New developments in the application of optimal control theory to therapeutic protocols.

Optimal control theory is one of the most important tools in the development of new therapeutic protocols for treating infections. In this work, we present an algorithm able to deal with high-dimensional problems with bounded controls. The optimal solution is obtained by minimizing a positive-definite treatment cost function. Our method, based on Pontryagin's Minimum Principle and the coordinate cyclic descent method, allows solving problems of varied nature. In this paper, and by way of example, therapeutic enhancement of the immune response to invasion by pathogenic attack is addressed as an optimal control problem. The generic mathematical model used describes the evolution of the disease by means of four non-linear, ordinary differential equations. The model is characterized by the concentration of pathogens, plasma cells, antibodies and a numerical value that indicates the relative characteristic of an organ damaged by disease. From a system theory point of view, drugs can be interpreted as control inputs. Therapies based on separate application of the agents are presented in previous studies. We shall present the more general problem in this paper, considering combined therapies and bounded controls. Finally, we present several numerical simulations.

Pleurodesis in the treatment of pneumothorax and pleural effusion.

Malignant pleural effusion and persistent and/or recurrent spontaneous pneumothorax are clinical entities requiring pleurodesis to avoid the accumulation of liquid and air, respectively. The objectives are to alleviate symptoms (dyspnea, pain and cough), decrease prolonged air leak, avoid recurrence and improve quality of life. Chemical pleurodesis utilizes chemical irritants. The most common of these is "talc" because of its efficiency and its success in lowering the rate of recurrence. Its main indication is in the palliative treatment of malignant pleural effusion. Other substances less frequently used because they are rarely used currently or under study are cytostatics, antibiotics, antiseptics and autologous blood. Surgical pleurodesis with mechanical abrasion by videothoracoscopy is indicated primarily in the treatment of spontaneous pneumothorax because it is highly efficient, easy to carry out, and has low morbidity when compared to pleurectomy. Using pleurodesis in benign effusion is highly controversial. Its principal indications are hepatic hydrothorax, chylothorax, and cardiac effusion that does not respond to medical treatment. Plasma determinations of systemic inflammatory markers and thoracic ultrasound studies can evaluate the efficacy of pleurodesis. We do not recommend the use of non-steroidal anti-inflammatory drugs in the postoperative period to avoid the possibility of interfering with hemostasis or the formation of adherences.