A tutorial review of mathematical techniques for quantifying tumor heterogeneity

Rebecca Everett; Kevin B. Flores; Nick Henscheid; John Lagergren; Kamila Larripa; Ding Li; John T. Nardini; Phuong T.T. Nguyen; E. Bruce Pitman; Erica M. Rutter

doi:10.3934/MBE.2020207

A tutorial review of mathematical techniques for quantifying tumor heterogeneity

Rebecca Everett, Kevin B. Flores, Nick Henscheid, John Lagergren, Kamila Larripa, Ding Li, John T. Nardini, Phuong T.T. Nguyen, E. Bruce Pitman, Erica M. Rutter

Research output: Contribution to journal › Review article › peer-review

9 Scopus citations

Abstract

Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weaknesses of each technique. We provide all code used in this review at https://github.com/jtnardin/TumorHeterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.

Original language	English
Pages (from-to)	3660-3709
Number of pages	50
Journal	Mathematical Biosciences and Engineering
Volume	17
Issue number	4
DOIs	https://doi.org/10.3934/MBE.2020207
State	Published - May 19 2020
Externally published	Yes

Funding

This research was also supported in part by the National Institutes of Health under grant number R01EB000803 (NH) and in part by the National Science Foundation grant number DMS-1514929 (KBF). SAMSI: This material was based upon work partially supported by the National Science Foundation under Grant DMS-1638521 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Funders	Funder number
National Science Foundation	DMS-1638521, DMS-1514929
National Institutes of Health
National Institute of Biomedical Imaging and Bioengineering	R01EB000803

Keywords

Bayesian estimation
Cancer heterogeneity
Generative adversarial networks
Glioblastoma multiforme
Machine learning
Mathematical oncology
Non-parametric estimation
Nonlinear mixed effects
Spatiotemporal data
Tumor growth
Variational autoencoders
Virtual populations

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.3934/MBE.2020207

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title = "A tutorial review of mathematical techniques for quantifying tumor heterogeneity",

abstract = "Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weaknesses of each technique. We provide all code used in this review at https://github.com/jtnardin/TumorHeterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.",

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AU - Nardini, John T.

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AU - Bruce Pitman, E.

AU - Rutter, Erica M.

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AB - Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weaknesses of each technique. We provide all code used in this review at https://github.com/jtnardin/TumorHeterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.

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A tutorial review of mathematical techniques for quantifying tumor heterogeneity

Abstract

Funding

Keywords

UN SDGs

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