Clifford S. Patlak

Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data

A theoretical model of blood–brain exchange is developed and a procedure is derived that can be used for graphing multiple-time tissue uptake data and determining whether a unidirectional transfer process was dominant during part or all of the experimental period. If the graph indicates unidirectionality of uptake, then an influx constant (Ki) can be calculated. The model is general, assumes linear transfer kinetics, and consists of a blood–plasma compartment, a reversible tissue region with an arbitrary number of compartments, and one or more irreversible tissue regions. The solution of the equations for this model shows that a graph of the ratio of the total tissue solute concentration at the times of sampling to the plasma concentration at the respective times (Cp) versus the ratio of the arterial plasma concentration–time integral to Cp should be drawn. If the data are consistent with this model, then this graph will yield a curve that eventually becomes linear, with a slope of Ki and an ordinate intercept less than or equal to the vascular plus steady-state space of the reversible tissue region.

Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data. Generalizations

The method of graphical analysis for the evaluation of sequential data (e.g., tissue and blood concentrations over time) in which the test substance is irreversibly trapped in the system has been expanded. A simpler derivation of the original analysis is presented. General equations are derived that can be used to analyze tissue uptake data when the blood–plasma concentration of the test substance cannot be easily measured. In addition, general equations are derived for situations when trapping of the test substance is incomplete and for a combination of these two conditions. These derivations are independent of the actual configuration of the compartmental system being analyzed and show what information can be obtained for the period when the reversible compartments are in effective steady state with the blood. This approach is also shown to result in equations with at least one less nonlinear term than those derived from direct compartmental analysis. Specific applications of these equations are illustrated for a compartmental system with one reversible region (with or without reversible binding) and one irreversible region.

Transport of α-Aminoisobutyric Acid across Brain Capillary and Cellular Membranes

The transport of α-aminoisobutyric acid (AIB), N-methyl-AIB (MeAIB), and diethylenetriaminepentaacetic acid (DTPA) from blood to brain was measured over different experimental periods in eight regions of the rat brain. Unidirectional transfer rate constants were determined from multiple-time/graphical and single-time analysis of the experimental data; values of 0,0018, 0,00057, and 0,000021 ml g−1 min−1, respectively, were obtained for the thalamus by graphical analysis, The initial distribution volume of AIB and MeAIB in brain tissue was several-fold greater than that of DTPA and the tissue plasma volume, and this difference was not accounted for by red blood cell uptake, This discrepancy could be due to rapid transport of AIB and MeAIB into brain endothelial cells in addition to the relatively rapid uptake by choroidal, meningeal, and ependymal associated tissues that was demonstrated by autoradiography. Thus, it may be misleading and erroneous to consider the blood–brain barrier (BBB) to be a simple, single-membrane structure when analyzing the blood–brain transfer data of solutes such as amino acids. The data from the ventriculocisternal perfusion experiments and previously published AIB uptake data in mouse brain slices were used to estimate the transfer rate constants across brain cell membranes. These studies indicated that the transport of AIB into brain cells was approximately 110 to 265 times greater than that across normal brain capillaries per unit mass of brain tissue, and that the BBB limits blood-to-brain cell transport of this amino acid. These observations (low rate of transport across normal brain capillaries and rapid concentrative uptake by brain cells) indicate that AIB is a good marker for measuring moderate to large increases in BBB permeability by experiments that require unidirectional flux of the tracer.

Fate of Cerebrospinal Fluid-Borne Amyloid β-Peptide: Rapid Clearance into Blood and Appreciable Accumulation by Cerebral Arteries

Abstract: In Alzheimers disease, the neuritic or senile amyloid plaques in hippocampus and association cortex, the diffuse plaques in brain areas such as the cerebellum and sensorimotor cortex, and the amyloid deposits in the walls of pial and parenchymal blood vessels are mainly composed of amyloid β‐peptides. In the present study, either soluble 40‐residue amyloid β‐peptide radiolabeled with 125I (I‐sAβ) or [14C]polyethylene glycol ([14C]‐PEG, a reference material) was briefly infused into one lateral ventricle of normal rats. By 3.5 min, 30% of the I‐sAβ was cleared from ventricular CSF into blood; another 30% was removed over the next 6.5 min. No [14C]PEG was lost from the CSF‐brain system during the first 5 min, and only 20% was cleared by 10 min. Much of the I‐sAβ that reached the subarachnoid space was retained by pial arteries and arterioles. Virtually no I‐sAβ was found in brain. The clearance of amyloid β‐peptides from the CSF‐brain system, reported herein for normal rats, may be reduced in Alzheimers disease, thus contributing to amyloid deposition in cerebral tissue and blood vessels.

A Critical Evaluation of the Principles Governing the Advantages of Intra-arterial Infusions

From the literature, there appears to be inadequate evidence supporting the clinical use of intraarterial infusions as a method of drug administration. This problem has been evaluated with consideration of the advantages gained in increased total drug delivery and increased drug effectiveness in the region supplied by the infused artery and consideration of the advantage of reduced systemic drug delivery following intraarterial infusion. Carefully chosen simplifying assumptions allow precise determination of the advantages of regional or systemic drug delivery when drug delivery is evaluated by the total time integral of drug concentration. Simplified experimental approaches are suggested for the precise measurement of these advantages. Drug effectiveness is more difficult to evaluate because of the usual nonlinear relationship between effect and concentration. However, certain relationships between the advantage of regional drug delivery and the advantage of regional drug effects are elucidated. This analysis offers new insight into the factors which determine the value of intraarterial drug administration and hopefully will help guide both future experimental studies in this area and clinical application of this method.

Hypoxia Increases Velocity of Blood Flow through Parenchymal Microvascular Systems in Rat Brain

The postulation that hypoxia increases local cerebral blood flow (lCBF) mainly by perfusing more capillaries (the capillary recruitment hypothesis) was tested in awake adult male Sprague–Dawley rats exposed to 10% O2 and control rats. The [14C]iodoantipyrine technique was used to measure lCBF. Local cerebral blood volume was determined by measuring plasma and red cell distribution spaces within the brain parenchyma with 125I-labeled serum albumin (RISA) and 55Fe-labeled red cells (RBC), respectively. Tissue radioactivity in 44 brain areas was estimated by quantitative autoradiography. Hypoxia raised lCBF by 25–90% in all brain areas. In about one-quarter of the brain areas, the rise in blood flow was associated with a small increase in microvascular plasma and blood volumes. This change in blood volume, which could be the result of perfusing more parenchymal microvessels and/or increasing parenchymal microvessel diameter, is not sufficient to account for the observed rise in lCBF. In the remaining areas the RISA, RBC, and blood spaces were either unchanged or only marginally increased by hypoxia. For this hypoxic perturbation, the major mechanism of raising blood flow appears to be increased velocity of microvessel perfusion and not perfusion of more capillaries. These findings provide only limited support for the capillary recruitment hypothesis.

Heuristic Modeling of Drug Delivery to Malignant Brain Tumors

It is apparent that chemotherapy against malignant brain tumors is generally ineffective. While some agents are more effective than others, none appreciably alters the clinical course of and the poor prognosis for patients with brain tumors. Even though new and more effective agents are being or will be developed, chemotherapy depends as much on the delivery of drug as it does on the drug used. Therefore, we have defined factors that we believe are of primary importance in drug delivery to brain tumors, and, using computer simulation, we have modeled the effects of these factors. In this article we discuss (a) the extent of the “breakdown” in the blood-brain barrier (BBB) that accompanies the development of malignant tumors in the brain, (b) factors that influence drug transport from tumor capillaries to tumor cells at varying distances from the capillaries, (c) the problems inherent in drug delivery from a well-vascularized tumor outward to normal brain tissue that might harbor malignant cells but that does not have leaky vessels (i.e., normal BBB), and (d) the difficulties in drug delivery from a well-perfused, highly permeable outer tumor shell to a central, poorly perfused tumor core.

Dexamethasone Effects on [125I]Albumin Distribution in Experimental RG-2 Gliomas and Adjacent Brain

A total of 72 RG-2 transplanted gliomas were studied in 58 rats at three time points (1, 30, 240 min) after intravenous injection of [125I]radioiodinated serum albumin ([125I]RISA). The animals were divided into two groups: a control group that received no treatment and a second group that was treated with five doses of 1.5 mg/kg of dexamethasone over 2.5 days. Local tissue concentrations of [125I]RISA were measured with quantitative autoradiography based on morphological features of the tumors and used to calculate the tissue distribution space. Two models were used to analyze the data. A two compartment model yielded estimates of local blood-to-tissue influx constants (K1), lower limit extracellular volumes (Ve), and plasma vascular volumes (Vp) in different tumor regions. Treatment with dexamethasone consistently reduced the RISA distribution space in the RG-2 tumors; the reduction in Ve was statistically significant in almost all tumor regions: whole tumor Ve (mean ± SE) was reduced from 0.14 ± 0.02 ml g−1 in control animals to 0.08 ± 0.01 ml g−1 in dexamethasone treated animals. K1 and Vp were also decreased in all tumor regions after treatment with dexamethasone (whole tumor K1 decreased from 2.36 ± 0.89 to 0.83 ± 0.29 μl g−1 min−1 and Vp decreased slightly from 0.016 ± 0.013 to 0.010 ± 0.005 ml g−1 after dexamethasone treatment), but these changes were not statistically significant. A comparison of the tumor influx constants in control animals and the aqueous diffusion constants of two different size molecules (RISA and aminoisobutyric acid) suggests that the “pores” across RG-2 capillaries are large and may not restrict the free diffusion of RISA (estimated minimum pore diameter > 36 nm) and that the total pore area is ∼6.2 × 10−5 cm2 g−1 in RG-2 tumor tissue. The second model, which allows for diffusion and solvent drag of RISA across tumor capillaries and through the tissue, was used to analyze the distribution profiles of RISA in peripheral tumor and adjacent brain. This analysis was consistent with a small bulk flow of plasma-derived edema fluid (capillary filtration rate ≈ 0.8 μl g−1 min−1) and a larger component of free diffusion of RISA (K ≈ 2 μl g−1 min−1) through pores in the tumor vessels of control animals. Dexamethasone treatment markedly reduced or eliminated the filtration of plasma-derived fluid across tumor capillaries and the movement of RISA through the extracellular space by solvent drag. These effects may be mediated by a reduction in the size of the extracellular space and/or a decrease in the pore size of tumor capillaries and could represent an important mechanism for corticosteroid control of tumor and peritumoral brain edema.

Striatal 18F-DOPA Uptake: Absence of an Aging Effect

l-[18F]6-Fluoro-DOPA (l-[18F]6-fluoro-3,4-dihydroxyphenylalanine; FDOPA) has been used with quantitative positron emission tomography (PET) to assess presynaptic nigrostriatal dopaminergic function in life. The relationship of estimated kinetic rate constants for striatal FDOPA uptake [Ki(FDOPA)] to the normal aging process has been the subject of conflicting reports. Resolution of this issue has been hampered by methodological differences in previous FDOPA/PET investigations. We studied 19 healthy normal subjects (aged 27–77 years) and measured striatal Ki-(FDOPA) according to each of the earlier methods. While significant correlations (p < 0.005) existed between Ki(FDOPA) values estimated by the various techniques, none correlated with normal aging. We conclude that normal striatal Ki(FDOPA) values estimated using quantitative FDOPA/PET are uncorrelated with the aging process.

An evaluation of errors in the determination of blood flow by the indicator fractionation and tissue equilibration (Kety) methods.

In this report, the effects of various errors and plasma time courses of indicator concentration on the accurate determination of cerebral blood flow (F) are theoretically analyzed for the tissue equilibration and the indicator fractionation techniques. For the indicator fractionation technique, the impact of sample timing and tissue assaying errors and of indicator backflux were examined; for the tissue equilibration method, errors in the value of the partition coefficient (Λ), sample timing, and tissue assaying were considered. The recommended ways to decrease the effects of errors in the indicator fractionation technique are to administer the indicator by an intravenous bolus and to sample the tissue about 10 s thereafter. Possible errors in the assessment of F by the tissue equilibration technique are diminished by using an indicator infusion schedule which yields a continuous rise in arterial concentration and by selecting a 30-s experiment duration. Surprisingly, the impact of sample timing errors is greater on the determination of F with the tissue equilibration method than with the indicator fractionation technique. For the chosen plasma time courses, there is always a backflux error in an indicator fractionation estimation of F, and this error increases as the flow rate increases. Thus, provided the sample timing and tissue assay errors are small and the value of Λ is known, the tissue equilibration method is the more accurate of the two. If Λ is unknown, then the indicator fractionation technique should be used. In many cases, the indicator fractionation method will provide as accurate an estimate of F as will the tissue equilibration method.