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The pathogenesis of pseudotumor cerebri
Journaf of the Neurological Sciences, 1980, 48:51-60 © Elsevier/North-Holland Biomedical Press
51
THE PATHOGENESIS OF PSEUDOTUMOR CEREBRI A Mathematical Analysis
ROBERT M. AISENBERG and DAVID A. ROTTENBERG
Departments of Neurology, Memorial Sloan-Kettering Cancer Center and Cornell University Medical College, New York, N Y (U.S.A.) (Received 29 January, 1980) (Accepted 7 May, 1980)
SUMMARY
Although the clinical and laboratory features of pseudotumor cerebri have been clearly delineated, the pathogenesis of idiopathic pseudotumor remains a mystery. A number of pathogenetic mechanisms have been proposed to account for some or all of the observed cases. We describe a model relating changes in CSF outflow resistance and/or dural sinus venous pressure to observed changes in (i) CSF pressure, (ii) cerebral blood volume and (iii) the volume and hydrodynamic flow resistance of the ventriculosubarachnoid space.
INTRODUCTION
Although the clinical and laboratory features of pseudomotor cerebri have been clearly delineated (Weisberg 1975; Bulens et al. 1979), the pathogenesis of idiopathic pseudotumor remains a mystery. On occasion, the clinical picture is atypical or confusing: the "disease process" may be asymptomatic (Bulens et al. 1979), and papilledema may be absent (Lipton and Michelson 1972). In most
Dr. Rottenberg is the recipient of Teacher Investigator Award No. 1 K07 NS00286-01 from the National Institute of Neurological and Communicative Disorders and Stroke. Address reprint requests to: David A. Rottenberg, M.D., Department of Neurology, Memorial Hospital, 1275 York Avenue, New York, NY 10021, U.S.A. Abbreviations : CBV, cerebral blood volume; CSF, cerebrospinal fluid; CSFP, cerebrospinal fluid pressure; ICP, intracranial pressure; If, rate of CSF formation; Pd, dural sinus venous pressure; PVI, pressure-volume index; Ra, arachnoid villous flow resistance; Rs, flow resistance of the convexity subarachnoid space; R~,. limiting value of R~; R t, total CSF outflow resistance; SVP, subarachnoid venous pressure.
52 TABLE 1 CSFP IN P S E U D O T U M O R CEREBRI
Pressure (mm CSF)
Patterson et al. (1961) a Johnston and Paterson (1974) b Foley (1975) a Weisberg (1975) c
Totals"
200-299
300 399
400 499
5(}0
2 2 2 12
3 5 3 72
7 3 3 30
3
6
18
83
43
~)
a Lumbar subarachnoid pressure. b Ventricular pressure. c Site of pressure measurement not specified.
instances, the electroencephalogram is normal, although intracranial pressure is markedly elevated (Table 1); neuroradiologic studies, including isotope cisternography, cerebral angiography and CT, are almost invariably normal or nondiagnostic (James et al. 1974; Weisberg 1975 ; Delaney and Schellinger 1976; Butens et al. 1979). Characteristically, the cerebrospinal fluid is of normal composition, though the protein concentration may be in the low-normal range. Even the designations "pseudotumor cerebri" and "benign intracranial hypertension" are misnomers: "Pseudotumor cerebri" erroneously implies that tumors - - in and of themselves - - increase intracranial pressure, whereas 'benign intracranial hypertension" reflects the prevailing but incorrect notion that afflicted individuals invariably recover without serious sequelae. In fact, brain tumors may be remarkably symptomatic in the absence of increased intracranial pressure (ICP) (Van Crevel 1975), and patients with pseudomotor cerebri may go blind or become chronically disabled by recurring symptoms (Foley 1977). Numerous hypotheses have been put forward to explain the pathogenesis of pseudotumor cerebri and its occasional relationship to anemia, endocrinopathy, vitamin and drug therapy, etc. The following pathogenetic mechanisms have been proposed to account for some or all of the observed cases: (1) increased cerebral blood volume (CBV) (Dandy 1937), (2) increased brain water content (cerebral edema) (Sahs and Joynt 1956; Raichle et al. 1978), (3) increased dural sinus venous pressure (Ray and Dunbar 1950; Marr and Chambers 1961), (4) CSF hypersecretion (Donaldson 1979), and (5) increased CSF outflow resistance (Johnston 1975; Johnston et al. 1975; Fishman 1979). Dural sinus thrombosis was initially implicated by Symonds (1937) and Gardner (1939) as a causative factor in patients with "otitic hydrocephalus" (Symonds 1931), but the vast majority of pseudotumor patients do not have otitic hydrocephalus. We [and others (Johnston 1975; Fishman 1979; Mann et al. 1979)] believe that pseudotumor cerebri results from an increase in
53
Fig. 1. The cerebrospinal fluid system. arachnoid villous flow resistance, Ra, and/or an increase in dural sinus venous pressure, Pd (Fig. 1). The following model relates changes in Ra and/or Pd to observed changes in CSF pressure (CSFP) and CBV and to the volume and hydrodynamic flow resistance of the ventriculosubarachnoid space. The etiology of these changes in R~ and/or Pd is not specifically considered. MODEL ASSUMPTIONS
(1) CSF statics In the steady state, CSFP may be described by Equation 1, CSFP = Po + ifRt,
[Equation 1]
where Pd is dural sinus venous pressure, If is the rate of CSF formation and Rt is total CSF outflow resistance (Marmarou et al. 1978). Sagittal sinus compression/ occlusion, dominant lateral sinus thrombosis or jugular venous obstruction may increase Pd (Rottenberg and Posner 1980). In the absence of a choroid plexus papilloma, If is rarely, if ever, increased. R,, which represents the resistance of the arachnoid villi, R~,,in series with the resistance of the convexity subarachnoid space, R~, may be increased by structural alterations in the arachnoid villi themselves (Hayes et al. 1971) or by compartmentalization or compromise of the cerebral subarachnoid space (see Mathematical Appendix).
54
(2) CSF dynamics In general, abrupt increases in the volume of the intracranial contents produce predictable changes in CSFP. That is, CSFP = Po. 106wPv~,
[Equation 2]
where Po is initial or resting CSFP, AV is the volume increment or decrement and PVI is the pressure-volume index [the volume increment or decrement required to raise or lower CSFP 10-fold (Marmarou et al. 1978)].
(3) The Monro-Kellie hypothesis The Monro-Kellie hypothesis refers to the concept of a rigid craniocerebral compartment within which the sum total of brain volume + CSF volume + CBV remains constant; any change in the volume of one of these compartments implies a compensatory change in the volume of either or both of the other compartments.
(4) The constancy of cerebral blood flow (CBF) Grubb et al. (1975) demonstrated that (at least in the Rhesus monkey) CBF remains constant until CSFP exceeds 70 torr. Also, Raichle et al. (1978) were unable to demonstrate significant short-term alterations in CBF in 3 pseudotumor patients studied before and after CSF removal.
(5) The vascular waterfall The movement of blood from convexity subarachnoid veins into the sagittal sinus is described by the Vascular Waterfall Hypothesis of Permutt and Riley (1963). According to this hypothesis, the driving pressure for flow through collapsible tubes with a higher pressure surrounding them than the outflow pressure is not the difference between the inflow and outflow pressures, but rather the difference between the inflow pressure and the critical closing pressure. It follows that since collapsible cerebral veins traverse the subarachnoid space before emptying into the sagittal sinus, changes in CSFP provoke changes in subarachnoid venous pressure (SVP); if CBF remains constant, CSFP-induced changes in SVP must entail a pressure redistribution across the cerebral vascular bed with consequent cerebral vasodilatation (Benabid 1974). Grubb et al. (1975) have provided a quantitative description of the relationship between CBV and CSFP during experimentally-induced intracranial hypertension in the Rhesus monkey, and Raichle et al. (1978), in a comprehensive analysis of cerebral hemodynamics and metabolism in 14 pseudotumor patients with mean CSPF = 27 mm Hg, demonstrated a highly significant increase ( > 30~) in CBV.
(6) Patency of the convexity subarachnoid space In patients with pseudotumor cerebri, the convexity subarachnoid space remains patent (James et al. 1974).
55
(7) Ventricular size Ventricular volume is normal or slightly reduced (Weisberg 1975; Delaney and Schellinger 1976; Hahn and Schapiro 1976). DISCUSSION
Based on existing clinical information and the assumptions mentioned above the pathogenesis of pseudotumor cerebri may be described as follows: Structural changes in the arachnoid villi increase arachnoid villous flow resistance, R~, and hence total CSF outflow resistance, Rt, and/or obstruction to cerebral venous outflow increases Pd- Whichever the precipitant, an increase in R t o r Po leads to an increase in CSFP, which, in turn, leads to an increase in SVP and, ultimately, to an increase in CBV. The magnitude of this latter increase can be calculated from the relationship ACBV = 2.44. Alog P,
[Equation 3]
based on the data of Grubb et al. (1975), where CBV is cerebral blood volume (ml/100 g) and P is CSFP (torr). Note that the slope of the line relating CBV to log P, 2.44, is the pressure-volume index per 100 g brain and that 2.44 is similar to the value of 1.79 ml/100 g obtained by dividing 25 ml, the PVI in normal human subjects (Shapiro et al. 1976), by a brain weight of 1400 g. Any increase in CBV compromises the cerebral subarachnoid space, provoking a further increase in R r In Fig. 2, Rs is graphed as a function of the volume of the convexity subarachnoid space. As is evident from the figure, CSF flow resistance does not become appreciable until the volume of the convexity subarachnoid space is reduced to approximately 10 ml. If the brain "swells" more or less uniformly following an increase in CBV, it may be assumed that the increased brain bulk encroaches on the ventricular system and convexity subarachnoid space
I I l
l
'
I I
~
Rs'
I 75ml
IOml
DecreosinoVolume of CerebrolSuborochnoidSpoce
•
Fig. 2. Hydrodynamic flow resistance of the convexity subarachnoid space, Rs, as a function of cerebral subarachnoid CSF volume, SV. Initially, R s increases slowly as SV decreases. W h e n SV approaches 10 ml, further decrements in SV result in large increases in R s. At some anatomically-determined limiting value of SV, R s reaches its limiting value, R~.
56 in proportion to their respective volumes. Given that the cerebral subarachnoid space contains 75 ml CSF (Weston 1921) and the ventricular system an additional 25 ml CSF (Last and Tompsett 1953), then an increase in brain volume of approximately 85 ml will be required to reduce the convexity subarachnoid space to l0 ml. Since CBV is normally about 75 ml (Fishman 1975), it would appear that cerebral blood volume must be doubled in order to produce an appreciable increase in Rt. The following hypothetical example illustrates the proposed pathogenetic sequence: one week after steroid withdrawal, a patient with bronchial asthma develops pseudotumor cerebri. K, initially 100 mm H20/ml/min, increases 15-fold to 1500 mm H20/ml/min. Pd and If remain unchanged (90 mm H20 and 0.35 ml/ rain, respectively), and CSFP increases from 125 to 615 mm H20. In consequence of this increase in CSFP, cerebral SVP rises, there is a redistribution of pressure gradients across the cerebrovascular bed, and CBV increases from 3.6 to 5.3 ml/100 g. This increase in CBV (1.7 ml/100 g) leads to a 24-ml reduction in the volume of the ventriculosubarachnoid space, which produces a small increase in R~, the hydrodynamic flow resistance of the convexity subarachnoid CSF pathways (Fig. 2), and in K. [A positive-feedback-loop situation develops when secondary increases in R increase R, and provoke further increases in CSFP and CBV. R, does not increase without bound, because R~ reaches a limiting value, PC, when the subarachnoid space is effectively replaced by secondary channels produced by infolding of the pia mater into the depths of cortical sulci (see Mathematical Appendix)]. The preceding considerations may be invoked to evaluate rationally the therapeutic efficacy of various proposed treatments for pseudotumor cerebri. In order successfully to lower chronically increased CSFP, one must lower R,, 1~ or P,~. Subtemporal decompression, which has no consistent effect on any of these 3 parameters, has little theoretical justification and equally little therapeutic success. Drainage of CSF by lumbar puncture, which results in a transient lowering of CSFP (unless a dural tear inadvertently provides an effective low resistance pathway to the spinal epidural space), may provide short-lived relief of symptoms but does not usually result in a permanent lowering of CSFP. A variety of drugs have been used to reduce l, (Pollay 1975). As might be expected from Equation 1, the scope of such treatment is limited. Moreover, the chronic administration ofacetazolamide, ethacrynic acid, corticosteroids, etc., entails a significant risk of serious sytemic side effects. In selected cases, the insertion of a ventriculosystemic shunt may provide a low-resistance pathway for CSF absorption. However, optimal shunt function - and appropriate lowering of CSFP - depends upon the relationship between R, and the effective shunt flow resistance. MATHEMATICAL APPENDIX
The subarachnoid space is approximated mathematically as the space between 2 rigid spherical shells, the inner shell representing the brain and pia mater and the outer shell representing the arachnoid membrane.
57
/ dd~
/ /
/
/
[0 "bzz j
J /
//
/
Fig. 3. A: The cerebral subarachnoid space modeled as the space between 2 rigid spherical shells (see Mathematical Appendix). If the shells are cut by cones as shown, the subarachnoid space will be defined by a series o f differential toroids. B: One of a series of toroids generated as described in A. A mathen~atical description of the flow o f CSF through the shaded volume is provided in the Appendix (Equations
4-8). If the shells are cut by cones, as illustrated in Fig. 3A, the subarachnoid space will be defined by a series of differential toroids; one such toroid is depicted in Fig. 3B. If the hydrodynamic flow resistance of each toroid is known, the resistance of the entire subarachnoid space can be determined by integration. Referring to Fig. 3B, the flow of CSF through the shaded differential volume may be calculated as follows: for an incompressible fluid of constant viscosity (assuming laminar flow and no end effects), the flow, Q, between two stationary parallel plates may be expressed as: - b c 3 c3p Q 12~t c~x' [Equation 4] where c is distance between the plates, b is width of the channel perpendicular to the direction of flow,/~ is viscosity and 0p/Ox is the pressure gradient in the direction of flow (Massey 1970). Applying Equation 4 to the shaded volume in Fig. 3B, 0p/0x = 0p/Dc~0. The distance between the 2 spheres is c, and since c ~ D, b may be approximated by Dcos0~ 4). Therefore, Equation 4 may be rewritten : dQ =
- c3(Dcos00 ~b) 0p 12/~ DO0"
[Equation 5]
58 Since p varies only with 0, we can rewrite the partial derivatives as simple derivatives. Integration from ~b = 0 to q5 = 2~ provides the following expression for Q, CSF flow through the differential toroid in Fig. 3B: Q =
- c3(2rtDcos0) dp 12/~ "Dd0'
[Equation 6]
The resistance of the differential toroid, dR, is then given by Equation 7: 12/iDd0 dR - c3(2nDeos0 ).
[Equation 7]
Integrating with respect to 0 gives the resistance of the entire subarachnoid space : 12# ~0~ dO c327z ~ cos0'
Rs
[Equation 8]
where 0j and 0 2 are the limits of integration for finite upper and lower orifices (foramen magnum and arachnoid villi, see below). If the area of each orifice is known, then A 0 = cos-l(1 - 2~-D5),
[Equation 9]
where 0 is the angle defining the orifice, A is the area of the orifice and D is the radius of the sphere. For the lower orifice, A is taken as the area of the foramen magnum. For the upper orifice, A is approximated as the total surface area of the arachnoid villi. To find this latter area, the arachnoid villi are modeled as simple cylinders, and the flow resistance of each individual villus, Rv, is calculated according to Poiseuille's law. Normally, CSF outflow resistance is determined by the physical characteristics of the arachnoid villi. If total CSF outflow resistance, R t , is wholly determined by the resistance of the individual villi, then 1
-
R,
n
[Equation 10]
Rv'
where n is the number of villi. The total surface area occupied by the arachnoid villi is then nnr 2, where r is the radius of a villus. Assuming that brain volume = 1400 ml, radius of the foramen magnum = 1.4 cm (Schmeltzer et al. 1971), radius of a single arachnoid villus = 12 x 10 -6 m (Welch and Friedman 1960), length of an arachnoid villus = 1 cm, R t --- 100 mm H20/ml/min (Ekstedt 1978), and CSF viscosity = 0.6915 x 10 -2 centipoise at 37°C, then 01 and 02 are equal to - 7 8 ° and 89 °, respectively. Inserting the values for 01 and 02 into Equation 8 and integrating yields R as a function of c: R
=
k/c 3 mm H20/ml/min,
59 where c is in cm and k = 1.54 x 10 _5 mm H20/min. The distance between the 2 spherical shells, c, is determined by the volumes of the brain and cerebral subarachnoid space. As the volume of the convexity subarachnoid space becomes very small, the assumption that this space can be modeled as the space between 2 rigid spheres breaks down; at such small volumes, gyral and sulcal irregularities play a dominant and, in effect, a limiting role. We have postulated the existence of preferential channels in the subarachnoid space through which CSF can flow when the subarachnoid space becomes highly attenuated. CSF outflow resistance is then equal to a series combination of the arachnoid villous resistance, R~, and the flow resistance, R'. of these preferential channels (Fig. 2).
REFERENCES Benabid, A. L., J. De Rougemont and M. Barge (1974) Pression veineuse c6r6brale, pression sinusale et pression intracrS.nienne, Neuro-chirurgie, 20: 623-632. Bulens, C., W. A. E. J. De Vries and H. Van Crevel (1979) Benign intracranial hypertension, J. neurol. Sci., 40: 147-157. Dandy, W. E. (1937) Intracranial pressure without brain tumor, Ann. Surg., 106: 492-513. Delaney, P. and D. Schellinger (1976) Computerized tomography and benign intracranial hypertension, J. Amer. med. Ass., 236:951 952. Donaldson, J. O. (1979) Cerebrospinal fluid hypersecretion in pseudotumor cerebri, Ann. Neurol., 6: 160. Ekstedt, J. (1978) CSF hydrodynamic studies in man, J. Neurol. Neurosurg. Psychiat., 41 : 345 353. Fishman, R.A. (1975) Brain edema, New Engl. J. Med., 293:70(~711. Fishman, R.A. (1979) Pathophysiology of pseudotumor, Ann. Neurol., 5: 496. Foley, K. M. (1977) Is benign intracranial hypertension a chronic disease? Neurology (Minneap.), 27: 388. Foley, K.M. and J.B. Posner (1975) Does pseudotumor cerebri cause the empty sella syndrome? Neurology ( Minneap.), 25: 565-569. Gardner, W.J. (1939) Otitic sinus thrombosis causing intracranial hypertension, Arch. Otolaryngol., 30:253 268. Grubb, Jr., R.L., M.E. Raichle, M.E. Phelps and R.A. Ratcheson (1975) Effects of increased intracranial pressure on cerebral blood volume, blood flow and oxygen utilization in monkeys, J. Neurosurg., 43 : 385-398. Hahn, F. J. Y. and R. L. Schapiro (1976) The excessively small ventricle on computed axial tomography of the brain, Neuroradiology, 12 : 13~139. Hayes, K.C., H.L. McCombs and T.P. Faherty (1971) The fine structure of vitamin A deficiency, Part 2 (Arachnoid granulations and CSF pressure), Brain, 94:213 224. James, A. E., J.C. Harbert, P.B. Hoffer and F.H. Deland (1974) CSF imaging in benign intracranial hypertension, J. Neurol. Neurosurg. Psychiat., 37: 1053-1058. Johnston, I. (1975) The definition of a reduced CSF absorption syndrome A reappraisal of benign intracranial hypertension and related conditions, Med. Hypotheses, 1 : 10 14. Johnston, I. and A. Paterson (1974) Benign intracranial hypertension Diagnosis and prognosis, Brain, 97 : 289-300. Johnston, I., D.L. Gilday and E.B. Hendrick (1975) Experimental effects of steroids and steroid withdrawal on cerebrospinal fluid absorption, J. Neurosurg., 42 : 690 695. Last, R. J. and D. H. Tompsett (1953) Casts of the cerebral ventricles, Brit. J. Surg., 40:525 543. Lipton, H. L. and P. E. Michelson (1972) Pseudotumor cerebri syndrome without papilledema, J. Amer. med. Ass., 220: 1591-1592. Mann, J.D., R.N. Johnson, A.B. Butler and N.H. Bass (1979) Impairment of cerebrospinal fluid circulatory dynamics in pseudotumor cerebri and response to steroid treatment, Neurology (Minneap.), 29: 550. Marmarou, A., K. Shulman and R.M. Rosende (1978) A nonlinear analysis of the cerebrospinal fluid system and intracranial dynamics, J. Neurosurg., 48:332 344.
60 Marr, W. G. and R.G. Chambers (1961) Pseudotumor cerebri syndrome, Amer. J. Ophth., 51:605 (~11 Massey, B. S. (1970) Mechanics o/Fluids, 2nd edition, Van Nostrand Reinhold Company, Ltd., kondoll, p. 149. Paterson, R., N. DePasquale and S. Mann (1961) Pseudotumor cerebri, Medicine :Baltimore j, 40: 85-99. Permutt, S. and R.L. Riley (1963) Hemodynamics of collapsible vessels with tone The vascular waterfall, J. appl. Physiol., 18 : 924-932. Pollay, M. (1975) Formation of cerebrospinal fluid Relation of studies of isolated choroid plexus to the standing gradient hypothesis, J. Neurosurg., 42 : 665 673. Raichle, M. E., R. L. Grubb, M. E. Phelps, M. H. Gado and J. J. Caronna (1978) Cerebral hemodynamics and metabolism in pseudotumor cerebri, Ann, Neural., 4: 104-111. Ray, B. S. and H. W. Dunbar (1951) Thrombosis of the dural venous sinuses as a cause of "pseudotumor cerebri", Ann. Surg., 134: 376-386. Rottenberg, D. A. and J. B. Posner (1980) lntracranial pressure control. In: J. E. Cottrell and H. Turndorf (Eds.), Anesthesia and Neurosurgery, The C. V. Mosby Company, Saint Louis. Sahs, A. L. and R.J. Joynt (1956) Brain swelling of unknown cause, Neurology (Minneap.), 6:791 803. Schmeltzer, A., E. Babin and J. J. Wenger (1971) Foramen magnum in children Measurements of the antero-posterior diameter on midsagittal pneumotomograms, Neuroradiology, 2: 162-163. Shapiro, K., A. Marmarou and K. Shulman (1976) Clinical applications of the pressure volume index, Presented at the 44th Annual Meeting c~/'the American Association (~/' Neurological Surgeons, San Francisco (Paper No. 75). Symonds, C. P. (1931) Otitic hydrocephalus, Brain, 54: 55-71. Symonds, C. P. (1937) Hydrocephalic and focal cerebral symptoms in relation to thrombophlebitis of the dural sinuses and cerebral veins, Brain, 60: 531-550. Van Crevel, H. (1975) Absence of papilloedema in cerebral tumours, J. Neural. Neurosurg. Ps:vchiat., 38:931 933. Weisberg, L.A. (1975) Benign intracranial hypertension, Medicine (Baltimore), 54: 197-207. Welch, K. and Friedman, V. (1960) The cerebrospinal fluid valves, Brain, 83: 454-469. Weston, P.G. (1921) Phenosulphonephthalein absorption from the subarachnoid space in paresis and dementia praecox. Arch. Neural. Po'chiat., 5 : 58-63.
51
THE PATHOGENESIS OF PSEUDOTUMOR CEREBRI A Mathematical Analysis
ROBERT M. AISENBERG and DAVID A. ROTTENBERG
Departments of Neurology, Memorial Sloan-Kettering Cancer Center and Cornell University Medical College, New York, N Y (U.S.A.) (Received 29 January, 1980) (Accepted 7 May, 1980)
SUMMARY
Although the clinical and laboratory features of pseudotumor cerebri have been clearly delineated, the pathogenesis of idiopathic pseudotumor remains a mystery. A number of pathogenetic mechanisms have been proposed to account for some or all of the observed cases. We describe a model relating changes in CSF outflow resistance and/or dural sinus venous pressure to observed changes in (i) CSF pressure, (ii) cerebral blood volume and (iii) the volume and hydrodynamic flow resistance of the ventriculosubarachnoid space.
INTRODUCTION
Although the clinical and laboratory features of pseudomotor cerebri have been clearly delineated (Weisberg 1975; Bulens et al. 1979), the pathogenesis of idiopathic pseudotumor remains a mystery. On occasion, the clinical picture is atypical or confusing: the "disease process" may be asymptomatic (Bulens et al. 1979), and papilledema may be absent (Lipton and Michelson 1972). In most
Dr. Rottenberg is the recipient of Teacher Investigator Award No. 1 K07 NS00286-01 from the National Institute of Neurological and Communicative Disorders and Stroke. Address reprint requests to: David A. Rottenberg, M.D., Department of Neurology, Memorial Hospital, 1275 York Avenue, New York, NY 10021, U.S.A. Abbreviations : CBV, cerebral blood volume; CSF, cerebrospinal fluid; CSFP, cerebrospinal fluid pressure; ICP, intracranial pressure; If, rate of CSF formation; Pd, dural sinus venous pressure; PVI, pressure-volume index; Ra, arachnoid villous flow resistance; Rs, flow resistance of the convexity subarachnoid space; R~,. limiting value of R~; R t, total CSF outflow resistance; SVP, subarachnoid venous pressure.
52 TABLE 1 CSFP IN P S E U D O T U M O R CEREBRI
Pressure (mm CSF)
Patterson et al. (1961) a Johnston and Paterson (1974) b Foley (1975) a Weisberg (1975) c
Totals"
200-299
300 399
400 499
5(}0
2 2 2 12
3 5 3 72
7 3 3 30
3
6
18
83
43
~)
a Lumbar subarachnoid pressure. b Ventricular pressure. c Site of pressure measurement not specified.
instances, the electroencephalogram is normal, although intracranial pressure is markedly elevated (Table 1); neuroradiologic studies, including isotope cisternography, cerebral angiography and CT, are almost invariably normal or nondiagnostic (James et al. 1974; Weisberg 1975 ; Delaney and Schellinger 1976; Butens et al. 1979). Characteristically, the cerebrospinal fluid is of normal composition, though the protein concentration may be in the low-normal range. Even the designations "pseudotumor cerebri" and "benign intracranial hypertension" are misnomers: "Pseudotumor cerebri" erroneously implies that tumors - - in and of themselves - - increase intracranial pressure, whereas 'benign intracranial hypertension" reflects the prevailing but incorrect notion that afflicted individuals invariably recover without serious sequelae. In fact, brain tumors may be remarkably symptomatic in the absence of increased intracranial pressure (ICP) (Van Crevel 1975), and patients with pseudomotor cerebri may go blind or become chronically disabled by recurring symptoms (Foley 1977). Numerous hypotheses have been put forward to explain the pathogenesis of pseudotumor cerebri and its occasional relationship to anemia, endocrinopathy, vitamin and drug therapy, etc. The following pathogenetic mechanisms have been proposed to account for some or all of the observed cases: (1) increased cerebral blood volume (CBV) (Dandy 1937), (2) increased brain water content (cerebral edema) (Sahs and Joynt 1956; Raichle et al. 1978), (3) increased dural sinus venous pressure (Ray and Dunbar 1950; Marr and Chambers 1961), (4) CSF hypersecretion (Donaldson 1979), and (5) increased CSF outflow resistance (Johnston 1975; Johnston et al. 1975; Fishman 1979). Dural sinus thrombosis was initially implicated by Symonds (1937) and Gardner (1939) as a causative factor in patients with "otitic hydrocephalus" (Symonds 1931), but the vast majority of pseudotumor patients do not have otitic hydrocephalus. We [and others (Johnston 1975; Fishman 1979; Mann et al. 1979)] believe that pseudotumor cerebri results from an increase in
53
Fig. 1. The cerebrospinal fluid system. arachnoid villous flow resistance, Ra, and/or an increase in dural sinus venous pressure, Pd (Fig. 1). The following model relates changes in Ra and/or Pd to observed changes in CSF pressure (CSFP) and CBV and to the volume and hydrodynamic flow resistance of the ventriculosubarachnoid space. The etiology of these changes in R~ and/or Pd is not specifically considered. MODEL ASSUMPTIONS
(1) CSF statics In the steady state, CSFP may be described by Equation 1, CSFP = Po + ifRt,
[Equation 1]
where Pd is dural sinus venous pressure, If is the rate of CSF formation and Rt is total CSF outflow resistance (Marmarou et al. 1978). Sagittal sinus compression/ occlusion, dominant lateral sinus thrombosis or jugular venous obstruction may increase Pd (Rottenberg and Posner 1980). In the absence of a choroid plexus papilloma, If is rarely, if ever, increased. R,, which represents the resistance of the arachnoid villi, R~,,in series with the resistance of the convexity subarachnoid space, R~, may be increased by structural alterations in the arachnoid villi themselves (Hayes et al. 1971) or by compartmentalization or compromise of the cerebral subarachnoid space (see Mathematical Appendix).
54
(2) CSF dynamics In general, abrupt increases in the volume of the intracranial contents produce predictable changes in CSFP. That is, CSFP = Po. 106wPv~,
[Equation 2]
where Po is initial or resting CSFP, AV is the volume increment or decrement and PVI is the pressure-volume index [the volume increment or decrement required to raise or lower CSFP 10-fold (Marmarou et al. 1978)].
(3) The Monro-Kellie hypothesis The Monro-Kellie hypothesis refers to the concept of a rigid craniocerebral compartment within which the sum total of brain volume + CSF volume + CBV remains constant; any change in the volume of one of these compartments implies a compensatory change in the volume of either or both of the other compartments.
(4) The constancy of cerebral blood flow (CBF) Grubb et al. (1975) demonstrated that (at least in the Rhesus monkey) CBF remains constant until CSFP exceeds 70 torr. Also, Raichle et al. (1978) were unable to demonstrate significant short-term alterations in CBF in 3 pseudotumor patients studied before and after CSF removal.
(5) The vascular waterfall The movement of blood from convexity subarachnoid veins into the sagittal sinus is described by the Vascular Waterfall Hypothesis of Permutt and Riley (1963). According to this hypothesis, the driving pressure for flow through collapsible tubes with a higher pressure surrounding them than the outflow pressure is not the difference between the inflow and outflow pressures, but rather the difference between the inflow pressure and the critical closing pressure. It follows that since collapsible cerebral veins traverse the subarachnoid space before emptying into the sagittal sinus, changes in CSFP provoke changes in subarachnoid venous pressure (SVP); if CBF remains constant, CSFP-induced changes in SVP must entail a pressure redistribution across the cerebral vascular bed with consequent cerebral vasodilatation (Benabid 1974). Grubb et al. (1975) have provided a quantitative description of the relationship between CBV and CSFP during experimentally-induced intracranial hypertension in the Rhesus monkey, and Raichle et al. (1978), in a comprehensive analysis of cerebral hemodynamics and metabolism in 14 pseudotumor patients with mean CSPF = 27 mm Hg, demonstrated a highly significant increase ( > 30~) in CBV.
(6) Patency of the convexity subarachnoid space In patients with pseudotumor cerebri, the convexity subarachnoid space remains patent (James et al. 1974).
55
(7) Ventricular size Ventricular volume is normal or slightly reduced (Weisberg 1975; Delaney and Schellinger 1976; Hahn and Schapiro 1976). DISCUSSION
Based on existing clinical information and the assumptions mentioned above the pathogenesis of pseudotumor cerebri may be described as follows: Structural changes in the arachnoid villi increase arachnoid villous flow resistance, R~, and hence total CSF outflow resistance, Rt, and/or obstruction to cerebral venous outflow increases Pd- Whichever the precipitant, an increase in R t o r Po leads to an increase in CSFP, which, in turn, leads to an increase in SVP and, ultimately, to an increase in CBV. The magnitude of this latter increase can be calculated from the relationship ACBV = 2.44. Alog P,
[Equation 3]
based on the data of Grubb et al. (1975), where CBV is cerebral blood volume (ml/100 g) and P is CSFP (torr). Note that the slope of the line relating CBV to log P, 2.44, is the pressure-volume index per 100 g brain and that 2.44 is similar to the value of 1.79 ml/100 g obtained by dividing 25 ml, the PVI in normal human subjects (Shapiro et al. 1976), by a brain weight of 1400 g. Any increase in CBV compromises the cerebral subarachnoid space, provoking a further increase in R r In Fig. 2, Rs is graphed as a function of the volume of the convexity subarachnoid space. As is evident from the figure, CSF flow resistance does not become appreciable until the volume of the convexity subarachnoid space is reduced to approximately 10 ml. If the brain "swells" more or less uniformly following an increase in CBV, it may be assumed that the increased brain bulk encroaches on the ventricular system and convexity subarachnoid space
I I l
l
'
I I
~
Rs'
I 75ml
IOml
DecreosinoVolume of CerebrolSuborochnoidSpoce
•
Fig. 2. Hydrodynamic flow resistance of the convexity subarachnoid space, Rs, as a function of cerebral subarachnoid CSF volume, SV. Initially, R s increases slowly as SV decreases. W h e n SV approaches 10 ml, further decrements in SV result in large increases in R s. At some anatomically-determined limiting value of SV, R s reaches its limiting value, R~.
56 in proportion to their respective volumes. Given that the cerebral subarachnoid space contains 75 ml CSF (Weston 1921) and the ventricular system an additional 25 ml CSF (Last and Tompsett 1953), then an increase in brain volume of approximately 85 ml will be required to reduce the convexity subarachnoid space to l0 ml. Since CBV is normally about 75 ml (Fishman 1975), it would appear that cerebral blood volume must be doubled in order to produce an appreciable increase in Rt. The following hypothetical example illustrates the proposed pathogenetic sequence: one week after steroid withdrawal, a patient with bronchial asthma develops pseudotumor cerebri. K, initially 100 mm H20/ml/min, increases 15-fold to 1500 mm H20/ml/min. Pd and If remain unchanged (90 mm H20 and 0.35 ml/ rain, respectively), and CSFP increases from 125 to 615 mm H20. In consequence of this increase in CSFP, cerebral SVP rises, there is a redistribution of pressure gradients across the cerebrovascular bed, and CBV increases from 3.6 to 5.3 ml/100 g. This increase in CBV (1.7 ml/100 g) leads to a 24-ml reduction in the volume of the ventriculosubarachnoid space, which produces a small increase in R~, the hydrodynamic flow resistance of the convexity subarachnoid CSF pathways (Fig. 2), and in K. [A positive-feedback-loop situation develops when secondary increases in R increase R, and provoke further increases in CSFP and CBV. R, does not increase without bound, because R~ reaches a limiting value, PC, when the subarachnoid space is effectively replaced by secondary channels produced by infolding of the pia mater into the depths of cortical sulci (see Mathematical Appendix)]. The preceding considerations may be invoked to evaluate rationally the therapeutic efficacy of various proposed treatments for pseudotumor cerebri. In order successfully to lower chronically increased CSFP, one must lower R,, 1~ or P,~. Subtemporal decompression, which has no consistent effect on any of these 3 parameters, has little theoretical justification and equally little therapeutic success. Drainage of CSF by lumbar puncture, which results in a transient lowering of CSFP (unless a dural tear inadvertently provides an effective low resistance pathway to the spinal epidural space), may provide short-lived relief of symptoms but does not usually result in a permanent lowering of CSFP. A variety of drugs have been used to reduce l, (Pollay 1975). As might be expected from Equation 1, the scope of such treatment is limited. Moreover, the chronic administration ofacetazolamide, ethacrynic acid, corticosteroids, etc., entails a significant risk of serious sytemic side effects. In selected cases, the insertion of a ventriculosystemic shunt may provide a low-resistance pathway for CSF absorption. However, optimal shunt function - and appropriate lowering of CSFP - depends upon the relationship between R, and the effective shunt flow resistance. MATHEMATICAL APPENDIX
The subarachnoid space is approximated mathematically as the space between 2 rigid spherical shells, the inner shell representing the brain and pia mater and the outer shell representing the arachnoid membrane.
57
/ dd~
/ /
/
/
[0 "bzz j
J /
//
/
Fig. 3. A: The cerebral subarachnoid space modeled as the space between 2 rigid spherical shells (see Mathematical Appendix). If the shells are cut by cones as shown, the subarachnoid space will be defined by a series o f differential toroids. B: One of a series of toroids generated as described in A. A mathen~atical description of the flow o f CSF through the shaded volume is provided in the Appendix (Equations
4-8). If the shells are cut by cones, as illustrated in Fig. 3A, the subarachnoid space will be defined by a series of differential toroids; one such toroid is depicted in Fig. 3B. If the hydrodynamic flow resistance of each toroid is known, the resistance of the entire subarachnoid space can be determined by integration. Referring to Fig. 3B, the flow of CSF through the shaded differential volume may be calculated as follows: for an incompressible fluid of constant viscosity (assuming laminar flow and no end effects), the flow, Q, between two stationary parallel plates may be expressed as: - b c 3 c3p Q 12~t c~x' [Equation 4] where c is distance between the plates, b is width of the channel perpendicular to the direction of flow,/~ is viscosity and 0p/Ox is the pressure gradient in the direction of flow (Massey 1970). Applying Equation 4 to the shaded volume in Fig. 3B, 0p/0x = 0p/Dc~0. The distance between the 2 spheres is c, and since c ~ D, b may be approximated by Dcos0~ 4). Therefore, Equation 4 may be rewritten : dQ =
- c3(Dcos00 ~b) 0p 12/~ DO0"
[Equation 5]
58 Since p varies only with 0, we can rewrite the partial derivatives as simple derivatives. Integration from ~b = 0 to q5 = 2~ provides the following expression for Q, CSF flow through the differential toroid in Fig. 3B: Q =
- c3(2rtDcos0) dp 12/~ "Dd0'
[Equation 6]
The resistance of the differential toroid, dR, is then given by Equation 7: 12/iDd0 dR - c3(2nDeos0 ).
[Equation 7]
Integrating with respect to 0 gives the resistance of the entire subarachnoid space : 12# ~0~ dO c327z ~ cos0'
Rs
[Equation 8]
where 0j and 0 2 are the limits of integration for finite upper and lower orifices (foramen magnum and arachnoid villi, see below). If the area of each orifice is known, then A 0 = cos-l(1 - 2~-D5),
[Equation 9]
where 0 is the angle defining the orifice, A is the area of the orifice and D is the radius of the sphere. For the lower orifice, A is taken as the area of the foramen magnum. For the upper orifice, A is approximated as the total surface area of the arachnoid villi. To find this latter area, the arachnoid villi are modeled as simple cylinders, and the flow resistance of each individual villus, Rv, is calculated according to Poiseuille's law. Normally, CSF outflow resistance is determined by the physical characteristics of the arachnoid villi. If total CSF outflow resistance, R t , is wholly determined by the resistance of the individual villi, then 1
-
R,
n
[Equation 10]
Rv'
where n is the number of villi. The total surface area occupied by the arachnoid villi is then nnr 2, where r is the radius of a villus. Assuming that brain volume = 1400 ml, radius of the foramen magnum = 1.4 cm (Schmeltzer et al. 1971), radius of a single arachnoid villus = 12 x 10 -6 m (Welch and Friedman 1960), length of an arachnoid villus = 1 cm, R t --- 100 mm H20/ml/min (Ekstedt 1978), and CSF viscosity = 0.6915 x 10 -2 centipoise at 37°C, then 01 and 02 are equal to - 7 8 ° and 89 °, respectively. Inserting the values for 01 and 02 into Equation 8 and integrating yields R as a function of c: R
=
k/c 3 mm H20/ml/min,
59 where c is in cm and k = 1.54 x 10 _5 mm H20/min. The distance between the 2 spherical shells, c, is determined by the volumes of the brain and cerebral subarachnoid space. As the volume of the convexity subarachnoid space becomes very small, the assumption that this space can be modeled as the space between 2 rigid spheres breaks down; at such small volumes, gyral and sulcal irregularities play a dominant and, in effect, a limiting role. We have postulated the existence of preferential channels in the subarachnoid space through which CSF can flow when the subarachnoid space becomes highly attenuated. CSF outflow resistance is then equal to a series combination of the arachnoid villous resistance, R~, and the flow resistance, R'. of these preferential channels (Fig. 2).
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