Combining Gompertzian growth and cell population dynamics
From MaRDI portal
Publication:1410348
DOI10.1016/S0025-5564(03)00094-4zbMath1021.92012OpenAlexW2018440559WikidataQ52010147 ScholiaQ52010147MaRDI QIDQ1410348
Željko Bajzer, Frank P. Kozusko
Publication date: 14 October 2003
Published in: Mathematical Biosciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0025-5564(03)00094-4
tumor growthordinary differential equationscell kineticsproliferationquiescenceGompertz growth model
Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).
Related Items (42)
Hazard function for cancer patients and cancer cell dynamics ⋮ Weighted maximum likelihood estimation for individual growth models ⋮ An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation ⋮ A new Gompertz-type diffusion process with application to random growth ⋮ A closed-form expression for the quantile function of the Gompertz-Makeham distribution ⋮ Profit optimization of cattle growth with variable prices ⋮ Optimal therapy protocols in the mathematical model of acute leukemia with several phase constraints ⋮ Tumor growth dynamics with nutrient limitation and cell proliferation time delay ⋮ Global dynamics of Nicholson-type delay systems with applications ⋮ Dynamics of almost periodic solutions for a discrete Fox harvesting model with feedback control ⋮ Nutrient limitations as an explanation of Gompertzian tumor growth ⋮ Density-dependence as a size-independent regulatory mechanism ⋮ A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers ⋮ A microenvironment based model of antimitotic therapy of Gompertzian tumor growth ⋮ Optimal control in a mathematical model for leukemia therapy with phase constraints ⋮ On strategies on a mathematical model for leukemia therapy ⋮ Modeling and analysis of a multilayer solid tumour with cell physiological age and resource limitations ⋮ Observer-based techniques for the identification and analysis of avascular tumor growth ⋮ A stochastic model in tumor growth ⋮ Inference on a stochastic two-compartment model in tumor growth ⋮ Parameter non-identifiability of the Gyllenberg-Webb ODE model ⋮ Solution of the feedback control problem in the mathematical model of leukaemia therapy ⋮ Mathematical modeling of biofilm structures using COMSTAT data ⋮ A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction in tumor size and rise in growth rate ⋮ Periodic Fox production harvesting models with delay ⋮ Spatial vs. non-spatial eco-evolutionary dynamics in a tumor growth model ⋮ Quiescence as an explanation of Gompertzian tumor growth revisited ⋮ Some Classes of Stochastic Differential Equations as an Alternative Modeling Approach to Biomedical Problems ⋮ A generalization of Gompertz law compatible with the Gyllenberg-Webb theory for tumour growth ⋮ A mathematical model to study the effects of drugs administration on tumor growth dynamics ⋮ Stochastic roots of growth phenomena ⋮ Modelling the balance between quiescence and cell death in normal and tumour cell populations ⋮ Accumulation of neutral mutations in growing cell colonies with competition ⋮ Asymptotic behaviour of solutions to abstract logistic equations ⋮ Goodness-of-fit testing for the Gompertz growth curve model ⋮ Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification ⋮ An Evolutionary Model of Tumor Cell Kinetics and the Emergence of Molecular Heterogeneity Driving Gompertzian Growth ⋮ A two-compartment model interacting with dynamic drugs ⋮ On the Gompertz-Makeham law: a useful mortality model to deal with human mortality ⋮ Two-compartment model interacting with proliferating regulatory factor ⋮ Entropy control of stochastic processes described by stochastic Gompertz equation based on Fokker-Planck equation ⋮ Stationary distribution and extinction for a stochastic two-compartment model of B-cell chronic lymphocytic leukemia
Cites Work
- Gompertzian growth as a consequence of tumor heterogeneity
- Diverse ideas on the growth kinetics of disseminated cancer cells
- Modeling tumor growth
- Stability analysis of normal and neoplastic growth
- Tumor growth \textit{in vivo} and as multicellular spheroids compared by mathematical models
- Conceptual frameworks for mathematical modeling of tumor growth dynamics
- A Theoretical Basis for Gompertz'S Curve
- A Cell Kinetics Justification for Gompertz’ Equation
- Allometric morphogenesis of complex systems: Derivation of the basic equations from first principles
- New Dimensions in Gompertzian Growth
This page was built for publication: Combining Gompertzian growth and cell population dynamics