Methods of Mathematical Oncology

2021 ◽  
Keyword(s):  
Mathematical Oncology

scholarly journals The 2019 mathematical oncology roadmap

2019 ◽  
Vol 16 (4) ◽  
pp. 041005 ◽  
Author(s):  
Russell C Rockne ◽  
Andrea Hawkins-Daarud ◽  
Kristin R Swanson ◽  
James P Sluka ◽  
James A Glazier ◽  
...  
Keyword(s):  
Mathematical Oncology

scholarly journals Introduction to Mathematical Oncology

2019 ◽  
pp. 1-4 ◽  
Author(s):  
Russell C. Rockne ◽  
Jacob G. Scott
Keyword(s):  
Mathematical Oncology

The Rise of Mathematical Oncology

2015 ◽  
Vol 4 (4) ◽  
pp. 293-296
Author(s):  
Kiran George ◽  
R. Malathi ◽  
J. Krishnan ◽  
Nisha Susan Thomas
Keyword(s):  
Mathematical Oncology

scholarly journals High school Internship Program in Integrated Mathematical Oncology (HIP IMO) – five-year experience at Moffitt Cancer Center

2020 ◽  
Author(s):  
Heiko Enderling ◽  
Philipp M. Altrock ◽  
Noemi Andor ◽  
David Basanta ◽  
Joel S. Brown ◽  
...  
Keyword(s):  
High School ◽  
High School Students ◽  
Cancer Biology ◽  
Cancer Center ◽  
Medical Sciences ◽  
School Students ◽  
Steep Learning Curve ◽  
Spatial And Temporal Scales ◽  
College Undergraduate ◽  
Mathematical Oncology

AbstractModern cancer research, and the wealth of data across multiple spatial and temporal scales, has created the need for researchers that are well-versed in the life sciences (cancer biology, developmental biology, immunology), medical sciences (oncology) and natural sciences (mathematics, physics, engineering, computer sciences). College undergraduate education is traditionally provided in disciplinary silos, which creates a steep learning curve at the graduate and postdoctoral levels that increasingly bridge multiple disciplines. Numerous colleges have begun to embrace interdisciplinary curricula, but students who double-major in mathematics (or other quantitative sciences) and biology (or medicine) remain scarce. We identified the need to educate junior and senior high school students about integrating mathematical and biological skills, through the lens of mathematical oncology, to better prepare students for future careers at the interdisciplinary interface. The High school Internship Program in Integrated Mathematical Oncology (HIP IMO) at Moffitt Cancer Center has so far trained 59 students between 2015 and 2019. We report here on the program structure, training deliverables, curriculum, and outcomes. We hope to promote such interdisciplinary educational activities early in a student’s career.

scholarly journals In Silico Assessment of 5-FU Therapy via A Mathematical Model with Fuzzy Uncertain Parameters

2020 ◽  
Author(s):  
Sajad Shafiekhani ◽  
Amir. H. Jafari ◽  
L. Jafarzadeh ◽  
N. Gheibi
Keyword(s):  
Differential Equation ◽  
Immune Cells ◽  
In Silico ◽  
Parametric Uncertainty ◽  
Testable Hypothesis ◽  
Model Parameters ◽  
Ode Model ◽  
Ode Models ◽  
Mathematical Oncology ◽  
Uncertainty Band

Abstract Background: Ordinary differential equation (ODE) models widely have been used in mathematical oncology to capture dynamics of tumor and immune cells and evaluate the efficacy of treatments. However, for dynamic models of tumor-immune system (TIS), some parameters are uncertain due to inaccurate, missing or incomplete data, which has hindered the application of ODEs that require accurate parameters. Methods: We extended an available ODE model of TIS interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. Fuzzy ODE (FODE) models, in comparison with the stochastic differential equation (SDE) models, assigns a fuzzy number instead of a random number (from a specific probability density function) to the parameters, to capture parametric uncertainty. We used FODE model to predict tumor and immune cells dynamics and assess the efficacy of 5-FU. The present model is configurable for 5-FU chemotherapy injection timing and propose testable hypothesis in vitro/ in vivo experiments. Result: FODE model was used to explore the uncertainty of cells dynamics resulting from parametric uncertainty in presence and absence of 5-FU therapy. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and NK cells, and decreasing that of myeloid-derived suppressor (MDSC) cells. We investigate the effect of perturbation on model parameters on dynamics of cells through global sensitivity analysis (GSA) and compute correlation between model parameters and cell dynamics. Conclusion: ODE models with fuzzy uncertain kinetic parameters cope with insufficient experimental data in the field of mathematical oncology and can predict cells dynamics uncertainty band. In silico assessment of treatments considering parameter uncertainty and investigating the effect of the drugs on movement of cells dynamics uncertainty band may be more appropriate than in crisp setting.

scholarly journals Edge effects in game-theoretic dynamics of spatially structured tumours

2015 ◽  
Vol 12 (108) ◽  
pp. 20150154 ◽  
Author(s):  
Artem Kaznatcheev ◽  
Jacob G. Scott ◽  
David Basanta
Keyword(s):  
Spatial Structure ◽  
Epithelial Mesenchymal Transition ◽  
Evolutionary Game ◽  
Prostate Adenocarcinoma ◽  
Mesenchymal Transition ◽  
Mathematical Oncology ◽  
Game Theoretic ◽  
Cellular Phenotypes ◽  
Neighbourhood Structure ◽  
Fixed System

Cancer dynamics are an evolutionary game between cellular phenotypes. A typical assumption in this modelling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard for local neighbourhood structure. We address this limitation by using the Ohtsuki–Nowak transform to introduce spatial structure to the go versus grow game. We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary—such as a blood vessel, organ capsule or basement membrane—we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (epithelial–mesenchymal transition-positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Our results caution that pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. Although we concentrate on applications in mathematical oncology, we expect our approach to extend to other evolutionary game models where interaction neighbourhoods change at fixed system boundaries.

scholarly journals Hybrid Automata Library: A modular platform for efficient hybrid modeling with real-time visualization

2018 ◽  
Author(s):  
Rafael Bravo ◽  
Etienne Baratchart ◽  
Jeffrey West ◽  
Ryan O. Schenck ◽  
Anna K. Miller ◽  
...  
Keyword(s):  
Hybrid Model ◽  
Spatial Dynamics ◽  
Spatial Models ◽  
Hybrid Models ◽  
Hybrid Modeling ◽  
Hybrid Automata ◽  
Agent Based ◽  
Link Type ◽  
Model Complex ◽  
Mathematical Oncology

AbstractThe Hybrid Automata Library (HAL) is a Java Library developed for use in mathematical oncology modeling. It is made of simple, efficient, generic components that can be used to model complex spatial systems. HAL’s components can broadly be classified into: on- and off-lattice agent containers, finite difference diffusion fields, a GUI building system, and additional tools and utilities for computation and data collection. These components are designed to operate independently and are standardized to make them easy to interface with one another. As a demonstration of how modeling can be simplified using our approach, we have included a complete example of a hybrid model (a spatial model with interacting agent-based and PDE components). HAL is a useful asset for researchers who wish to build efficient 1D, 2D and 3D hybrid models in Java, while not starting entirely from scratch. It is available on github at https://github.com/MathOnco/HAL under the MIT License. HAL requires at least Java 8 or later to run, and the Java JDK version 1.8 or later to compile the source code.1Author SummaryIn this paper we introduce the Hybrid Automata Library (HAL) with the purpose of simplifying the implementation and sharing of hybrid models for use in mathematical oncology. Hybrid modeling is used in oncology to create spatial models of tissue, typically by modeling cells using agent-based techniques, and by modeling diffusible chemicals using partial differential equations (PDEs). HAL’s key components are designed to run agent-based models, PDEs, and visualization. The components are standardized and are completely decoupled, so models can be built with any combination of them. We first explore the philosophy behind HAL, then summarize the components. Lastly we demonstrate how the components work together with an example of a hybrid model, and a walk-through of the code used to construct it. HAL is open-source and will produce identical results on any machine that supports Java 8 and above, making it highly portable. We recommend HAL to modelers interested in spatial dynamics, even those outside of mathematical oncology, as the components are general enough to facilitate a variety of model types. A community page that provides a download link and online documentation can be found at https://halloworld.org [1].

scholarly journals Mathematical Oncology

2018 ◽  
Vol 80 (5) ◽  
pp. 945-953 ◽  
Author(s):  
Alexander R. A. Anderson ◽  
Philip K. Maini
Keyword(s):  
Mathematical Oncology
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