Mixed immunotherapy and chemotherapy of tumors: feedback design and model updating schemes

In this paper, a recently developed model governing the cancer growth on a cell population level with combination of immune and chemotherapy is used to develop a reactive (feedback) mixed treatment strategy. The feedback design proposed here is based on nonlinear constrained model predictive control together with an adaptation scheme that enables the effects of unavoidable modeling uncertainties to be compensated. The effectiveness of the proposed strategy is shown under realistic human data showing the advantage of treatment in feedback form as well as the relevance of the adaptation strategy in handling uncertainties and modeling errors. A new treatment strategy defined by an original optimal control problem formulation is also proposed. This new formulation shows particularly interesting possibilities since it may lead to tumor regression under better health indicator profile.     

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.     

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.     

The optimal dose of CAF regimen in adjuvant chemotherapy for breast cancer patients at stage IIB

This paper deals with the idea of balancing drug effects on tumor and normal cell populations based on a variety of criteria, which is evaluated by the oncologist for breast cancer patients at stage IIB. In this paper, the optimal controller represents the optimal drug dosage of CAF (Cyclophosphamide, Adriamycin and Fluorouracil) regimen in adjuvant chemotherapy after surgery for these patients. We determined the doses of CAF regimen by minimizing a cost function with some constraints. The cost function includes the cancer cell and the normal cell growth dynamics with prescribed weighting coefficients for each patient. The physician determines these weighting coefficients based on some individual parameters. The optimal treatment schedules are computed based on a trade-off between the cancer cell reduction and the normal cell preserving. Numerical simulations are given to illustrate the accuracy of the optimal controller.     

Fastest Time to Cancer by Loss of Tumor Suppressor Genes

Genetic instability promotes cancer progression (by increasing the probability of cancerous mutations) as well as hinders it (by imposing a higher cell death rate for cells susceptible to cancerous mutation). With the loss of tumor suppressor gene function known to be responsible for a high percentage of breast and colorectal cancer (and a good fraction of lung cancer and other types as well), it is important to understand how genetic instability can be orchestrated toward carcinogenesis. In this context, this paper gives a complete characterization of the optimal (time-varying) cell mutation rate for the fastest time to a target cancerous cell population through the loss of both copies of a tumor suppressor gene. Similar to the (one-step) oncogene activation model previously analyzed, the optimal mutation rate of the present two-step model changes qualitatively with the convexity of the (mutation rate-dependent) cell death rate. However, the structure of the Hamiltonian for the new model differs significantly and intrinsically from that of the one-step model, and a completely new approach is needed for the solution of the present two-step problem. Considerable insight into the biology of optimal switching (between corner controls) is extracted from numerical results for cases with nonconvex death rates.     

Recovery of normal hemopoiesis in disseminated cancer therapy--a model

The strategy of normal cell regeneration with recombinant hematopoietic growth factors during cancer chemotherapy is investigated by superimposing a treatment protocol on a simple model that describes an expanding malignant cell population that is coexisting with and inhibiting the population of normal cells. The model predictions suggest that the strategy of normal cell stimulation, possibly with growth factors, and possibly carried out within an intensive treatment framework may be a worthwhile chemotherapeutic option. Under this protocol, the model also predicts a minimum time interval for active treatment, a time to discontinue treatment, and a rest period during treatment in order to guarantee patient safety and recovery. Consequently, by relating and comparing model predictions to patient data, model simulations forecast that treatment could be shortened by 1-2 weeks if organized over or in the neighborhood of a predicted optimal time interval. Following this, it is conjectured that such an approach engendered by the model could produce outcomes that may have an edge over outcomes arising from therapeutic strategies that are executed over time frames that are relatively longer or significantly shorter than the predicted optimal time.     

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.     

世代重叠群体多个QTL最优化选择

一种扩展的方法能够在一个世代重叠的群体内对多个数量性状位点选择进行最优化,目的是为了在整个计划期内获得最大的累积反应加权和。该模型允许群体有多个性别年龄组、公母畜间有不同的年龄组数、各年龄组有不同的遗传贡献。整个最优化问题被描述成一个多阶段系统优化控制问题,通过一个向前和向后的迭代循环解决。用一个世代重叠的实际育种猪群的参数来评价该方法的选择效果,并和标准QTL选择和常规BLUP选择进行比较。模拟结果表明,优化选择要优于标准QTL选择和常规BLUP选择。群体结构对优化选择的影响比较明显。优化QTL选择和标准QTL选择在世代重叠的群体内比在世代离散的群体内的选择优势更明显,相对于常规BLUP选择,能够获得更大的选择优势。在世代重叠群体内随着2岁公畜遗传贡献的增大,优化选择相对于常规BLUP选择的优势越明显。     

Optimizing Selection on Multiple Identified Quantitative Trait Loci in Population with Overlapping Generations

A method was developed to model and optimize selection on multiple identified quantitative trait loci (QTLs) and polygenic estimated breeding value, in order to maximize a weighted sum of cumulative response to selection over multiple years in a population with overlapping generations. The model allows for a population with multiple sex-age classes, different number of age class between sires and dams, and varied genetic contribution of the age class. The optimization problem was formulated as a multiple-stage optimal control problem and solved by a forward and backward iteration loop. The practical utility of this method was illustrated in an example of pig breeding population with overlapping generations. The selection response of this method was compared with standard QTL selection and conventional best linear unbiased prediction (BLUP) selection. Simulation results show that optimal selection achieved greater selection response than either standard QTL or conventional BLUP selections. The influence of population structure on optimal selection was significant. Optimal QTL selection and standard QTL selection were more favorable in a population with overlapping generations than discrete generations, and obtained more benefits relative to conventional BLUP selection in a population with overlapping generations. Optimal QTL selection relative to conventional BLUP selection is also more favorable following increase of genetic contribution of two-year-old boars and sows in a population with overlapping generations.     

A Mathematical Model of Cell Cycle Effects in Gastric Cancer Chemotherapy

A mathematical model is presented to investigate the relationship between drug order and treatment response in gastric cancer chemotherapy involving a taxane (either paclitaxel or docetaxel) coupled with flavopiridol. To model treatment effects, we simulate treatment by bolus injection and employ a pulsing condition to indicate cell kill as well as instantaneous changes to the cell’s transition rates. Cell population growth is described using an ordinary differential equation model whereby we examine the treatment effects upon cells in various stages of the cell cycle. Ultimately, the results generated support prior clinical investigations which indicate that for an enhanced synergistic effect, flavopiridol must be administered following taxane therapy.     

A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease

A previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis by effector cells. The model exhibits bistability where a tumour-cell population threshold exists. A tumour with an initial cell population below the threshold can be controlled by the immune system and remains microscopic and asymptomatic called cancer without disease while that above the threshold grows to lethal size. Bifurcation analysis shows that (a) the chemotherapy-induced damage may cause a microscopic tumour, which would never grow to become lethal if untreated, to grow to lethal size, (b) applying chemotherapy alone requires a large dosage to be successful, (c) immunotherapy is ineffective, and (d) a combination of chemotherapy and immunotherapy can produce a synergistic effect on the outcome of a treatment.     

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.     

Synchronized mammalian cell culture: Part II—population ensemble modeling and analysis for development of reproducible processes

The consideration of inherent population inhomogeneities of mammalian cell cultures becomes increasingly important for systems biology study and for developing more stable and efficient processes. However, variations of cellular properties belonging to different sub‐populations and their potential effects on cellular physiology and kinetics of culture productivity under bioproduction conditions have not yet been much in the focus of research. Culture heterogeneity is strongly determined by the advance of the cell cycle. The assignment of cell‐cycle specific cellular variations to large‐scale process conditions can be optimally determined based on the combination of (partially) synchronized cultivation under otherwise physiological conditions and subsequent population‐resolved model adaptation. The first step has been achieved using the physical selection method of countercurrent flow centrifugal elutriation, recently established in our group for different mammalian cell lines which is presented in Part I of this paper series. In this second part, we demonstrate the successful adaptation and application of a cell‐cycle dependent population balance ensemble model to describe and understand synchronized bioreactor cultivations performed with two model mammalian cell lines, AGE1.HN_AAT and CHO‐K1. Numerical adaptation of the model to experimental data allows for detection of phase‐specific parameters and for determination of significant variations between different phases and different cell lines. It shows that special care must be taken with regard to the sampling frequency in such oscillation cultures to minimize phase shift (jitter) artifacts. Based on predictions of long‐term oscillation behavior of a culture depending on its start conditions, optimal elutriation setup trade‐offs between high cell yields and high synchronization efficiency are proposed. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:175–185, 2015     

Variable responsiveness of hormone-inducible hybrid genes in different cell lines

Altered steroid responsiveness leads to various pathological conditions and is a particular problem for the treatment of cancers arising in steroid-sensitive cells. To develop cellular model systems for the analysis of the molecular mechanisms mediating altered steroid responses, we have analyzed the inducibility of a steroid-responsive promoter in different cell lines. In vitro constructs containing the mouse mammary tumor virus promoter fused to the herpes simplex virus thymidine kinase gene or the bacterial neo gene were transfected into four different cell lines [Rat-2, CHO chinese hamster ovary cells, F9, and T47D). Thymidine kinase+ clones and neo-resistant clones were selected in the presence of dexamethasone (dex) and/or other steroid hormones. We find that the mouse mammary tumor virus promoter activity is completely dependent on the presence of dex in Rat-2 cells but is constitutively active in CHO cells and is inactive in F9 teratocarcinoma cells in the presence and absence of dex. In the human breast cancer cell line T47D, we observe no response to dex but do observe an inducibility by progesterone. Examination of glucocorticoid receptors in these cell lines showed that Rat-2, CHO, and F9 cells contain sufficient receptors to allow a hormonal response, whereas in T47D cells several glucocorticoid binding activities appear to be present. Our results indicate that the presence of receptor in cells is not always sufficient to allow hormonal activation and that, in some cell lines, like CHO, other factors are present that can substitute for an activated steroid hormone receptor complex.(ABSTRACT TRUNCATED AT 250 WORDS)     

Role of optimal control theory in cancer chemotherapy

This paper presents a review of the ways in which optimal control theory interacts with cancer chemotherapy. There are three broad areas of investigation. One involves miscellaneous growth kinetic models, the second involves cell cycle models, and the third is a classification of "other models." Both normal and tumor cell populations are included in a number of the models. The concepts of deterministic optimal control theory are applied to each model in such a way as to present a cohesive picture. There are applications to both experimental and clinical tumors. Suggestions for designing better chemotherapy strategies are presented.     

Implications of a simple mathematical model to cancer cell population dynamics

Recent research in cancer progression and treatment indicates that many forms of cancer arise from the development of a small subpopulation of abnormal cancer stem cells (CSCs) that promote cancer growth and spread. Many potential treatments preferentially interact with cells at certain stages of the cell cycle by either selective killing or halting the cell cycle, such as intense, nanosecond-duration pulsed electric fields (nsPEFs). Simple mathematical models of unfed cancer cell populations at the plateau of their growth characteristics may estimate the long-term consequences of these treatments on proliferating and quiescent cell populations. Applying such a model with no transition from the quiescent to proliferating state shows that it is possible for the proliferating cell population to fall below 1 if the quiescent cell population obtains a sufficient competitive advantage with respect to nutrient consumption and/or survival rate. Introducing small, realistic transition rates did not appreciably alter short-term or long-term population behaviour, indicating that the predicted small cell population behaviour (< 1 cell) is not an artefact of the simpler model. Experimental observations of nsPEF-induced effects on the cell cycle suggest that such a model may serve as a first step in assessing the viability of a given cancer treatment in vitro prior to clinical application.     

Addition of Valproic Acid to CHO Cell Fed-Batch Cultures Improves Monoclonal Antibody Titers

Improving the productivity of a biopharmaceutical Chinese hamster ovary (CHO) fed-batch cell culture can enable cost savings and more efficient manufacturing capacity utilization. One method for increasing CHO cell productivity is the addition of histone deacetylase (HDAC) inhibitors to the cell culture process. In this study, we examined the effect of valproic acid (VPA, 2-propylpentanoic acid), a branched-chain carboxylic acid HDAC inhibitor, on the productivity of three of our CHO cell lines that stably express monoclonal antibodies. Fed-batch shake flask VPA titrations on the three different CHO cell lines yielded cell line-specific results. Cell line A responded highly positively, cell line B responded mildly positively, and cell line C did not respond. We then performed factorial experiments to identify the optimal VPA concentration and day of addition for cell line A. After identifying the optimal conditions for cell line A, we performed verification experiments in fed-batch bioreactors for cell lines A and B. These experiments confirmed that a high dose of VPA late in the culture can increase harvest titer >20 % without greatly changing antibody aggregation, charge heterogeneity, and N-linked glycosylation profiles. Our results suggest that VPA is an attractive and viable small molecule enhancer of protein production for biopharmaceutical CHO cell culture processes.