Bridging blood cancers and inflammation: The reduced Cancitis model

Johnny T. Ottesen, Rasmus Kristoffer Pedersen, Zamra Sajid, Johanne Gudmand-Høyer, Katrine O. Bangsgaard, Vibe Skov, Lasse Kjær, Trine A. Knudsen, Niels Pallisgaard, Hans Hasselbalch, Morten Wienecke Andersen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.
Original languageEnglish
JournalJournal of Theoretical Biology
Volume2019
Issue number465
Pages (from-to)90-108
Number of pages19
ISSN0022-5193
DOIs
Publication statusPublished - 2019

Cite this

Ottesen, Johnny T. ; Pedersen, Rasmus Kristoffer ; Sajid, Zamra ; Gudmand-Høyer, Johanne ; Bangsgaard, Katrine O. ; Skov, Vibe ; Kjær, Lasse ; Knudsen, Trine A. ; Pallisgaard, Niels ; Hasselbalch, Hans ; Wienecke Andersen, Morten. / Bridging blood cancers and inflammation : The reduced Cancitis model. In: Journal of Theoretical Biology. 2019 ; Vol. 2019, No. 465. pp. 90-108.
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abstract = "A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.",
author = "Ottesen, {Johnny T.} and Pedersen, {Rasmus Kristoffer} and Zamra Sajid and Johanne Gudmand-H{\o}yer and Bangsgaard, {Katrine O.} and Vibe Skov and Lasse Kj{\ae}r and Knudsen, {Trine A.} and Niels Pallisgaard and Hans Hasselbalch and {Wienecke Andersen}, Morten",
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language = "English",
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Bridging blood cancers and inflammation : The reduced Cancitis model. / Ottesen, Johnny T.; Pedersen, Rasmus Kristoffer; Sajid, Zamra; Gudmand-Høyer, Johanne; Bangsgaard, Katrine O.; Skov, Vibe; Kjær, Lasse; Knudsen, Trine A.; Pallisgaard, Niels ; Hasselbalch, Hans; Wienecke Andersen, Morten.

In: Journal of Theoretical Biology, Vol. 2019, No. 465, 2019, p. 90-108.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Bridging blood cancers and inflammation

T2 - The reduced Cancitis model

AU - Ottesen, Johnny T.

AU - Pedersen, Rasmus Kristoffer

AU - Sajid, Zamra

AU - Gudmand-Høyer, Johanne

AU - Bangsgaard, Katrine O.

AU - Skov, Vibe

AU - Kjær, Lasse

AU - Knudsen, Trine A.

AU - Pallisgaard, Niels

AU - Hasselbalch, Hans

AU - Wienecke Andersen, Morten

PY - 2019

Y1 - 2019

N2 - A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

AB - A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

U2 - 10.1016/j.jtbi.2019.01.001

DO - 10.1016/j.jtbi.2019.01.001

M3 - Journal article

VL - 2019

SP - 90

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JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

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