Integrative cybernetic model of oxygen homeostasis

The paper presents an integrative cybernetic model of the complex physiological process generically called "oxygen homeostasis". The model has been designed in such a manner as to enable a mathematical approach, in quantitative terms, to the various functions involved in the generation and uninterrupted functioning of the mentioned process. Those functions are: pulmonary and tissular respiratory function, blood circulation, transport, erythropoiesis, as well as other functions involved in the blood pH regulation at renal and hepatic level (the resorption of Na+ ions from the glomerular filtrate and the ammonio-genetic functions of the kidneys and, respectively, the glyco-genetic, ureo-genetic and metabolization functions of the liver). All of these functions have been assumed as regulated and controlled within a unitary cybernetic system, interpreted as an open, dynamic system. That system consists of seven multicompartment subsystems which are open and interconnected by means of exchange relations, biophysical and biochemical processes involved in the performance of the respective function. Special attention was given to the mathematical modelling of the exchange processes going on in the erythrocytic membrane as part of the transport function of the circulating blood. The mathematical description of the entire homeostatic system operation was done by means of a set of differential and algebraic equations. Some of those equations (those describing the continuity of several chemical species in a compartment of the circulatory system and those characterizing the state of thermodynamic balance of the blood subsystem within the respective compartment) enable one to determine the value of the state parameters at a given moment, as a function of the external and internal conditions and as a function of the intensity of processes specific to the subsystems considered. There are other equations (equations of regulation and control devices) that enable one to determine the variations in intensity of the processes mentioned that are necessary in order to restore the system to its "normal" state, in case of possible deregulations caused by disturbing factors.