Uncertainty Analysis in Tumor Model with Fuzzy Parameters

Esmaili, Somayeh Saraf; Nasrabadi, Ali Motie

doi:10.1109/cise.2009.5365495

Cited by 4 publications

(5 citation statements)

References 17 publications

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“…The concept of fuzzy is logic that is used to designate fuzziness rather than logic that is fuzzy. In oncology, related to tumor growth, fuzzy mathematical models have been used by A.M Nasarbadi in 2009 and 2010 in which fuzzy differential equations have been solved for tumor growth solutions [46,47].…”

Section: Fuzzy Theory and Applicationsmentioning

confidence: 99%

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Khaliq

Iqbal

Bhat

2021

Preprint

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Most of the cancer growth models have described the exponential growth patterns at the very initial stage with low cell population density. Eventually, decreasing the tumor growth rate at higher cell population densities because of deficiency in resources such as space and nutrients. However, recent studies at clinical and preclinical investigations of cancer initiation or reappaearance showed a population dynamics evincing that the growth rate increases as cell number increases. Hence, showing behaviour analogous to cooperative mechanism in the ecosystem and ecological effect called Allee effect. Based on these observations with two arguments i.e. change in initial population and growth rate. In this paper, the novel mathematical model of tumor growth kinetics with Allee effect under fuzzy environment is proposed. In this model the Generalized Hukuhara derivative approach is utilized to solve the fuzzy differential equations. Moreover, it is showen that the change in initial value and growth rate affects the cell density with the Allee effect under the fuzzy environment. Finally the superiority of model has been showen with the help of numerical simulation.

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Section: Fuzzy Theory and Applicationsmentioning

confidence: 99%

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Khaliq

Iqbal

Bhat

2021

Preprint

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“…This feature has prompted several recent contributions to develop mathematical models that integrate ambiguity to understand evolutionary processes using differential equations.The traditional perspective of uncertainty has been transformed, and the usual view regards uncertainty as undesirable in research efforts and must be eradicated by all feasible measures. The contemporary viewpoint accepts ambiguity and thinks that science should solve it [9][10][11][12]. Possibility theory focuses on ambiguity inherent in natural languages and is "possibilistic" rather than probabilistic.…”

Section: Introductionmentioning

confidence: 99%

“…To forecast cell proliferation and tumor development models, the idea of fuzzy differential inclusion has been applied. The generalized Seikkala differentiability approach and the Zadeh extension rule are used to determine deterministic solutions in another attempt to solve fuzzy differential equations [20][21][22][23][24][25][26][27]. This study discusses the influence of fuzzy uncertainty in the Gompertz growth equation, which is used in a variety of fields, including statistical mechanics, medicine (tumor growth rate), chemistry (response models), and ecology (population growth) [28,29].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Sheergojri

Iqbal

Agarwal

et al. 2022

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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For treating cancer, tumor growth models have shown to be a valuable resource, whether they are used to develop therapeutic methods paired with process control or to simulate and evaluate treatment processes. In addition, a fuzzy mathematical model is a tool for monitoring the influences of various elements and creating behavioral assessments. It has been designed to decrease the ambiguity of model parameters to obtain a reliable mathematical tumor development model by employing fuzzy logic.The tumor Gompertz equation is shown in an imprecise environment in this study. It considers the whole cancer cell population to be vague at any given time, with the possibility distribution function determined by the initial tumor cell population, tumor net population rate, and carrying capacity of the tumor. Moreover, this work provides information on the expected tumor cell population in the maximum period. This study examines fuzzy tumor growth modeling insights based on fuzziness to reduce tumor uncertainty and achieve a degree of realism. Finally, numerical simulations are utilized to show the significant conclusions of the proposed study.

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“…For the first time in 2004, K. Kumar Majumdar and D. Dutta Majumder in one grade differential equation tumor model proposed the idea of using fuzzy differential equations and the advantages of its use in modeling [10,11,13]. In 2009, we simulated and analyzed that model by using fuzzy differential inclusion method [14].…”

Section: Introductionmentioning

confidence: 99%

Different initial conditions in fuzzy Tumor model

Esmaili¹,

Nasrabadi²

2010

JBiSE

Self Cite

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One of the best ways for better understanding of biological experiments is mathematical modeling. Modeling cancer is one of the complicated biological modeling that has uncertainty. Therefore, fuzzy models have studied because of their application in achievement uncertainty in modeling. Overall, the main purpose of this modeling is creating a new view of complex phenomena. In this paper, fuzzy differential equation model consisting of tumor, the immune system and normal cells has been studied. Model derived from a classical model DePillis in 2003, which some parameters from a clinical point of view can be described in the region. In this model, by considering fuzzy parameters from clinical point of view, the three-dimensional fuzzy tumor cells in terms of time and membership function are pictured and region of uncertainties are determined. To access the uncertainty area we use fuzzy differential inclusion method that is one of the including methods of solving differential equations. Also, different initial conditions on the model are inserted and the results of them are analyzed because tumor has different treatment in different initial conditions. Results show that fuzzy models in the best way justify what happens in the reality

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Uncertainty Analysis in Tumor Model with Fuzzy Parameters

Cited by 4 publications

References 17 publications

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

A Novel Mathematical Model of Tumor Growth Kinetics with Allee Effect under Fuzzy Environment

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Different initial conditions in fuzzy Tumor model

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