Stochastic model of tumor-induced angiogenesis: Ensemble averages and deterministic equations

Terragni, Filippo; Carretero, Manuel; Capasso, Vincenzo; Bonilla, L. L.

doi:10.1103/physreve.93.022413

Cited by 22 publications

(92 citation statements)

References 32 publications

(110 reference statements)

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“…For details on the latter two ingredients, we refer to [10]. Let X i (t) and v i (t) be the position and the velocity of the ith tip at time t. The extension of this vessel is given by…”

Section: The Stochastic Modelmentioning

confidence: 99%

“…Initial and boundary conditions for the TAF field C have been proposed in [10]. The initial and boundary conditions for Equations (4) and (5) will be specified later.…”

Section: The Stochastic Modelmentioning

confidence: 99%

“…The reference values for x, v, t, and C are those considered in [10], as we will use the same numerical setting. These values are consistent with Stokes and Lauffenburger's experiments [5].…”

Section: Remarkmentioning

confidence: 99%

“…We are assuming Table 3. Dimensionless parameters in the hybrid model as given in [10,13,15]. The nondimensional equations for TAF, FN and MDE are…”

Section: Dimensionless Equationsmentioning

confidence: 99%

“…Capasso and Morale also attempted to derive a continuum equation for the density of moving tip cells from the stochastic equations but could not account for branching and anastomosis [7]. Recently, we have derived a deterministic description for the average vessel tip density of a related hybrid stochastic tip cell model for tumor-induced angiogenesis that includes chemotaxis but not haptotaxis [9,10]. We have shown that the density of active vessel tips advances toward the tumor as a soliton-like wave [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

Bonilla

Carretero

Terragni

2017

Entropy

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Abstract:In this work, we present a numerical study of the influence of matrix degrading enzyme (MDE) dynamics and haptotaxis on the development of vessel networks in tumor-induced angiogenesis. Avascular tumors produce growth factors that induce nearby blood vessels to emit sprouts formed by endothelial cells. These capillary sprouts advance toward the tumor by chemotaxis (gradients of growth factor) and haptotaxis (adhesion to the tissue matrix outside blood vessels). The motion of the capillaries in this constrained space is modelled by stochastic processes (Langevin equations, branching and merging of sprouts) coupled to continuum equations for concentrations of involved substances. There is a complementary deterministic description in terms of the density of actively moving tips of vessel sprouts. The latter forms a stable soliton-like wave whose motion is influenced by the different taxis mechanisms. We show the delaying effect of haptotaxis on the advance of the angiogenic vessel network by direct numerical simulations of the stochastic process and by a study of the soliton motion.

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“…For details on the latter two ingredients, we refer to [10]. Let X i (t) and v i (t) be the position and the velocity of the ith tip at time t. The extension of this vessel is given by…”

Section: The Stochastic Modelmentioning

confidence: 99%

“…Initial and boundary conditions for the TAF field C have been proposed in [10]. The initial and boundary conditions for Equations (4) and (5) will be specified later.…”

Section: The Stochastic Modelmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

“…We are assuming Table 3. Dimensionless parameters in the hybrid model as given in [10,13,15]. The nondimensional equations for TAF, FN and MDE are…”

Section: Dimensionless Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

Bonilla

Carretero

Terragni

2017

Entropy

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Multiscale modeling methods in biomechanics

Bhattacharya

Viceconti

2017

WIREs Mechanisms of Disease

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More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space–time continuum. We are forced to consider multiple space–time continua, each representing the phenomenon of interest at a characteristic space–time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: ‘causal confirmation,’ where multiscale models are used as materializations of the causation theories; ‘predictive accuracy,’ where multiscale modeling is aimed to improve the predictive accuracy; and ‘determination of effect,’ where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space–time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375For further resources related to this article, please visit the WIREs website.

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