Summary: All tracer-kinetic models currently employed with positron-emission tomography (PET) are based on compartmental assumptions. Our first indication that a compartmental model might suffer from severe limita tions in certain circumstances when used with PET oc curred when we implemented the Kety tissue-autoradiog raphy technique for measuring CBF and observed that the resulting CBF estimates, rather than remaining con stant (to within predictable statistical uncertainty) as ex pected, fe ll with increasing scan duration T when T > 1 min . After ruling out other explanations, we concluded that a one-compartment model does not possess suffi cient realism for adequately describing the movement of labeled water in brain. This article recounts our search for more realistic substitute models. We give our deriva tions and results for the residue-detection impulse re sponses for unit capillary-tissue systems of our two can didate distributed-parameter models. In a sequence of trials beginning with the simplest, we tested fo ur progres-The measurement of CBF is important not only because of the information it provides about the normal and diseased brain, but also because it is essential to other important measurements (e.g. , rate of oxygen consumption). Tr acer-kinetic models are employed with external radiation-detection de vices to interpret dynamic imaging data in terms of the movements of radiolabeled water (H 2 1 50) or other diffusible tracer (e.g. , [ 1 8F] fluoromethane) for the purpose of inferring CBF. The tracer-kinetic model currently employed with positron-emission tomography (PET) for this purpose is based on 443sively more detailed candidate models against data fr om appropriate residue-detection experiments. In these, we generated high-temporal-resolution counting-rate data re flecting the history of radiolabeled-water uptake and washout in the brains of rhesus monkeys. We describe our treatment of the data to yield model-independent em pirical values of CBF and of other parameters. By substi tuting these into our trial-model fu nctions , we were able to make direct comparisons of the model predictions with the experimental dynamic counting-rate histories, con firming that our reservations concerning the one-com partment model were well founded and obliging us to re ject two others . We conclude that a two-barrier distrib uted-parameter model has the potential of serving as a substitute for the Kety model in PET measurements of CBF in patients, especially when scan durations for T> 1 min are desired. Key Words: Cerebral blood flow-Dis tributed-parameter models-Po sitron-emission tomog raphy-Tissue heterogeneity-Tr acer kinetics. compartmental assumptions; that is , tracer is as sumed to move between discrete subvolumes, or "compartments," within each of which tracer is assumed to distribute instantaneously upon arrival. Thus, in a compartmental model, gradients of con centration are assumed to be zero (i.e. , their spatial profiles flat) within each compartment at all times. The compartmental mode...

A method for the in vivo determination of cerebral blood volume was tested in 15 adult rhesus monkeys. The technique utilized external residue detection and required the serial measurement of two mean transit times, namely, that of an intravascular tracer, C I5 O-hemoglobin, and that of a diffusible tracer, H 2 15 O. In computing the mean transit time for the intravascular tracer, the conventional Hamilton extrapolation of the downslope of the recording obtained for the washout of the tracer from the brain subsequent to an intracarotid bolus injection was found to be inadequate, yielding a mean transit time that systematically underestimated that parameter. Alternatively, the use of a power law extrapolation, as proposed by Huang, allowed a more accurate prediction of the vascular mean transit time. The preliminary studies testing the method predicted that the relationship between cerebral blood volume (CBV) and cerebral blood flow (CBF) was adequately represented by the equation CBV = 0.80CBF 038 , with a correlation coefficient of r = 0.90 for the cerebral blood flow range of 16 to 134 ml/100 g min~' with a normocapnic cerebral blood volume of 3.5 ml/100 g perfused brain tissue (arterial Pco 2 = 37 torr, CBF = 50 ml/100 g min" 1 ).• Cerebral blood volume is considered an important factor in cerebral hemodynamics, but its assessment is a difficult undertaking. Various methods have been proposed for the in vivo measurement of cerebral blood volume, and some disparity exists in the reported results (Table 1). In the present study, the cerebral blood volume of rhesus monkeys was determined by an in vivo tracer method using radioactive oxygen-15 ( labeled with (1) C 15 0-hemoglobin and (2) H 2 15 0, respectively, in 15 adult rhesus monkeys. To facilitate the injection of the labeled materials into the internal carotid artery, all branches of the right external carotid artery were ligated 2 weeks prior to the experiments. The tracers were then injected into the common carotid artery through a small (0.21 cm in diameter) catheter inserted in the femoral artery and positioned in the common carotid artery under fluoroscopic observation.The monkeys were anesthetized with phencyclidine, paralyzed with gallamine, and passively ventilated with 100% oxygen. End-tidal carbon dioxide tension (Pco 2 ), arterial blood pressure, and rectal temperature were continuously monitored. Temperature was maintained between 37 and 39 °C with a heating pad. Arterial pH, Pco 2 , and oxygen tension (Po 2 ) were measured before and after each injection.The time course of each tracer through the injected hemisphere was monitored with a 3 x 2-inch Nal(Tl) scintillation detector appropriately collimated and positioned to ensure essentially uniform detection efficiency for the injected hemisphere. The detector signal was routed through a pulse-height analyzer with an energy window of acceptance adjusted symmetrically around the 511-kev photopeak (481-541 kev) to eliminate scattered radiation. The accepted events (counts) per time frame we...

Summary: Dopaminergic ligands labeled with positron emitting radionuclides have been synthesized for quanti tative evaluation of dopaminergic binding in vivo. Two different methods, the explicit method and an operation ally simplified ratio method , have been proposed for anal ysis of these positron emission tomographic (PET) data.The basis for both methods is the same three-compart ment model. The two methods differ in the assumptions necessary for practical implementation. We have com pared these two approaches using PET data obtained in our laboratory. Sequential scans and serial arterial blood samples from a baboon following intravenous injection of [1BF]spiroperidol were collected. Application of the two methods to the same data yielded different values for corresponding parameters. Values calculated by the ratio Until recently, investigation of diseases in humans thought to involve dopaminergic receptors has been limited to postmortem studies. A method for quantitative measurement of dopaminergic binding in vivo would be of great value in eluci dating the role of dopaminergic receptors in the pathogenesis of these diseases and in defining the alterations induced by their pharmacological treat ment.Numerous investigators have synthesized dopa minergic ligands labeled with positron-emitting ra dionucJides for the measurement of dopaminergic binding in vivo using positron emission tomography (PET) (Tewson et al ., 1980;Wagner et al ., 1983; Received June 19, 1985; accepted November 18, 1985. 154method for the specific rate constant describing receptor binding varied depending upon the time after tracer injec tion , thus demonstrating an internal inconsistency in this approach. Tracer metabolism markedly affected the binding measurements calculated with either method and thus cannot be ignored. Our results indicate that the adoption of simplifying assumptions for operational con venience can lead to substantial errors and must be done with caution. Alternatively, we present simple new ana lytical solutions of the tracer conservation equations de scribing the complete , unsimplified three-compartment model that vastly reduce the computations necessary to implement the explicit method. Key Words: Dopamine Metabolism-Modeling-Positron emission tomog raphy-Receptors. Kilbourn et al ., 1984; Mintun et al ., 1984;Arnett et al ., 1985;Baron et al., 1985). The requirements of desirable radiopharmaceuticals for these studies have been reviewed recently (Arnett et al., 1985). The most important of these is that the ligand have a relatively higher degree of binding to specific re ceptor sites in vivo than to nonspecific nonreceptor sites. In vivo studies suggest that the labeled dopa minergic ligands [ISF]spiroperidol and [ l IC]N-meth ylspiroperidol are superior to others such as [ l IC]pimozide and [1sF]haloperidol in this regard (Welch et al ., 1983;Arnett et al., 1985;Baron et al ., 1985). PET images obtained 30-60 min after the in travenous injection of these radiotracers show re gional radioactivity distribution...

We investigated the movement of 13 N-labeled ammonia from blood to brain, in vivo, in adult rhesus monkeys. For this purpose, we monitored the behavior of the tracer by using external detection of the 511-keV annihilation-radiation photons of nitrogen-13 following rapid bolus injection into the internal carotid artery. Our data reveal a diffusion limitation for the transport of ammonia from blood to brain. We attribute this to the low permeability of the blood-brain barrier for the ammonium cation. At a measured cerebral blood flow of 51 (ml/min) per hg (hg = hectogram), for example, only 35% of the injected tracer leaves the vasculature and is incorporated into brain tissue. Further, this extracted fraction not only decreases with increasing cerebral blood flow, but is also influenced by the pH of the blood perfusing the brain and by the integrity of the blood-brain barrier. We have interpreted our data on the basis of a new regional model of the cerebral circulation that takes into account both capillary heterogeneity within an external detector spatial-resolution element and the effects of shifts in the degree of ionization of vascular radioammonia due to the existence of pH gradients along the direction of flow in capillary blood. We have thus obtained, apparently for the first time, estimates for the individual permeability coefficient-specific surface-area products for diffusive transport across the blood-brain barrier of the two aqueous solution ammonia species, NH 3 and NH^. These estimates, denoted PoS and P+S, respectively, are regional averages; our values and associated standard deviations are P 0 S = 0.12 ± 0.02 ml/sec per g and P+S = (5.5 ± 4.9) x 10" 4 ml/sec per g. Assuming a regional average brain capillary specific surface area, S, of 100 cm 2 /g, these data yield the tentative values P^ = (1.2 ± 0.4) x 10~3 cm/sec and P + = (6 ± 5) x lO" 6 cm/sec.

Regional cerebral blood flow (rCBF) provides important information about local neuronal functional and cerebrovascular status. Determination of rCBF requires sequential measurements of tracer concentration in arterial blood and brain tissue unless the tracer is trapped in the brain in proportion to rCBF. Since gadopentate dimeglumine is not trapped within brain tissue, we have developed the simultaneous dual FLASH pulse sequence (SDFLASH) which sequentially measures the MR signal change in both the internal carotid artery and brain parenchyma simultaneously during the passage of a bolus of paramagnetic contrast material.

Attempts to measure blood-to-brain glucose transport and cerebral glucose metabolism with 11C-glucose have been hampered by methods that require jugular venous sampling or do not adequately account for the efflux of labeled metabolites from the brain. We performed eight positron emission tomography studies with 1-11C-D-glucose in macaques at arterial plasma glucose concentrations of 8.43 to 1.51 mumol ml-1 (152-27 mg dl-1) using a model that includes a fourth rate constant to account for regional egress of all 11C-metabolites. Values for blood-to-brain glucose influx, cerebral glucose metabolism, and brain free glucose concentration agreed closely with values obtained in mammals by other investigators. Values for net extraction fraction corresponded closely to simultaneously measured arteriovenous values. We demonstrated that utilization of a model that includes a fourth rate constant to account for regional egress of all 11C-metabolites with positron emission tomography and 1-11C-D-glucose provides accurate measurements of blood-to-brain glucose transport and cerebral glucose metabolism in vivo without need for jugular venous sampling, even under conditions of severe hypoglycemia.

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A new method for analysis of electron microscope autoradiographs is described which is based on the maximum-likelihood method of statistics for estimating the intensities of radioactivity in organelle structures. We adopted a Poisson statistical model to describe the autoradiographic grain distributions that we prove results from the underlying Poisson nature of the radioactive decays as well as the additive errors introduced during the formation of grains. Within the model, an iterative procedure derived from the expectation-maximization algorithm of mathematical statistics is used to generate the maximum-likelihood estimates. The algorithm has the properties that at every stage of the iteration process the likelihood of the data increases; and for all initial nonzero starting points the algorithm converges to the maximum-likelihood estimates of the organelle intensities.The maximum-likelihood approach differs from the mask-analysis method, and other published quantitative algorithms in the following ways: (1) In deriving estimates of the radioactivity intensities the maximum-likelihood algorithm requires that we obtain the actual locations of the grains as well as the micrograph geometries; each micrograph is digitized so that both the grain locations as well as the geometries of the organelle structures can be used. (2) The maximum-likelihood algorithm iteratively computes the minimum-meansquared-error estimate of the underlying emission locations that resulted in the observed grain distributions, from which intensity estimates are generated; this algorithm does not minimize a chi-squared error statistic. (3) The maximum-likelihood approach is based on a Poisson model and is therefore valid for low-count experiments; there are no minimum constraints on data collection for any single organelle compartment. (4) The maximum-likelihood algorithm requires the form of the point-spread function describing the emission spread; a probability matrix based on the use of overlay masks is not required. (5) The maximum-likelihood algorithm does not change for different organelle geometries; arbitrary geometries are incorporated by maximizing the likelihood-function subject to the geometry constraints.We have performed a preliminary evaluation of the quantitative accuracy of the maximum-likelihood and mask-analysis algorithms. Based on two different phantoms in which we compared the squared error resulting from the two algorithms, we find that the new maximum-likelihood approach provides substantially improved estimates of the radioactivity intensities of the phantoms.