## Measurement of cerebral blood flow

The theoretical bases of all methods which utilize diffusible tracers are similar, and are based on the Fick principle which can be expressed mathematically as follows:

where CBF is the cerebral blood flow and has the dimensions of mass or volume per unit time, Qt is the quantity of the tracer which is taken up in the tissue in unit time t, and Ca and Cv are the arterial and venous concentrations respectively over a short period of time d t.

Unlike the kidney, the brain does not specifically and selectively remove foreign substances from the blood and excrete them—a process which would permit accurate measurement. What the brain can do, however, is absorb (in physical solution) an inert gas when it is presented to the brain via the lungs and/or circulation. Thus the amount of the tracer absorbed by the brain will be independent of the state of mental activity and, since the tracer is inert, will not itself alter the metabolic rate (and hence the blood flow) of the brain. The numerator of the Fick equation ( Qt) is determined by the concentration of the tracer in the brain, the weight of the brain, and the blood-brain partition coefficient (l) for the tracer:

In practice, the concentration of tracer can be measured directly or calculated from arteriovenous differences over a timed period. The mass of tissue (brain) can rarely be defined; thus perfusion is calculated as a flow per unit mass ( W) of tissue (traditionally 100 g). As a result, it is customary to express flow ( F) as milliliters of blood per 100 g brain tissue per minute, such that

This equation is valid only if the partition coefficient is the same throughout the tissue to be measured, the blood flow is uniform in the tissue, and diffusion equilibrium is achieved between the arterial supply and the tissue. Thus the ideal freely diffusible tracer ( Table 1) would equilibrate with the entire volume of tissue under investigation and have a 100 per cent extraction efficiency, such that by the end of the first circulation the arterial input would be in diffusion equilibrium with the tissue. Subsequently, there should be a linear relationship between the washout of the tracer and perfusion throughout the range of physiological measurement. Unfortunately, no such ideal tracer exists. Moreover, as far as the brain is concerned, gray matter, white matter, skull, and scalp have different partition coefficients and blood flows, as do normal brain, edematous brain, ischemic brain, and compressed brain. Furthermore, estimations of cerebral perfusion are complicated further by the recirculation of tracer and scatter due to extra- and intracranial activity. However, despite these valid considerations, estimates of cerebral blood flow can be made in clinical practice with sufficient reproducibility to permit decisions in relation to treatment and, as alluded to earlier, can be of value in the management of specific patients.

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Rea^ptfie. ifoofjue, uflinr-Kw Table 1 Characteristics of an ideal tracer

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