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formation (Cutler and Spertell) Electrolytes enter the ventricles somewhat more readily than they enter the subarachnoid space (water does the opposite) It is also known that the penetration of certain drugs and metabolites is in direct relation to their lipid solubility Ionized compounds, such as hexoses and amino acids, being relatively insoluble in lipids, enter the CSF slowly unless facilitated by a membrane transport system This type of facilitated (carrier) diffusion is stereospeci c; ie, the carrier (a speci c protein or proteolipid) binds only with a solute having a speci c con guration and carries it across the membrane, where it is released into the CSF and intercellular uid Diffusion gradients appear to determine the entry of serum proteins into the CSF and also the exchanges of CO2 Water and sodium diffuse as readily from blood to CSF and intercellular spaces as in the reverse direction This explains the rapid effects of intravenously injected hypotonic and hypertonic uids Studies using radioisotopic tracer techniques have shown that the various constituents of the CSF (see Table 2-1) are in dynamic equilibrium with the blood Similarly, CSF in the ventricles and subarachnoid spaces is in equilibrium with the intercellular uid of the brain, spinal cord, and olfactory and optic nerves Certain structures that were thought to maintain this equilibrium namely, the blood-CSF barrier and brain CSF barrier are now subsumed under the term blood-brain barrier, which is used to designate all of the interfaces between blood, brain, and CSF The site of the barrier varies for the different plasma constituents One is the endothelium of the choroidal and brain capillaries; another is the plasma membrane and adventitia (Rouget cells) of these vessels; a third is the pericapillary foot processes of astrocytes Large molecules such as albumin are prevented from entry by the capillary endothelium, and this is the barrier also for such molecules as are bound to albumin, eg, aniline dyes (trypan blue), bilirubin, and many drugs Other smaller molecules are blocked from entering the brain by the capillary plasma membrane or astrocytes The various substances formed in the nervous system during its metabolic activity diffuse rapidly into the CSF Thus, the CSF has a kind of sink action, to use Davson s term, by which the products of brain metabolism are removed into the bloodstream as CSF is absorbed Circulation Harvey Cushing aptly termed the CSF the third circulation, comparable to that of the blood and lymph From its principal site of formation in the choroid plexus of the lateral ventricles, the CSF ows downward through the third ventricle, aqueduct, fourth ventricle, and foramens of Magendie (medially) and Luschka (laterally) at the base of the medulla, to the perimedullary and perispinal subarachnoid spaces, thence around the brainstem and rostrally to the basal and ambient cisterns, through the tentorial aperture, and nally to the lateral and superior surfaces of the cerebral hemispheres, where most of it is absorbed (Fig 30-1) The pressure is highest in the ventricles and diminishes successively along the subarachnoid pathways Arterial pulsations of the choroid plexuses help drive the uid from the ventricular system The spinal uid is everywhere in contact with the extracellular uid of the brain and spinal cord, but the extent of bulk ow of the CSF through the brain parenchyma is small under normal conditions The periventricular tissues offer considerable resistance to the entrance of CSF, and although the pressure difference between the ventricles and the subarachnoid spaces (transmantle pressure) is only slightly above zero, the open ventricular-foraminal-subarachnoid pathway directs the bulk of CSF ow in this direction.

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Figure 30-1 A Schematic representation of the three components of the intracranial contents: the incompressible brain tissue (shaded); the vascular system; and the CSF (dotted) B With ventricular obstruction C With obstruction at or near the points of outlet of the CSF D With obstruction of the venous out ow (Redrawn by permission from Foley)

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Only if this conduit is obstructed does the transmantle pressure rise, compressing the periventricular tissues and leading to ventricular enlargement and transependymal ow of CSF Absorption Absorption of CSF is through the arachnoid villi These are microscopic excrescences of arachnoid membrane that penetrate the dura and protrude into the superior sagittal sinus and other venous structures Multiple villi are aggregated in these locations to form the pacchionian granulations or bodies, some of them large enough to indent the inner table of the calvarium The arachnoid villi, most numerous on both sides of the superior sagittal sinus, are present at the base of the brain and around the spinal cord roots and have been thought to act as functional valves that permit unidirectional bulk ow of CSF into the vascular lumen However, electron microscopic studies have shown that the arachnoid villi have a continuous membranous covering This layer is extremely thin, and CSF passes through the villi at a linearly increasing rate as CSF pressures rise above 68 mmH2O This passive route is not the only manner in which CSF water and other contents are transported Tripathi and Tripathi, in serial electron micrographs, found that the mesothelial cells of the arachnoid villus continually form giant cytoplasmic vacuoles that are capable of transcellular bulk transport Certain substances, such as penicillin and organic acids and bases, are also absorbed by cells of the choroid plexus; the bidirectional action of these cells resembles that of the tubule cells of the kidneys Some substances have been shown in pathologic specimens to pass between the ependymal cells of the ventricles and to enter subependymal capillaries and venules By infusing and withdrawing CSF under controlled circumstances, the resistance to CSF absorbtion and its rate of replacement can be calculated The resistance to the passage of CSF into the.

where the nomenclatnrefi(l) designatesthat this is a iirst-order polynomial Equation (1520) is refered to as the LinearLagrangeinterpolatingpolynomial The samestrategycan be employedto fit a parabola throughthreepointsFor this case threeparabolas would be usedwith eachone passingthroughone of the points and equaling zero at the othertwo Their sum would thenrepresent uniqueparabola the that connects the threepoints Such a second-order Lagrangeinterpolatingpolynomial can be written as

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