000098218 001__ 98218
000098218 005__ 20230126102837.0
000098218 0247_ $$2doi$$a10.1371/JOURNAL.PONE.0224978
000098218 0248_ $$2sideral$$a121879
000098218 037__ $$aART-2019-121879
000098218 041__ $$aeng
000098218 100__ $$aSelva Castañeda, A.R.
000098218 245__ $$aNew formulation of the Gompertz equation to describe the kinetics of untreated tumors
000098218 260__ $$c2019
000098218 5060_ $$aAccess copy available to the general public$$fUnrestricted
000098218 5203_ $$aBackground
Different equations have been used to describe and understand the growth kinetics of undisturbed malignant solid tumors. The aim of this paper is to propose a new formulation of the Gompertz equation in terms of different parameters of a malignant tumor: the intrinsic growth rate, the deceleration factor, the apoptosis rate, the number of cells corresponding to the tumor latency time, and the fractal dimensions of the tumor and its contour.
Methods
Furthermore, different formulations of the Gompertz equation are used to fit experimental data of the Ehrlich and fibrosarcoma Sa-37 tumors that grow in male BALB/c/Cenp mice. The parameters of each equation are obtained from these fittings.
Results
The new formulation of the Gompertz equation reveals that the initial number of cancerous cells in the conventional Gompertz equation is not a constant but a variable that depends nonlinearly on time and the tumor deceleration factor. In turn, this deceleration factor depends on the apoptosis rate of tumor cells and the fractal dimensions of the tumor and its irregular contour.
Conclusions
It is concluded that this new formulation has two parameters that are directly estimated from the experiment, describes well the growth kinetics of unperturbed Ehrlich and fibrosarcoma Sa-37 tumors, and confirms the fractal origin of the Gompertz formulation and the fractal property of tumors.
000098218 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77735-C3-1-P
000098218 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000098218 590__ $$a2.74$$b2019
000098218 591__ $$aMULTIDISCIPLINARY SCIENCES$$b27 / 71 = 0.38$$c2019$$dQ2$$eT2
000098218 592__ $$a1.023$$b2019
000098218 593__ $$aMultidisciplinary$$c2019$$dQ1
000098218 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000098218 700__ $$aRamírez Torres, E.
000098218 700__ $$aVilla Goris, N.A.
000098218 700__ $$aMorales González, M.
000098218 700__ $$aBory Reyes, J.
000098218 700__ $$aSierra González, V.G.
000098218 700__ $$aSchonbek, M.
000098218 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, J.I.$$uUniversidad de Zaragoza
000098218 700__ $$aBerges Cabrales, L.E.
000098218 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000098218 773__ $$g14, 11 (2019), e0224978 [17 pp]$$pPLoS One$$tPLoS ONE$$x1932-6203
000098218 8564_ $$s941408$$uhttps://zaguan.unizar.es/record/98218/files/texto_completo.pdf$$yVersión publicada
000098218 8564_ $$s2234226$$uhttps://zaguan.unizar.es/record/98218/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000098218 909CO $$ooai:zaguan.unizar.es:98218$$particulos$$pdriver
000098218 951__ $$a2023-01-26-09:54:42
000098218 980__ $$aARTICLE