scholarly journals Macroscopic limit of a kinetic model describing the switch in T cell migration modes via binary interactions

2021 ◽  
pp. 1-27
Author(s):  
G. ESTRADA-RODRIGUEZ ◽  
T. LORENZI
Keyword(s):  
Immune Response ◽  
Kinetic Model ◽  
Coupled System ◽  
Search Pattern ◽  
Balance Equations ◽  
Diffusion Term ◽  
Migration Patterns ◽  
Running Time ◽  
Immune Response To Cancer ◽  
Non Local

Experimental results on the immune response to cancer indicate that activation of cytotoxic T lymphocytes (CTLs) through interactions with dendritic cells (DCs) can trigger a change in CTL migration patterns. In particular, while CTLs in the pre-activation state move in a non-local search pattern, the search pattern of activated CTLs is more localised. In this paper, we develop a kinetic model for such a switch in CTL migration modes. The model is formulated as a coupled system of balance equations for the one-particle distribution functions of CTLs in the pre-activation state, activated CTLs and DCs. CTL activation is modelled via binary interactions between CTLs in the pre-activation state and DCs. Moreover, cell motion is represented as a velocity-jump process, with the running time of CTLs in the pre-activation state following a long-tailed distribution, which is consistent with a Lévy walk, and the running time of activated CTLs following a Poisson distribution, which corresponds to Brownian motion. We formally show that the macroscopic limit of the model comprises a coupled system of balance equations for the cell densities, whereby activated CTL movement is described via a classical diffusion term, whilst a fractional diffusion term describes the movement of CTLs in the pre-activation state. The modelling approach presented here and its possible generalisations are expected to find applications in the study of the immune response to cancer and in other biological contexts in which switch from non-local to localised migration patterns occurs.

scholarly journals Thermovaccination, thermoheliox as a stimulant of immune response. Kinetic model of process development

2020 ◽  
Vol 69 (9) ◽  
pp. 1811-1815 ◽  
Author(s):  
S. D. Varfolomeev ◽  
A. A. Panin ◽  
V. I. Bykov ◽  
S. B. Tsybenova
Keyword(s):  
Immune Response ◽  
Kinetic Model ◽  
Process Development

scholarly journals Turbulence through the Spyglass of Bilocal Kinetics

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 539 ◽  
Author(s):  
Gregor Chliamovitch ◽  
Yann Thorimbert
Keyword(s):  
Turbulent Flows ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Pressure Tensor ◽  
Kinetic Description ◽  
Balance Equations ◽  
Coupling Term ◽  
Navier Stokes Equation ◽  
Local Character ◽  
Non Local

In two recent papers we introduced a generalization of Boltzmann’s assumption of molecular chaos based on a criterion of maximum entropy, which allowed setting up a bilocal version of Boltzmann’s kinetic equation. The present paper aims to investigate how the essentially non-local character of turbulent flows can be addressed through this bilocal kinetic description, instead of the more standard approach through the local Euler/Navier–Stokes equation. Balance equations appropriate to this kinetic scheme are derived and closed so as to provide bilocal hydrodynamical equations at the non-viscous order. These equations essentially consist of two copies of the usual local equations, but coupled through a bilocal pressure tensor. Interestingly, our formalism automatically produces a closed transport equation for this coupling term.

Current Concepts of Tumor Immunology III. Immune Therapy

1978 ◽  
Vol 87 (1) ◽  
pp. 138-141 ◽  
Author(s):  
Charles J. Krause ◽  
John O. Nysather
Keyword(s):  
Immune Response ◽  
Radiation Therapy ◽  
Tumor Cells ◽  
Tumor Immunology ◽  
Normal Tissue ◽  
Immune Therapy ◽  
Great Promise ◽  
Adjacent Normal Tissue ◽  
Immune Response To Cancer ◽  
Treatment Surgery

It is apparent that development of consistently effective methods of immunotherapy must await a more thorough understanding of the immune response to cancer. However, even those forms of immunotherapy which have been developed to date indicate a tremendous potential. It appears that immunotherapy may be most useful as an adjuvant to established forms of treatment. Surgery, radiation therapy and/or chemotherapy are used to remove all of the gross tumor, with immune therapy then employed to destroy the small foci of tumor which remain. As methods are developed which are effective in counteracting the immunosuppression of tumors, other means of immunotherapy may be found which are capable of destroying tumor cells while not affecting the adjacent normal tissue. Thus, the future of immune therapy holds great promise. As more is learned about the immune response to cancer, advances in therapy will certainly follow.

Asymptotic Analysis of the Drift-Diffusion Equations and Hamilton–Jacobi Equations

1997 ◽  
Vol 07 (01) ◽  
pp. 61-80 ◽  
Author(s):  
Ph. Montarnal ◽  
B. Perthame
Keyword(s):  
Asymptotic Behavior ◽  
Coupled System ◽  
Limit Problem ◽  
Diffusion Equations ◽  
Drift Diffusion ◽  
Diffusion Term ◽  
Electronic Concentration ◽  
New Variables ◽  
Jacobi Equations ◽  
Original Approach

We study the asymptotic behavior of the semiconductor drift-diffusion (DD) equations with a vanishing diffusion term. In order to obtain a closed limit problem, we need to introduce two new variables involving the logarithm of the electronic concentration. We show that the limit problem is a coupled system of Hamilton–Jacobi equations and variational inequalities. In the mono-dimensional case, we show that this limit problem has a unique solution, which allows us to prove the convergence of the DD model for vanishing viscosities. Our method, which is an extension of previous asymptotic studies, sheds new light on the convergence of the electronic concentration, improves some necessary mathematical hypotheses and provides an original approach to the problem, well suited for numerical purposes.

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