Commutativity, time-reflection, and impulse-behavior
of pharmacokinetic reactions

Horst Melcher and Ewald Gerth
1. Pädagogische Hochschule Erfurt-Mühlhausen, Germany
2. Academy of Sciences of the GDR, Central Institute of Astrophysics, Potsdam (GDR)

Abstract
Pharmacokinetics opens up concepts and methods of research and examination of general process kinetics for matters of medicine, specifically those of pharmacology.

Reaction kinetics - originally developed for the specific problem of physical chemistry - is nowadays no longer bound to a certain discipline. It has, moreover, already turned into a multivalent instrument of the treatment of diverse and complicated problems of processes, so that it appears not only in natural sciences as for example in chemistry, physics and biology, but also in other areas like, e.g., in meteorology, population statistics, and even in social history.

In continuation of former works of the authors in other fields of physics, it is shown that the matrix-calculation can be applied profitably also to problems in the pharmacology. That refers above all to the concepts of commutativity and non-commutativity as well as to the impulse-behavior by giving different pharmacological drugs.

The main focus of the present work is put on the analytic representation of reaction systems and reaction processes. An adequate analytical formulation and treatment of kinetic reaction processes is given by the matrix-calculation, which implies the extremely important non-commutativity of multiplication of matrices.

The reaction process is pursued in positive time-progression and in negative direction of time by time-reflection. The relevant differential equation systems are formulated as vector-transformations of the ''concentration-vector'' in the multidimensional ''reaction-space''.

The reaction-matrix is considered also for temporally variable transition coefficients. With the reference to such phenomena like the propagating and spreading of concentration impulses in the reaction medium, also oscillating reactions are represented as effects brought about by intermittently given pharmacological drugs, showing a characteristic impulse-behavior. Thus, biorhythms, periodical seasons of the year and the day, with averaging, resonance, and aftereffect, can be described analytically and - using special computer programs for the solution of systems of differential equations - could be calculated numerically.

The article was published in German in the journal
,,Wissenschaftliche Zeitschrift der Pädagogischen Hochschule Erfurt-Mühlhausen'':

P 56. Melcher, H., Gerth, E.:
Kommutativität, Zeitspiegelung und Impulsverhalten pharmakokinetischer Reaktionen
Wiss. Z. PH Erfurt-Mühlhausen 19 (1983) 30-46
Abstract:
Commutativity, time-reflection, and impulse-behavior
of pharmacokinetic reactions

This is the last and most comprehensive article in a series of publications on reaction kinetics composed
by Horst Melcher and Ewald Gerth, which use the consecutive and non-commutative character of the dynamic process.

References

P 39. Melcher H., Gerth E.:
Behandlung von Strahlungstransportproblemen mit Matrixfunktionen
Wiss. Z. PH Erfurt-Mühlhausen 8 (1972) 3-10
Abstract:
Analytical treatment of the radiative transfer by means of matrix functions

P 42. Melcher H., Gerth E.:
Lösung des Strahlungstransportproblems für Energiestreuung mit Hilfe von Matrixfunktionen
Kernenergie 16 (1973) 47-52
Abstract:
Solution of the stationary radiation transport problem
for energy scattering using matrix functions
Quoted by: Energy Citations Database

P 44. Melcher H., Gerth E.:
Analytische Behandlung und numerische Berechnung
der Umwandlungsreihen von Radionukliden
mit Hilfe von Matrixfunktionen
Wiss. Z. PH Erfurt-Mühlhausen 9 (1973) 21-30
Abstract:
Analytical treatment and numerical calculation
of conversion series of radionuclides
by means of matrix functions

P 46. Melcher H., Gerth E.:
Darstellung von Schwingungsvorgängen als Transformationsproblem
Wiss. Z. PH Erfurt-Mühlhausen 11 (1975) 67-71
Abstract:
Oscillation processes represented as transformations of matrices

P 47. Melcher, H., Gerth, E.:
Ein heuristisches Modell für Linienprofile
Exper. Techn. Phys. 25 (1977) 521-525
Abstract:
A heuristic model for spectral line profiles

P 48. Melcher, H., Gerth, E.:
Darstellung von Linienprofilen durch Lorentz-Funktionen n-ten Grades
Exper. Techn. Phys. 25 (1977) 527-538
Abstract:
Representation of Spectral-Line-Profiles by Means of the Lorentz-Function of the n-th Degree

The numbers of the references are related to the Register of Published Articles of E. Gerth.

The seven articles referred above are put together to a booklet with the title:
Seven articles on reaction kinetics