Novel Multiscale Analysis and Modelling in Tumour Development: from Spatio Temporal-Structural Mechanics to Multiscale Moving-Boundary Dynamics in Cancer Invasion (Keynote Speaker Talk)

TY - CONF

T1 - Novel Multiscale Analysis and Modelling in Tumour Development: from Spatio Temporal-Structural Mechanics to Multiscale Moving-Boundary Dynamics in Cancer Invasion (Keynote Speaker Talk)

AU - Trucu, Dumitru

PY - 2022/7/11

Y1 - 2022/7/11

N2 - Despite recent mathematical modelling advances, the understanding of the biologically multiscale process of cancer invasion remains a multifaceted open question, with challenges ranging from the understanding of the spatio-temporal-structural dynamics of tumour growth to its naturally emerging multiscale moving boundary progression within the surrounding tissue. In this series of lectures we will embark on an exciting journey within novel structural and multiscale mathematical modelling and analysis approaches for solid tumour invasion. Specifically, we will start these lectures with a first part that focused on exploring the dynamic interplay between collective cell movement and various key molecules involved in the accompanying cell signalling mechanisms which play a crucial role in cancer development. Information about the various structures embedded within these processes enables a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this part we establish a novel general spatio-temporal-structural mathematical modelling framework that enables the description of surface-bound reaction processes coupled within the cancer cell population dynamics. The second part of the lecture series will be focused on the novel multiscale moving boundary approaches for cancer invasion that we recently introduced, which explores the dynamic interactions that the migratory cancer cells population and the accompanying matrix degrading enzymes(MDEs) have with the extracellular matrix (ECM) components, and in particular with the ECM fibres. These complex two-scale interactions are explored via two multiscale systems that share (and contribute to) the same macro-dynamics but have independent in nature micro-dynamics. Specifically, on the bulk of the tumour, this explores the dynamics fibres degradation and realignment occurring at cell-scale (and induced by the spatial flux of invading cancer cells) as well as the immediate impact that this continuously changing field of oriented ECM fibres has over the tumour macro- dynamics. On the other hand, the cell-scale proteolytic micro-dynamics occurring at the tumour invasive edge interacts with the peritumoural ECM fibres through the molecular fluxes of MDEs. This interfacial cell-scale interaction not only results in changes of the micro-scale distribution of peritumoural ECM fibres, but also influences directly the changes of the overall tumour morphology. The new multiscale modelling framework will be accompanied by details of the computational approach and a discussion of the numerical simulation results. Finally, besides the rigorous derivation of the novel spatio-temporal structural and multiscale-moving boundary modelling approaches for cancer invasion, a special attention will also be paid to the new three-scale convergence concept and its wider implications for multiscale analysis for general heterogeneous processes that this work has triggered. This is a genuine invitation to novel mathematics obtained purely by challenging the frontiers of knowledge in our quest for gaining a deeper understanding for the tremendous real-world problem of cancer invasion.

AB - Despite recent mathematical modelling advances, the understanding of the biologically multiscale process of cancer invasion remains a multifaceted open question, with challenges ranging from the understanding of the spatio-temporal-structural dynamics of tumour growth to its naturally emerging multiscale moving boundary progression within the surrounding tissue. In this series of lectures we will embark on an exciting journey within novel structural and multiscale mathematical modelling and analysis approaches for solid tumour invasion. Specifically, we will start these lectures with a first part that focused on exploring the dynamic interplay between collective cell movement and various key molecules involved in the accompanying cell signalling mechanisms which play a crucial role in cancer development. Information about the various structures embedded within these processes enables a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this part we establish a novel general spatio-temporal-structural mathematical modelling framework that enables the description of surface-bound reaction processes coupled within the cancer cell population dynamics. The second part of the lecture series will be focused on the novel multiscale moving boundary approaches for cancer invasion that we recently introduced, which explores the dynamic interactions that the migratory cancer cells population and the accompanying matrix degrading enzymes(MDEs) have with the extracellular matrix (ECM) components, and in particular with the ECM fibres. These complex two-scale interactions are explored via two multiscale systems that share (and contribute to) the same macro-dynamics but have independent in nature micro-dynamics. Specifically, on the bulk of the tumour, this explores the dynamics fibres degradation and realignment occurring at cell-scale (and induced by the spatial flux of invading cancer cells) as well as the immediate impact that this continuously changing field of oriented ECM fibres has over the tumour macro- dynamics. On the other hand, the cell-scale proteolytic micro-dynamics occurring at the tumour invasive edge interacts with the peritumoural ECM fibres through the molecular fluxes of MDEs. This interfacial cell-scale interaction not only results in changes of the micro-scale distribution of peritumoural ECM fibres, but also influences directly the changes of the overall tumour morphology. The new multiscale modelling framework will be accompanied by details of the computational approach and a discussion of the numerical simulation results. Finally, besides the rigorous derivation of the novel spatio-temporal structural and multiscale-moving boundary modelling approaches for cancer invasion, a special attention will also be paid to the new three-scale convergence concept and its wider implications for multiscale analysis for general heterogeneous processes that this work has triggered. This is a genuine invitation to novel mathematics obtained purely by challenging the frontiers of knowledge in our quest for gaining a deeper understanding for the tremendous real-world problem of cancer invasion.

KW - Keynote Speaker

UR - https://sites.google.com/site/marinliviu/regional-french-romanian-summer-school-on-applied-mathematics/7th-french-romanian-summer-school-on-applied-mathematics-6-14-july-2022?authuser=0

UR - https://drive.google.com/file/d/1bjqUAwTR7tz9-1ErjgBF4PY3gv-4reJD/view

M3 - Paper

T2 - 7th French –<br/>Romanian Summer School on Applied Mathematics

Y2 - 6 July 2022 through 14 July 2022

ER -