The two faces of pharmacokinetics.

There are two main branches of Mathematics: Calculus and Geometry; in Physics there are Constructive Theories and Principle Theories. Similarly in Pharmacokinetics we can build models with two opposite approaches, the bottom-up and the top-down point of view. In this short opinion article I will try to show, with the help of a few examples, the advantages of each one of the two approaches.

Compartmental analysis and its manifold applications to pharmacokinetics.

In this paper, I show how the concept of compartment evolved from the simple dilution of a substance in a physiological volume to its distribution in a network of interconnected spaces. The differential equations describing the fate of a substance in a living being can be solved, qualitatively and quantitatively, with the help of a number of mathematical techniques. A number of parameters of pharmacokinetic interest can be computed from the experimental data; often, the data available are not sufficient to determine some parameters, but it is possible to determine their range.

Kinetic modeling in support of radionuclide dose assessment.

In this review, we trace the origins of mathematical modeling methods and pay particular attention to radiotracer applications. Nuclear medicine has been advanced greatly by the efforts of the Society of Nuclear Medicine's Medical Internal Radiation Dose Committee. Well-developed mathematical methods and tools have been created in support of a wide range of applications. Applications of mathematical modeling extend well beyond biology and medicine and are essential to analysis is a wide range of fields that rely on numerical predictions, eg, weather, economic, and various gaming applications. We start with the discovery of radioactivity and radioactive transformations and illustrate selected applications in biology, physiology, and pharmacology. We discuss compartment models as tools used to frame the context of specific problems. A definition of terms, methods, and examples of particular problems follows. We present models of different applications with varying complexity depending on the features of the particular system and function being analyzed. Commonly used analysis tools and methods are described, followed by established models which describe dosimetry along gastrointestinal and urinary excretory pathways, ending finally with a brief discussion of bone marrow dose. We conclude pointing to more recent, promising methods, not yet widely used in dosimetry applications, which aim at coupling pharmacokinetic data with other patient data to correlate patient outcome (benefits and risk) with the type, amount, kind and timing of the therapy the patient received.

On the use of pharmacokinetic models.

Extensive use of models in pharmacology, in physiology and in radiotherapy raises some questions on the nature and utility of models in general and of compartmental models in particular. In this paper I will define in a simple and logical way a set of useful pharmacokinetic parameters and show how their estimation depends on the assumed model. A special problem arises when some parameters are not identifiable; in that case I will show how it is possible to determine a range for them. Two examples are used to illustrate how to compute the value of the identifiable parameters and the range of the non-identifiable ones, when the available experimental data are not sufficient to identify a model.

Bioequivalence of Two Recombinant Human Growth Hormones in Healthy Male Volunteers after Subcutaneous Administration.

The bioequivalence of recombinant human growth hormone (rhGH) (somatropin) and its N-methionyl variant (Met-hGH) [Protropin((R)) (somatrem for injection)] was determined in 42 healthy male volunteers (n = 21 per treatment) who were randomized to receive either protein by subcutaneous administration of 0.1 mg kg(minus sign1). Serum samples were collected over 24 h after the injection, and the concentration of human growth hormone (hGH) were determined by an immunoradiometric assay. Bioequivalence of the two proteins was assessed by determining whether the 90% confidence limits for the ratio of geometric means using logarithmically transformed AUC and C(max) parameters (log(10)AUC(0--24), log(10)AUC(0--infty infinity), and log(10)C(max)) were within the 80--125% range. The bioequivalence of the two treatments was also tested by calculating a bioequivalance index (xi(2)) that measured the difference between the two mean concentration-time profiles. The 90% confidence intervals for the ratios of the geometric means for AUC were within the prescribed 80--125% range for bioequivalence. The upper limit of the 90% confidence interval for the ratio of the geometric means for C(max) fell slightly outside the 125% criterion even though the geometric mean itself, 106.6%, was very close to the ideal of 100%. There was a larger standard error associated with C(max) than with the AUCs, and this marginally larger confidence limit for C(max) resulted more from the variance among the subject than to the difference in the means. In fact, the bioequivalence index, xi(2), was 0.075, indicating that the mean curves after rhGH and Met-hGH are essentially superimposable.