Regional Cerebral Blood Flow: Estimation by Means of Noametabolized Diffusible Tracers-An Orerview

T" E FJrrRQUS OXIDE technique' useful for th nmswmmt of blood hw, o x y d

and @cwa canswmpih of tfia human brain as a ww was inapb ie of mmuring these fun& rims in imjividnd small regions througfimt the b h W h n the technique was applied to tbe study of schizophrenia, tbe valuwr for b l d flow amd wgen consumption were w i t h the normal mmjp2 1t was pOintcd out that this did not mle ont cbanges in particular regions of tha braia, and the next obpctive btmnt the -t and study of regional b l d Bow and metabdim. The m a t promisiing approach a m m d to lie in a more exhaustive study of the

pwaaarses on which the nitrous oxide tdmiiuc was kd, ie, the errchange of nmme- tab&&, diffusible molecula bcbetwecn capihry a d h u c 3

In the dwetoprncnt of the nitrous oxide tech- nique, the familiar Fick principle had been cm- v m d to differential fm and made appliable to the atrmmulation of an exogenous noamp. tabolizad substance in the brain, rather than the a h p t i o a of oxygen in the lungs, ie:

w h Qb. C,, and C, rcprestnt the quantity of the substance in the brain and its concentration in arterial and mixed cerebral venous blood, mpctively, and F represents total cerebral b l d h. To solve the rsulting expmion Tor cerebral

Mood How it was necessary to evaluate Eoncen-

From t b N a t l d l ~ ~ i t w ~ of Health, tkihesdu, MD. Addmss rgpdnf requests to s 4 y m S. KCIF, MD,

NmeoAol Imihrre of Muntal Health. N a r i o ~ l Inrrlrures oj H d t h . Bcrkrsd~. MD 20205.

htim of the traw in ar~erial and mixed ccre bPal venous Mood, both dwbicb wmobtakble, but also the amunt taka up by the brain as a whole. For a mdimctiw gas like N#, w M cwld not b mwurod by uxtsrrial W m , Ihh could mvsrthsl;~ bt dona ky continuing ifs inhalation at a cornstant low ~~~lcuntration until the brain mid ib eauent blood were in virtual equiIibrium, at w h a time Q would bt qml to GWX, where W repmsents the wtigbt of the brain and A, the partition & a t of the subtance ktween mixed brain t h e and b l d . Thus,

F/W - A C ~ / r (G - GI dt 121

where F/W representti mean Bow ptr unit weight of brain, and T rtpmmts the time required after the onset of inhalation of a oonsmt partial p m u m of nitom oxide for cqnilibrium to be achieved. h a p c m of equilibration e x w i n g over several minutes, the limiting lactor is not diffwion between capillaria and their s u m n d - in8 tissue, but the disparities between tissua with dflefent ptrfusion rates and partition cuef- ficients and the rate at which the tissue with the slowest perfusion approaches the mt of the b i n in respct of tracer comntration. It was shown rheoAcally, and v e W experimeotally, that for the normal brain, and for most abtlormal situations aside from major cerebral infarction, Icn minut- of equilibration L sufficient for a masurement d avcmgc cerebral blood flow with an mar of 5%. In tbe development of the principle for mm-

surernmt of blood flow in s d regions tbrougb- out the brain, quation 1 led directly tu the exprdon for the conantratioo of tracw in an individual tissue region (C,):

Tho situation was different here from that for blood flow in the brain as a whole, wberc the cunccntration of tracer in the arterial and duent venom blood was a d b l e to measure- ma14 and a mans had to be devised for =timat- iag the mean nncantm tim of tracer in the whole brain. In the case of an individual small region, on theother band, there a p p d to be no way of measuring the concentration of tracer in the d3ucnt b l d , but by using a radioactive tram It should be passible to measure its regional concentration in tht brain by autoradiography in animals and by external detectors in man. Under oppnqnkte conditions it would thern be p i b l e ta derive the conmtration of tracer in the venous W from a small region through its tissue cmecntration. Where diffwion is not significantly limiting, a

traccr in the entering capillary blood will achieve practical quilibiium with the surrounding h u e at &the time of its exit, ie. - C,/X(. Substitut- ing, rearranging, and integmting yielded an expression for the concentration of tracer in a mil tissue regionat a time IT) in terms of blood h w though the region, partition coefficient of the tracer Wwaen the tissue and blood, and the past history of the tram in the arterial b l d from the timeof its introduction2:

whert 4 - Fi/bWi. In the simple special case where the tracer is

being cleared from the tissue in the prtsence of a negligible arterial concantration, equation 4 rcdacw to:

Thig equation was derived in 1949' for the clear- am~ of wa from an intramuscular injection site. Thdrt is some diffusion limitation for d i u m ion through the capillary wall, however, m the assumption of inatantancous capil1ary:tis- sue cquiJibrium could not be made. and a factor (m)' was intduced representing the fraction of amp1ete equilibrium achieved by a particular substance in each passage through the tissue, k now becoming mF/XW for each region. The technique was later improved by Lassen t t als who substituted a radiaisrrtope of an inert gas for the sodium ion.

It was de~irable to elucidate the physical and biological factors on which the capiUwy:hue equilibrium of a diffusible and unmetablized substance depends, and to ascertain the condi- tions under which it would not be limiting, ie, where m would be sufficiently close to unity that it could bt neglected. Thirty years before, Krogh6 had used a mdeI consisting of paraljd capillar- ies, each with a cylinder of surrounding tissue, to calculate tbe diffusion gradients of oxygen in muscle. Earlier, JWr7 had demibcd the eqnili- bration of pulmonary mpillary b I d with a l v n Iar oxygen in terms of its diffusion d d e n t , capillary geometry, b l d flow, and the capacity of hemoglobin lor oxygen. I n a steady state, oxygen gradients would k comtant, but in the case of an unmatabolized substance the gradients would change with time and intrduce another level of complexity. By building on Bohr's derivation, and with the

use of KrOgh's rncdel, it was pssible to derive an expression for the exchange d an inm but diffusible tracer between flowing capillary b j d and the surrounding tissue3 in terms ~f perfusion rate (F), the capillary diffusing surface (S), and the diffusion cmficient of the traccr through the capillary membrane (D'):

m - 1 - exp (-WS/F).

That derivation was a first approximation because it made two simplifying assumptions: that, after diffusing through the capilIary wall, the tracer was iristantaneously dispersed uni- formly throughout the external phase, and that its concentration there did not change appre ciably in the time of a single transit of blood through the capillary. Since the capillary volume in the brain is less than 5% of the parenchyma, the latter assumption should introduce a ncgligi- blt error. In respect or tbt first assumption, Copperman' made further calculations, taking jnta mnsideration radial diffusion from the capi1- lary through the tissue. Since the capillaries of the brain ate arranged in baskets around the cellular components rather than in parallel along muscle fibers, radial diffusion processes should be the better model. These calculations s u p ported the prediction that inert gases and other substances with a high lipid solubility would achieve practical equilibrium between each tis- sue in the brain and tbe perfusing blood during a

single pwage. For a wide range of other sub- taacwr to whicb the capillary wall was less per- mble, t he expression for m became a measure of their capillary permeabilityP

The first application of the principles described above was in 1955 by Landau e t a1," with the measurement of blood flow in 28 strut- turas in the brain of the cat. The radioactive tracer u d was the gas trifluoriodomethane k W with I3'I, administered intravenoudy in solution. At tht end of one minute, during whicb the arterial concentration of the radioactive gas was monitorad, the animal was killed and the head sectioned and frozen in liquid nitrogen. Autoradiograms were made at law temperatures and from these, vatu= for mean concentration in the various structures were obtained with refer- ence to radioactive "'I standards incorporated in cacB section. The tissue:bld partition coefi- citnt for each structure was obtained from aut* radiograms prepared after complete equilibra- tion.

Among the most significant observations made with the use of Lha original technique were those reported by Sokoloff ' on the effects of th iop ta l and photic stimulation. Thiopcnlal anesthaia differentially roducui blood flow in mid regions and subcortical structures sub serving sensory functions, while photic stimula- tion was axmiatd witb marked increases in peafusion of the striate cortex, lateral gcniculate ganglia, and supriot colliculi. Allhough thert had h e n a few reports suggesting an increase in perfusion accompanying increased functional activity, this was the first clear demonstratjon of thnt important homeostatic relationship, and of the perceptive inference by Roy and Sherring- ton'' nearly 100 years ago that lmal neuronnl activity, metabolic rate, and perfusion were c l d y oouplcd. That early demonstration of the ampling 6f functional activity and local cerebral pwfwion was s u c d e d 16 years Later by auto- radiograms of the stimulated visual system using '%dmyglucosc, and demanstrating with high d u t i o n the optical dominance culumns in the visual cx~rttx.''

The original tracer (F,'"IC) was unsatisfac- twy for a number of reasons. As a gas at rmm tempemture, it required that autoradiograms be m a at -40 OC, and the radioisotope emitted a h a ray so penetrating as to impair the resolu-

tion of the image. Posternak" improved the image considerably with the use of "C ethanol, and Reivich et all5 used I4C-antipyrine in studies of regional cerebral blaod Row in slow wave and rapid eye movement (REMI sleep. Because the latter substance was diffusion limited at higher flows, Sakurnda et all6 substituted iodeJ4C- antipyrine, to which the capillary wall was con- siderably more permeable.

Jngvar and Lassen," in 1961, were the k t to apply the princip t es of ixpillary:tissue exchange of an inert gas to measurement of regional b l d flow in man, using "Kr. It was later found that I3'Xe was more satisfacmy.'' The tracer dim solved in saline wns administered by intracarotid injection in conjunction with cerebra1 angiogra- phy. CorticaI blood flow was memured as the initial semi-logarithmic slope of the clearance of the tracer from theregion under study. By inject- ing the radioisotope into the internal m t i d , background f m the cont rala teral hemisphere, extracranial structures, and respiratory system was minimized. and the measurement waa made in less than one minute. The rbchnique has been widely used in neurologic and psychophysiobgic studies, and has demonstrated the localization and extent of changtx in perfusion, reflecting neuronal activity i n n wide range of psychologic states.

Much effort bas been placed on developing less invasivc techniques for regional blood flow mcasurernent in the human brain. In 1965, Veal1 and Mallett'' administered la3Xe by inhalation, monitored the levels in the brain by external counting, and analyzed the resultant curve by means of a two-compartment modal. Obrist el alZ0 simplified this appraach by monitoring arte- rial concentration of the 88s through end-tidal air sampling, and estimated wrtical blood Bow from an early tangent of the semi-logarithmk clearance curve. The procedure is noninvasive and relatively inexpensive; i t has been used extensively in neuropsychiatric disorders and in studies of pychologic function. It is subject to certain potential errors, however, which with sufficient care can be minimized. Background radioactivity Irom the other hemisphert may account for as much as 25% of the counts record&; that from tbe respiratory tract may not be completely eliminated by ignoring the first 30 w x n d s of the clearance curve. That expedient,

w the other hand. may diminish the influence of the most rapid perfusion rates while the back- grwnd from extracerebral tissues of the head, magnified by proximity tb the counters, may unduly reducc the values obtained from the portion of tbe clearan% curve used in the m1w- Iations. Each of these sources of error would tend to d u c e values for mrtid Wood Bow obtained by moans of this technique.

Positron mission tomogtaphy offers the mst a d d and theoretically soundat apprcach to the noainwsivc measurement of regional cere bml blood flow in man which is presently avail- able. Background problems are minimal, and the mlution is higher than that which has been obtained with earlier methods of external counting. Water labeled with the pitran emit- ting isotope of oxygen (''0) has been the tracer most ~ s t d . * ' ~ ' ~ Tomita and GotohU have a d d r d some or the theoretic sources of error in the application of equation 4 lo clinical stud- ies, finding tbem small enough to be negligible, axccpt for cclnditions of severe ischemia and infarction. Hcrscovitch, Raichlt, and their m workers- have examined the several assump riom inherent in rht derivation and evaluated their vdidi ty both theoretically and cxperimen-

tally. They found that heterogeneity of tissue in the minimum volume examined by the technique intrduces an error of less than 4% if the duration of measurement is maintained at one minutc or less as used in the original autoradiographic application. With appropriate correction for the fact that water, in contrast to krypton or xenon, d m not diffuse freely through the entire apil- lary wall and has a value for m which is appre- ~ i a b l y lw than 1 , regional blood flow m w u m ment with H2'O is accurate over a range of 10 to 155 mL/lW g/rnin. In a fruitful collaboration with the department of psychiatry, Raichlt and Herscrwitch used tbis technique and demon- strated a significant abnormal right:leh asym- metry discretely Iacalized to the parshippocam- gal gyms in patients with lactatesensitive panic d i ~ o r d e r . ~

Two other approaches currently in use for measuring regional cerebral circulation depend upon the rapid and almost total uptake by the tissues of certain radioactively-labeled sub stances, or the equilibrium concentration of an extremely short-lived tracer in the tissue. Their application in clinical studies is described in some of the fallowing reviews.

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