Estimating intratumoral heterogeneity from spatiotemporal data

Rutter, Erica M.; Banks, Harvey Thomas; Flores, Kevin

doi:10.1007/s00285-018-1238-6

Cited by 8 publications

(5 citation statements)

References 63 publications

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“…This case is going to be investigated in a forthcoming paper. Moreover, there have been a plethora of studies trying to quantify intratumoral heterogeneity, see [33][34][35][36], nevertheless our method is able to include the existing literature and analyze the impact of data-driven heterogeneity distribution in more realistic tumor models. For instance, data regarding the invasive behavior heterogeneity, e.g., migration speed distribution, of tumor cells can be easily integrated and analyzed from our framework, such as in [37].…”

Section: Discussionmentioning

confidence: 99%

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A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

2021

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Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account.

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Section: Discussionmentioning

confidence: 99%

“…We consider ω ∈ Ω, where Ω is introduced in Remark 4. Now (35) entails that for any fixed ω ∈ Ω, fixed 2n , there exists Nk (ω) such that for each N > Nk (ω)…”

Section: The Novel Averaging Principlementioning

confidence: 99%

A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

2021

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“…However, the assumption of white noise is the worst possible scenario related to tumor heterogeneity, and therefore other noise distributions should be analyzed such as Gaussian noise. Moreover, there have been a plethora of studies trying to quantify intratumoral heterogeneity, see, 1,20,22,24 nevertheless our method is able to include the existing literature and analyze the impact of data-driven heterogeneity distribution in more realistic tumor models. Furthermore, our method can be also implemented to investigate the long-time dynamics of the full GoG system (5.1)-(5.2), which will be the subject of a forthcoming work.…”

Section: Discussionmentioning

confidence: 99%

A novel averaging principle provides insights in the impact of intratumoral heterogeneity on tumor progression

Leocata

Alfonso

Kavallaris

et al. 2019

Preprint

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Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is non-linearly integrated in the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied on RODEs. To exemplify the importance of our method, we apply it in an important biomedical problem, i.e. the assessment of intratumoral heterogeneity impact on tumor dynamics. In particular, we model gliomas according to a well-known Go or Grow (GoG) model and tumor heterogeneity is modelled as a stochastic process. It has been shown that this GoG model exhibits an emerging Allee effect (bistability). We analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to a monostable tumor growth. This monostability behaviour is also derived even when spatial cell diffusion is taking into account.

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“…While previous studies have shown that the Fisher-KPP equation is clinically relevant [56,39,4], the model assumes an intratumor homogeneous cellular behavior that might not be true in GBM populations [48]. As a result, many PDE models have been introduced to account for the population heterogeneity in GBM populations [48,30,35,42,2,50,17,44,54,40].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Multicellular Tumor Spheroids Quantifies Inter-Patient and Inter-Tumor Heterogeneity

Malik,

Nguyen,

Nardini

et al. 2024

Preprint

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In the study of brain tumors, patient-derived three-dimensional sphere cultures provide an important tool for studying emerging treatments. The growth of such spheroids depends on the combined effects of proliferation and migration of cells, but it is often challenging to make accurate distinctions between increase in cell number versus the radial movement of cells. To address this, we formulate a novel model (which we refer to as the reaction-diffusion, advection-reaction-diffusion model) in the form of a system of two partial differential equations (PDEs) and show that it more accurately fits our data as compared to simpler PDE models, including the reaction-diffusion model that has been found to be clinically relevant. We propose a numerical approach for calculating travelling-wave speeds, which are shown to be strongly associated with population heterogeneity. Having fitted the model to our dataset we show that a subset of the cell lines are best described by a “Go-or-Grow”-type model, which constitutes a special case of our model. Finally, we investigate whether our fitted model parameters are correlated with patient age at diagnosis and survival. Multiple model parameters are correlated with patient age, and a single model parameter with patient survival. Our work improves on current modelling approaches, and provides a novel step towards understanding associations between mathematical model parameters and clinical data.

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Estimating intratumoral heterogeneity from spatiotemporal data

Cited by 8 publications

References 63 publications

A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

A novel averaging principle provides insights in the impact of intratumoral heterogeneity on tumor progression

Mathematical Modeling of Multicellular Tumor Spheroids Quantifies Inter-Patient and Inter-Tumor Heterogeneity

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