A mathematical model of absorbing Markov chains to understand the routes of metastasis

Margarit, David Hipólito; Romanelli, L.

doi:10.11145/j.biomath.2016.07.281

Cited by 7 publications

(7 citation statements)

References 22 publications

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“…Cisneros and Newman ( 2014 ) proposed another stochastic model that used a birth–death process to investigate whether metastasis occurs from many poorly adapted cancer cells or from a few well-adapted cancer cells. Finally, Margarit and Romanelli ( 2016 ) developed a patient-statistics-based absorbing Markov Chain model to analyse the metastatic routes between principal organs.…”

Section: The Mathematical Modelling Frameworkmentioning

confidence: 99%

A Mathematical Framework for Modelling the Metastatic Spread of Cancer

et al. 2019

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Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network, they can spread to distant secondary sites in the body. This process, known as metastatic spread , is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer . To shed light on the metastatic process, we present a mathematical modelling framework that captures for the first time the interconnected processes of invasion and metastatic spread of individual cancer cells in a spatially explicit manner—a multigrid, hybrid, individual-based approach. This framework accounts for the spatiotemporal evolution of mesenchymal- and epithelial-like cancer cells, membrane-type-1 matrix metalloproteinase (MT1-MMP) and the diffusible matrix metalloproteinase-2 (MMP-2), and for their interactions with the extracellular matrix. Using computational simulations, we demonstrate that our model captures all the key steps of the invasion-metastasis cascade, i.e. invasion by both heterogeneous cancer cell clusters and by single mesenchymal-like cancer cells; intravasation of these clusters and single cells both via active mechanisms mediated by matrix-degrading enzymes (MDEs) and via passive shedding; circulation of cancer cell clusters and single cancer cells in the vasculature with the associated risk of cell death and disaggregation of clusters; extravasation of clusters and single cells; and metastatic growth at distant secondary sites in the body. By faithfully reproducing experimental results, our simulations support the evidence-based hypothesis that the membrane-bound MT1-MMP is the main driver of invasive spread rather than diffusible MDEs such as MMP-2.

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Section: The Mathematical Modelling Frameworkmentioning

confidence: 99%

A Mathematical Framework for Modelling the Metastatic Spread of Cancer

et al. 2019

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“…Cisneros and Newman (2014) proposed another stochastic model that used a birth-death process to investigate whether metastasis occurs from many poorly adapted cancer cells or from a few well-adapted cancer cells. Finally, Margarit and Romanelli (2016) developed a patient-statistics-based absorbing Markov Chain model to analyse the metastatic routes between principal organs.…”

Section: The Mathematical Modelling Frameworkmentioning

confidence: 99%

A mathematical framework for modelling the metastatic spread of cancer

Franssen

Lorenzi

Burgess

et al. 2018

Preprint

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Cancer is a complex disease that starts with mutations of key genes in one cell or a small group of cells at a primary site in the body. If these cancer cells continue to grow successfully and, at some later stage, invade the surrounding tissue and acquire a vascular network (tumour-induced angiogenesis), they can spread to distant secondary sites in the body. This process, known as metastatic spread, is responsible for around 90% of deaths from cancer and is one of the so-called hallmarks of cancer.To shed light on the metastatic process, we present a mathematical modelling framework that captures for the first time the interconnected processes of invasion and metastatic spread of individual cancer cells in a spatially explicit manner -a multi-grid, hybrid, individual-based approach. This framework accounts for the spatio-temporal evolution of mesenchymal-and epithelial-like cancer cells, as well as MT1-MMP and MMP-2 dynamics, and interactions with the extracellular matrix.Using computational simulations, we demonstrate that our model captures all the key steps of the invasion-metastasis cascade, i.e. invasion by both heterogeneous cancer cell clusters and by single mesenchymal-like cancer cells; intravasation of these clusters and single cells both via active mechanisms mediated by matrix degrading enzymes (MDEs) and via passive shedding; circulation of cancer cell clusters and single cancer cells in the vasculature with the associated risk of cell death and disaggregation of clusters; extravasation of clusters and single cells; and metastatic growth at distant secondary sites in the body. By faithfully reproducing experimental results, our simulations support the evidence-based hypothesis that the membrane-bound MT1-MMP is the main driver of invasive spread rather than diffusible MDEs like MMP-2.Keywords Metastatic spread · Mathematical oncology · Tumour microenvironment · Individual-based model · Multi-grid framework LCF is funded by the Engineering and Physical Sciences Research Council (EPSRC). MAJC gratefully acknowledges the support of EPSRC Grant

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“…In previous work, we used Markov Chains for statistics of Argentina [10]. Now, having into account the importance of modelling mathematically routes the metastasis in childhood cancer, we analyse metastatic pathways in the main haematological and solid cancers for children aged 0-14 years.…”

Section: Introductionmentioning

confidence: 99%

The role of Absorbing Markov Chains in childhood cancer

Margarit

Reale

Scagliotti

et al. 2022

Preprint

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Absorbing Markov Chains are an important mathematical tool used for different applications in science. On the other hand, cancer and its metastases in children have a significant impact on health due to their degree of lethality. Therefore, the aim of this work is to model the metastatic pathways of the main childhood cancers worldwide. The probabilities of generating metastases, from a primary site to secondary and tertiary sites, were characterized by constructing a directed graph and the associated transition matrix. In addition, the time of absorption and the probabilities of absorption by each absorbing state were calculated.

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A mathematical model of absorbing Markov chains to understand the routes of metastasis

Cited by 7 publications

References 22 publications

A Mathematical Framework for Modelling the Metastatic Spread of Cancer

A Mathematical Framework for Modelling the Metastatic Spread of Cancer

A mathematical framework for modelling the metastatic spread of cancer

The role of Absorbing Markov Chains in childhood cancer

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