Optimal control analysis in the chemotherapy of IgG multiple myeloma

This paper uses the Gompertzian model for the growth of a cancer cell population subject to losses due to the action of cycle nonspecific therapy for the determination of a chemotherapy program obtained from optimal control theory. Application of the analysis to control of the bone cancer IgG multiple myeloma is presented. The program obtained from optimal control theory is compared with clinical results.     

Optimal control problems arising in cell-cycle-specific cancer chemotherapy

We explore mathematical properties of models of cancer chemotherapy including cell-cycle dependence. Using the mathematical methods of control theory, we demonstrate two assertions of interest for the biomedical community: 1 Periodic chemotherapy protocols are close to the optimum for a wide class of models and have additional favourable properties. 2 Two possible approaches, (a) to minimize the final count of malignant cells and the cumulative effect of the drug on normal cells, or (b) to maximize the final count of normal cells and the cumulative effect of the drug on malignant cells, lead to similar principles of optimization. From the mathematical viewpoint, the paper provides a catalogue of simplest mathematical models of cell-cycle dependent chemotherapy. They can be classified based on the number of compartments and types of drug action modelled. In all these models the optimal controls are complicated by the singular and periodic trajectories and multiple solutions. However, efficient numerical methods have been developed. In simpler cases, it is also possible to provide an exhaustive classification of solutions. We also discuss developments in estimation of cell cycle parameters and cell-cycle dependent drug action.     

Metronomic Chemotherapy: Possible Clinical Application in Advanced Hepatocellular Carcinoma

Hepatocellular carcinoma (HCC) is a hypervascular highly angiogenic tumor usually associated with liver cirrhosis. Vascular endothelial growth factor plays a critical role in vascular development in HCC. In contrast to the treatment of early-stage HCC, the treatment options for advanced HCC are limited and prognosis is often poor, which contributes to this tumor type being the third leading cause of cancer-related deaths worldwide. Metronomic chemotherapy, which was originally designed to inhibit angiogenesis, involves low-dose chemotherapeutic agents administered in a frequent regular schedule with no prolonged breaks and minimizes severe toxicities. We reviewed the potential effects and impact of metronomic chemotherapy in preclinical studies with HCC models and in patients with advanced HCC, especially when combined with a molecular targeted agent. Metronomic chemotherapy involves multiple mechanisms that include antiangiogenesis and antivasculogenesis, immune stimulation by reducing regulatory T cells and inducing dendritic cell maturation, and possibly some direct tumor cell targeting effects, including the cancer stem cell subpopulation. The total number of preclinical studies with HCC models shows impressive results using metronomic chemotherapy-based protocols, especially in conjunction with molecular targeted agents. Four clinical trials and two case reports evaluating metronomic chemotherapy for HCC indicate it to be a safe and potentially useful treatment for HCC. Several preclinical and clinical HCC studies suggest that metronomic chemotherapy may become an alternative type of chemotherapy for advanced unresectable HCC and postsurgical adjuvant treatment of HCC.     

Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function

In this article, four different mathematical models of chemotherapy from the literature are investigated with respect to optimal control of drug treatment schedules. The various models are based on two different sets of ordinary differential equations and contain either chemotherapy, immunotherapy, anti-angiogenic therapy or combinations of these. Optimal control problem formulations based on these models are proposed, discussed and compared. For different parameter sets, scenarios, and objective functions optimal control problems are solved numerically with Bock’s direct multiple shooting method.In particular, we show that an optimally controlled therapy can be the reason for the difference between a growing and a totally vanishing tumor in comparison to standard treatment schemes and untreated or wrongly treated tumors. Furthermore, we compare different objective functions. Eventually, we propose an optimization-driven indicator for the potential gain of optimal controls. Based on this indicator, we show that there is a high potential for optimization of chemotherapy schedules, although the currently available models are not yet appropriate for transferring the optimal therapies into medical practice due to patient-, cancer-, and therapy-specific components.     

Mathematical approaches to optimization of cancer chemotherapy

This paper uses optimal control theory in conjunction with a Gompertzian type model for cellular growth to determine the optimal method of administering cycle non-specific chemotherapy or more generally the optimal durations of treatment and rest periods during chemotherapy. The performance critera employed to determine the relative merits of the therapy include not only the destruction of malignant cells, but also the sparing of a critical normal tissue. Since these criteria are at odds with one another, the solutions are found which satisfy the Pareto optimality conditions.     

What is optimal about motor control?

This article poses a controversial question: is optimal control theory useful for understanding motor behavior or is it a misdirection? This question is becoming acute as people start to conflate internal models in motor control and perception (Poeppel et?al., 2008; Hickok et?al., 2011). However, the forward models in motor control are not the generative models used in perceptual inference. This Perspective tries to highlight the differences between internal models in motor control and perception and asks whether optimal control is the right way to think about things. The issues considered here may have broader implications for optimal decision theory and Bayesian approaches to learning and behavior in general.     

Single cell studies of the cell cycle and some models

Analysis of growth and division often involves measurements made on cell populations, which tend to average data. The value of single cell analysis needs to be appreciated, and models based on findings from single cells should be taken into greater consideration in our understanding of the way in which cell size and division are co-ordinated. Examples are given of some single cell analyses in mammalian cells, yeast and other microorganisms. There is also a short discussion on how far the results are in accord with simple models.     

An integrated scheduling and control model for multi-mode projects

In today’s highly competitive uncertain project environments, it is of crucial importance to develop analytical models and algorithms to schedule and control project activities so that the deviations from the project objectives are minimized. This paper addresses the integrated scheduling and control in multi-mode project environments. We propose an optimization model that models the dynamic behavior of projects and integrates optimal control into a practically relevant project scheduling problem. From the scheduling perspective, we address the discrete time/cost trade-off problem, whereas an optimal control formulation is used to capture the effect of project control. Moreover, we develop a solution algorithm for two particular instances of the optimal project control. This algorithm combines a tabu search strategy and nonlinear programming. It is applied to a large scale test bed and its efficiency is tested by means of computational experiments. To the best of our knowledge, this research is the first application of optimal control theory to multi-mode project networks. The models and algorithms developed in this research are targeted as a support tool for project managers in both scheduling and deciding on the timing and quantity of control activities.     

Optimal control of the chemotherapy of HIV

 Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system composed of four ordinary differential equations and four adjoint ordinary differential equations. Received 5 July 1995; received in revised form 3 June 1996     

Low-intensity combination chemotherapy maximizes host survival time for tumors containing drug-resistant cells

Recent clinical trials have shown that for some cancers, high-intensity alternating chemotherapy does not significantly improve either survival times or response rates compared with nonalternating therapy. The current study uses optimal control to determine the best way to treat a tumor that contains drug-resistant cells that cannot be destroyed. The delivery of two non-cross-resistant chemotherapeutic agents is limited by bounds on the drug concentration and the dose intensity. This ensures that the drug toxicity stays within a tolerable range. The aim of the therapy is to maximize the host survival time, defined as the time over which the tumor burden can be kept below a fixed bound. The model is posed as a free terminal time, optimal parameter selection problem in which the constraints are continuously parametrized by time and the number of courses of therapy is free to vary. New theory is developed so that the optimal parameter selection problem can be solved as a sequence of fixed terminal time problems using existing optimal control software. Numerical simulations of Gompertz tumor growth showed that a treatment maintaining a high tumor burden doubled and sometimes tripled with survival time under aggressive therapy. When these simulations were repeated using exponential and logistic tumor growth models, the tumor burden during treatment had little influence upon survival time. In all simulations, survival time was not extended by delivering the anticancer drugs concurrently instead of staggering the treatment arms.     

Some optimal control problems in cancer chemotherapy with a toxicity limit

We investigate some models of a cancer chemotherapy problem where the normal cell population must be maintained above a lower limit and a measure of the total drug use is bounded as a limit of toxicity. Three sets of objective functions are analyzed, and some numerical solutions are provided for the last case. In all cases the structure of the optimal solution is similar, including a bolus application of drug followed later by continuous infusion.     

Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method

In this paper, two cancer therapies are investigated through their mathematical models. Namely, angiogenesis inhibition (P. Hahndfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 1999, 4770-4775) and tumor-immune interactions with chemotherapy (L. De Pillis, W. Gu, K.R. Fister, T. Head, K. Maples, A. Murugan, T. Neal, K. Yoshida, Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math. Biosci. 209 (1), 2007, 292-315). The feedback protocols are determined by using a control set-valued method whose mathematical foundations are stated in (K. Kassara, A unified set-valued approach to control immunotherapy, SIAM J. Contr. Optim. 48 (2), 2009, 909-924), and which is demonstrated to be well suited for cancer control.     

Machine learning-based model predictive controller design for cell culture processes

The biopharmaceutical industry continuously seeks to optimize the critical quality attributes to maintain the reliability and cost-effectiveness of its products. Such optimization demands a scalable and optimal control strategy to meet the process constraints and objectives. This work uses a model predictive controller (MPC) to compute an optimal feeding strategy leading to maximized cell growth and metabolite production in fed-batch cell culture processes. The lack of high-fidelity physics-based models and the high complexity of cell culture processes motivated us to use machine learning algorithms in the forecast model to aid our development. We took advantage of linear regression, the Gaussian process and neural network models in the MPC design to maximize the daily protein production for each batch. The control scheme of the cell culture process solves an optimization problem while maintaining all metabolites and cell culture process variables within the specification. The linear and nonlinear models are developed based on real cell culture process data, and the performance of the designed controllers is evaluated by running several real-time experiments.     

Design of optimal cancer chemotherapy using a continuous-time state model of cell kinetics

A continuous bilinear model in state space is used to describe the cell kinetics of a tumor-cell population under the effects of chemotherapy. Firstly, the time-course behavior of a Chinese-hamster-ovary (CHO) cell population is simulated to demonstrate the utility of the model. Then, an optimal strategy for cancer treatment is derived, based on the need to balance the effects on both cancerous and normal tissues. The performance index minimized is the sum of the weighted tumor population and the weighted total drug dosage. The optimization problem has resulted in a two-point boundary-value problem (TPBVP) with a bang-bang control policy, which is solved by the switching-time variation method (STVM). Computer simulation of CHO cells is also carried out as a numerical example of determining optimal cancer chemotherapy.     

Control and integration of cell signaling pathways during C. Elegans vulval development

Vulval development in the Caenorhabditis elegans hermaphrodite represents a simple, genetically tractable system for studying how cell signaling events control cell fata decisions. Current models suggest that proper specification of vulval cell fates relies on the integration of multiple signaling systems, including one that involves a receptor tyrosine kinase (RTK)→Ras→mitogen activated protein kinase (MAPK) cascade and one that involves a LIN-12/Notch family receptor. In this review, we first discuss how genetic strategies are being used to identify and analyze components that control vulval cell fate decisions. We then describe the different signaling systems that have been elucidated and how they relate to one another. Finally, we highlight several recently characterized genes that encode positive regulators, negative regulators or potential targets of the RTK→Ras→MAPK cascade involved in vulval induction.     

Reusing and composing models of cell fate regulation of human bone precursor cells

In order to treat osteoporosis and other bone mass disorders it is necessary to understand the regulatory processes that control the cell fate decisions responsible for going from bone precursor cells to bone tissue. Many processes interact to regulate cell division, differentiation and apoptosis. There are models for these basic processes, but not for their interactions. In this work we use the theory of switched systems, reuse and composition of validated models to describe the cell fate decisions leading to bone and fat formation. We describe the differentiation of osteo-adipo progenitor cells by composing its model with differentiation stimuli. We use the activation of the Wnt pathway as stimulus to osteoblast lineage, including regulation of cell division and apoptosis. This model is our first step to simulate physiological responses in silico to treatments for bone mass disorders.     

Dynamic decision-making in uncertain environments I. The principle of dynamic utility

Understanding the dynamics or sequences of animal behavior usually involves the application of either dynamic programming or stochastic control methodologies. A difficulty of dynamic programming lies in interpreting numerical output, whereas even relatively simple models of stochastic control are notoriously difficult to solve. Here we develop the theory of dynamic decision-making under probabilistic conditions and risks, assuming individual growth rates of body size are expressed as a simple stochastic process. From our analyses we then derive the optimization of dynamic utility, in which the utility of weight gain, given the current body size, is a logarithmic function: hence the fitness function of an individual varies depending on its current body size. The dynamic utility function also shows that animals are universally sensitive to risk and display risk-averse behaviors. Our result proves the traditional use of expected utility theory and game theory in behavioral studies is valid only as a static model.     

The role of radiation therapy for carcinoma of the lung

A large proportion of patients with carcinoma of the lung may benefit from the use of radiation therapy. Operable patients have not been shown to benefit from preoperative irradiation, but postoperative irradiation has improved survival in those found to have involvement of hilar or mediastinal lymph nodes. Radiation therapy is the only potentially curative treatment for patients who are inoperable, but do not have distant metastasis. Control of the local tumor is very dependent upon dose-fractionation-time relationships. Patients who are relatively asymptomatic, i.e., they have a high performance status, are curable if treated promptly with radiation therapy. Small cell carcinoma requires both radiation therapy and chemotherapy. The optimal method of combining the two modalities is yet to be determined, but prophylactic cranial irradiation is necessary to control microscopic metastases that are not affected by systemic chemotherapy, and thoracic irradiation is necessary to give the highest probability of control of the primary tumor. Prophylactic cranial irradiation has also been shown to reduce the frequency of brain metastasis in patients with squamous carcinoma, large cell carcinoma, and adenocarcinoma; it may become more important in these cell types when more effective chemotherapy is developed.     

The HtrA family of proteases: implications for protein composition and cell fate

Cells precisely monitor the concentration and functionality of each protein for optimal performance. Protein quality control involves molecular chaperones, folding catalysts, and proteases that are often heat shock proteins. One quality control factor is HtrA, one of a new class of oligomeric serine proteases. The defining feature of the HtrA family is the combination of a catalytic domain with at least one C-terminal PDZ domain. Here, we discuss the properties and roles of this ATP-independent protease chaperone system in protein metabolism and cell fate.