u003eThe input parameters are unchanged from the previous study [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] and will only be briefly described as the details can be obtained from the original study. This study is based on a middle aged individual with a brain size of 1500g. A normal global CBF is 50 ml/100g/min [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], giving a normal cerebral blood arterial inflow of 750 ml/min. The normal mean arterial inflow pressure is 100 mmHg [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. The normal precapillary bed pressure is 32 mmHg [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. The end capillary pressure is estimated to be 15 mmHg [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. The normal CSF pressure in middle age is 11.5 mmHg [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e] and the normal pressure gradient from the CSF to the superior sinus lumen is 4 mmHg, [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] giving a normal sinus pressure by subtraction of 7.5 mmHg [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. The normal transmural pressure of the subarachnoid cortical veins in primates is 2.5 mmHg [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Using this figure for the model, it can be seen that the pre-venous outflow cuff pressure is 14 mmHg by addition of the TMP to the ICP.\u003c/p\u003e \u003cp\u003eIn a 1500g brain, the total CBV would be 51 ml [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Hua et al. found the arterial component of the CBV to be 25% [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e] or 12.8 ml in total. This leaves the remaining 75% for the capacitance vessels, including the veins and capillaries or 38.2 ml. The estimated percentage of this latter figure for the capillaries is 53% [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e], giving a total capillary blood volume of 20.3 ml and a total venous blood volume of 17.9 ml.\u003c/p\u003e \u003cp\u003eThe normal CSF outflow resistance (R\u003csub\u003eout\u003c/sub\u003e) has been found to depend linearly with age, with the regression line being: [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\:{R}_{out}=0.075\\times\\:Age+9.88$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThis gives a normal R\u003csub\u003eout\u003c/sub\u003e for a 40 year old of 13 mmHg/ml/min. The normal CSF formation rate is 0.35 ml/min [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eVessel responses to transmural pressure variations\u003c/h2\u003e \u003cp\u003eIt is assumed that variations in the arterial resistance and volume in this model depend entirely on the arterial autoregulation and muscle tone and not the vessel transmural pressure. As the arterial pressure is always much higher than the ICP, the arterial transmural pressure will have no effect on the outcome of the current modelling study.\u003c/p\u003e \u003cp\u003eIn the capillary bed, the vessels do not actively alter their diameter [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e], indicating they react purely to their transmural pressure. In a rat model, extreme hyperventilation decreased the PCO\u003csub\u003e2\u003c/sub\u003e from 40 to 21.6 mmHg without affecting PO\u003csub\u003e2\u003c/sub\u003e, the capillary size was not significantly different to controls despite the expected arteriolar constriction [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. However, in the opposite case, in rats made extremely hypercapnic secondary to hypoventilation, the PCO\u003csub\u003e2\u003c/sub\u003e increased to 95.6 mmHg but PO\u003csub\u003e2\u003c/sub\u003e was normal, the capillary diameter increased by 20% consistent with a 44% increase in volume compared to known control values [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. Thus, a moderate reduction in capillary TMP does not change the capillary size but a maximal increase in TMP increases their volume by 44%. To simplify the current study, it is assumed the volume of the capillaries vary between normal and maximally dilated as a linear function of their transmural pressure. A previous study indicated an increase in capillary TMP from 12 to 37.9 mmHg would increase the capillary volume by 44% or a 1.7% increase in volume for each 1 mmHg pressure rise. Below a TMP of 12 mmHg the volume is unchanged at 20.3 ml and above a TMP of 37.9 the elastic limit is reached and the volume is set to 29.2 ml.\u003c/p\u003e \u003cp\u003eSimilar to the capillaries, the veins alter their size purely depending on their transmural pressures. In a previous modelling study [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] the function for the outflow vein dilatation was found to be summarized by Eq.\u0026nbsp;(\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e12\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAt the distal end of the cortical veins, as they join the sinus wall, the outflow cuff segment resides. The collapse of this segment occurs physiologically and is passively modulated by the transmural pressure between the ICP and the sinus pressure, which is usually negative [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. The segment is very short, and as it is mostly under a state of collapse with physiological ICPs, the change in volume from this segment will be ignored in this model. However, its resistance will be taken into consideration. In the previous study four differing cuff transmural pressures resulted in 4 differing resistances [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. When these points were plotted, a line with R\u003csup\u003e2\u003c/sup\u003e of 0.998 resulted, suggesting the cuff resistance varies as a linear function of the cuff TMP (see Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Thus giving Eq.\u0026nbsp;14:\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{cuf}=-2.71\\times\\:{TMP}_{cuf}\\)\u003c/span\u003e\u003c/span\u003e+0.008 (14)\u003c/p\u003e \u003cp\u003eWhere R\u003csub\u003ecuf\u003c/sub\u003e is the cuff resistance and TMP\u003csub\u003ecuf\u003c/sub\u003e is the cuff transmural pressure.\u003c/p\u003e \u003cp\u003eThe sagittal sinus pressure will be varied as per the literature being modelled.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eThe arterial inflow in IIH\u003c/h2\u003e \u003cp\u003eIt has been argued that there are actually two populations within most studies where cerebral blood flow has been measured in IIH [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. Capel et al. measured CBF in 13 patients with IIH [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. Their data were consistent with two populations, a larger one with reduced CBF, and two outliers with a larger CBF [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. Bicakci et al. found an overall normal CBF in IIH [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. However, of the 16 patients they studied, there were 6 with a blood flow two standard deviations below the mean compared to the controls, 8 with flow in the normal range and two with flow greater than 8 standard deviations above the mean compared to the controls [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. The largest study quantifying the arterial inflow in IIH patients was performed by one of the current authors describing 40 patients [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The pooled data from this study is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e. A Shapiro- Wilk test confirms the control data in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e4\u003c/span\u003e to be a normal distribution, with the CBF averaging 920\u0026thinsp;\u0026plusmn;\u0026thinsp;108 ml/min and the ages averaging 33.1\u0026thinsp;\u0026plusmn;\u0026thinsp;12 years. A Tukey test indicated the IIH data had a single outlier at 2000 ml/min which will be removed from further evaluation. The remaining data showed a bimodal distribution with the first mode at 800 ml/min and the second at 1300 ml/min. There was a gap with no IIH patient at 950 ml/min. A Shapiro-Wilk test confirmed the patients with a CBF below 950 ml/min (the oligemic group) conformed to a normal distribution with the CBF 13% below the controls (p\u0026thinsp;=\u0026thinsp;0.0006), their age was 30.6\u0026thinsp;\u0026plusmn;\u0026thinsp;10.3 years. The average ICP for the oligemic group was 33.3\u0026thinsp;\u0026plusmn;\u0026thinsp;24.5 mmHg. The patients with a CBF above 950 ml/min also conformed to a normal distribution with the CBF averaging 35% above the controls (p\u0026thinsp;\u0026lt;\u0026thinsp;0.0001), their age averaged 31\u0026thinsp;\u0026plusmn;\u0026thinsp;12.4 years and the ICP 31\u0026thinsp;\u0026plusmn;\u0026thinsp;22.8 mmHg. Given that most studies seem to indicate that the oligemic patients predominate, a CBF 13% below normal will be utilized in this study.\u003c/p\u003e \u003c/div\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eBBB, blood brain barrier; CBF, cerebral blood flow; CBV, cerebral blood volume; CSF, cerebrospinal fluid; CSF\u003csub\u003efr\u003c/sub\u003e, cerebrospinal fluid formation rate; ICP, intracranial pressure; IIH, idiopathic intracranial hypertension; \u0026nbsp;min, minute; ml, milliliter; mm, millimeters; mmHg, millimeters of mercury; R\u003csub\u003eout\u003c/sub\u003e, CSF outflow resistance; TMP, transmural pressure.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analysed during this study are available within the original paper or on reasonable request to the corresponding author GAB.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor\u0026rsquo;s contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualisation and design GAB, ARB. Modelling GAB, ARB. Writing original draft GAB. Review and editing all authors. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eN/A\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u0026nbsp;\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJohnston, I., Hawke, S., Halmagyi, M. \u0026amp; Teo, C. The pseudotumor syndrome. 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A scoping review of the discrepancies in the measurement of cerebral blood flow in idiopathic intracranial hypertension: oligemia, euvolemia or hyperemia? \u003cem\u003eFluids Barriers CNS\u003c/em\u003e \u003cstrong\u003e20\u003c/strong\u003e, 63, doi:10.1186/s12987-023-00465-w (2023).\u003c/li\u003e\n\u003cli\u003eCapel, C.\u003cem\u003e et al.\u003c/em\u003e Cerebrospinal Fluid and Cerebral Blood Flows in Idiopathic Intracranial Hypertension. \u003cem\u003eActa Neurochir Suppl\u003c/em\u003e \u003cstrong\u003e126\u003c/strong\u003e, 237-241, doi:10.1007/978-3-319-65798-1_48 (2018).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"cerebral blood flow, idiopathic intracranial hypertension, CSF formation rate, blood brain barrier, tetracycline, retinoic acid","lastPublishedDoi":"10.21203/rs.3.rs-4626772/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4626772/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStudies simultaneously measuring the intracranial pressure (ICP) and sagittal sinus pressures in idiopathic intracranial hypertension (IIH), suggest either a reduction in the CSF outflow resistance or the CSF formation rate. A study maintaining the ICP at zero showed a significantly elevated CSF formation rate. The purpose of this study is to define the most feasible explanation for these findings. A lumped parameter model originally developed to study normal pressure hydrocephalus was extended to investigate IIH. The model was used to estimate the CSF formation rate and the capillary transmural pressure (TMP), utilizing the data from 4 experiments published within the literature. When the CSF formation rates of these 4 studies were plotted against the estimated capillary transmural pressures, a straight line with an R\u003csup\u003e2\u003c/sup\u003e of 0.999 was returned. The model suggests the CSF formation rate in IIH varies with the capillary TMP. A reduced capillary TMP secondary to a reduced blood flow in IIH moderates the ICP. The variation in formation rate is most likely a function of the blood brain barrier (BBB) breakdown known to occur in this disease. Drugs which stabilize the BBB may trigger IIH.\u003c/p\u003e","manuscriptTitle":"A Lumped Parameter Modelling Study of Idiopathic Intracranial Hypertension: Does the CSF Formation Rate vary with the Capillary Transmural Pressure?","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-15 19:39:35","doi":"10.21203/rs.3.rs-4626772/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"21558dd3-e64f-415f-9746-22edfdd4fb26","owner":[],"postedDate":"August 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":35833283,"name":"Health sciences/Diseases"},{"id":35833284,"name":"Health sciences/Neurology"},{"id":35833285,"name":"Health sciences/Pathogenesis"}],"tags":[],"updatedAt":"2024-10-11T08:23:33+00:00","versionOfRecord":[],"versionCreatedAt":"2024-08-15 19:39:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4626772","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4626772","identity":"rs-4626772","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}