<p>Angiogenesis is a multiscale process by which a blood vessel emits secondary blood capillaries that move towards a region where cells need oxygen and nutrients. Angiogenesis can be physiological as in organ growth and repair or pathological when it is induced by a cancerous tumor. Analysis of a simple stochastic model shows that the density of active capillaries moves as a soliton attractor of a deterministic system of partial differential equations. Here we show that a linear feedback control applied to the deterministic system can freeze or even kill the soliton at a final time. While the linear control is too costly when used as a nonlinear control, it is possible to analyze differently the nonlinear problem. By interpreting the stochastic equations associated to the nonlinear system as an optimal filtering problem, we can derive the associated Kushner equation and equations for the mean and variance. The resulting equation for the estimator is formally identical to the result of an optimal control problem driven by the noise correlations of the filtering problem. Then we can freeze or annihilate the soliton (and therefore the angiogenic network) with this nonlinear control.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Control of the soliton attractor in a model of angiogenesis

  • B. Birnir,
  • L. L. Bonilla,
  • M. Carretero,
  • F. Terragni

摘要

Angiogenesis is a multiscale process by which a blood vessel emits secondary blood capillaries that move towards a region where cells need oxygen and nutrients. Angiogenesis can be physiological as in organ growth and repair or pathological when it is induced by a cancerous tumor. Analysis of a simple stochastic model shows that the density of active capillaries moves as a soliton attractor of a deterministic system of partial differential equations. Here we show that a linear feedback control applied to the deterministic system can freeze or even kill the soliton at a final time. While the linear control is too costly when used as a nonlinear control, it is possible to analyze differently the nonlinear problem. By interpreting the stochastic equations associated to the nonlinear system as an optimal filtering problem, we can derive the associated Kushner equation and equations for the mean and variance. The resulting equation for the estimator is formally identical to the result of an optimal control problem driven by the noise correlations of the filtering problem. Then we can freeze or annihilate the soliton (and therefore the angiogenic network) with this nonlinear control.