Skip to main content



The Statistical Analysis of Pharmacokinetic Data

Virtually all of the practical applications of pharmacokinetic data analysis involve two parts, one is the mathematical modelling of the underlying pharmacokinetic system and the other is the statistical analysis of pharmacokinetic data. The mathematical modelling has received great attention in the literature and has produced many practically useful and mathematically elegant models. The mathematical modelling of compartmental systems is described in (1–6). However, the statistical analysis of pharmacokinetic data has received relatively little attention in the literature. The limited attention that it has received usually addresses one of the following questions.
James H. Matis, Thomas E. Wehrly, Kenneth B. Gerald

Mathematical Methods in The Formulation of Pharmacokinetic Models

The first quantitative analysis in pharmacokinetics was made by Widmark (1), who studied both theoretically and experimentally the kinetics of distribution of several narcotics, in particlar acetone. He studied the concentration curve of acetone in the blood after a single dose administration, and assumed that the fall of the curve was due principally to elimination from the lungs and chemical metabolism. The mathematical model used by Widmark was
$$ \begin{gathered} dx/dt = - \beta x - \gamma x\;x\left( 0 \right) = {x_0} \hfill \\ dy/dt = \beta x\quad \;y\left( 0 \right) = 0 \hfill \\ dz/dt = \gamma x\quad \;z\left( 0 \right) = 0 \hfill \\ \end{gathered} $$
where x,y,z are the amount of acetone in the body, exhaled, and metabolized, respectively; xo is the amount administered initially. From the knowledge of the time behavior of the concentration c(t) of the acetone in the blood and of the so-called “reduced body volume” m, where m = x/c, Widmark computed the time behavior of x,y,z in several experimental conditions.
Aldo Rescigno, Richard M. Lambrecht, Charles C. Duncan

New Approaches to Uptake by Heterogeneous Perfused Organs: From Linear to Saturation Kinetics

The central problem of modeling biochemical kinetics in intact organs is to put the corresponding test-tube kinetics (known or postulated) into the appropriate physiological setting, and hence to deduce relations between quantities observable on the organ. Some normal or pathological features of the physiological setting can then be quantified from experimental data. Such work must navigate between the Scylla of losing the physiology in over-simplifications, and the Charybdis of so complicating the modeling for the sake of realism that the multitude of adjustable parameters can get no grip on the data (see especially Sections 7 and 10).
Ludvik Bass, Anthony J. Bracken, Conrad J. Burden

Basic Principles Underlying Radioisotopic Methods for Assay of Biochemical Processes in Vivo

Radioisotopes are frequently used to facilitate the assay of biochemical reactions. Usually they are used to study chemical reactions in vitro, and the procedure is to label one of the reactants and to measure the rate of accumulation of a labeled product (see General Equation in Fig.IB). From assay or knowledge of the specific activity of the reactant molecule, the rate of the overall reaction rate can be calculated from the rate of radioactive product formation. The application of this approach generally necessitates, however, specialized biochemical procedures to isolate and identify the labeled product and to limit the measurement of the radioactivity to the chemical product of the reaction.
Louis Sokoloff, Carolyn B. Smith

Tracer Studies of Peripheral Circulation

Studying the blood flow of the various tissues by tracers (also called indicators) one assumes steady state conditions for the system. It means, that the relevant parameters of the system are taken to be constant, the flow, oxygen uptake, etc. Systemic steady state is elementary for deriving the basic equations. It must persist during the time needed for making the measurement. This does not mean, however, that some degree of variability of the systemic parameter in question cannot be allowed. Consider for example the determination of cardiac output by injection of below-body-temperature saline in the right side of the heart with downstream temperature measurement in the pulmonary artery (“heat” clearance). In this case the flow rate of the blood in the system measured oscillates enormously. Yet, because the duration of the period of oscillation is fairly short relative to the duration of the heat clearance curve itself, one can get a good estimate of the average blood flow. In contrast to the systemic parameters, the tracer parameters, as for example the blood concentration, often vary as a function of time, i.e. for the tracer the steady state condition does not (in many cases) pertain.
Niels A. Lassen, Ole Henriksen

Tracer Kinetic Modeling in Positron Computed Tomography

The tracer technique uses a measurable substance to trace a dynamic process, such as flow, transport, or chemical reactions. The technique is neither new nor rarely used. For example, it has been used in our daily lives to estimate intuitively the flow speed in a river by observing the drifting of floats in the river. The application of the technique to physiological systems in the 19th century by injecting dye in the circulatory system to measure cardiac output(1, 2). The success of this application has led to many biomedical tracer techniques, including the measurement of cerebral blood flow in man(3). After the development of radioisotope tracer techniques(4) and external detection capabilities, tracer techniques have become widely used in many applications(5–9). With the recent development of positron emission computed tomography, i.e., positron CT(10), tracer techniques became an essential, integral part of this new technique for measuring many physiologic or biochemical parameters in man(ll, 12). Studies dealing with the principles and treatment of tracer techniques developed in parallel and have become more rigorous (13–17).
Sung-Cheng Huang, Richard E. Carson, Michael E. Phelps

Pharmacokinetic Models and Positron Emission Tomography: Studies of Physiologic and Pathophysiologic Conditions

Because of the structurally and functionally heterogeneous nature of the brain, it is necessary to measure changes in physiologic and biochemical parameters in the human brain on a regional basis. Such information is important in furthering our understanding of the normal function of the brain and the derangements that occur in various pathologic conditions. The development of the Kety-Schmidt technique for the quantitative measurement of cerebral blood flow in man, made it possible to determine the average rates of glucose and oxygen utilization and blood flow in the brain as a whole (1). Using these same principles a method to measure hemispheric changes in these parameters has been developed (2). Regional methods for the determination of cerebral blood flow using diffusable tracers have also been developed (3–5). These methods, however, do not provide 3-dimensional resolution by which it is possible to determine the physiologic and metabolic parameters in specific structural and functional subunits of the brain. With the development of the 18F-fluorodeoxyglucose technique it became possible to do this in terms of glucose metabolism in the human brain (6).
Martin Reivich, Abass Alavi

Kinetic Analysis of the Uptake of Glucose and Some of its Analogs in the Brain Using the Single Capillary Model: Comments on Some Points of Controversy

In 1961 Crone (1) demonstrated that the glucose transport across the blood-brain barrier occurs by facilitated diffusion. Since then, many studies with a variety of techniques have confirmed this observation and extended our knowledge of the process in details (2, 3, 4, 5, 6, 7, 8). In particular, the finding that glucose analogs share the facilitated transport mechanism has proven fertile. It forms the basis for Sokoloff’S ingenious autoradiographic method of determining the local rate of glucose metabolism (ICGU) in animals by measuring the rate of phosphorylation of the analog 2-deoxyglucose (2DG) which is trapped in brain (9). Using positron-emitting derivatives, this method has even been applied to man, yielding spectacular maps of the local rates of metabolism, the intensity of which change during changes of brain activity of motor, sensory, or mental type (10). It is perhaps worth noting, however, that the facilitated diffusion of glucose, one of the major prerequisites of the model on which the method is based, never has been documented in man. The use of positron emission technology would be one approach to the solution of this problem.
Niels A. Lassen, Albert Gjedde

The Use of 11C-Methyl-D-Glucose for Assessment of Glucose Transport in the Human Brain; Theory and Application

Imbalance between perfusion, transport and metabolism may determine the ultimate damage in ischemic brain disease (1,2). Therefore, for the quantitative assessment of ischemic brain disorders the knowledge of at least two parameters is necessary. One is local perfusion. The second parameter should relate to tissue metabolism, for example, to the glucose utilisation rate (3,4,5) or to the local unidirectional glucose transport rate (6,7,8,9).
Karel Vyska, Miroslav Profant, Franz Schuier, C. Freundlieb, Anton Höck, Hans-U. Thal, Veit Becker, Ludwig E. Feinendegen

The Indicator Dilution Method: Assumptions and Applications to Brain Uptake

Evaluation of vascular permeability can be made using intraarterial injection of two tracers, i.e. a test and an impermeable reference substance, and measurements of their concentrations in the venous outflow following a single passage through the organ, as first introduced by Chinard and co-workers (1,2). In his careful evaluation of this method, Crone made quantitative measurement possible and applied this to studies of blood-brain barrier glucose permeability (3,4).
Olaf B. Paulson, Marianne M. Hertz

Measurement of Receptor-Ligand Binding: Theory and Practice

The word “receptor” may seem at times to mean something different to almost everyone; this is not particularly surprising, since investigators in a wide variety of separate fields routinely employ the term to refer to something they work with. They may use it to refer to cellular components that specifically bind neurotransmitters; classical hormones; other hormone-like agents, such as paracrines, growth factors, and interferons; plant and bacterial toxins; lectins; antigens; antibodies; transported molecules and ions; second messengers; and ultimately the entire spectrum of drugs and poisons. In short, the concept of a “receptor” is truly protean (some might prefer to call it lipoprotean).
David E. Schafer


Weitere Informationen