{"title":"冈伯兹生长是一个自相似异速生长过程。","authors":"Z Bajzer","doi":"","DOIUrl":null,"url":null,"abstract":"<p><p>The Gompertz law of growth has puzzled scientists for decades: while it successfully described growth kinetics of various biological systems (e.g., tumor growth), its foundation has remained unclear. In this paper I recognize the Gompertzian growth as founded on self-similarity, which is so abundant in natural phenomena that it justifiably represents a fundamental natural paradigm. The self-similarity leads to an allometric principle: the sizes of a given biological system at different times are related by a simple power law. The stated relation can be also viewed as basic functional growth equation with unique nonconstant solutions being the Gompertz and the exponential functions. This equation also provides the description of growth and regression dynamics in terms of a difference equation which already has found practical application in characterizing tumor growth kinetics.</p>","PeriodicalId":55080,"journal":{"name":"Growth Development and Aging","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1999-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gompertzian growth as a self-similar and allometric process.\",\"authors\":\"Z Bajzer\",\"doi\":\"\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The Gompertz law of growth has puzzled scientists for decades: while it successfully described growth kinetics of various biological systems (e.g., tumor growth), its foundation has remained unclear. In this paper I recognize the Gompertzian growth as founded on self-similarity, which is so abundant in natural phenomena that it justifiably represents a fundamental natural paradigm. The self-similarity leads to an allometric principle: the sizes of a given biological system at different times are related by a simple power law. The stated relation can be also viewed as basic functional growth equation with unique nonconstant solutions being the Gompertz and the exponential functions. This equation also provides the description of growth and regression dynamics in terms of a difference equation which already has found practical application in characterizing tumor growth kinetics.</p>\",\"PeriodicalId\":55080,\"journal\":{\"name\":\"Growth Development and Aging\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1999-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Growth Development and Aging\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Growth Development and Aging","FirstCategoryId":"1085","ListUrlMain":"","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Gompertzian growth as a self-similar and allometric process.
The Gompertz law of growth has puzzled scientists for decades: while it successfully described growth kinetics of various biological systems (e.g., tumor growth), its foundation has remained unclear. In this paper I recognize the Gompertzian growth as founded on self-similarity, which is so abundant in natural phenomena that it justifiably represents a fundamental natural paradigm. The self-similarity leads to an allometric principle: the sizes of a given biological system at different times are related by a simple power law. The stated relation can be also viewed as basic functional growth equation with unique nonconstant solutions being the Gompertz and the exponential functions. This equation also provides the description of growth and regression dynamics in terms of a difference equation which already has found practical application in characterizing tumor growth kinetics.