Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy.

The high failure rates encountered in the chemotherapy of some cancers suggest that drug resistance is a common phenomenon. In the current study, the tumor burden during therapy is used to slow the growth of the drug-resistant cells, thereby maximizing the survival time of the host. Three types of tumor growth model are investigated--Gompertz, logistic, and exponential. For each model, feedback controls are constructed that specify the optimal tumor mass as a function of the size of the resistant subpopulation. For exponential and logistic tumor growth, the tumor burden during therapy is shown to have little impact upon survival time. When the tumor is in Gompertz growth, therapies maintaining a large tumor burden double and sometimes triple the survival time under aggressive therapies. Aggressive therapies aim for a rapid reduction in the sensitive cell subpopulation. These conclusions are not dependent upon the values of the model constants that determine the mass of resistant cells. Since treatments maintaining a high tumor burden are optimal for Gompertz tumor growth and close to optimal for exponential and logistic tumor growth, it may no longer be necessary to know the growth characteristics of a tumor to schedule anticancer drugs.     

Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method

The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a “healthy” steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.     

A mathematical model of cancer chemotherapy with an optimal selection of parameters

An optimal parameter selection model of cancer chemotherapy is presented which describes the treatment of a tumor over a fixed period of time by the repeated administration of a single drug. The drug is delivered at evenly spaced intervals over the treatment period at doses to be selected by the model. The model constructs a regimen that both minimizes the tumor population at the end of the treatment and satisfies constraints on the drug toxicity and intermediate tumor size. Numerical solutions show that an optimal regimen withholds the bulk of the doses until the end of the treatment period. When a drug used is of either moderate or low effectiveness, an optimal regimen is superior to a schedule that delivers all of the drug at the beginning of the treatment. This study questions whether the current method for the administration of chemotherapy is optimal and suggests that alternative regimens should be considered.     

Exploiting the Synergy between Carboplatin and ABT-737 in the Treatment of Ovarian Carcinomas

Platinum drug-resistance in ovarian cancers mediated by anti-apoptotic proteins such as Bcl-xL is a major factor contributing to the chemotherapeutic resistance of recurrent disease. Consequently, concurrent inhibition of Bcl-xL in combination with chemotherapy may improve treatment outcomes for patients. Here, we develop a mathematical model to investigate the potential of combination therapy with ABT-737, a small molecule inhibitor of Bcl-xL, and carboplatin, a platinum-based drug, on a simulated tumor xenograft. The model is calibrated against in vivo experimental data, wherein xenografts established in mice were treated with ABT-737 and/or carboplatin on a fixed periodic schedule. The validated model is used to predict the minimum drug load that will achieve a predetermined level of tumor growth inhibition, thereby maximizing the synergy between the two drugs. Our simulations suggest that the infusion-duration of each carboplatin dose is a critical parameter, with an 8-hour infusion of carboplatin given weekly combined with a daily bolus dose of ABT-737 predicted to minimize residual disease. The potential of combination therapy to prevent or delay the onset of carboplatin-resistance is also investigated. When resistance is acquired as a result of aberrant DNA-damage repair in cells treated with carboplatin, drug delivery schedules that induce tumor remission with even low doses of combination therapy can be identified. Intrinsic resistance due to pre-existing cohorts of resistant cells precludes tumor regression, but dosing strategies that extend disease-free survival periods can still be identified. These results highlight the potential of our model to accelerate the development of novel therapeutics such as BH3 mimetics.     

Optimal response to chemotherapy for a mathematical model of tumor–immune dynamics

An optimal control problem for cancer chemotherapy is considered that includes immunological activity. In the objective a weighted average of several quantities that describe the effectiveness of treatment is minimized. These terms include (i) the number of cancer cells at the terminal time, (ii) a measure for the immunocompetent cell densities at the terminal point (included as a negative term), (iii) the overall amount of cytotoxic agents given as a measure for the side effects of treatment and (iv) a small penalty on the terminal time that limits the overall therapy horizon which is assumed to be free. This last term is essential in obtaining a well-posed problem formulation. Employing a Gompertzian growth model for the cancer cells, for various scenarios optimal controls and corresponding responses of the system are calculated. Solutions initially follow a full dose treatment, but then at one point switch to a singular regimen that only applies partial dosages. This structure is consistent with protocols that apply an initial burst to reduce the tumor volume and then maintain a small volume through lower dosages. Optimal controls end with either a prolonged period of no dose treatment or, in a small number of scenarios, this no dose interval is still followed by one more short burst of full dose treatment.     

Optimal control for a cancer chemotherapy problem with general growth and loss functions

We investigate a model of a cancer chemotherapy problem where the aim is to minimize the tumor burden at the end of the treatment period while maintaining a normal cell population above a lower level as a limit of toxicity. The analysis is performed for general classes of growth and loss functions. The optimal drug dose is maximum initially so that the normal cell population is driven down to its lower level, and then the drug level is chosen to maintain the normal cell population there until the end of treatment. During treatment the number of tumor cells is always decreasing.     

The numerical method for the optimal supporting position and related optimal control for the catalytic reaction system

This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method.     

A paradigm for therapy-induced microenvironmental changes in solid tumors leading to drug resistance

Intrinsic alterations in the tumor microenvironment are known to contribute to various forms of drug resistance. For example, tumor hypoxia, due to abnormal or sluggish blood flow within areas of solid tumors, can result in both microenvironment-mediated radiation and chemotherapeutic drug resistance. In contrast, acquired resistance to chemotherapy is generally considered to be the result of the gradual selection of mutant subpopulations having genetic mutations and biochemical alterations responsible for the resistant phenotype. Here we present a paradigm for therapyinduced microenvironment-mediated acquired drug resistance. It is based on the results showing that tumor cells appear to be heterogeneous in their relative dependence on adjacent tumor-associated vasculature for survival. Some tumor cells are highly vessel dependent, whereas some are significantly less so, and thus can survive in more hypoxic regions of tumors, distal from such tumor vessels. Hence, it is possible that variant tumor cells that are less vessel dependent may therefore be selected for over time by successful antiangiogenic drug therapies. This results in loss of response or attenuated responses to the therapy. Preliminary evidence is summarized in support of this hypothesis, using paired human colon cancer (HCT116) cell lines that contain two copies of either the wild-type or the disrupted p53 tumor suppressor gene. The mutant cells were found to be less responsive to antiangiogenic therapy, compared to the wild-type cells, and could be progressively selected for in mixed cell populations. Because p53 inactivation can lead to resistance to hypoxia-mediated apoptosis, the results suggest that a protracted and successful antiangiogenic therapy may create more hypoxic tumor microenvironments, thereby creating the necessary conditions to accelerate the selection of mutant tumor cells that are more adept in surviving and growing in such environments. As such, consideration might be given to the combined use of bioreductive hypoxic cell cytotoxic drugs and angiogenesis inhibitors to prolong the efficacy of antiangiogenic therapeutics.     

Influence of interferon-α on the expression of the cancer stem cell markers in pancreatic carcinoma cells

The cytokine interferon-α (IFNα) belongs to the group of type I interferons already used in cancer therapy. This drug possesses radio- and chemo-sensitizing, and shows anti-angiogenic properties. Cancer stem cells (CSC) are a unique population of tumor cells that initiate secondary tumors, and are responsible for metastasis formation. Patients with pancreatic ductal adenocarcinoma (PDAC) have an especially poor prognosis, with 5-year survival rates of only ~1% and median survival of 4–6 months. PDAC is characterized by the presence of CSC. In this work we demonstrate for the first time that IFNα up-regulates the expression of the CSC markers CD24, CD44 and CD133 in in vitro and in vivo models of PDAC. We showed the IFNα effects on the migration and invasion of PDAC cells, which is associated with the level of the CSC marker expression. In vivo, this drug inhibits tumor growth but promotes metastasis formation in the early stage of tumor growth. We propose that IFNα may enhance the enrichment of CSC in PDAC tumors. Additionally we also suggest that in combination therapy of solid tumors with IFNα, this drug should be given to patients prior to chemotherapy to achieve the CSC activation.     

Inhibition of ABL tyrosine kinase potentiates radiation-induced terminal growth arrest in anaplastic thyroid cancer cells

Gleevec, a selective tyrosine kinase inhibitor, retarded the growth of anaplastic thyroid cancer cell lines in vitro and in vivo through selective inhibition of ABL tyrosine kinase activity. In the present study, we investigated the ability of Gleevec to modulate the in vitro and in vivo radiation response of anaplastic thyroid cancer cells. Cell growth assays, colony formation assays and xenograft models were used to quantify the radiosensitizing effect of Gleevec in cells of the anaplastic thyroid cancer cell lines ARO and FRO. FACS, Western blotting and histochemical techniques were employed to study the mechanisms of radiation response after exposure to Gleevec. Gleevec (7.0 microM) increased the anti-proliferative effect of radiation on the growth ARO and FRO cells in vitro. Clonogenic analysis demonstrated that Gleevec reduced cell survival after irradiation. Gleevec combined with radiation produced an increase in tumor growth inhibition compared to treatment with either modality alone in mice bearing anaplastic thyroid cancer xenografts. The drug suppressed radiation-induced ABL activation and promoted CDKN1A (p21(cip1)) accumulation in irradiated anaplastic thyroid cancer cells. Gleevec had an additional effect on radiation-induced apoptosis in cells of both cell lines and potentiated the induction of terminal growth arrest accompanied by the expression of senescence-associated beta-galactosidase. The antitumor effect of Gleevec is potentiated in adjunctive therapy with radiation not only due to inhibition of proliferative cell growth with transient cell cycle arrest and apoptosis, but also due to the terminal growth arrest associated with senescence, suggesting that tumor cell senescence is a mechanism for tumor targeting therapy in combination with ionizing radiation.     

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.     

Optimized adoptive T-cell therapy for the treatment of residual mantle cell lymphoma

Mantle cell lymphoma (MCL) is an aggressive B-cell neoplasm with few patients achieving long-term survival with current treatment regimens. High-dose therapy is effective in reducing the tumor burden; however, patients eventually relapse due to minimal residual disease. Having demonstrated efficacy in other malignancies, the effectiveness of dendritic cell-based immunotherapy for minimal residual MCL was examined. We demonstrated that dendritic cells (DC) primed with MCL antigens stimulated the activation of MCL-specific T cells that recognized and destroyed both MCL cell lines and primary MCL in vitro. In addition, in vivo studies demonstrated that adoptively transferred MCL-specific T cells were able to significantly inhibit tumor growth in mice with minimal residual MCL. Subsequently, when combined with CHOP chemotherapy, adoptive T-cell therapy was able to significantly extend the survival of the mice by further reducing the tumor burden. These results clearly show that MCL-specific cellular immunotherapy is effective in treating minimal residual MCL, paving the way for future clinical studies.     

Cellular Uptake and Antitumor Activity of DOX-hyd-PEG-FA Nanoparticles

A PEG-based, folate mediated, active tumor targeting drug delivery system using DOX-hyd-PEG-FA nanoparticles (NPs) were prepared. DOX-hyd-PEG-FA NPs showed a significantly faster DOX release in pH 5.0 medium than in pH 7.4 medium. Compared with DOX-hyd-PEG NPs, DOX-hyd-PEG-FA NPs increased the intracellular accumulation of DOX and showed a DOX translocation from lysosomes to nucleus. The cytotoxicity of DOX-hyd-PEG-FA NPs on KB cells was much higher than that of free DOX, DOX-ami-PEG-FA NPs and DOX-hyd-PEG NPs. The cytotoxicity of DOX-hyd-PEG-FA NPs on KB cells was attenuated in the presence of exogenous folic acid. The IC₅₀ of DOX-hyd-PEG-FA NPs and DOX-hyd-PEG NPs on A549 cells showed no significant difference. After DOX-hyd-PEG-FA NPs were intravenously administered, the amount of DOX distributed in tumor tissue was significantly increased, while the amount of DOX distributed in heart was greatly decreased as compared with free DOX. Compared with free DOX, NPs yielded improved survival rate, prolonged life span, delayed tumor growth and reduced the cardiotoxicity in tumor bearing mice model. These results indicated that the acid sensitivity, passive and active tumor targeting abilities were likely to act synergistically to enhance the drug delivery efficiency of DOX-hyd-PEG-FA NPs. Therefore, DOX-hyd-PEG-FA NPs are a promising drug delivery system for targeted cancer therapy.     

Robustness and Efficiency of D‐optimal Experimental Designs in a Growth Problem

To assess tree growth, for example in diameter, a forester typically measures the trees at regular time points. We call such designs equidistant. In this paper we look at the robustness and efficiency of several experimental designs, using the D‐optimality criterion, in a case study of diameter growth in cork oaks. We compare D‐optimal designs (unrestricted and replication‐free) with equidistant designs. We further compare designs in different experimental regions. Results indicate that the experimental region should be adequate to the problem, and that D‐optimal designs are substantially more efficient than equidistant designs, even under parameter mis‐specification.     

Proteins expressed in osteosarcoma and serum levels as prognostic factors

Osteosarcoma is the most frequent highly malignant bone-tumor with a peak manifestation during the second and third decade of life. Although survival rate increased up to 60-70% within the last 20 years, the problem of non-response to chemotherapy remains. Initial tumor size and response to neoadjuvant chemotherapy are the most accepted prognostic factors used for postoperative stratification of chemotherapy. The identification of patients with a bad response to therapy at the time of diagnosis would facilitate already a preoperative stratification of chemotherapy or a more aggressive regime to increase survival. This review reflects on recently described molecular markers but not on clinical parameters in human osteosarcoma with respect to their prognostic potential. This includes p53, the p-glycoprotein, the multidrug resistance gene, the humen epidermal growth factor receptor and metallothionein expression. Heat shock proteins have recently become important in osteosarcoma because of their prognostic value and their role in drug resistance. A short overview of serological markers is also given. Further results on drug resistance and survival may be provided by ongoing studies, which investigate the role of proteins of the apoptotic and antiapoptotic families in human osteosarcoma.     

Doubly penalized buckley-james method for survival data with high-dimensional covariates.

Recent interest in cancer research focuses on predicting patients' survival by investigating gene expression profiles based on microarray analysis. We propose a doubly penalized Buckley-James method for the semiparametric accelerated failure time model to relate high-dimensional genomic data to censored survival outcomes, which uses the elastic-net penalty that is a mixture of L1- and L2-norm penalties. Similar to the elastic-net method for a linear regression model with uncensored data, the proposed method performs automatic gene selection and parameter estimation, where highly correlated genes are able to be selected (or removed) together. The two-dimensional tuning parameter is determined by generalized crossvalidation. The proposed method is evaluated by simulations and applied to the Michigan squamous cell lung carcinoma study.     

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.     

P-loop Conformation Governed Crizotinib Resistance in G2032R-Mutated ROS1 Tyrosine Kinase: Clues from Free Energy Landscape

Tyrosine kinases are regarded as excellent targets for chemical drug therapy of carcinomas. However, under strong purifying selection, drug resistance usually occurs in the cancer cells within a short term. Many cases of drug resistance have been found to be associated with secondary mutations in drug target, which lead to the attenuated drug-target interactions. For example, recently, an acquired secondary mutation, G2032R, has been detected in the drug target, ROS1 tyrosine kinase, from a crizotinib-resistant patient, who responded poorly to crizotinib within a very short therapeutic term. It was supposed that the mutation was located at the solvent front and might hinder the drug binding. However, a different fact could be uncovered by the simulations reported in this study. Here, free energy surfaces were characterized by the drug-target distance and the phosphate-binding loop (P-loop) conformational change of the crizotinib-ROS1 complex through advanced molecular dynamics techniques, and it was revealed that the more rigid P-loop region in the G2032R-mutated ROS1 was primarily responsible for the crizotinib resistance, which on one hand, impaired the binding of crizotinib directly, and on the other hand, shortened the residence time induced by the flattened free energy surface. Therefore, both of the binding affinity and the drug residence time should be emphasized in rational drug design to overcome the kinase resistance.     

Algorithms for efficient near-perfect phylogenetic tree reconstruction in theory and practice

We consider the problem of reconstructing near-perfect phylogenetic trees using binary character states (referred to as BNPP). A perfect phylogeny assumes that every character mutates at most once in the evolutionary tree, yielding an algorithm for binary character states that is computationally efficient but not robust to imperfections in real data. A near-perfect phylogeny relaxes the perfect phylogeny assumption by allowing at most a constant number of additional mutations. We develop two algorithms for constructing optimal near-perfect phylogenies and provide empirical evidence of their performance. The first simple algorithm is fixed parameter tractable when the number of additional mutations and the number of characters that share four gametes with some other character are constants. The second, more involved algorithm for the problem is fixed parameter tractable when only the number of additional mutations is fixed. We have implemented both algorithms and shown them to be extremely efficient in practice on biologically significant data sets. This work proves the BNPP problem fixed parameter tractable and provides the first practical phylogenetic tree reconstruction algorithms that find guaranteed optimal solutions while being easily implemented and computationally feasible for data sets of biologically meaningful size and complexity.