A multiphase model for exploring tumor cell migration driven by autologous chemotaxis

Waldeland, Jahn Otto; Evje, Steinar

doi:10.1016/j.ces.2018.06.076

Cited by 28 publications

(17 citation statements)

References 23 publications

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“…A rather general cell-fluid-ECM model was proposed in Waldeland and Evje (2018a) and further developed in Waldeland and Evje (2018b) and Evje and Waldeland (2019) to shed light on the above-mentioned competing cell migration mechanisms governed by interstitial fluid flow. A gently simplified version of the model, where we ignore certain details of the biochemical part by assuming that chemokine C is directly produced by the tumor cells instead of being released from ECM, takes the following form:…”

Section: A General Cell-fluid-ecm Modelmentioning

confidence: 99%

“…From the two momentum equations (1.1) 3,4 , we can compute explicit expressions for the cell and fluid velocity, respectively, u c and u w (Waldeland and Evje 2018a). The following expressions are found: 3) used in Waldeland and Evje (2018b) and where the total velocity U T = α c u c + α w u w is determined from the equation U T = −λ T ∇ P w −λ c ∇( P + ) and the fact that ∇ •U T = 0.…”

Section: A General Cell-fluid-ecm Modelmentioning

confidence: 99%

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Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow

Evje

Winkler

2020

J Nonlinear Sci

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Recent experimental work has revealed that interstitial fluid flow can mobilize two types of tumor cell migration mechanisms. One is a chemotactic-driven mechanism where chemokine (chemical component) bounded to the extracellular matrix (ECM) is released and skewed in the flow direction. This leads to higher chemical concentrations downstream which the tumor cells can sense and migrate toward. The other is a mechanism where the flowing fluid imposes a stress on the tumor cells which triggers them to go in the upstream direction. Researchers have suggested that these two migration modes possibly can play a role in metastatic behavior, i.e., the process where tumor cells are able to break loose from the primary tumor and move to nearby lymphatic vessels. In Waldeland and Evje (J Biomech 81:22-35, 2018), a mathematical cell-fluid model was put forward based on a mixture theory formulation. It was demonstrated that the model was able to capture the main characteristics of the two competing migration mechanisms. The objective of the current work is to seek deeper insight into certain qualitative aspects of these competing mechanisms by means of mathematical methods. For that purpose, we propose a simpler version of the cell-fluid model mentioned above but such that the two competing migration mechanisms are retained. An initial cell distribution in a one-dimensional slab is exposed to a constant fluid flow from one end to the other, consistent with the experimental setup. Then, we explore by means of analytical estimates the long-time behavior of the two competing migration mechanisms for two different scenarios: (i) when the initial cell volume fraction is low and (ii) when the initial cell volume fraction is high. In particular, it is demonstrated in a strict mathematical sense that for a sufficiently low initial cell volume fraction, the downstream migration dominates in the sense that the solution converges to a downstream-dominated steady state as time elapses. On the other hand, with a sufficiently high initial cell volume fraction, the upstream migration mechanism is the stronger in the sense that the solution converges to an upstream-dominated steady state. Communicated by Alain Goriely.

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Section: A General Cell-fluid-ecm Modelmentioning

confidence: 99%

Section: A General Cell-fluid-ecm Modelmentioning

confidence: 99%

Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow

Evje

Winkler

2020

J Nonlinear Sci

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“…The purpose of the present study is to investigate how far the evolution of singular structures may be affected by the presence of logistic-type growth restrictions. In fact, a large literature suggests that accordingly obtained logistic Keller-Segel systems can be viewed as a natural first step to adapt the prototypical and hence quite simple model (1.1) so as to account for mechanisms of competition-induced overcrowding prevention which seem virtually ubiquitous in numerous situations of biological relevance (see, e.g., [11,35,39] or [32] for some examples, or also [15,30] for a broader overview). In fact, several precedents have been indicating that on the way from (1.1) to fully realistic models, despite their increased complexity and especially their apparent lack of appropriate energy structures, such logistic chemotaxis systems remain accessible to a considerably large variety of mathematical tools; accordingly, not only quite comprehensive conclusions are available in the fields of global classical solvability for smooth data [28,38,41,48], of constructing attractors [1,28,29], and of proving asymptotic homogenization in cases of strong dampening [9,43] (cf.…”

Section: Main Results: Detecting Additional Regularization Effects Ofmentioning

confidence: 99%

How strong singularities can be regularized by logistic degradation in the Keller–Segel system?

Winkler

2019

Annali di Matematica

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“…This was carefully explored in the two recent works. 35,36 Through that study, the model was trained with data from relevant in vitro experiments and insight was gained for setting various model parameters. However, the experimental setup in Refs.…”

Section: Methodsmentioning

confidence: 99%

How Tumor Cells Can Make Use of Interstitial Fluid Flow in a Strategy for Metastasis

Evje

Waldeland

2019

Cel. Mol. Bioeng.

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Introduction-The phenomenon of lymph node metastasis has been known for a long time. However, the underlying mechanism by which malignant tumor cells are able to break loose from the primary tumor site remains unclear. In particular, two competing fluid sensitive migration mechanisms have been reported in the experimental literature: (i) autologous chemotaxis (Shields et al. in Cancer Cell 11:526-538, 2007) which gives rise to downstream migration; (ii) an integrin-mediated and strain-induced upstream mechanism (Polacheck et al. in PNAS 108:11115-11120, 2011). How can these two competing mechanisms be used as a means for metastatic behavior in a realistic tumor setting? Excessive fluid flow is typically produced from leaky intratumoral blood vessels and collected by lymphatics in the peritumoral region giving rise to a heterogeneous fluid velocity field and a corresponding heterogeneous cell migration behavior, quite different from the experimental setup. Method-In order to shed light on this issue there is a need for tools which allow one to extrapolate the observed single cell behavior in a homogeneous microfluidic environment to a more realistic, higher-dimensional tumor setting. Here we explore this issue by using a computational multiphase model. The model has been trained with data from the experimental results mentioned above which essentially reflect one-dimensional behavior. We extend the model to an envisioned idealized two-dimensional tumor setting. Result-A main observation from the simulation is that the autologous chemotaxis migration mechanism, which triggers tumor cells to go with the flow in the direction of lymphatics, becomes much more aggressive and effective as a means for metastasis in the presence of realistic IF flow. This is because the outwardly directed IF flow generates upstream cell migration that possibly empowers small clusters of tumor cells to break loose from the primary tumor periphery. Without this upstream stress-mediated migration, autologous chemotaxis is inclined to move cells at the rim of the tumor in a homogeneous and collective, but space-demanding style. In contrast, inclusion of realistic IF flow generates upstream migration that allows two different aspects to be synthesized: maintain the coherency and solidity of the the primary tumor and at the same time cleave the outgoing waves of tumor cells into small clusters at the front that can move collectively in a more specific direction.

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A multiphase model for exploring tumor cell migration driven by autologous chemotaxis

Cited by 28 publications

References 23 publications

Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow

Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow

How strong singularities can be regularized by logistic degradation in the Keller–Segel system?

How Tumor Cells Can Make Use of Interstitial Fluid Flow in a Strategy for Metastasis

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