Confinement of plasma along shaped open magnetic fields from the centrifugal force of supersonic plasma rotation.

Interferometric density measurements in plasmas rotating in shaped, open magnetic fields demonstrate strong confinement of plasma parallel to the magnetic field, with density drops of more than a factor of 10. Taken together with spectroscopic measurements of supersonic E × B rotation of sonic Mach 2, these measurements are in agreement with ideal MHD theory which predicts large parallel pressure drops balanced by centrifugal forces in supersonically rotating plasmas.

Role of optimal control theory in cancer chemotherapy.

This paper presents a review of the ways in which optimal control theory interacts with cancer chemotherapy. There are three broad areas of investigation. One involves miscellaneous growth kinetic models, the second involves cell cycle models, and the third is a classification of "other models." Both normal and tumor cell populations are included in a number of the models. The concepts of deterministic optimal control theory are applied to each model in such a way as to present a cohesive picture. There are applications to both experimental and clinical tumors. Suggestions for designing better chemotherapy strategies are presented.

The diffusion of an inhibitor in a spherical tumor.

The purpose of this paper is to show the correct mathematical behavior of the solution to a diffusion equation that has previously been used in a modeling situation involving a spherical tumor.

Optimal control applications in the chemotherapy of multiple myeloma.

There is an increasing interest in the use of therapeutic devices which deliver chemotherapeutic agents in a continuous manner. In this paper the Gompertz model of cancer growth with a loss term depending on a cancer chemotherapeutic agent is applied to human multiple myeloma. Three different performance criteria are introduced which measure the influence of the anti-cancer drug in driving the tumor population level to a desired target level. Engineering optimal control theory is used to produce expressions for the continuous-time optimal control. A comparison is made between the natures of the controller for the three problems considered. Parameter values used in the models are based on patient data. Results of the present study may be useful in the construction of algorithms for use with drug delivery devices that incorporate a microprocessor. Use of such devices may be useful in improving the treatment schedules and treatment outcome of cancer patients.

Optimal control analysis of a cancer chemotherapy problem.

The biologically based model due to Cox and co-workers is used in this study of a cancer chemotherapy problem involving the continuous delivery of an anticancer drug. A performance criterion is introduced to measure the effectiveness of therapy while penalizing excessive usage of drug. Optimal control theory is used to obtain information on the nature of the controller, which is related to the amount of drug to be infused from a drug-delivery device.

General applications of optimal control theory in cancer chemotherapy.

There are an increasing number of clinical papers dealing with the continuous delivery of an anticancer drug to patients. In this paper, two basic theoretical models are presented of cancer growth under the action of a continuously delivered anticancer drug. The therapeutic objective is to obtain the nature of the control agent that can drive the tumour population to a desired level so as to penalize excessive usage of the drug and to keep deviations of the tumour population from the desired level to a minimum. This gives rise to a certain type of optimal control problem. The nature of the optimal controller for each model is presented. The optimal control approach leads to a therapeutic strategy that may be of relevance to the clinical studies and this is investigated.