The Model Muddle: In Search of Tumor Growth Laws

Gerlee, Philip

doi:10.1158/0008-5472.can-12-4355

Cited by 274 publications

(287 citation statements)

References 13 publications

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“…Among six growth models reported in the literature, three were found to describe our data significantly better than the others, namely the Bertalanffy, West, and Gompertz models. Because of the close resemblance of three-parameter tumor growth models, some authors have cast doubts on their distinguishability (4,32). It is thus remarkable that our data permitted this distinction.…”

Section: Discussionmentioning

confidence: 99%

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Mathematical Modeling of Tumor Growth and Metastatic Spreading: Validation in Tumor-Bearing Mice

et al. 2014

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Defining tumor stage at diagnosis is a pivotal point for clinical decisions about patient treatment strategies. In this respect, early detection of occult metastasis invisible to current imaging methods would have a major impact on best care and long-term survival. Mathematical models that describe metastatic spreading might estimate the risk of metastasis when no clinical evidence is available. In this study, we adapted a top-down model to make such estimates. The model was constituted by a transport equation describing metastatic growth and endowed with a boundary condition for metastatic emission. Model predictions were compared with experimental results from orthotopic breast tumor xenograft experiments conducted in Nod/Scidg mice. Primary tumor growth, metastatic spread and growth were monitored by 3D bioluminescence tomography. A tailored computational approach allowed the use of Monolix software for mixed-effects modeling with a partial differential equation model. Primary tumor growth was described best by Bertalanffy, West, and Gompertz models, which involve an initial exponential growth phase. All other tested models were rejected. The best metastatic model involved two parameters describing metastatic spreading and growth, respectively. Visual predictive check, analysis of residuals, and a bootstrap study validated the model. Coefficients of determination were R 2 ¼ 0:94 for primary tumor growth and R 2 ¼ 0:57 for metastatic growth. The data-based model development revealed several biologically significant findings. First, information on both growth and spreading can be obtained from measures of total metastatic burden. Second, the postulated link between primary tumor size and emission rate is validated. Finally, fast growing peritoneal metastases can only be described by such a complex partial differential equation model and not by ordinary differential equation models. This work advances efforts to predict metastatic spreading during the earliest stages of cancer. Cancer Res; 74(22); 6397-407. Ó2014 AACR.

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Section: Discussionmentioning

confidence: 99%

“…On a purely macroscopic level, the Gompertz model, exhibiting a sigmoidal growth curve, has been used first (2). Many other sigmoidal growth curves have also been proposed (3,4). Some of these models are derived on a mechanistic basis, such as the von Bertalanffy (5) and West (6, 7) models, which assume an auto-similar tissue organization.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Tumor Growth and Metastatic Spreading: Validation in Tumor-Bearing Mice

et al. 2014

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“…Many mathematical models of tumor growth at different levels from gene expression to the macroscopic tumor development have been formulated, [1][2][3][4][5][6][7][8][9][10][11]. Recently, mathematical models of tumor-immune interactions have also been considered to evaluate the efficacy of immunotherapy in the context of tumor challenge.…”

Section: Introductionmentioning

confidence: 99%

The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study

Saccomani

Thomaseth

2018

Complexity

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Mathematical models are increasingly proposed to describe tumor's dynamic response to treatments with the aims of improving their efficacy. The most widely used are nonlinear ODE models, whose identification is often difficult due to experimental limitations. We focus on the issue of parameter estimation in model-based oncological studies. Given their complexity, many of these models are unidentifiable having an infinite number of parameter solutions. These equivalently describe experimental data but are associated with different dynamic evolution of unmeasurable variables. We propose a joint use of two different identifiability methodologies, structural identifiability and practical identifiability, which are traditionally regarded as disjoint. This new methodology provides the number of parameter solutions, the analytic relations between the unidentifiable parameters useful to reduce model complexity, a ranking between parameters revealing the most reliable estimates, and a way to disentangle the various causes of nonidentifiability. It is implementable by using available differential algebra software and statistical packages. This methodology can constitute a powerful tool for the oncologist to discover the behavior of inaccessible variables of clinical interest and to correctly address the experimental design. A complex model to study "in vivo" antitumor activity of interleukin-21 on tumor eradication in different cancers in mice is illustrated.

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“…However, the logistic model does not fit very well in cases where there are more complex relationships acting as interactions within food webs or several features that occur in most cases in nature dependencies [5,6,7,8,9,22]. Aiming to generalize the logistic equation and give a better description for some of those events, El-Sayed, at all [5], studied the corresponding fractional-order logistic by a numerical analyze.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this paper is to present the analytic solution of the fractional logistic equation, in the inverse form, and analyze the applicability of this fractional equation to improve the description of the dynamic of cancer tumor and compare this model with some classical models presented in the literature [9,18], and is organized as follows. In Section 1 we make a brief introduction to our work.…”

Section: Introductionmentioning

confidence: 99%

A Prelude to the Fractional Calculus Applied to Tumor Dynamic

Camargo

Gomes

Varalta

2014

Tend. Mat. Apl. Comput.

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ABSTRACT. In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α ≤ 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.

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The Model Muddle: In Search of Tumor Growth Laws

Cited by 274 publications

References 13 publications

Mathematical Modeling of Tumor Growth and Metastatic Spreading: Validation in Tumor-Bearing Mice

Mathematical Modeling of Tumor Growth and Metastatic Spreading: Validation in Tumor-Bearing Mice

The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study

A Prelude to the Fractional Calculus Applied to Tumor Dynamic

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