Ci(T) = λikiCa(µ)e^-kj(T-µ)dµ

where flow is Fi = λiki. The input functions for this equation are the partition coefficient (λi ) the flow rate constant (ki), the time­dependent tracer concentration in the arterial blood Ca(µ). and the time-dependent tracer concentration in the venous blood. For this relationship the tissue concentration (C,T) is assumed to be equal to the venous blood content divided by λ. This equation is then valid for saturation or desaturation studies depending on the boundary conditions that are set. This measurement of global cerebral blood flow with nitrous oxide required the following assumptions: (1) blood flow is in a steady state during the period of study and is not affected by the tracer. (2) the venous blood from the superior internal jugular vein is representative of the mixed cerebral venous blood with no contamination from extracerebral blood, (3) the period of measurement is long enough to allow equilibration of gas in the brain with the cerebral venous blood, (4) no significant arterial-venous shunts are present in the brain, and (5) the value of the partition coefficient of the inert gas is representative of the entire brain. The initial studies with nitrous oxide demonstrated that blood flow studies with this tracer did meet the above assumptions under most situations, the exception being in a region of disturbed physiology, where arteriovenous shunting may be significant and where the partition coefficient is likely to be altered.

A major advance toward the broad clinical application of cerebral blood flow measurement came with the substitution of radio­labeled ⁸⁵Kr for nitrous oxide and scintillation counting as the direct measure of tracer movement within the tissue, the latter measure being substituted for the difference of the arterial and venous concentrations of the tracer. This approach provided a regionality of blood flow determination that was lacking in the global blood flow measures provided by nitrous oxide, but this was significantly hampered by a weak signal and contamination from extracranial emissions. Initially this was dealt with experimentally by the injection of ⁸⁵Kr directly into the internal carotid artery and by scintillation counting over the cortex. Subsequently with the substitution of the gamma emitter. 133Xe. for 85Kr. higher and more adequate counting rates were obtained through the skull. The application of this technique with internal carotid artery injection then became widely utilized. both clinically and experimentally, as a means of obtaining regional CBF measurements. Because this approach requires an internal carotid artery catheter, its application has generally remained limited to situations where patients were undergoing angiography.

A broader approach became possible, however, with the work of Obrist, who, utilizing a multi compartmental analysis of the Kety-Schmidt equation, was able to divide the washout curve into three components, with the extracranial contamination appearing as a well-defined, late washout. If this contamination is subtracted from the remaining fast (gray matter) and slow (white matter) curves, an analysis of flow can then be done, with an additional correction being made for the recirculation of gas. The later measure was made by a separate recording of the end tidal ¹³³Xe concentration as an indirect measure of the capillary (and therefore arterial) concentration of the gas. As a "noninvasive" inhalation study, ¹³³Xe inhalation flow determinations have been shown to maintain the numerical reliability of the intracarotid injection method. In recent years most centres have turned to intravenous bolus introduction of ¹³³Xe as a simpler means of delivering the tracer. Refinements have permitted a relatively short period of data acquisition (10 min) during the clearance phase in which only the fast "gray matter" flows are extracted, again without significant loss of validity against the intracarotid technique. Commercially available units utilizing this methodology commonly incorporate about 16 to 32 NaI scintillation counters, which are placed about both hemispheres so that each is perpendicular to the surface of the brain. The ultimate in collimation was developed in Lassen's laboratory. where 254 independent collimators were made into a unilateral array. Elegant studies of regional flow disturbance in disease and during activation studies of physiologic stimulation have been demonstrated with this technique. Portable ¹³³Xe cerebral blood flow units utilizing four to five probes over each hemisphere are now available, permitting studies to be performed at the bedside.

The ¹³³Xe methodology, however, suffers from a number of significant limitations. Counts arising from extracranial tissues still provide a signal contamination, as do emissions arising  from the opposite hemisphere. This technique is dependent on the use of "normal" partition coefficients, which in diseased states can alter flow values by as much as 50 percent. Although a careful analytic approach to data analysis with this technique has been able to positively identify the side of a cerebral infarction in 80% of the cases in which a stroke was evident on computed tomography, regions of no flow may be totally missed. This technique may detect raised or normal flow in a region of no flow because counts from the hyperaemic rim can overshadow the area of low , or no  flow just below it. As a major limitation of this technique, this "look­through" phenomenon has prompted the development of a single photon emission computed tomography (SPECT) imaging system for ¹³³Xe. Due to Compton scatter and a weaker signal from central regions, ¹³³Xe SPECT still suffers from poor resolution, especially centrally within the brain. This technology is also limited because of independence on "normal" partition coefficient values (λ). Tomographic CBF measurements with ¹³³Xe are best acquired with dedicated multi-head rotating cameras. A single rotating gamma camera can be utilized with ¹³³Xe, but the time for adequate data acquisition may be over 1 h compared with 20 to 30 min for multi-head units.

Other quantitative and regionally specific techniques for blood flow determination include positron emission tomography (PET)²  and stable xenon-enhanced tomography (Xe/CT). The major of PET is its ability to measure not only flow, but also a  theoretically limitless list of other potentially vital parameters at the same time. The relatively high cost of acquisition and its requirement for short-lived isotopes make PET a demanding technology requiring a team of individuals, thus limiting its potential for wide availability. Inter­pretation of PET-derived physiologic data is also limited due to a lack of direct anatomic correlation, and quantitative reliability is weakened by a dependence on numerous physiologic assumptions which do not necessarily pertain in disease states.

Another tomographic approach for acquiring cerebral blood flow information involves the inhalation of 26 to 33 percent stable xenon, an inert radiodense gas which is highly lipid-soluble, as a marker of flow combined with transmission computed tomography. For this technique, CT scans obtained before and during approximately 4.5 min of xenon-oxygen inhalation are utilized to record the movement of this lipid-soluble and radiodense gas into the brain substance. Because the relatively slow process of diffusion of this agent is being characterized, scans obtained at 1-min intervals, provide the required data. Rapid scanning techniques with incremental table movements permit data acquisition at three or more additional levels during each inhalation sequence. The end tidal xenon concentration as measured by a thermoconductivity analyzer is utilized to indirectly record the arterial concentration during the buildup and/or washout of xenon. This information, plus the degree of image enhancement, is then used to derive λ and the local cerebral blood flow by multi variable analysis. Concurrent studies using radiolabeled microspheres, iodoantipyrine. and ¹³³Xe have shown excellent correlation with Xe/CT CBF. Anatomic resolution is high, approaching the resolution of the CT scanners, with equal quantitative accuracy within the center and on the surface of the brain. Clinical studies suggest that this method has the potential for broad application as a noninvasive, repeatable means of obtaining clinically useful CBF information. Although it has been shown that xenon moderately alters cerebral blood flow and may alter the sensorium of 10 to 15 percent of individuals, moderate flow activation does not significantly alter flow values. although sensorial effects can at times make it difficult to obtain studies without motion.

Qualitative information about cerebral blood flow is also being provided by two older and four newer approaches. Clearance curves of ^99mTc-labeled technetium pertechnetate combined with rapid data acquisition on a single-crystal Anger camera has been utilized for a decade to provide information about the movement of blood within comparative blood pools. The absence of supratentorial flow by this technique has become a standard test for brain death. The same type of data, but with better localization, is also being provided by rapid CT scanning following an intravenous iodine bolus. Studies at the level of the middle cerebral arteries or at the level of the brain stem have been shown to provide a readily accessible means of evaluating regional asymmetries of movement within blood pools. Because of the broad availability of this technology and the possible importance of flow asymmetry, this technique has a broad potential application for the assessment of regional blood flow.

New radiopharmaceuticals combined with SPECT imaging have received much attention of late. SPECT CBF derived with radiolabeled isotopes that behave as biological microspheres today provide relatively high-resolution three-dimensional qualitative CBF imaging. While rotating angle cameras provide information for the entire intracranial volume, such studies require prolonged acquisition times (>40 to 60 min). Newer dedicated multihead SPECT units provide more rapid acquisition and higher resolution. Normally, repeat studies are performed at 24-h intervals, allowing tracer clearance. Repeat studies at briefer intervals can be performed using the fractional dosing of a single study. Quantitative data can be obtained if a reference arterial blood curve for tracer activity is acquired.

Diffusion imaging with magnetic resonance imaging provides information concerning the presence or absence of blood movement. The combination of excellent anatomic imaging and the ability to identify the absence of flow should have direct clinical utility, especially if linked to MR spectroscopy. At this time, MRI is unable to differentiate gradients of flow unless diffusible tracers of CBF such as fluorocarbons are combined with imaging.

Direct monitoring of cortical blood flow is available today utilizing either thermal dilution or laser Doppler technologies. Both techniques are able to record flow changes repeatedly and provide information from a very focused region of only the outer few millimetres of the cerebral cortex. Both are limited by the inability to maintain fixation with the cortical surface, so that the interpretation of variations in flow may be complicated by uncertainty as to whether the probe has remained in position.

Transcranial Doppler (TCD) velocity measurement of intracranial vessels in and directly about the circle of Willis is now widely available. This relatively simple and low-cost bedside measurement can be made frequently or continuously. Although a single velocity measurement is not tightly linked to CBF, the change of velocity induced by a physiologic challenge is related to a proportional CBF change. This provides a valuable means of assessing the response to diagnostic and therapeutic efforts. TCD has also been very useful for recording the occurrence of cerebral emboli.

Three additional approaches to cerebral blood flow measurement are applicable only in the laboratory.These are autoradiography with iodo[¹⁴C]antipyrine, sequential injections of different radiolabeled isotope microspheres, and hydrogen clearance techniques.

Autoradiography utilizing iodo[¹⁴C]antipyrine as a diffusible indicator of flow has proved to be a highly quantitative means of obtaining data concerning flow with a high degree of spatial resolution. For this study the animal needs to be sacrificed shortly after the intravenous injection of iodo[¹⁴C]antipyrine. The brain is then removed and frozen to -70°, followed by thin sectioning and application of tissue slices to radiographic plates for 5 to 6 days. Multiple sequential arterial blood samples are used to provide the arterial input function. The emission densities on the photographic plates are then interpretable as measures of blood flow which contain a high degree of spatial resolution. The major limitation of this approach is that it permits a measure of flow at only one point in time, although some work has suggested that two isotopes with differential counting can be used to record flow at two points in time.

Radiolabeled microspheres measuring 6 to 8 µm in diameter provide a nondiffusible means of measuring flow. Microspheres of this size are extracted into the microcirculation at a rate of over 90 percent for a single pass through the cerebral circulation. By recording the rate of extraction of radiolabeled isotopes from the arterial circulation and then directly counting the number of counts in each tissue volume, blood flow data are obtained. Currently up to five independent isotope injections ¹⁴¹Ce, ¹³³Sn, ⁸⁵Sr, ⁹⁵Nb, ⁴⁶Sc) and therefore blood flow determinations can be made after isotope separation utilizing a matrix algebra approach for the solution of simultaneous equations. The major disadvantage of this approach in a laboratory is that a volume of 8 x 8 x 8 mm is typically required to obtain adequate counts for reliable statistical determinations.

The third approach involves measuring the clearance of hydrogen gas from about a reference platinum-iridium probe previously placed within the brain substance. Fine probe diameters (0.01 in) with exposure of only the terminal 2 mm are commonly being utilized. An array of as many as six simultaneous probes are currently being used, and this approach has been shown to provide a highly reproducible and locally specific means of repeatedly determining local cerebral blood flow. This technique has the advantage of repeatability with the opportunity to make flow calculations every 10 to 15 min for days or even weeks. A critical review of this topic has suggested that the tissue volume of study may be 5 x 5 x 5 mm. The only major limitation to this approach is that the data acquisition is limited to only the immediate region about the tip of the probe, which does require disturbance of the tissue to be studied by its placement.

Blood flow is an important monitor of cerebral function and impaired blood flow is often the pathway through which cerebral injury occurs. Many technologies, each having advantages and disadvantages, have become available for the measurement of CBF. Choosing the most appropriate CBF tool will depend on the particular study subject and the specific question to be answered.