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Displaying 1261 –
1280 of
1854
The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for objects implies the existence of an optimum chemical balance weighing design for objects are given. The existence of an optimum chemical balance weighing design for objects implies the existence of an optimum chemical...
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are...
In this paper, we look at a model depicting the relationship of cancer cells in different
development stages with immune cells and a cell cycle specific chemotherapy drug. The
model includes a constant delay in the mitotic phase. By applying optimal control theory,
we seek to minimize the cost associated with the chemotherapy drug and to minimize the
number of tumor cells. Global existence of a solution has been shown for this model and
existence...
We consider optimal control problems for the bidomain equations of cardiac electrophysiology together with two-variable ionic models, e.g. the Rogers–McCulloch model. After ensuring the existence of global minimizers, we provide a rigorous proof for the system of first-order necessary optimality conditions. The proof is based on a stability estimate for the primal equations and an existence theorem for weak solutions of the adjoint system.
A distributed optimal control problem on and inside a homogeneous skin tissue is solved subject to Pennes' equation with Dirichlet boundary condition at one end and Rubin condition at the other end. The point heating power induced by conducting heating probe inserted at the tumour site as an unknown control function at specific depth inside biological body is preassigned. Corresponding pseudo-port Hamiltonian system is proposed. Moreover, it is proved that bioheat transfer equation forms a contraction...
In this paper we construct a model to describe some
aspects of the
deformation of the central region of the human lung
considered as a
continuous
elastically deformable medium. To achieve this purpose, we study
the interaction
between the pipes composing the tree and the fluid that goes
through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key...
We consider a size structured cell population model where a mother cell gives birth to
two daughter cells. We know that the asymptotic behavior of the density of cells is given by the
solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives
the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on
the division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) or
asymmetric. We use a...
We present a model for describing the spread of an infectious disease with public
screening measures to control the spread. We want to address the problem of determining an
optimal screening strategy for a disease characterized by appreciable duration of the
infectiveness period and by variability of the transmission risk. The specific disease we
have in mind is the HIV infection. However the model will apply to a disease for which
class-age structure...
The scheduling of angiogenic inhibitors to control a vascularized tumor is analyzed as an optimal control problem for a mathematical model that was developed and biologically validated by Hahnfeldt et al. [Cancer Res. 59 (1999)]. Two formulations of the problem are considered. In the first one the primary tumor volume is minimized for a given amount of angiogenic inhibitors to be administered, while a balance between tumor reduction and the total amount of angiogenic inhibitors given is minimized...
The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique...
The chronotherapy concept takes advantage of the circadian rhythm of
cells physiology in maximising a treatment efficacy on its target
while minimising its toxicity on healthy organs. The
object of the present paper is to investigate mathematically and
numerically optimal strategies in cancer chronotherapy. To this
end a mathematical model describing the time evolution of efficiency
and toxicity of an oxaliplatin anti-tumour treatment has been derived.
We then applied an optimal control...
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1854