Minaya Villasana

Heuristic design of cancer chemotherapies

A methodology using heuristic search methods is proposed for optimizing cancer chemotherapies with drugs acting on a specific phase of the cell cycle. Specifically, two evolutionary algorithms, and a simulated annealing method are considered. The methodology relies on an underlying mathematical model for tumor growth that includes cycle phase specificity, and multiple applications of a single cytotoxic agent. The goal is to determine effective protocols for administering the agent, so that the tumor is eradicated, while the immune system remains above a given threshold. Results confirm that modern heuristic methods are a good choice for optimizing complex systems. The three algorithms considered produced effective solutions, and provided drug schedules suitable for practice, although some methods excelled others in performance. A discussion of comparative results is presented.

An evolutionary approach to cancer chemotherapy scheduling

In this paper, we investigate the employment of evolutionary algorithms as a search mechanism in a decision support system for designing chemotherapy schedules. Chemotherapy involves using powerful anti-cancer drugs to help eliminate cancerous cells and cure the condition. It is given in cycles of treatment alternating with rest periods to allow the body to recover from toxic side-effects. The number and duration of these cycles would depend on many factors, and the oncologist would schedule a treatment for each patient’s condition. The design of a chemotherapy schedule can be formulated as an optimal control problem; using an underlying mathematical model of tumour growth (that considers interactions with the immune system and multiple applications of a cycle-phase-specific drug), the objective is to find effective drug schedules that help eradicate the tumour while maintaining the patient health’s above an acceptable level. A detailed study on the effects of different objective functions, in the quality and diversity of the solutions, was performed. A term that keeps at a minimum the tumour levels throughout the course of treatment was found to produce more regular treatments, at the expense of imposing a higher strain on the patient’s health, and reducing the diversity of the solutions. Moreover, when the number of cycles was incorporated in the problem encoding, and a parsimony pressure added to the objective function, shorter treatments were obtained than those initially found by trial and error.

An extension of the Kermack–McKendrick model for AIDS epidemic

We propose an SI epidemic model for AIDS that would take into account factors such as preventive education and the infection through the use of needles (transfusions and drug use). The model is analyzed from a dynamical systems point of view and is further applied to specific data for China, Spain and Venezuela.

Modeling and optimization of combined cytostatic and cytotoxic cancer chemotherapy

OBJECTIVES This study extends a previous mathematical model of cancer cytotoxic chemotherapy, which considered cycling tumor cells and interactions with the immune system, by incorporating a different type of drug: a cytostatic agent. The effect of a cytostatic drug is to arrest cells in a phase of their cycle. In consequence, once tumor cells are arrested and synchronized they can be targeted with a cytotoxic agent, thus maximizing cell kill fraction and minimizing normal cell killing. The goal is to incorporate the new drug into the chemotherapy protocol and devise optimal delivery schedules. METHODS The problem of designing efficient combined chemotherapies is formulated as an optimal control problem and tackled using a state-of-the-art evolutionary algorithm for real-valued encoding, namely the covariance matrix adaptation evolution strategy. Alternative solution representations and three formulations of the underlying objective function are proposed and compared. RESULTS The optimization problem was successfully solved by the proposed approach. The encoding that enforced non-overlapping (simultaneous) application of the two types of drugs produced competitive protocols with significant less amount of toxic drug, thus achieving better immune system health. When compared to treatment protocols that only consider a cytotoxic agent, the incorporation of a cytostatic drug dramatically improved the outcome and performance of the overall treatment, confirming in silico that the combination of a cytostatic with a cytotoxic agent improves the efficacy and efficiency of the chemotherapy. CONCLUSION We conclude that the proposed approach can serve as a valuable decision support tool for the medical practitioner facing the complex problem of designing efficient combined chemotherapies.

Multi-objective pole placement with evolutionary algorithms

Multi-Objective Evolutionary Algorithms (MOEA) have been succesfully applied to solve control problems. However, many improvements are still to be accomplished. In this paper a new approach is proposed: the Multi-Objective Pole Placement with Evolutionary Algorithms (MOPPEA). The design method is based upon using complex-valued chromosomes that contain information about closed-loop poles, which are then placed through an output feedback controller. Specific cross-over and mutation operators were implemented in simple but efficient ways. The performance is tested on a mixed multi-objective H2/H∞ control problem.

Maxentropic solution of fractional moment problems

The problem of reconstructing a function from the knowledge of a few of its moments is a special case of the problem inverting an integral transform when there are finitely many data points. The classical method of maximum entropy and the method of maximum entropy in the mean are well suited to attack these problems. What is interesting is that when we are free to choose the data points, the choice can be made to improve the quality of the reconstruction when the method of maximum entropy is used too. In this note we review how to apply these methods and compare them in a couple of examples.

Solving Multi-Objective Linear Control Design Problems Using Genetic Algorithms

Abstract Two multi-objective genetic algorithms, an elitist version of MOGA and NSGA-II, were applied to solve two linear control design problems. The first was a H 2 problem with a PI controller structure, for a first order stable plant. The second was a mixed H 2 /H ∞ control problem. In both cases, three indicators were used to evaluate each algorithm performance: Set coverage, spread and hypervolume. It was found that NSGA-II shows better performance indicators. Moreover, for the second problem, a new controller representation was proposed with corresponding cross-over and mutation operators. This approach was able to find solutions as good as those previously published. The main advantage is that the stability restriction disappears, allowing to deal with an unconstrained optimization problem.

Population-based optimization of cytostatic/cytotoxic combination cancer chemotherapy

This article studies the suitability of modern population based algorithms for designing combination cancer chemotherapies. The problem of designing chemotherapy schedules is expressed as an optimization problem (an optimal control problem) where the objective is to minimize the tumor size without compromising the patient’s health. Given the complexity of the underlying mathematical model describing the tumor’s progression (considering two types of drugs, the cell cycle and the immune system response), analytical and classical optimization methods are not suitable, instead, stochastic heuristic optimization methods are the right tool to solve the optimal control problem. Considering several solution quality and performance metrics, we compared three powerful heuristic algorithms for real-parameter optimization, namely, CMA evolution strategy, differential evolution, and particle swarm pattern search method. The three algorithms were able to successfully solve the posed problem. However, differential evolution outperformed its counterparts both in quality of the obtained solutions and efficiency of search.

Using a model comparison approach to describe the assembly pathway for histone H1

Histones H1 or linker histones are highly dynamic proteins that diffuse throughout the cell nucleus and associate with chromatin (DNA and associated proteins). This binding interaction of histone H1 with the chromatin is thought to regulate chromatin organization and DNA accessibility to transcription factors and has been proven to involve a kinetic process characterized by a population that associates weakly with chromatin and rapidly dissociates and another population that resides at a binding site for up to several minutes before dissociating. When considering differences between these two classes of interactions in a mathematical model for the purpose of describing and quantifying the dynamics of histone H1, it becomes apparent that there could be several assembly pathways that explain the kinetic data obtained in living cells. In this work, we model these different pathways using systems of reaction-diffusion equations and carry out a model comparison analysis using FRAP (fluorescence recovery after photobleaching) experimental data from different histone H1 variants to determine the most feasible mechanism to explain histone H1 binding to chromatin. The analysis favors four different chromatin assembly pathways for histone H1 which share common features and provide meaningful biological information on histone H1 dynamics. We show, using perturbation analysis, that the explicit consideration of high- and low-affinity associations of histone H1 with chromatin in the favored assembly pathways improves the interpretation of histone H1 experimental FRAP data. To illustrate the results, we use one of the favored models to assess the kinetic changes of histone H1 after core histone hyperacetylation, and conclude that this post-transcriptional modification does not affect significantly the transition of histone H1 from a weakly bound state to a tightly bound state.

The Minimal Model of Glucose Disappearance in Type I Diabetes

In this chapter we evaluate the ability of the minimal model of glucose disappearance to describe experimental data collected from 9 diabetic patients controlled subcutaneously by an insulin pump. Two versions of the minimal model are used: the nonlinear classic minimal model developed by Bergman et al. (MM) and the linear approximation proposed by Fernandez et al. (LMM). All data windows (n = 13) show residuals that are correlated for both the LMM and MM (p-value 0.05). This study confirms that the minimal model of glucose disappearance, either the classic or linear version, is unable to describe the observed experimental data possibly as a result of the physiological constraints imposed by the minimal model approach on the system dynamics, together with possible errors derived from the unmeasured insulin dynamics. Further testing on more complex models should be performed.