Modeling and Dose Schedule Design for Cycle-Specific Chemotherapeutics

Model-based optimal control has been used to synthesize chemotherapy treatment schedules. Constraints on drug delivery or states are used to maintain drug administration within toxicity limits, and the objective function usually minimizes the tumor volume at a prespecified final time. These solutions predict a characteristic 3-phase treatment profile: maximum initial drug delivery; a non-dosing period; and the remainder of the drug delivered at the end of the treatment window. Ethically, however, a doctor cannot allow a tumor to grow untreated, thereby invalidating the controller formulation. Dose schedule development, therefore, requires an alternative formulation to obtain clinically relevant dosing schedules. Dose schedule design for the therapeutic tamoxifen (TM) was investigated using nonlinear model predictive control (NMPC) and a tumor regressionreference trajectory. Performance was dependent on accurate incorporation of the pharmacodynamic (PD) effect, and the desired trajectory was tracked. The techniques evaluated could be adapted to other therapeutics administered over regular intervals, though alterations to the objective function would be necessary forclinical implementation.More detailed cell-level tumor growth models were investigated using population balance equations.Individual cell cycle states were included within the model, as were saturating growth rates representative of Gompertzian growth seen from solid tumors. Open-loop simulations involving two cycle specific therapeutics (S- and M-phase active) questioned the simultaneous adminstration of therapeutics which predicted the largest final tumor volumes. These results require additional investigation, as does the accuracy of the bilinear PD effect structure.A physiologically-based pharmacokinetic (PBPK) model for docetaxel (Doc) disposition in SCID mice was developed based on collected plasma, tumor, and tissue concentration data. This model was scaled to humans and compared against patient Doc plasma data from several clinical trials as well as Doc plasma predictions from other models in the literature. A low-order neutrophil model from the literature was tailored to patient neutrophil samples from the clinical study. The human-scaled PBPK Doc and neutrophil PD models were combined and used to evaluate Doc regimens from the literature. Finally, a nonlinear model predictive controller (NMPC) was synthesized based on the PBPK and PD models and used to develop clinically-relevant dosing regimens under PD constraints

Optimal Dosing of Breast Cancer Chemotherapy Using Robust MPC Based on Linear Matrix Inequalities

In this paper, we consider an application of robust model predictive control to optimal dosing of breast cancer chemotherapy. The model-patient mismatch is handled by computing an ellipsoidal invariant set containing the measured patient's states at each sampling time. An optimal dose of chemotherapeutic agent is obtained by solving a convex optimization problem subject to linear matrix inequalities. In the case study of simulated patients, the results show that the tumor volume can be reduced to a specified target with up to 30% model-patient mismatch. Moreover, the robust model predictive control algorithm can achieve better treatment results as compared with the nonlinear model predictive control algorithm while the on-line computational time is significantly reduced

Model--Based Design of Cancer Chemotherapy Treatment Schedules

Cancer is the name given to a class of diseases characterized by an imbalance in cell proliferation and apoptosis, or programmed cell death. Once cancer has reached detectable sizes ($10^{6}$ cells or 1 mm$^3$), it is assumed to have spread throughout the body, and a systemic form of treatment is needed. Chemotherapy treatment is commonly used, and it effects both healthy and diseased tissue. This creates a dichotomy for clinicians who need develop treatment schedules which balance toxic side effects with treatment efficacy. Nominally, the optimal treatment schedule --- where schedule is defined as the amount and frequency of drug delivered --- is the one found to be the most efficacious from the set evaluated during clinical trials. In this work, a model based approach for developing drug treatment schedules was developed. Cancer chemotherapy modeling is typically segregated into drug pharmacokinetics (PK), describing drug distribution throughout an organism, and pharmacodynamics (PD), which delineates cellular proliferation, and drug effects on the organism. This work considers two case studies: (i) a preclinical study of the oral administration of the antitumor agent 9-nitrocamptothecin (9NC) to severe combined immunodeficient (SCID) mice bearing subcutaneously implanted HT29 human colon xenografts; and (ii) a theoretical study of intravenous chemotherapy from the engineering literature.Metabolism of 9NC yields the active metabolite 9-aminocamptothecin (9AC). Both 9NC and 9AC exist in active lactone and inactive carboxylate forms. Four different PK model structures are presented to describe the plasma disposition of 9NC and 9AC: three linear models at a single dose level (0.67 mg/kg 9NC); and a nonlinear model for the dosing range 0.44 -- 1.0 mg/kg 9NC. Untreated tumor growth was modeled using two approaches: (i) exponential growth; and (ii) a switched exponential model transitioning between two different rates of exponential growth at a critical size. All of the PK/PD models considered here have bilinear kill terms which decrease tumor sizes at rates proportional to the effective drug concentration and the current tumor size. The PK/PD model combining the best linear PK model with exponential tumor growth accurately characterized tumor responses in ten experimental mice administered 0.67 mg/kg of 9NC myschedule (Monday-Friday for two weeks repeated every four weeks). The nonlinear PK model of 9NC coupled to the switched exponential PD model accurately captured the tumor response data at multiple dose levels. Each dosing problem was formulated as a mixed--integer linear programming problem (MILP), which guarantees globally optimal solutions. When minimizing the tumor volume at a specified final time, the MILP algorithm delivered as much drug as possible at the end of the treatment window (up to the cumulative toxicity constraint). While numerically optimal, it was found that an exponentially growing tumor, with bilinear kill driven by linear PK would experience the same decrease in tumor volume at a final time regardless of when the drug was administered as long as the {it same amount} was administered. An alternate objective function was selected to minimize tumor volume along a trajectory. This is more clinically relevant in that it better represents the objective of the clinician (eliminate the diseased tissue as rapidly as possible). This resulted in a treatment schedule which eliminated the tumor burden more rapidly, and this schedule can be evaluated recursively at the end of each cycle for efficacy and toxicity, as per current clinical practice.The second case study consists of an intravenously administered drug with first order elimination treating a tumor under Gompertzian growth. This system was also formulated as a MILP, and the two different objectives above were considered. The first objective was minimizing the tumor volume at a final time --- the objective the original authors considered. The MILP solution was qualitatively similar to the solutions originally found using control vector parameterization techniques. This solution also attempted to administer as much drug as possible at the end of the treatment interval. The problem was then posed as a receding horizon trajectory tracking problem. Once again, a more clinically relevant objective returned promising results; the tumor burden was rapidly eliminated

A model-based clinically-relevant chemotherapy scheduling algorithm for anticancer agents

Chemotherapy is the most commonly employed method for systemic cancer treatment of solid tumors and their metastases. The balance between cancer cell elimination and host toxicity minimization remains a challenge for clinicians when deploying chemotherapy treatments. Our approach explicitly incorporates treatment-induced toxicities into the schedule design. As a case study, we synthesize administration schedules for docetaxel, a widely used chemotherapeutic employed as a monoagent or in combination for the treatment of a variety of cancers. The primary adverse effect of docetaxel treatment is myelosuppression, characterized by neutropenia, a low plasma absolute neutrophil count (ANC). Through the use of model-based systems engineering tools, this thesis provides treatment schedules for docetaxel and its combination therapies that reduce toxic side effects and improve patient outcomes. The current algorithm employs models of tumor growth, drug pharmacokinetics, and pharmacodynamics for both anticancer effects and toxicity, as characterized by ANC. Also included is a toxicity-rescue therapy, with granulocyte colony stimulating factor (G-CSF) that serves to elevate ANC. The single-agent docetaxel chemotherapy schedule minimizes tumor volume over a multi-cycle horizon, subject to toxicity and logistical constraints imposed by clinical practice.This single-agent chemotherapy scheduling formulation is extended to combination chemotherapy using docetaxel-cisplatin or docetaxel-carboplatin drug pairs. The two platinum agents display different toxicities, with cisplatin exhibiting kidney function damage and carboplatin demonstrating the same myelosuppression effects as docetaxel. These case studies provide two different challenges to the algorithm: (i) cisplatin scheduling significantly increases the number of variables and constraints, thereby challenging the computational engine and formulation; (ii) carboplatin's overlapping toxicity tests the ability of the algorithm to schedule drugs with different mechanisms of action (they act in different phases of the cellular growth cycle) with the same toxic side effects. The simulated results demonstrate the algorithms flexibility, in scheduling both docetaxel and cisplatin or carboplatin treatments for effective tumor elimination and clinically acceptable toxicties. Overall, a clinically-relevant chemotherapy scheduling optimization algorithm is provided for designing single agent and combination chemotherapies, when toxicity and pharmacokinetic/pharmacodynamic information is available. Furthermore, the algorithm can be extended to patient-specfic treatment by updating the pharmacokinetic/pharmacodynamic models as data are collected during treatment

Readings in Advanced Pharmacokinetics

This book, “Readings in Advanced Pharmacokinetics - Theory, Methods and Applications”, covers up to date information and practical topics related to the study of drug pharmacokinetics in humans and in animals. The book is designed to offer scientists, clinicians and researchers a choice to logically build their knowledge in pharmacokinetics from basic concepts to advanced applications. This book is organized into two sections. The first section discusses advanced theories that include a wide range of topics; from bioequivalence studies, pharmacogenomics in relation to pharmacokinetics, computer based simulation concepts to drug interactions of herbal medicines and veterinary pharmacokinetics. The second section advances theory to practice offering several examples of methods and applications in advanced pharmacokinetics

Pharmacokinetic Scaling of Anticancer Drugs in Dogs

Anticancer drugs are characterized by a narrow therapeutic index and wide inter-individual variability in therapeutic outcome, disposition, and toxicity. The accurate calculation and administration of anticancer drugs from the initiation of treatment is necessary to attain a good therapeutic outcome. Currently, the doses of anticancer drugs are calculated based on the body surface area approach, which requires prior dose escalation studies to establish the maximum tolerated dose. In addition, several studies have questioned the ability of standard dosing methods to adequately normalize drug exposure for several anticancer drugs. As with most drugs, the efficacy of anticancer drugs correlates best with total drug exposure, or the area under the plasma concentration versus time curve. If the clearance of a drug is accurately known, then the dose required to produce a desired total drug exposure can be calculated accordingly. Therefore, it is important to understand the factors that influence the clearance of aVeterinary Pathobiolog

The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study

Mathematical models are increasingly proposed to describe tumor’s dynamic response to treatments with the aims of improving their efficacy. The most widely used are nonlinear ODE models, whose identification is often difficult due to experimental limitations. We focus on the issue of parameter estimation in model-based oncological studies. Given their complexity, many of these models are unidentifiable having an infinite number of parameter solutions. These equivalently describe experimental data but are associated with different dynamic evolution of unmeasurable variables. We propose a joint use of two different identifiability methodologies, structural identifiability and practical identifiability, which are traditionally regarded as disjoint. This new methodology provides the number of parameter solutions, the analytic relations between the unidentifiable parameters useful to reduce model complexity, a ranking between parameters revealing the most reliable estimates, and a way to disentangle the various causes of nonidentifiability. It is implementable by using available differential algebra software and statistical packages. This methodology can constitute a powerful tool for the oncologist to discover the behavior of inaccessible variables of clinical interest and to correctly address the experimental design. A complex model to study “in vivo” antitumor activity of interleukin-21 on tumor eradication in different cancers in mice is illustrated

Quantitative approaches in support of the early development of T-cell redirecting therapies

T-cell redirecting therapies such as CD3-bispecific antibodies and CAR-T cells are promising assets in our fight against cancer. By redirecting T-cells towards tumour cells, these therapies induce efficient eradication of tumours. Many questions remain regarding their efficacy and safety in patients. The success of a drug candidate starts with nonclinical investigations before going into patients. This work focused on developing tools to improve the translatability of nonclinical research of T-cell redirecting therapies. In this work, a mechanistic in silico model was developed that integrates an in vitro dataset of the pharmacology of cibisatamab, a CD3-bispecific antibody. The model may serve as a tool in early development to explore and quantify the impact of target expression densities on the pharmacology of CD3-bispecifics. Also, this work proposed the collection of data over multiple time points and designed a new experimental setup and analysis that allows assessing the pharmacology in an unbiased and time-independent manner. As such, the kinetics of experimental readouts can be considered to make informed decisions about the development of the compound and assist in dose selection. Lastly, the work presents a fresh look on cytokine release syndrome and identifies drug-target disease related factors and individual risk factors as the root cause of CRS. It postulates a combination of mechanistic modelling with real world data to enable individualized risk assessment.Gerichtete T-Zell-Therapien sind ein vielversprechendes Mittel im Kampf gegen Krebs. Bei dieser Therapie werden T-Zellen auf Tumorzellen gerichtet, was zu einer hocheffizienten Abtötung des Tumors führt. Es bleiben viele Fragen bezüglich ihrer Wirksamkeit und Sicherheit offen. Der Erfolg eines Arzneimittels beginnt mit nichtklinischen Untersuchungen. Diese Dissertation konzentrierte sich auf die Entwicklung Instrumente zur Verbesserung der nichtklinischen Forschung von gerichtete T-Zell-Therapien. In dieser Dissertation wurde ein mechanistisches In-silico-Modell entwickelt, das einen in-vitro-Datensatz zur Pharmakologie von cibisatamab integriert. Das Modell kann als Werkzeug in der Entwicklung dienen, um die Auswirkungen der Targetdichten auf die Pharmakologie von CD3-bispezifischen Antikörpern zu quantifizieren. In dieser Dissertation wurde auch ein neuer Versuchsaufbau und Analyse entwickelt, die eine unverzerrte und zeitunabhängige Bewertung der pharmakologischen Aktivität ermöglicht. Auf diese Weise kann die Kinetik der Messwerte berücksichtigt werden. Dies ist von Bedeutung, um fundierte Entscheidungen über die Entwicklung der Wirkstoffe und die Dosisauswahl zu treffen. Schließlich wirft die Arbeit einen Blick auf das Cytokine Release Syndrome und identifiziert Risikofaktoren als Ursache für CRS und empfiehlt eine Kombination von Modellierung und real-world Daten zur Ermöglichung einer individuellen CRS Risikobewertung bei der Behandlung mit gerichteten T-Zell-Therapien

Characterization and informed design of downregulating anti-epidermal growth factor receptor antibodies

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Biological Engineering, 2011.Cataloged from PDF version of thesis. Vita.Includes bibliographical references.Due to its common dysregulation in epithelial-based cancers and the extensive characterization of its role in tumor growth, epidermal growth factor receptor (EGFR) has long been an attractive target for monoclonal antibodies. Intense research has culminated in the approval of two antibody-based drugs against EGFR for cancer treatment, with numerous others in clinical trials. However, therapeutic efficacy of these drugs has been disappointingly low due to autocrine signaling, receptor mutation, and transport limitations, necessitating novel antibody designs and mechanisms of action. Recently, it was reported that treatment with combinations of antibodies can induce receptor clustering, leading to synergistic receptor downregulation and anti-tumor activity. The aim of this thesis is to elucidate the details of this phenomenon and to exploit this mechanism to design more effective therapeutic antibodies targeting EGFR. We first illuminate several key aspects of combination antibody-induced clustering. By screening a panel of pairwise combinations, we show that the most potently downregulating pairs consist of two non-competitive antibodies that target EGFR extracellular domain 3. We further find the mechanism underlying downregulation to be consistent with recycling inhibition. Lastly, in contrast to the agonism associated with ligand-induced downregulation, we demonstrate that combination mAb-induced downregulation does not activate EGFR or its downstream effectors and it leads to synergistic reduction in migration and proliferation of cells that secrete autocrine ligand. To enhance antibody binding and induced receptor clustering, we design multispecific antibodybased constructs that engage up to four distinct epitopes on EGFR. We engineer two classes of constructs: one consisting of a full EGFR-specific antibody fused to the variable domain of a second anti-EGFR antibody and the other consisting of a full EGFR-specific antibody fused to one or more EGFR-targeted tenth type three domains of human fibronectin. Both classes of constructs induce robust receptor clustering and downregulation in the absence of signal activation. In vitro downregulation correlates well with in vivo inhibition of tumor growth in several mouse xenograft tumor models and mutational analysis demonstrates that the efficacy of our fusions is attributable to both signaling effects and antibody-dependent cell-mediated cytotoxicity. Our multi-epitopic strategy may be readily applied to other receptor systems to form the basis for a new category of antibody-based therapeutics.by Jamie Berta Spangler.Ph.D

Improving the use of G-CSF during chemotherapy using physiological mathematical modelling : a quantitative systems pharmacology approach

La diminution des doses administrées ou même la cessation complète d'un traitement chimiothérapeutique est souvent la conséquence de la réduction du nombre de neutrophiles, qui sont les globules blancs les plus fréquents dans le sang. Cette réduction dans le nombre absolu des neutrophiles, aussi connue sous le nom de myélosuppression, est précipitée par les effets létaux non spécifiques des médicaments anti-cancéreux, qui, parallèlement à leur effet thérapeutique, produisent aussi des effets toxiques sur les cellules saines. Dans le but d'atténuer cet impact myélosuppresseur, on administre aux patients un facteur de stimulation des colonies de granulocytes recombinant humain (rhG-CSF), une forme exogène du G-CSF, l'hormone responsable de la stimulation de la production des neutrophiles et de leurs libération dans la circulation sanguine. Bien que les bienfaits d'un traitement prophylactique avec le G-CSF pendant la chimiothérapie soient bien établis, les protocoles d'administration demeurent mal définis et sont fréquemment déterminés ad libitum par les cliniciens. Avec l'optique d'améliorer le dosage thérapeutique et rationaliser l'utilisation du rhG-CSF pendant le traitement chimiothérapeutique, nous avons développé un modèle physiologique du processus de granulopoïèse, qui incorpore les connaissances actuelles de pointe relatives à la production des neutrophiles des cellules souches hématopoïétiques dans la moelle osseuse. À ce modèle physiologique, nous avons intégré des modèles pharmacocinétiques/pharmacodynamiques (PK/PD) de deux médicaments: le PM00104 (Zalypsis®), un médicament anti-cancéreux, et le rhG-CSF (filgrastim). En se servant des principes fondamentaux sous-jacents à la physiologie, nous avons estimé les paramètres de manière exhaustive sans devoir recourir à l'ajustement des données, ce qui nous a permis de prédire des données cliniques provenant de 172 patients soumis au protocol CHOP14 (6 cycles de chimiothérapie avec une période de 14 jours où l'administration du rhG-CSF se fait du jour 4 au jour 13 post-chimiothérapie). En utilisant ce modèle physio-PK/PD, nous avons démontré que le nombre d'administrations du rhG-CSF pourrait être réduit de dix (pratique actuelle) à quatre ou même trois administrations, à condition de retarder le début du traitement prophylactique par le rhG-CSF. Dans un souci d'applicabilité clinique de notre approche de modélisation, nous avons investigué l'impact de la variabilité PK présente dans une population de patients, sur les prédictions du modèle, en intégrant des modèles PK de population (Pop-PK) des deux médicaments. En considérant des cohortes de 500 patients in silico pour chacun des cinq scénarios de variabilité plausibles et en utilisant trois marqueurs cliniques, soient le temps au nadir des neutrophiles, la valeur du nadir, ainsi que l'aire sous la courbe concentration-effet, nous avons établi qu'il n'y avait aucune différence significative dans les prédictions du modèle entre le patient-type et la population. Ceci démontre la robustesse de l'approche que nous avons développée et qui s'apparente à une approche de pharmacologie quantitative des systèmes (QSP). Motivés par l'utilisation du rhG-CSF dans le traitement d'autres maladies, comme des pathologies périodiques telles que la neutropénie cyclique, nous avons ensuite soumis l'étude du modèle au contexte des maladies dynamiques. En mettant en évidence la non validité du paradigme de la rétroaction des cytokines pour l'administration exogène des mimétiques du G-CSF, nous avons développé un modèle physiologique PK/PD novateur comprenant les concentrations libres et liées du G-CSF. Ce nouveau modèle PK a aussi nécessité des changements dans le modèle PD puisqu’il nous a permis de retracer les concentrations du G-CSF lié aux neutrophiles. Nous avons démontré que l'hypothèse sous-jacente de l'équilibre entre la concentration libre et liée, selon la loi d'action de masse, n'est plus valide pour le G-CSF aux concentrations endogènes et mènerait en fait à la surestimation de la clairance rénale du médicament. En procédant ainsi, nous avons réussi à reproduire des données cliniques obtenues dans diverses conditions (l'administration exogène du G-CSF, l'administration du PM00104, CHOP14). Nous avons aussi fourni une explication logique des mécanismes responsables de la réponse physiologique aux deux médicaments. Finalement, afin de mettre en exergue l’approche intégrative en pharmacologie adoptée dans cette thèse, nous avons démontré sa valeur inestimable pour la mise en lumière et la reconstruction des systèmes vivants complexes, en faisant le parallèle avec d’autres disciplines scientifiques telles que la paléontologie et la forensique, où une approche semblable a largement fait ses preuves. Nous avons aussi discuté du potentiel de la pharmacologie quantitative des systèmes appliquées au développement du médicament et à la médecine translationnelle, en se servant du modèle physio-PK/PD que nous avons mis au point.Dose-limitation or interruption of chemotherapeutic treatment is most often prompted by a decrease in circulating neutrophils, the most abundant white blood cell in the human body. Myelosuppression, or a reduction in absolute neutrophil counts (ANCs) by anti-cancer treatments, is precipitated by the nonspecific killing effect of chemotherapeutic drugs which have toxic effects on noncancerous cells. To mitigate this myelosuppressive effect, patients are frequently administered recombinant human granulocyte colony-stimulating factor (rhG-CSF), an exogenous form of the cytokine G-CSF, which stimulates neutrophil production and release into the blood stream. While the benefits of adjuvant treatment rhG-CSF during chemotherapy are well recognised, the protocols with which it is administered are not well defined and are frequently determined ad libitum by clinicians. To quantify and address the optimisation of the administration of rhG-CSF during chemotherapeutic treatment, we developed a physiological model of granulopoiesis which incorporates the contemporary understanding of the production of neutrophils from the hematopoietic stem cells in the bone marrow. To this physiological model, we incorporated mechanistic pharmacokinetic/pharmacodynamic (PK/PD) models of two drugs, PM00104 (Zalypsis), a chemotherapeutic drug, and rhG-CSF (filgrastim). Through exhaustive parameter estimation using first principles and no data fitting, we successfully predicted clinical data from 172 patients for an average patient undergoing the CHOP14 protocol (6 cycles of 14-day periodic chemotherapy with rhG-CSF administered on days 4-13 post-chemotherapy). We then demonstrated that delaying the administration of rhG-CSF to 6 or 7 days post-chemotherapy allowed for a reduction in the number of filgrastim administrations from ten to four or even three while maintaining or improving the neutrophil nadir. We also investigated the effects of PK variability on the model's predictions by incorporating population PK (PopPK) models of both drugs. Using five different variability scenarios and cohorts of 500 in silico patients per scenario, we established that there are no statistically significant differences between a typical patient and the population in the model's predictions with respect to three crucial clinical endpoints, namely the time to ANC nadir, the ANC nadir, and the area under the concentration-effect curve. The model's robustness to PK variability allows for the scaling up from the individual to population level. Motivated by the use of rhG-CSF in other disease-states, namely periodic pathologies like cyclical neutropenia, we next endeavoured to contextualise the model within dynamic diseases. By bringing to light that the cytokine paradigm is broken when exogenous cytokine mimetics are administered, we developed a novel physiological PK model for G-CSF incorporating both unbound and bound concentrations. The updated PK model prompted changes to the PD model since we could now track the concentrations of bound G-CSF. We showed that the mass-action equilibrium hypopthesis for bound and unbound drugs is not valid and led to overestimations of the renal clearance of G-CSF. We also successfully reproduced clinical data in a variety of settings (exogenous G-CSF alone, PM00104 alone, CHOP14 protocol) and clarified the mechanisms underlying the body's response to both drugs. Lastly, we discussed the potential of quantitative systems pharmacology in both drug development and translational medicine by using the physiological PK/PD model we developed