We can see that the sagittal sinus pressure is an important element in the calculation of R
out but the sinus pressure is almost never measured. It is either calculated from Davson’s equation itself (circular reasoning) or assumed to be a constant. Calculations of the sagittal sinus pressure by Ekstedt suggested that the sinus pressure does not change throughout life [
3] but as already discussed, this would appear to be unlikely. The purpose of the current study was to estimate the sinus pressure using a non-invasive technique based on a modified Poiseuille equation, which is therefore independent of Davson’s equation. This will be used to test how well infusion studies perform throughout life and following the development of communicating hydrocephalus.
The current study utilised a modification of Poiseuille’s equation using vascular area and blood flow data obtained from the current study. The proportionality constant in the equation was derived from manometry pressure measurements in children obtained from the literature (see methods). The mean sinus pressure for normal children obtained from the literature was 10.5 mmHg. The derived equation was then used to predict the sinus pressures in a normal adult cohort independent of the literature. A mean value of 7.7 mmHg was obtained. This compares well to Ekstedt’s reference value for the sinus pressure of 7.5 mmHg [
3]. Martins
et al. measured the sagittal sinus pressure in adults aged 18 to 60 yr and found that in the 9 individuals where the CSF pressure was independent of the ICP, the sinus pressure averaged 8.0 mmHg [
15] which again is very similar to the figure predicted by the current study. Iwabuchi
et al. found the sinus pressure to be between 4.8 and 9.1 mmHg in adults of mean age 45 years, the range depending on the technique used [
14]. Therefore, the current technique appears to correlate well with the available literature for adults indicating an acceptable precision. These findings indicate that the sinus pressure is reduced with age. The cross-sectional area of the sinuses does not appear to change from the first decade to the fifth, indicating the venous outflow resistance is unchanged throughout this period of normal life. The reduction in pressure appears to be directly proportional to the reduction in blood flow.
Davson’s equation revisited
Having established a normal range for sinus pressures, we can test Davson’s equation by utilising the most up to date figures available in the literature for the ICP, R
out and FR
CSF and calculate the sinus pressure using this technique. In a large study, the average CSF pressure in 10-year old children was found to be 14.6 mmHg [
16]. The R
out has been found to depend linearly with age, with the regression line being; 9.88 + 0.075 × Age in mmHg/ml/min [
17]. This gives a R
out of 10.63 mmHg/ml/min at 10 years. The CSF formation rate is highest in children and young adults, being about 0.4 ml/min and decreases with age to about 50% of this value at age 70 years [
18]. Therefore, Davson’s equation predicts an average sinus pressure of 10.3 mmHg (14.6- 10.63× 0.4) in children with a pressure gradient across the arachnoid granulations of 4.3 mmHg for CSF to flow. This sinus pressure correlates well with the literature (10.5 mmHg). Similarly, in normal middle age, the CSF pressure in a very large study averaged 11.5 mmHg at 45 years [
19]. Using the equation as discussed above, the R
out at 45 years would be 13.3 mmHg/ml/min. The CSF formation rate is reduced by 50% in old age, and its reduction is said to be linear throughout life [
20]. Therefore, we can estimate a 25% reduction in middle age giving a figure of 0.3 ml/min. Thus, Davson’s equation estimates the sinus pressure to be 7.5 mmHg (11.5- 13.3× 0.3) with a pressure gradient of 4 mmHg across the arachnoid granulations in middle age. This sinus pressure is similar to the published literature, and the findings in the current study (7.7 mmHg), indicating that CSF infusion studies are probably quite accurate in normal individuals.
In patients with chronic hydrocephalus of average age 54 years, the average CSF pressure was found to be 1.5 mmHg higher than the control group [
20], which would give a CSF pressure of 13 mmHg at 45 years. The average CSF formation rate in the hydrocephalus patients was 0.25 ml/min [
20]. In the Dutch normal-pressure hydrocephalus study, a good outcome from treatment of NPH was found to be in individuals with a R
out greater than 18 mmHg/ml/min but averaging approximately 24 mmHg/ml/min [
21]. Similarly, Czosnyka
et al. noted that the upper limit of normal for R
out is about 12 mmHg/ml/min, with NPH patients often being twice this amount [
22]. Thus, the R
out in chronic hydrocephalus is about 24 mmHg/ml/min. Therefore, Davson’s equation estimates the venous pressure to be 7 mmHg (13-24× 0.25) in chronic hydrocephalus with a pressure gradient across the arachnoid granulations of 6 mmHg. We can see there is a discrepancy between the current study and infusion studies in hydrocephalus. Infusion studies predict a normal sagittal sinus pressure in hydrocephalus (7 mmHg) but the estimation of the sinus pressure based on flow and area of the sinuses suggests 10.2 mmHg or 3.2 mmHg higher. Which figure is correct? There is almost no information in the literature regarding sinus pressure in chronic hydrocephalus. Hash
et al. noted that an attempt to shunt CSF directly into the sagittal sinus in a patient with NPH failed because the sinus pressure was 1 mmHg higher than the CSF pressure (i.e. elevated) and there was no pressure gradient for CSF absorption [
23]. In another study, a prediction of an elevation in sinus pressure of 3–4 mmHg above normal in chronic hydrocephalus was made based on evidence of increased collateral flow bypassing the sinuses [
24]. In a kaolin dog model of chronic hydrocephalus, the initial phase was associated with an elevation in CSF and sinus venous pressure, with a normal CSF to sagittal sinus gradient. In the chronic phase, the CSF pressure returned to normal and there was some reduction in sinus pressure but it remained elevated with loss of the pressure gradient across the arachnoid granulations [
25]. Similarly, in a rat model of hydrocephalus, there was loss of the pressure gradient between the CSF and sinus during infusion studies with the venous pressure rising linearly with CSF pressure [
26]. The illustrative case in the current study appears similar to this literature. Without a shunt, the sinus pressure was 11 mmHg and the CSF pressure 13–14 mmHg, giving a gradient across the arachnoid granulations of 2–3 mmHg. We know from the predictions of Davson’s equation that in normal middle aged subjects, a gradient pressure of about 4 mmHg is required for CSF to flow. Therefore, the lack of absorption at the vertex appears to be due to an unfavourable pressure gradient and not blocked granulations in this case (in the later instance the gradient pressure should have been increased). Similarly, the pooled data suggests a CSF pressure of 13 mmHg in chronic hydrocephalus with a sinus pressure of 10.2 mmHg, giving a gradient across the granulations of 2.8 mmHg and therefore no CSF flow.
The current study would tend to suggest that infusion studies underestimate the venous pressure in hydrocephalus. If we corrected Davson’s equation for a sinus pressure of 10.2 mmHg, then in order for the equation to balance, either the R
out or the CSF formation rate must have been over estimated. The estimate of the CSF formation rate is made by reducing the CSF pressure significantly and measuring the CSF flow required to maintain this pressure. It is said the CSF formation rate is not altered by CSF pressure, so it is unlikely to be overestimated [
27]. In the illustrative case the CSF formation rate was 0.22 ml/min which compares well with the literature [
20]. Thus, the R
out is probably at fault. The R
out corrected for a sinus pressure of 10.2 mmHg would average 11.2 mmHg/min/min ((13–10.2)/0.25) for the hydrocephalus cohort in order to balance Davson’s equation. Thus, if the sinus pressure figure of 10.2 mmHg is correct, then the R
out in chronic hydrocephalus is actually normal. Therefore, it is being overestimated two fold by infusion studies. In the illustrative case, the ICP whilst the ventricular drain was monitored averaged 13.5 mmHg, the formation rate was 0.22 ml/min and the sinus pressure was 11 mmHg. Therefore Davson’s equation gives the actual R
out to be (13.5-11)/ 0.22 = 11.4 mmHg/ml/min in this case which is normal and similar to the pooled data figure just discussed.
A cause for Rout overestimation
In a recent study, R
out was found to be overestimated if the venous pressure increased during the course of the infusion study. The degree of this overestimation was dependent on the proportion of the CSF pressure which was fed back to the sinuses. In pseudotumor cerebri, if 80% of the increase in CSF pressure occurring during the study was fed back to the sinuses then the R
out was overestimated 5 fold i.e. if the CSF pressure was raised by 10 mmHg during the test and collapse of the sinuses allowed them to increase in pressure by 8 mmHg, then the test would overestimate a normal R
out as being elevated five times normal [
5]. The two fold overestimation found in the current study could be accounted for by a feedback percentage of 50%. In the illustrative case, whilst the shunt was working the CSF pressure was set by the valve at about 7 mmHg and the estimate of the sinus pressure was 7.9 mmHg. When the shunt was removed, the CSF pressure went up to about 13.5 mmHg or an increase of 6.5 mmHg. The sinus pressure went up to 11 mmHg or an increase in pressure of 3.1 mmHg. Therefore, the increase in CSF pressure increased the sinus pressure by passive collapse. The feedback percentage was 50%. Thus, if an infusion study were performed it would overestimate the R
out, in this case two fold due to the collapse of the sinuses (i.e. to about 22.8 mmHg/ml/min).
How wide spread is this problem? Obviously if infusion studies are accurate in normal patients, then the sinuses of normal patients do not collapse to any significant degree. In a study where ICP was altered by the addition or removal of CSF, nine of twelve patients showed no change in sinus pressure, despite the CSF pressure being raised by up to 75 mmHg. Therefore, there was no venous collapse in these cases and an infusion study would be accurate. In the remaining three patients the sagittal sinus pressure increased by 12 mmHg during a 20 mmHg elevation in CSF pressure (about a 60% feedback fraction). In one of these patients, a venogram showed a partial collapse of both the sagittal and transverse sinuses during the raised CSF pressure [
15] (similar to the illustrative case). If an infusion study were performed on these three individuals it would overestimate R
out by over two fold.
The underlying pathophysiology of chronic hydrocephalus
If the venous pressures rise by 3 mmHg in chronic hydrocephalus, why do the CSF pressures increase by only 1.5 mmHg [
20]? A moderation of the CSF pressure would require a parallel CSF outflow pathway, other than the arachnoid granulations, to reduce the total outflow resistance and make up for the unfavourable gradient pressure across the granulations. We know there is transependymal CSF absorption in hydrocephalus [
28] and this may provide a parallel pathway. It has been suggested that capillary absorption is not possible because the CSF pressure would need to be above the capillary pressure and the capillaries would collapse [
29]. However, the absorption of water across a capillary bed depends on all the Starling forces not just the hydrostatic pressure. It has been estimated that no net absorption or filtration of water would occur with an average capillary bed pressure of 32 mmHg in the brain [
30]. If the capillary bed were reduced from 32 mmHg to anywhere above 13 mmHg, then the capillaries would absorb water but maintain their blood flow at a lower level. Below 13 mmHg the capillaries would start to collapse and blood flow would cease. In chronic hydrocephalus the subependymal white matter is ischemic [
31,
32]. Therefore, there is a reduction in blood flow at a reduced capillary pressure, bringing about bulk water absorption and moderating the CSF pressure.
If the venous pressure is raised why don’t all patients have small ventricles like pseudotumor cerebri? Whether or not the ventricles dilate depends on brain turgor. If the brain is stiff the ventricles will not dilate, if it is more compliant they will. Brain turgor is predominantly affected by the medullary venous pressure [
5]. If the sinuses collapse during an elevation in CSF pressure and 80-90% of the CSF pressure is fed back to the veins, then the medullary veins will be close to CSF pressure and no ventricular dilatation will ensue i.e. pseudotumor cerebri or slit ventricle syndrome [
5]. If the feedback fraction is 50% then the venous pressure will lag behind the CSF pressure. Also, the subependymal white matter is ischemic. Therefore, the medullary pressure is lower, so brain turgor is less in this region, and the ventricles may enlarge [
5].
Study limitations
The present study limits its scope to patients between the ages of 30 and 65 years because of the risk of significant co-morbidity from dementia and atrophy in older patients. Therefore, the applicability to NPH patients in the age group over 65 may be limited until further research is done. The methods utilise MRI, which requires quiet respiration in a supine patient, so it is difficult to draw conclusions as to how the sinuses may react to the upright posture or valsalva manoeuvre. These limitations are common to most hydrocephalus research. The central venous pressures were not measured directly but estimated to be normal, given the patients were not morbidly obese or in right heart failure, this is probably justified.
Poiseuille’s equation assumes laminar flow in a uniform cylinder with rigid smooth walls. It is obvious that the sinuses have bends in the sigmoid region, there is some irregularity to the walls and probably wall movement. Thus, the calculations can only be a first approximation to reality. The flow is probably laminar in the sinuses due to the low Reynold’s numbers involved. The wall irregularity and bends would be similar between the controls and test patients but the wall pulsation is probably greater in the more compliant sinus walls in the hydrocephalus patients. The flexible walls of the sinus distort in the hydrocephalus patients and the sinuses become more triangular and less cylindrical compared to the controls. As triangular pipes are less efficient, the effect may have been to underestimate the resistance slightly in the hydrocephalus group compared to the controls.
The outflow resistance of both transverse sinuses was added together and both sinuses assumed to act as a single resistor because this considerably simplified the calculations. This would be a reasonable assumption if the ratio of the resistances between the right and left sinuses remained the same in the control and test groups. If there was a significant variation, then depending on the magnitude, the pressure would be over or under estimated. The ratio of the average right and left transverse sinus resistances for the adult controls was 2.2:1 and for the hydrocephalus patients 1.56:1. Recalculating the pressure gradient across the sinuses in the hydrocephalus patients taking the parallel resistances into account provided an estimate of 9.95 mmHg compared to the quoted figure of 10.2 mmHg or a 2.5% error which did not affect the outcome of the study.