Using a probabilistic approach to derive a two-phase model of flow-induced cell migration

Area of Science:

• Biophysics
• Mathematical Biology
• Cancer Research

Background:

• Interstitial fluid flow is prevalent in solid tumors.
• Tumor cell migration is influenced by fluid flow, exhibiting complex behaviors.
• Tensotaxis and autologous chemotaxis are key competing mechanisms governing cell movement in flow.

Purpose of the Study:

• To develop a probabilistic-continuum, two-phase model for cell migration in response to interstitial fluid flow.
• To investigate the transition between upstream and downstream cell migration based on varying conditions.
• To identify the key factors influencing the directionality of tumor cell movement.

Main Methods:

• Developed a probabilistic-continuum, two-phase model using a kinetic description for cell velocity.
• Modeled flow-dependent mechanical and chemical stimuli as forcing terms.
• Employed velocity-space averaging to derive continuum equations for cell volume fraction and flux.
• Utilized numerical simulations and asymptotic analysis for a one-dimensional cell layer model.

Main Results:

• The model predicts downstream chemotactic migration at low cell volume fractions.
• Upstream tensotactic migration is predicted at higher cell volume fractions, consistent with experimental observations.
• The transition point is significantly influenced by the ratio of chemokine secretion and advection rates.
• Tensotaxis-dominated migration is transient, transitioning to chemotaxis-dominated migration due to cell diffusion.

Conclusions:

• The developed model accurately captures the dual nature of cell migration in response to interstitial fluid flow.
• Cell volume fraction, chemokine dynamics, and cell diffusion are critical determinants of migration direction.
• Understanding these dynamics is crucial for predicting and potentially controlling tumor cell dissemination.