@article{oai:nagoya.repo.nii.ac.jp:00016502, author = {OGAWA, SYUHEI and YAMADA, KOZO}, issue = {2}, journal = {Nagoya Journal of Medical Science}, month = {Sep}, note = {There are numerous empirical knowledge in the field of clinical medicine. In this article the authors intend to analyze such knowledge logically. A mathematical structure of an organism is proposed, using the "theory of sets", and the development of axiom was adopted into practice for the analysis of obese-diabetic and obese·normal constitutions. Define X, Y and Z as the sets of genetic, environmental factors and of vital phenomena; x, y, and z the elements in each set and t as time factor of aging, when z can be shown by the formula: Of course, the law given to "correspondence" f is of paramount importance. An organism is at least representing itself as having the responses of fitness to y within some limits by its x at t in the physiologic state. Therefore, the authors gave correspondence f, the law, that an organism would fitly respond to y or its own x with deficiency of minimal type. This axiom should not be applied to the pathologic state-that is, vital phenomena with cancer, autoimmunity or functio laesa etc. A man with glucokinase (GK) deficiency and without others will become a hyperinsulinar obese-diabetic; a man with deficiencies of phosphofructokinase (PFK) or pyruvate kinase (PK) in the liver, or of both enzymes, will become a hyperinsulinar obese-normal subject. One will recognize hyperinsulinism (one element in set Z) to be a response of fitness (correspondence f) in a person with any deficiency of hepatic key glycolytic enzymes, GK, PFK, and PK, (one element in set X), because insulin is the inducer of biosynthesis of hepatic key glycolytic enzymes. It is well known that rats fed on high fat diet show a diabetic status. Weber et al. reported that the hepatic key glycolytic enzymes, GK, PFK, and PK, were inhibited by physiological concentrations of fatty acids. Without genetic deficiencies, however, these organisms will become normal by removal of the insults. Thus, diets of environmental factors in set Y can regulate the appearance of genetic factors quantitatively, but not qualitatively. An enzyme with deficient activity needs to be produced in a larger quantity in order to compensate for the deficiency. Therefore, a person with GK deficiency shows hyperinsulinism. It is reported that insular function of pancreas decreases with age even in normal man and suggested that senile changes in the insular apparatus are significant factors in the development of diabetes. A person with hyperinsulinism will show a decrease in insular function with age more rapidly than a normal man will. Therefore, diabetes and obesity are in conformity with the "wear and tear theory" as a mechanism underlying the aging process. Thus, a constitution is composed of combinations of abnormal key enzymes and the interrelations between these enzymes and neural or hormonal systems which work on these key enzymes. Furthermore, the great variety of combinations between abnormality of elements in set X and modifications by elements in set Y should decrease or increase the time factor "t" when a pathologic state should occur.}, pages = {157--168}, title = {Analysis of Constitutions by Mathematical Principles :I. The Analysis of Obese-Diabetic and Obese Normal Constitutions}, volume = {30}, year = {1967} }