Discrete-time MPC for switched systems with applications to biomedical problems

Switched systems in which the manipulated control action is the time-dependingswitching signal describe many engineering problems, mainly related to biomedical applications. In such a context, to control the system means to select an autonomous system - at each time step - among a given finite family. Even when this selection can be done by solving a Dynamic Programming (DP) problem, such a solution is often difficult to apply, and state/control constraints cannot be explicitly considered. In this work a new set-based Model Predictive Control (MPC) strategy is proposed to handle switched systems in a tractable form. The optimization problem at the core of the MPC formulation consists in an easy-to-solve mixed-integer optimization problem, whose solution is applied in a receding horizon way. Two biomedical applications are simulated to test the controller: (i) the drug schedule to attenuate the effect of viralmutation and drugs resistance on the viral load, and (ii) the drug schedule for Triple Negative breast cancer treatment. The numerical results suggest that the proposed strategy outperform the schedule for available treatments.Fil: Anderson, Alejandro Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Ferramosca, Antonio. Universidad Tecnológica Nacional; ArgentinaFil: Hernandez Vargas, Esteban Abelardo. Frankfurt Institute For Advanced Studies-fias; Alemani

An Engineering Approach Towards Personalized Cancer Therapy

Cells behave as complex systems with regulatory processes that make use of many elements such as switches based on thresholds, memory, feedback, error-checking, and other components commonly encountered in electrical engineering. It is therefore not surprising that these complex systems are amenable to study by engineering methods. A great deal of effort has been spent on observing how cells store, modify, and use information. Still, an understanding of how one uses this knowledge to exert control over cells within a living organism is unavailable. Our prime objective is "Personalized Cancer Therapy" which is based on characterizing the treatment for every individual cancer patient. Knowing how one can systematically alter the behavior of an abnormal cancerous cell will lead towards personalized cancer therapy. Towards this objective, it is required to construct a model for the regulation of the cell and utilize this model to devise effective treatment strategies. The proposed treatments will have to be validated experimentally, but selecting good treatment candidates is a monumental task by itself. It is also a process where an analytic approach to systems biology can provide significant breakthrough. In this dissertation, theoretical frameworks towards effective treatment strategies in the context of probabilistic Boolean networks, a class of gene regulatory networks, are addressed. These proposed analytical tools provide insight into the design of effective therapeutic interventions

Mathematical Models Of The Tumor Ecosystem

The cellular composition of tumors is highly heterogeneous, involving not only divergent lineages of transformed cancer cells, but also host cells of the stroma and immune system. The complicity of protumoral host cells is essential for conferring malignancy and promoting progression in tumor in a wide range of solid tissues, including breast, pancreas, and brain. This understanding has led to the concept of ecological treatment: that is, molecular therapies aimed not directly at the destruction of cancer cells, but at disrupting interactions between tumor cells and host cells or the microenvironment, in effect creating a microenvironment unfavorable for tumor progression. In order to design effective eco- logical interventions and predict the course of progression of complex tumors, a quantitative understanding of the interactions between cellular subpopulations in tumors is essential. The theoretical branch of ecology has long established a history of using mathematical modeling to describe and predict the behavior of heterogeneous populations consisting of myriad interacting individuals each susceptible to noise in their responses to local stimuli, and complex systems comprised of different subpopulations engaged in asymmetrical interactions. We adapt some of these models--specifically, an agent-based self-propelled particle model and a population dynamics differential equation model--to the problems of stromal cell-dependent cancer cell migration and growth. From the former study, I find that paracrine signaling between tumor cells and in- creases the stability and efficiency of a preexisting tumor cell collective migration phenotype, rendering the net comigratory behavior more robust against microenvironmental fluctuations. From the latter study, I find that gliomas de- pendent upon protumoral tumor-associated macrophages for growth undergo multi-phasic growth dynamics. I also conclude that macrophage-targeted treat- ment of such tumors in a linear stage of progression leads to tumor reduction dependent on the size and composition of the tumor at the time of treatment initiation, and that tumors exhibiting weak response to such a treatment may harbor hidden vulnerability to combinatorial therapy. In addition, I infer from these theoretical studies possible methods of intervening in protumoral ecological interactions

Organizing timely treatment in multi-disciplinary care

Healthcare providers experience an increased pressure to organize their processes more efficiently and to provide coordinated care over multiple disciplines. Organizing multi-disciplinary care is typically highly constrained, since multiple appointments per patient have to be scheduled with possible restrictions between them. Furthermore, schedules of professionals from various facilities or with different skills must be aligned. Since it is important that patients are treated on time, access time targets are set on the time between referral to the facility and the actual start of the treatment. These targets may vary per patient type: e.g., urgent patients have shorter access time targets than regular patients. In this thesis, we use operations research methods to support multi-disciplinary care settings in providing timely treatments with an excellent quality of care, against affordable costs, while taking patient and employee satisfaction into account. We consider settings in rehabilitation care and radiotherapy, but the underlying planning problems are applicable to many other multi-disciplinary care settings, such as cancer care or specialty clinics. The developed models are applied to case studies in the Sint Maartenskliniek Nijmegen, the AMC Amsterdam and a BCCA cancer clinic in Vancouver, Canada. The results of the thesis demonstrate that adequate admission policies and capacity allocation to different activities and stages in complex treatment processes can improve compliance with access time targets for multi-disciplinary care systems considerably, while using the available resource capacities and taking patient and employee satisfaction into account

Selected Topics on Mathematical Models in Immunology and Medicine

In 1988 the new IIASA project on System Immunology was inaugurated. The new activity focuses theoretical and experimental research in immunology and system mathematics to experimental planning and prediction for relevant disease applications and systematic understanding of immunology. IIASA analysis and simulation should lead to an effective plan of successive experiments to identify and to quantify particularly sensitive parameters in this most complex system of information processing, decision and control. The integration of such diverse disciplines is extremely difficult but some basis has already been established. For several years IIASA has sponsored international workshops dealing with dynamical systems and their applications to biology. These include: (1) The conference on "Dynamics of Macrosystems"; (2) The Working Conference on "Theoretical Immunology"; (3) The Workshop on "Selected Topics in Biomathematics"; The present volume contains the proceedings of the latest Workshop "Mathematical Modelling in Immunology and Medicine", Part 1 deals with the mathematical models of autoimmune, infectious diseases and AIDS. The models are studied with the intent to establish a basis for more effective treatment. In Part 2, questions of computer simulation and data analysis in cancer research are analyzed. Part 3 is devoted to the models for antibody binding, immunoassay dynamics and immunogenetic systems. The problems of system analysis and medical decision making are discussed in Part 4

Systems Medicine: An Integrated Approach with Decision Making Perspective

Two models are proposed to describe interactions among genes, transcription factors, and signaling cascades involved in regulating a cellular sub-system. These models fall within the class of Markovian regulatory networks, and can accommodate for different biological time scales. These regulatory networks are used to study pathological cellular dynamics and discover treatments that beneficially alter those dynamics. The salient translational goal is to design effective therapeutic actions that desirably modify a pathological cellular behavior via external treatments that vary the expressions of targeted genes. The objective of therapeutic actions is to reduce the likelihood of the pathological phenotypes related to a disease. The task of finding effective treatments is formulated as sequential decision making processes that discriminate the gene-expression profiles with high pathological competence versus those with low pathological competence. Thereby, the proposed computational frameworks provide tools that facilitate the discovery of effective drug targets and the design of potent therapeutic actions on them. Each of the proposed system-based therapeutic methods in this dissertation is motivated by practical and analytical considerations. First, it is determined how asynchronous regulatory models can be used as a tool to search for effective therapeutic interventions. Then, a constrained intervention method is introduced to incorporate the side-effects of treatments while searching for a sequence of potent therapeutic actions. Lastly, to bypass the impediment of model inference and to mitigate the numerical challenges of exhaustive search algorithms, a heuristic method is proposed for designing system-based therapies. The presentation of the key ideas in method is facilitated with the help of several case studies

Network resilience

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.Comment: Review chapter