Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations
2020
A systems pharmacology model to improve clinical outcomes in non-small cell lung cancer
Benjamin Karl Schneider Iowa State University
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Recommended Citation Schneider, Benjamin Karl, "A systems pharmacology model to improve clinical outcomes in non-small cell lung cancer" (2020). Graduate Theses and Dissertations. 18397. https://lib.dr.iastate.edu/etd/18397
This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. A systems pharmacology model to improve clinical outcomes in non-small cell lung cancer
by
Benjamin Karl Schneider
A dissertation submitted to the graduate faculty
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
Major: Biomedical Sciences – Pharmacology
Program of Study Committee: Jonathan Paul M Mochel, Major Professor Sébastien Benzekry Amy G Froelich Joshua Ryan Beck Karin Allenspach-Jorn
The student author, whose presentation of the scholarship herein was approved by the program of study committee, is solely responsible for the content of this dissertation. The Graduate College will ensure this dissertation is globally accessible and will not permit alterations after a degree is conferred.
Iowa State University
Ames, Iowa
2020
Copyright © Benjamin Karl Schneider, 2020. All rights reserved. ii
DEDICATION
Robin Schneider, abruptly missing and forever missed (11/19/1955 – 5/22/2000).
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TABLE OF CONTENTS
Page
LIST OF FIGURES...... vi
LIST OF TABLES ...... viii
NOMENCLATURE ...... ix
ABSTRACT ...... x
CHAPTER 1. GENERAL INTRODUCTION ...... 1 References ...... 7
CHAPTER 2. MODEL-BASED REVERSE TRANSLATION BETWEEN VETERINARY AND HUMAN MEDICINE: THE ONE HEALTH INITIATIVE ...... 9 Abstract ...... 9 Improving the Predictability of Animal Models Used in Preclinical Research ...... 9 One Health and Comparative Medicine to Support Drug R&D ...... 11 Cancer Research ...... 11 Inflammatory Bowel Disease ...... 13 Congestive Heart Failure ...... 13 Opening the “Black Box” of Complex Biological Networks...... 14 Conclusion ...... 15 Acknowledgments ...... 16 Conflicts of Interest ...... 16 Author Contributions ...... 16 Tables and Figures ...... 16 References ...... 18
CHAPTER 3. IN VITRO CYTOTOXICITY AND PHARMACOKINETIC EVALUATION OF PHARMACOLOGICAL ASCORBATE IN DOGS ...... 20 Abstract ...... 20 Introduction ...... 21 Methods ...... 23 Experimental Animals ...... 23 Ascorbate Administration...... 24 Plasma Ascorbate Sample Preparation and Analysis ...... 24 Pharmacokinetic Modeling ...... 26 In Vitro Ascorbate Analysis – Cell Lines and Reagents ...... 27 In Vitro Ascorbate Analysis – Clonogenic Survival Assay ...... 28 In Vitro Ascorbate Analysis – B1 Feeder Layer Cells ...... 29 Statistical Analysis ...... 30 Results ...... 30 Safety ...... 30 Clonogenic Assay ...... 32 iv
Discussion ...... 33 Data Availability Statement ...... 40 Ethics Statement ...... 40 Conflict of Interest ...... 41 Author Contributions ...... 41 Funding ...... 41 Tables and Figures ...... 42 References ...... 46
CHAPTER 4. OPTIMAL SCHEDULING OF BEVACIZUMAB AND PEMETREXED/CISPLATIN DOSING IN NON‐SMALL CELL LUNG CANCER ...... 53 Abstract ...... 53 Introduction ...... 54 Methods ...... 56 Experimental Procedure ...... 56 PK/PD Structural Model Building and Evaluation ...... 57 Simulations ...... 59 Quality Assessment ...... 60 Results ...... 60 Error Model ...... 60 PKPD Structural Model Building ...... 61 Simulations ...... 63 Discussion ...... 64 Acknowledgements ...... 68 Conflicts of Interest ...... 68 Author Contributions ...... 68 Supplementary Methods ...... 68 Simulation Details ...... 68 Further Justification and Limitations of Scaling Procedure ...... 70 Tables and Figures ...... 73 References ...... 82 Supplementary ...... 87
CHAPTER 5. COMPREHENSIVE JOINT MODELING OF FIRST-LINE THERAPEUTICS IN NON-SMALL CELL LUNG CANCER ...... 89 Abstract ...... 89 Reference Nomenclature and Abbreviations for Equations ...... 90 Introduction ...... 91 Methods ...... 95 Literature Search and Review ...... 95 Data Processing and Collation ...... 96 Non-Linear Mixed Effects Modeling and Characterizing Individual Variation ...... 97 Model Building ...... 98 Model Evaluation ...... 100 Clinical Trial Simulations ...... 101 Study Details ...... 101 Results ...... 106 v
Data Summary ...... 106 PKPD Model Building ...... 108 Model Diagnostics ...... 112 Clinical Trial Simulations ...... 113 Discussion ...... 114 Tables and Figures ...... 117 References ...... 127
CHAPTER 6. GENERAL CONCLUSION ...... 130 Perspectives and Next Steps ...... 133 vi
LIST OF FIGURES
Page
Figure 2.1 Translational vs. Reverse Translational Sciences ...... 18
Figure 3.1 In Vivo Pharmacokinetics of Two Doses of Pharmacological Ascorbate in Eight Healthy Beagle Dogs ...... 43
Figure 3.2 Pharmacokinetic Schematic Representation of the Two-Compartment Model Developed in this Study ...... 44
Figure 3.3 Individual Predicted Concentration of Ascorbate in Plasma ...... 44
Figure 3.4 Prediction of Ascorbate Distribution ...... 45
Figure 3.5 Pharmacological Ascorbate Treatment Results in Selective Clonogenic Cell Death in Canine Osteosarcoma Cell Lines ...... 45
Figure 3.S1 Assessment of Quality of Model Fit ...... 46
Figure 4.1 Structural Model Diagram ...... 76
Figure 4.2 Standard Goodness-of-Fit Diagnostic Plots...... 76
Figure 4.3 Sample of Individual Fits ...... 77
Figure 4.4 Combined and Stratified Visual Predictive Checks ...... 77
Figure 4.5 Human Pharmacodynamic and Pharmacodynamic Simulations Summary ...... 78
Figure 4.S1 Comparison of Error Models ...... 79
Figure 4.S2 Correlation Between Parameter Estimates ...... 80
Figure 4.S3 SAEM Convergence Diagnosis ...... 80
Figure 4.S4 Simulated Tumor Growth and Response – Mouse Model ...... 81
Figure 4.S5 Simulated Tumor Growth and Response – Humans ...... 82
Figure 5.1 Model Diagram ...... 120
Figure 5.2 SAEM Search ...... 121
Figure 5.3 Sample of Individual Fits ...... 121 vii
Figure 5.4 Observations vs. Predictions by Patients Receiving Therapeutic ...... 122
Figure 5.5 Visual Predictive Check ...... 123
Figure 5.6 Summary of Simulation Outcomes with Box and Whiskers Plots 1 ...... 124
Figure 5.7 Summary of Simulation Outcomes with Box and Wiskers Plots 2 ...... 125
Figure 5.8 A Pair of Illustrative Examples ...... 126 viii
LIST OF TABLES
Page
Table 2.S1 Examples of Diseases that Have Clinical Analogs in Dogs ...... 16
Table 3.1 Arterial Blood Gas and Electrolyte Abnormalities Observed in 8 Beagle Dogs After Receiving Pharmacological Ascorbate (2200 mg/kg) ...... 42
Table 3.2 Model Pharmacokinetic Parameter Estimates as Determined by the Stochastic Approximation Expectation-Maximization Algorithm ...... 42
Table 3.3 Noncompartmental Analysis Pharmacokinetic Parameters ...... 43
Table 4.1 PD Model Parameters for Tumor Proliferation in NSCLC-Xenografted Mice ...... 73
Table 4.2 Parameterization for Simulations of NSCLC treated with BEV-PEM/CIS in Humans ...... 73
Table 4.S1 Administration (adm) Schedule for the Five Experimental Groups ...... 74
Table 4.S2 Administration (adm) schedule for the simulated human individual ...... 75
Table 4.S3 Pharmacokinetic parameters for pemetrexed, cisplatin, and bevacizumab in mice ...... 75
Table 5.1 Pharmacokinetic Parameters ...... 117
Table 5.2 Pharmacodynamic Parameters ...... 118
Table 5.3 Summary of Simulation Outcomes 1 ...... 119
Table 5.4 Summary of Simulation Outcomes 2 ...... 120
ix
NOMENCLATURE adm Administer, Administered, Administration,
Etc.
BIC Bayesian Information Criteria
BSA Body Surface Area
CT Combined Therapy or Combination Therapy
DNA Deoxyribonucleic acid gap Frequently Refers to Gap in Time Between
Sequential Administration of Therapeutics
IP Intraperitoneal
IIV Inter-Individual Variability
IOV Inter-Occasion Variability
IV Intravenous
NLME Nonlinear Mixed-Effects
NSCLC Non-Small Cell Lung Carcinoma
PD Pharmacodynamic(s)
PK Pharmacokinetic(s)
PKPD Pharmacokinetic-Pharmacodynamic(s)
ROS Reactive Oxygen Species
RFU Relative Fluorescence Units
(s)GOF (standard) Goodness-of-Fit
VPC Visual Predictive Check
x
ABSTRACT
Each year, more patients die from lung cancer than die from any other type of cancer (1). Non-small cell lung carcinoma (NSCLC) is the most common form of lung cancer, accounting for approximately 85% of cases. Developing reliable therapeutics for
NSCLC has proven to be perniciously difficult, with the 5-year survival rate for metastatic NSCLC being less than 5%. Because patients with NSCLC do not typically exhibit obvious symptoms, the disease is often not detected in its early stages (2). The majority of NSCLC is intrinsically multi-drug resistant. When therapeutics do prove effective NSCLC, drug resistance is rapidly acquired. Patients regularly must be put on experimental therapies because of the high failure-rate of first-line and second-line therapies. And, those experimental therapies themselves often fail. Very few experimental therapies make it past the third phase of clinical trialing. Even when treatments are effective for NSCLC patients, dosages are often suboptimal because of the general intolerability of chemotherapeutics. Chemotherapeutics are commonly administered in combination with one or more targeted therapies to reduce the necessary dosage of each. This is meant to reduce the number of side-effects from chemotherapy the patient must endure (3).
Mechanistic modeling is an ideal method for making informed decisions in clinical trial design, optimizing dosages, and individualizing therapy (4–6). The common framework for supporting mathematical modeling of pharmaceuticals is non-linear mixed effects modeling (NLME). The kinetic properties of a therapeutic – absorption, distribution, metabolism, and elimination – are called pharmacokinetics (PK). The biological dynamics resulting from the biodistribution of a pharmaceutical are called xi pharmacodynamics (PD). Using NLME modeling, one can simultaneously describe both the pharmacokinetics and pharmacodynamics of a pharmaceutical, even if the patients being modeled have disparate individual characteristics and the sampling schedule is sparse. After initially parameterizing a population model, the model can easily be updated and expanded by either incorporating new data or further informing the model structure with disease biology and therapeutic properties. Parameterized, i.e. fit, models can be used to simulate hypothetical clinical trials, giving an approximate answer without the costly need for clinical experiments. The more mechanistic the model, the more accurate the simulated clinical trials become. As a graduate student, the primary aim of the research I have been involved with was to better characterize the PKPD of various therapies for NSCLC using population modeling. After fitting the models featured in each study, we used simulation to answer questions about optimal dosing regimens. Optimizing a dosing regimen reduces the side-effect burden in the patient, increases efficacy of the therapy, and – if the drug is still in development – reduces the chance that an effective therapy might fail in clinical trials due to an ineffective dosing schedule.
The present body of work is a collection of four papers from my time as a graduate student. They nominally demonstrate both in-depth knowledge of modeling pharmaceuticals as well as summarize related findings in NSCLC research.
Concurrently, they were selected to give insight into each stage of population modeling relative to clinical pharmaceutical development. After a hypothesis is proposed, preclinical modeling is used to develop mathematical descriptions of PKPD, and xii eventually the model is translated into a clinical setting to answer hypothetical questions about therapeutic safety and efficacy. 1
CHAPTER 1. GENERAL INTRODUCTION
Developing effective therapeutic strategies for non-small lung carcinoma
(NSCLC) is one of the most pressing needs in pharmacology today. This year, in the
United States alone, it is estimated that there will be 228,820 new cases of lung cancer and 135,720 people will die from lung cancer (2). Cigarettes and other forms of combustible recreational products are growing in popularity and they substantially increase the risk that a user develops NSCLC. Beyond risk of NSCLC from recreational products, several rapidly-expanding industries – including manufacturing, mining, farming, transportation, and electricity production – generate a great volume of aerosolized carcinogens. Exposure to these industrial air pollutants greatly increases the chances that both laborers, as well as fence-line community members, in these industries develop NSCLC during their life (7).
The development rate of therapeutics for NSCLC has been rapidly-accelerating in recent decades; many contemporary first-line therapeutic strategies are combination therapies. Historically, cutting-edge oncology research focused on refining surgical resection of the primary tumor as well as radiology. In the midcentury, the oncology community adopted cytotoxics as a concurrent course of treatment with surgery and radiology. The impetus for including chemotherapy in the surgical/radiological treatment regimen common in oncology was the observation that primary tumor resection did not typically save the life of patients. Especially since most patients do not have symptoms until the cancer has already metastasized. For most cancer patients, the ultimate causes of death are the metastases and as well as micro-infiltration of neoplasms into surrounding tissues (8). 2
Cytotoxic therapies are generalized therapies that accumulate in and preferentially kill rapidly-dividing cell populations. When used in cancer patients, cytotoxics disrupt and limit the growth of tumors, metastases, and micro-infiltration of neoplasms into surrounding tissues, increasing the probability of survival after primary tumor removal. However, several populations of rapidly-dividing endogenous cells are harmed by cytotoxics, e.g. hematopoietic stem cells. This puts hard limits on the feasibility of scaling dosages in cytotoxic therapy without the side-effect burden of the therapy putting patient survival at risk. Scaling dosages upward is sometimes an option for increasing response in patients (9). Accordingly, several adjunct and combination therapies involving were developed to increase the efficacy of cytotoxics either synergistically or additively. The two primary classes of adjunct therapies in NSCLC are targeted therapies and immune-checkpoint inhibitors. Targeted therapies are aimed at exploiting unique biological features of cancer physiology to combat the disease. For example, bevacizumab attenuates hypoxia signaling from the tumor to the body. In the short-term bevacizumab therapy increases the efficiency of drug delivery to the tumor by normalizing tumor vasculature, and in the long-term deprives the tumor of oxygen as the tumor blood supply recedes. Immune-checkpoint inhibitors instead decrease the ability of cancer cells to evade the host immune system. Currently, a broad combination of surgery, radiology, chemotherapy, targeted therapy, and immune checkpoint inhibitors are employed in treating NSCLC. The diverse array of combination therapies, and experimental therapies, being used to treat NSCLC make anti-NSCLC therapeutics an ideal target for mathematical modeling studies (4,5,10,11). 3
Building comprehensive population-level, mathematical descriptions of the PKPD of a therapeutic allows researchers to accelerate the resolution of important clinical hypotheses about pharmaceutical safety and efficacy by simulating virtual clinical trials.
The statistical framework for population modeling is nonlinear mixed-effects (NLME) modeling. NLME modeling of PKPD is especially important with respect to cytotoxic drugs – as well as other cancer therapies – for four reasons. First, sampling in cancer patients tends to be sparse and noisy, and there is significant variation between individual patient pathology. NLME modeling is an ideal framework for pooling and performing statistical analysis on a sparsely sampled, noisy, and highly variable dataset
(12). Second, antiproliferative drugs induce heavy side-effect burdens. With a combination of preclinical data and sparse clinical sampling, the dosages which produce plasma concentrations over the minimum concentration required to achieve effect and below the toxicity threshold (i.e. within the therapeutic window) can be quickly identified.
Third, research in cancer is extremely resource intensive and prone to failure.
Therefore, it is important to optimize study design. For experimental therapies, optimizing trial design via simulation reduces the chance that an effective therapy would fail in clinical trials due to underdosing or inefficient regimen. Simulation can also be used to quickly disqualify drugs which would likely prove to be ineffective. And lastly, when therapeutics prove effective in an individual patient, the effectiveness might only be marginal, and the cancer can rapidly develop resistance. NLME modeling can be used to optimize therapies on an individual level, increasing base effectiveness and reducing the necessary timespan of treatment; the longer treatment persists, the more likely the cancer develops resistance to the treatment (6). 4
The basic structure underlying most pharmaceutical modeling is two-part. First, drugs have kinetic properties resulting from both their chemical properties and the biological actions of the body on the drug. The study of pharmaceutical kinetics is called pharmacokinetics (PK). For example, when a small polar molecule is injected intravenously, basic laws of thermodynamics govern the distribution of the pharmaceutical throughout the cardiovascular system. The body ultimately takes some action on that drug which effectively removes it from circulation – either degrading it, excreting it, or sequestering it. The stages of pharmacokinetics are absorption, distribution, metabolism, and elimination. The second concept underlying most pharmaceutical modeling is pharmacodynamics (PD). Drugs have actions on the bodies of patients resulting in predictable dynamics, usually by interaction with cellular receptors or intercellular signals. For example, bevacizumab binds to and disables vascular endothelial growth factor (VEGF). VEGF is a cellular signaling medium which communicates the need for new vasculature (i.e. hypoxia). When VEGF signaling is attenuated, vascular growth is limited. The studies presented in this dissertation invariably use NLME models with this two-part (PKPD) structure to solve problems in modeling and simulation of therapeutics (6).
In the first publication presented in this dissertation, my coauthors and I outline the philosophical framework that we have used to solve research problems in PKPD modeling using population models. The traditional experimental paradigm for developing pharmaceuticals in humans requires first to induce a coarse reproduction of the disease in mice and then to treat the mice with a broad range of dosages to determine if there is therapeutic potential i.e. symptom reduction. Then, simple 5 allometric scaling is used to estimate effective human dosages. However, the rodent model has several broad limitations when modeling disease. Some brief examples: the human body is much larger than the rodent body (so the pharmacokinetics are largely incomparable), rodents do not spontaneously develop the majority of human diseases so they must be artificially induced, and clinical lab values differ significantly between rodents and humans. We propose several modifications to the traditional paradigm.
Creating parallel NLME models of the animal model pathology and human pathology better accounts for biological differences between the animal model and humans.
Ideally, the animal model used in therapeutic development is of spontaneously developed disease mirrored between the human and the animal model e.g. type I diabetes is a disease common in both humans and in cats. If the disease is shared between humans and the animal model, the number of assumptions made when translating results from the animal model to humans is drastically reduced. And, the experiments themselves reduce needless harm as the animal models are being treated in a veterinary clinic – rather than tested bench-side. In this setting, therapeutics can be jointly developed to both solve problems in human and veterinary medicine. Usually, researchers only consider translational research, where findings in veterinary medicine are applied to human medicine. However, when using spontaneous animal disease as a model instead of induced disease, findings can be reverse translated i.e. findings from experimental pharmaceuticals being developed preclinically, as well as clinically, are used to support the development of pharmaceuticals for veterinary use.
In the second publication, we detail a pharmacokinetics experiment in high-dose pharmacological ascorbate. Several human clinical trials are currently evaluating the 6 potential cytotoxic properties of pharmacological ascorbate for NSCLC. By evaluating the pharmacokinetics in dogs, we have built a mathematical model that can be translated to human patients. We found that pharmacological ascorbate is both preferentially cytotoxic to in vitro canine cancer cells and can be administered at therapeutic levels, safely. More research must be completed to establish the validity of this therapeutic for canine cancer, but our findings indicate that some spontaneous canine cancers might in the future serve as an ideal preclinical model for their human analog when evaluating pharmacological ascorbate. It also opens the possibility for future reverse translation from human findings in pharmacological ascorbate to veterinary medicine.
In the third publication, we report a preclinical experiment in bevacizumab- pemetrexed/cisplatin combination therapy for NSCLC and the mathematical modeling and simulations which were developed using that experimental data. Various publications have suggested that administering bevacizumab at a gap of one or more days before pemetrexed/cisplatin enhances the efficacy of their combined use. An attractive feature of optimizing the scheduling of bevacizumab-pemetrexed/cisplatin is that dosages can potentially be reduced, improving the tolerability of the therapy. We used a NSCLC-xenografted mouse model to experimentally measure the improvement resulting from sequential bevacizumab-pemetrexed/cisplatin. In the experiment, small, human NSCLC tumors were xenografted onto 90 mice. The mice were randomized into several treatment groups in which bevacizumab was administered either concurrently, or sequentially at a gap of one or more days. We found a significant increase in efficacy when bevacizumab was administered sequentially with pemetrexed/cisplatin, rather 7 than concomitantly. We next used the data to a fit a semi-mechanistic NLME PKPD model of bevacizumab-pemetrexed/cisplatin against NSCLC in xenografted mice. After obtaining a satisfactory fit, we translated the model to humans using sparse data collected in a separate study. With the final clinical model, we predicted that over 85 days, optimizing sequential bevacizumab-pemetrexed/cisplatin therapy resulted in an approximately 48% increase in tumor volume reduction.
In the final manuscript presented in this dissertation, we used an expansive dataset collated from several clinical trials in anti-NSCLC therapies to develop a comprehensive model of NSCLC therapeutics. Within clinical trials and between clinical trials, there is significant variation in scheduling of therapeutics for patients. Our goal in this study was to leverage that natural variation in scheduling to explain varied outcomes in tumor reduction. We modeled that variation in response in terms of both individual variability in medication response and in terms of efficiency gained from optimized scheduling. Building on our previous findings, we were especially interested in optimizing sequential scheduling of bevacizumab with various anti-proliferatives.
References
[1] Ferlay J, Ervik M, Lam F, Colombet M, Mery L, Piñeros M, et al. Cancer today [Internet]. Global Cancer Observatory: Cancer Today. Lyon, France: International Agency for Research on Cancer. [cited 2020 Nov 20]. Available from: http://gco.iarc.fr/today/home
[2] Siegel RL, Miller KD, Jemal A. Cancer statistics, 2020. CA: A Cancer Journal for Clinicians. 2020;70(1):7–30.
[3] Chang A. Chemotherapy, chemoresistance and the changing treatment landscape for NSCLC. Lung Cancer. 2011 Jan;71(1):3–10.
[4] Barlesi F, Imbs D-C, Tomasini P, Greillier L, Galloux M, Testot-Ferry A, et al. Mathematical modeling for Phase I cancer trials: A study of metronomic vinorelbine for advanced non-small cell lung cancer (NSCLC) and mesothelioma patients. Oncotarget. 2017 May 2;8(29):47161–6. 8
[5] Ciccolini J, Benzekry S, Lacarelle B, Barbolosi D, Barlési F. Improving efficacy of the combination between antiangiogenic and chemotherapy: Time for mathematical modeling support. PNAS. 2015 Jul 7;112(27):E3453–E3453.
[6] Mould DR, Upton RN. Basic Concepts in Population Modeling, Simulation, and Model-Based Drug Development. CPT Pharmacometrics Syst Pharmacol. 2012 Sep;1(9):e6.
[7] Dela Cruz CS, Tanoue LT, Matthay RA. Lung Cancer: Epidemiology, Etiology, and Prevention. Clinics in Chest Medicine. 2011 Dec;32(4):605–44.
[8] DeVita VT, Chu E. A History of Cancer Chemotherapy. Cancer Res. 2008 Nov 1;68(21):8643–53.
[9] Chemotherapy and You: Support for People With Cancer - National Cancer Institute [Internet]. 2014 [cited 2020 May 4]. Available from: https://www.cancer.gov/publications/patient-education/chemo-and-you
[10] Agur Z, Elishmereni M, Foryś U, Kogan Y. Accelerating the Development of Personalized Cancer Immunotherapy by Integrating Molecular Patients’ Profiles with Dynamic Mathematical Models. Clinical Pharmacology & Therapeutics. 2020;108(3):515–27.
[11] Benzekry S, Lamont C, Beheshti A, Tracz A, Ebos JML, Hlatky L, et al. Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth. PLOS Computational Biology. 2014 Aug 28;10(8):e1003800.
[12] Pawitan Y. In All Likelihood: Statistical Modelling and Inference Using Likelihood. OUP Oxford; 2013. 655 p.
9
CHAPTER 2. MODEL-BASED REVERSE TRANSLATION BETWEEN VETERINARY AND HUMAN MEDICINE: THE ONE HEALTH INITIATIVE
Authors and Affiliations
Benjamin Schneider1, Violeta Balbas-Martinez2, Albert E Jergens3, Inaki F.
Troconiz2, Karin Allenspach3, and Jonathan P Mochel1*
1Department of Biomedical Sciences, Iowa State University College of Veterinary
Medicine, Ames, Iowa, USA; 2Department of Pharmacy and Pharmaceutical
Technology, Pharmacometrics and Systems Pharmacology, University of Navarra,
Pamplona, Spain; 3Department of Veterinary Clinical Sciences, Iowa State University
College of Veterinary Medicine, Ames, Iowa, USA. *Correspondence: J. P. Mochel
Modified from a manuscript published in Clinical Pharmacology and
Therapeutics: Pharmacometrics & Systems Pharmacology.
Abstract
There is growing concern about the limitations of rodent models with regard to recapitulation of human disease pathogenesis. Computational modeling of data from humans and animals sharing similar diseases provides an opportunity for parallel drug development in human and veterinary medicine. This “reverse translational” approach needs to be supported by continuing efforts to refine the in silico tools that allow extrapolation of results between species.
Improving the Predictability of Animal Models Used in Preclinical Research
Translational research remains the consensual model to develop candidate drugs into clinical therapeutics. In the translational framework, drug pharmacokinetics
(PKs) and pharmacodynamics (PDs) are first characterized in animal models, and the 10 results of those preclinical studies are then extrapolated to humans. Currently, out of the few candidates that move forward to the development stage, 35% attrition in phase II studies are caused by failure to demonstrate clinical efficacy [1]. These high failure rates, combined with few relevant translational animal models in preclinical research, highlight the need for alternative approaches at the early stage of the research and development (R&D) lifecycle. One such approach is the reverse translational model.
A well‐known application of the reverse translational paradigm consists in the prediction of drug side effects and/or efficacy for individual patients using specific single nucleotide polymorphism information. The scope of reverse translation is actually broader, as we see it as an opportunity to synergize the information available from humans and animals sharing analogous diseases to develop improved predictions and therapies for both human and veterinary patients (figure 3.1).
The innovative nature of this approach, underpinned by the “One Health” initiative, is based on the underlying hypothesis that the use of animal models that spontaneously develop similar diseases to humans will improve the predictability of preclinical models used for biomedical research purposes. In return, quantitative PK/PD information gathered from human clinical studies present an opportunity to stimulate veterinary drug development, thus optimizing the utilization of existing resources and the application of available knowledge (i.e., from humans to animals and vice versa).
This contrasts starkly with the common translational practice of developing genetically engineered animal models of disease in preclinical research.
In reverse translational pharmacology, computational modeling of drug PK/PD assists in the selection of promising therapeutic candidates and the prediction of their 11 optimal dosing schedules (i.e., dose and frequency) in humans and animals. This is achieved through extrapolation of disposition kinetics, efficacy, and safety data from/to spontaneous animal models of the human disease pathophysiology to/from the clinic.
One Health and Comparative Medicine to Support Drug R&D
One Health is a cross‐disciplinary effort aiming to improve the assessment, treatment, and prevention of disease in people and animals [2]. An important subfield of
One Health is comparative medicine, which offers the possibility to use spontaneous animal models with naturally occurring diseases for drug R&D. These animal models have unique experimental advantages, especially over the mouse, which may provide insight into previously intractable diseases. In particular, many human disorders, including cancer, diabetes mellitus, chronic enteropathies (e.g., inflammatory bowel diseases (IBD)), hypertension, and congestive heart failure have well‐studied clinical analogs in dogs (supplementary table 3.S1). Domesticated animals also share several environmental risk factors with humans, simplifying experimental controls. In addition, biological relevance of genomic data can be supported by identifying human‐animal genetic homologs, as is the case in IBD, in which the importance of genetic susceptibility in disease development has been established in both species. Below, we highlight three examples of diseases in which reverse translational modeling have been used to support pharmaceutical research.
Cancer Research
About 6 million dogs are diagnosed with cancer each year, and >50% of dogs of
10 years or more will develop cancers, such as lymphoma, osteosarcoma, and melanoma [3]. Although murine models have been extremely useful for studying the biology of cancer development, mice usually do not adequately represent many of the 12 features constitutive of human cancers, including genomic instability and tumor heterogeneity [4]. In dogs, cancers develop naturally within a syngeneic host and tumor microenvironment, and in the context of an intact immunity. Dogs and human cancers share similar features, such as background genetics, histological appearance, therapeutic response, and acquired resistance [4]. One good example of the use of canine models to support cancer therapy pertains to the development of the inflammatory cytokine interleukin (IL)‐12 as a potential treatment for malignant melanoma. The use of cytokines to enhance antitumor immunity has been recognized as an important immunomodulatory approach in cancer management. Yet, historically, the high risk for systemic toxicity presented by IL‐12 dosing has prevented development of this cytokine into a therapeutic. A strong genetic similarity exists between canine and human IL‐12 (i.e., 84% homology for the ligand and 68% homology for the receptor), whereas dogs develop spontaneous malignant melanoma with similar biology to human tumors. These analogies provided impetus for the characterization of IL‐12 PK/PD, efficacy, and toxicity in canine clinical trials [5]. Results from the dog study showed that high levels of IL‐12 could be safely administered subcutaneously to patients with malignant melanoma, while maintaining both systemic immunological and clinical activity. This was demonstrated by measuring serum IL‐12 and other representative biomarkers (e.g., IL‐10) over time, and establishing PK/PD models of IL‐12. These findings in dogs were key to guide the sponsor's decision to move forward with a phase
I clinical trial in humans. In turn, preliminary studies focusing on IL‐12 gene electrotransfer in dog patients with melanoma have shown promising results for the treatment of spontaneous canine tumors [6]. 13
Inflammatory Bowel Disease
IBD is a highly prevalent disorder in both humans and dogs. Importantly, dogs with IBD exhibit similar clinical symptoms, show involvement of the same cells, inflammatory genes and molecular pathways, and have a time course of disease progression similar to humans. In fact, a copious amount of literature has established that human and canine IBD have common clinical and molecular features, such that clinical trials in dogs with IBD are particularly relevant to study the efficacy and safety of candidate drugs intended for use in humans [7]. In a recent collaboration between the
Iowa State University and the University of Navarra, IBD was modeled using a network systems approach based on Boolean equations [8]. The model was used to simulate the effect of a noncompetitive antagonist of the purinergic receptor P2X7 and guide dose selection for an upcoming clinical study in IBD in dogs. The model used inflammatory biomarkers IL‐1β and IL‐18 as well as the tissue damage biomarkers matrix metalloproteinases as surrogate end points of efficacy. Assuming that matrix metalloproteinases levels are associated with clinical disease activity, results from the simulations showed that the selected dose of the drug candidate should antagonize at least 75% of the target receptor. These findings will now inform the design of a proof‐of‐ concept study in IBD dogs prior to clinical development in humans.
Congestive Heart Failure
Another therapeutic indication in which modeling efforts have been made to better characterize the effects of drugs in naturally occurring animal models of human disease is congestive heart failure (CHF). In humans and dogs, CHF is often synergistic with renin angiotensin aldosterone system (RAAS) overactivation. This is due to the excessive release of renin from the juxtaglomerular apparatus, a well‐described 14 compensatory mechanism to the reduced cardiac output observed in symptomatic stages of CHF. Although there is no mathematical description of the PK/PD of angiotensin‐converting enzyme (ACE) inhibitors in spontaneous cases of canine CHF, the kinetics and effects of benazeprilat have been characterized in a low‐salt diet model of RAAS activation [9]. Similar to humans, ACE inhibitors are commonly dosed in the morning in dogs. However, using a nonlinear mixed‐effect model to describe the dynamics of RAAS biomarkers in dogs, Mochel et al [9] have shown that the timing of food intake exerts a synchronizing effect on the RAAS, such that dosing with ACE inhibitors should be adjusted according to the time of food intake. Using a mechanism‐ based PK/PD model, the authors further established that ACE activity alone was not a predictive marker of RAAS activity in dogs because, as reported in humans, benazeprilat exerts a moderate effect on angiotensin II and aldosterone, despite a complete and long‐lasting inhibition of ACE.
Opening the “Black Box” of Complex Biological Networks
The reductionist approach to biomedical research has been successful in identifying key mechanisms contributing to disease modulation. However, it has become increasingly apparent that a more integrated approach is required to characterize the pathophysiology of complex biological systems. This was nicely illustrated with the IBD example above for which a systems pharmacology model comprised of 43 nodes and
298 interactions was developed by combining human and animal data on a large number of cytokines, immune cells, and proteins to predict the therapeutic efficacy of prospective candidate drugs. As high‐throughput sequencing and metabolomics techniques continue to improve, this mechanistic model could be expanded further to 15 decipher the mechanisms by which diet and genetic backgrounds impact disease susceptibility [10].
Conclusion
Reverse translational pharmacology is an expanding field of research with the promise to improve existing preclinical models for better characterizing the efficacy and safety of candidate drugs and, ultimately, selecting the most promising therapeutics intended for use in humans. In return, from the perspective of developing veterinary pharmaceuticals for spontaneous diseases in animals, reverse translational pharmacology also presents an opportunity to leverage information from PK and PD studies in humans for the benefit of veterinary medicine. The success of the reverse translational paradigm relies on more systematic interdisciplinary research and cross talks among physicians, veterinarians, and quantitative scientists. To achieve this, the
Comparative Oncology Program of the National Cancer Institute has established a multicenter collaborative network of 22 veterinary academic partners known as the
Comparative Oncology Trials Consortium. The mission of the Comparative Oncology
Trials Consortium is to answer biological questions geared to inform the development path of chemotherapeutics for future use in human patients with cancer. Additional initiatives from the National Institute of Health include several multimillion‐dollar funding opportunities to foster collaborative programs for multidisciplinary teams (e.g., PAR‐17–
340 and RFA‐CA‐17‐002). Active participation of industrial partners is also key to the success of reverse translational research. This was exemplified by the 5‐year
Cooperative Research and Development Agreement between the US Food and Drug
Administration Center of Veterinary Medicine and Certara (www.certara.com) aiming to 16 deliver physiologically based PK dog models and assesses the impact of polymorphic variations on interspecies extrapolation. Regulatory incentives to develop parallel
(veterinary and human) drug development programs could present an opportunity to encourage such collaborations in the future.
Acknowledgments
The authors would like to thank Jordan Gongora (Biomedical Sciences, Iowa
State University) for her graphic design support.
Conflicts of Interest
The authors declared no conflicts of interest.
Author Contributions
All co‐authors participated in the writing and technical editing of the manuscript.
Tables and Figures
Table 2.S1 Examples of Diseases that Have Clinical Analogs in Dogs References can be accessed online using; Riviere et al., 2017 J Vet Pharmacol Ther 18(4): 347-360. Cancer Lymphoma Ito D et al., Vet Immunol Immunopathol. 2014 Jun 15;159(3-4):192- 201 Melanoma Atherton MJ et al., Vet Immunol Immunopathol. 2016 Jan;169:15-26 Osteosarcoma Roy J et al., PLoS One. 2017 Sep 14;12(9):e0183930 Colorectal Cancer Colorectal Cancer Gastrointestinal Stromal Tumors Gregory-Bryson E et. al., BMC Cancer. 2010 Oct 15;10:559
Cardiovascular Diseases Congestive Heart Failure Haidara MA et al., Curr Vasc Pharmacol. 2015;13(5):658-69 Metabolic Syndrome Montoya-Alonso JA et al., Front Vet Sci. 2017 Apr 25;4:59 Chronic Kidney Disease Martinez-Hernández L et al., Vet J. 2017 Mar;221:1-5 Pulmonary Hypertension Stenmark KR et al., Vet Pathol. 2016 Jul;53(4):707-10
17
Table 2.S1 Continued Gastrointestinal Diseases Inflammatory Bowel Disease Jergens AE et al., Front Biosci (Elite Ed). 2012 Jan 1;4:1404-19. Idiopathic Chronic Hepatitis Bexfield N, Vet Clin North Am Small Anim Pract. 2017 May;47(3):645-663 Pancreatitis Waltson P, J Small Anim Pract. 2015 Jan;56(1):3-12 Gastrointestinal Ulcers Fitzgerald E, et al., J Small Anim Pract. 2017 Apr;58(4):211-218
Endocrine Disorders Type 1 Diabetes O'Kell AL, et al., Sci Rep. 2017 Aug 25;7(1):9467 Addison's Disease Hanson JM, et al., J Vet Intern Med. 2016 Jan-Feb;30(1):76-84 Cushing's Syndrome Galac S, Mol Cell Endocrinol. 2016 Feb 5;421:34-9 Hypothyroidism Hypothyroidism
Neurological Disease Cognitive Dysfunction Schütt T, et al., J Alzheimers Dis. 2016 Mar 15;52(2):433-49 (Resembling Alzheimer's Disease) Epilepsy Marios Charalambous, etl al., BMC Vet Res. 2014; 10: 257 Polyneuropathy Vitale CL, Olby NJ, J Vet Intern Med. 2007 Nov-Dec;21(6) Meningoencephalitis Uchida K, et al. Vet J. 2016 Jul;213:72-7 18
Figure 2.1 Translational vs. Reverse Translational Sciences Reverse translational sciences is a bidirectional approach in which clinical findings from patients are used to design early studies in relevant animal models of (spontaneous) disease. The information generated in animal studies will later be used to predict the efficacy and safety of future therapeutics in human clinical trials.
References
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19
[2] National Center for Emerging and Zoonotic Infectious Diseases (17 May 2012). Centers for Disease Control and Prevention.
[3] Jacob, J.A. Researchers turn to canine clinical trials to advance cancer therapies. JAMA 315, 1550– 1552 (2016).
[4] Gordon, I., Paoloni, M., Mazcko, C. & Khanna, C. The Comparative Oncology Trials Consortium: using spontaneously occurring cancers in dogs to inform the cancer drug development pathway. PLoS Med. 6, e1000161 (2009).
[5] Paoloni, M. et al. Defining the pharmacodynamic profile and therapeutic index of NHS‐IL12 immunocytokine in dogs with malignant melanoma. PLoS One 10, e0129954 (2015).
[6] Lampreht, U. et al. Gene electrotransfer of canine interleukin 12 into canine melanoma cell lines. J. Membr. Biol. 248, 909– 917 (2015).
[7] Jergens, A.E. et al. Intestinal cytokine mRNA expression in canine inflammatory bowel disease: a meta‐analysis with critical appraisal. Comp. Med. 59, 153– 162 (2009).
[8] Balbas Martinez, V., Allenspach, K., Kingsbury, D., Jergens, A.E., Troconiz, I. & Mochel, J.P. One Health: translational and reverse translational modeling of inflammatory bowel disease using an advanced Boolean network. Population Approach Group in Europe Meeting, Budapest, Hungary.
[9] Mochel, J.P., Fink, M., Peyrou, M., Soubret, A., Giraudel, J.M. & Danhof, M. Pharmacokinetic/pharmacodynamic modeling of renin‐angiotensin aldosterone biomarkers following angiotensin‐converting enzyme (ACE) inhibition therapy with benazepril in dogs. Pharm. Res. 32, 1931– 1946 (2015).
[10] Swanson, K.S. & Schook, L.B. Canine nutritional model: influence of age, diet, and genetics on health and well‐being. Curr. Nutr. Food Sci. 2, 115– 126 (2006).
20
CHAPTER 3. IN VITRO CYTOTOXICITY AND PHARMACOKINETIC EVALUATION OF PHARMACOLOGICAL ASCORBATE IN DOGS
Authors and Affiliations
Margaret L. Musser1*, Alyssa L. Mahaffey1, Melissa A. Fath2, Garry R. Buettner2,
Brett A. Wagner2, Benjamin K. Schneider3, Yeon-Jung Seo3, Jonathan P. Mochel3, and
Chad M. Johannes1
1Veterinary Clinical Sciences, Iowa State University, Ames, IA, United States;
2Free Radical and Radiation Biology Program, The University of Iowa, Iowa City, IA,
United States; 3Biomedical Sciences, Iowa State University, Ames, IA, United States;
*Correspondence: Margaret L. Musser, [email protected]
Modified from a manuscript published in Frontiers in Veterinary Science,
Veterinary Pharmacology and Toxicology.
Abstract
High-dose, pharmacological ascorbate (P-AscH−) is preferentially cytotoxic to human cancer cells in vitro. Investigations on the efficacy of P-AscH− as an adjuvant treatment for multiple human cancers are on-going, but has yet to be formally investigated in dogs. The primary objectives of this study were to determine the pharmacokinetic (PK) profile of P-AscH− in healthy Beagle dogs and the effects of P-
AscH− on canine osteosarcoma cells in vitro.
In pursuit of these ends, eight purpose-bred, healthy, spayed female Beagle dogs, between 20 and 21 months old, and 8–10 kg were administered two doses of P-
AscH− (550 or 2,200 mg/kg) via intravenous infusion over 6 h, on separate days.
Plasma ascorbate concentrations were measured at 12 time points during and after infusion for PK analysis using nonlinear mixed-effects (NLME) and non-compartmental 21 analysis (NCA). Clonogenic assays were performed on 2 canine osteosarcoma cell lines (D-17 and OSCA-8) and canine primary dermal fibroblasts after exposure to high concentrations of ascorbate (75 pmoles/cell).
Plasma ascorbate levels in the dogs peaked at approximately 10 mM following
2,200 mg/kg and returned to baseline 6–8 h after dosing. Minor adverse effects were seen in two dogs. Ascorbate (75 pmoles/cell) significantly decreased survival in both the osteosarcoma cell lines (D-17 63% SD 0.010, P = 0.005; OSCA-8 50% SD 0.086, P =
0.026), compared to normal fibroblasts (27% SD 0.056).
From these results, we have concluded that pharmacological ascorbate is preferentially cytotoxic to canine-derived cancer cells, and high levels of ascorbate can be safely administered to dogs. Further studies are needed to determine the effects of
P-AscH− on canine patients.
Introduction
The potential benefit of high-dose intravenous (IV) pharmacological ascorbate
(P-AscH−, vitamin C) for patients with cancer was first reported in the 1970s [1,2].
Subsequent clinical trials failed to show substantial improvement in outcome [3], stalling its clinical use [4]. However, P-AscH− continued to be a popular alternative cancer therapy [5,6]. The potential anti-cancer properties of P-AscH− are being reevaluated.
Several human clinical trials are examining the efficacy and safety of P-AscH−, for example in non-small cell lung carcinoma (NSCLC) [7], glioblastoma multiforme (GBM)
[7], and pancreatic cancer [8,9], indicating renewed interest in the therapeutic use of P-
AscH− for human cancer patients. 22
Ascorbic acid is a weak acid with pKa1 of about 4.2 [8]. Thus, at the near-neutral pH of mammalian biology, greater than 99.9% will be present as the monoanion, i.e., ascorbate. The biochemistry for the functions of vitamin C is principally the biochemistry of ascorbate. In this work, we use the term pharmacological ascorbate, P-AscH−, to distinguish the functioning of ascorbate as a drug from its biochemistry as vitamin C
[10,11]. When at normal, healthy physiologic levels ascorbate functions as a reducing agent and donor antioxidant [12]; however, at supraphysiological concentrations, P-
− AscH can produce high fluxes of H2O2 via its oxidation [8,9,13]. The cytotoxic
− mechanism of P-AscH appears to be due to these fluxes of H2O2 and, in part, to alterations in cancer cell oxidative metabolism, allowing for increased steady-state
∙− levels of O2 and H2O2 within tumor cells [7,14,15]. These alterations disrupt intracellular iron metabolism, sensitizing cells to the effects of the oxidation of P-AscH− [7,14,15].
Multiple in vitro studies have confirmed the cytotoxic effects of P-AscH− on human and murine tumor cells, and the sparing effect on normal cells [10,11,14,15].
Human studies of P-AscH− have determined that therapeutic, cytotoxic plasma levels (≥≈20 mM) cannot be achieved through oral administration (PO) [16]. Therefore,
IV or intraperitoneal (IP) injection is required [16,17]. In addition, high-dose IV P-AscH− infusions (15–125 g), given over hours, are required to achieve and maintain proposed therapeutic plasma levels due to the rapid clearance of ascorbate [7,16–19]. The optimal dose of P-AscH−, frequency, and duration of administration have yet to be determined [20]. 23
Pharmacological ascorbate is generally well-tolerated and appears to have no dose-limiting toxicities in humans [6]. Adverse effects that have been described include vomiting, diarrhea, weight loss, leukopenia, and neutropenia [6,7,10,21].
Canine pharmacokinetic (PK) analysis of PO ascorbate, but not P-AscH−, has been scientifically evaluated [22]. In 4 Greyhounds that were treated with 1 g of ascorbate PO or IV, peak ascorbate plasma concentrations were significantly greater when ascorbate was administered IV (mean 0.33 ± 0.06 mM) compared to PO (mean
0.03 ± 0.01 mM) and was achieved within 6 min, falling rapidly back to baseline (mean
0.01 mM) within 6 h [23]. Recently, seven dogs were reported to have received various doses of IV ascorbate for the adjuvant treatment of multiple cancers with minimal side effects [24]. Data regarding the PK of P-AscH− in dogs, and if P-AscH− would be a feasible treatment option for our canine patients, are lacking.
The purpose of this study was two-fold: (1) determine the PK profile of P-AscH− in healthy Beagle dogs; and (2) determine the effects of P-AscH− on canine osteosarcoma cells. Given the lack of significant adverse side effects reported in humans, we hypothesized that IV P-AscH− would be safe for use in dogs and that in vitro, P-AscH− would cause significant cytotoxicity to canine osteosarcoma cells. The
PK data presented here can guide the development of treatment protocols that are feasible for use in the veterinary clinical setting.
Methods
Experimental Animals
Eight purpose-bred, spayed female Beagles, between 20 and 21 months old, and
8–10 kg were used in this study. The dogs were obtained from Ridglan Farms, Mt.
Horeb, WI. The use of the Beagles for this study was approved by the Iowa State 24
University Institutional Animal Care and Use Committee. Compliance with the US
National Research Council's Guide for the Care and Use of Laboratory Animals was maintained throughout the study. The Beagle dogs were group-housed in the same conditions and fed the same Royal Canin® diet for the duration of the study. Prior to infusions of P-AscH− and collection of blood samples, dogs were fasted overnight with free choice water available at all times.
Ascorbate Administration
Two doses of injectable L-ascorbic acid, 500 mg/mL (Mylan Institutional LLC,
Canonsburg, PA), were administered on two separate days. (Although labeled as
Ascorbic Acid for Injection, the contents are at near-neutral pH, thus vials contain ascorbate.) A low dose (550 mg/kg) was administered on the first trial day. This dose was escalated to 2,200 mg/kg for administration on the second trial day, as previously reported [24]. At least a two-day washout period was given between each dose.
Administration of ascorbate was performed through a 20 gauge, peripheral short IV catheter in the left or right cephalic vein of each dog. Pharmacological ascorbate was combined with sterile water to achieve a 500 mg ascorbate per mL solution with a targeted osmolarity between 500 and 900 mOsm/L [7]. The infusion was given over 6 h
(12.5 mL/h for the 550 mg/kg dose; 50 mL/h for the 2,200 mg/kg dose) via an IV infusion pump in order to achieve a steady-state plasma ascorbate concentration. Dogs were continuously monitored during the infusion and intermittently for 24 h post infusion for adverse clinical signs.
Plasma Ascorbate Sample Preparation and Analysis
To evaluate plasma ascorbate concentrations throughout and after infusion, blood was sampled at 12 time points: immediately prior to the ascorbate infusion, a 25 baseline venous sample was obtained; venous blood was sampled at 0.5, 1, 3, 5, and 6 h during the infusion period; and at 6.5, 7, 8, 10, 12, and 16 h during the post-infusion period. Prior to the higher dose infusion (2,200 mg/kg), and at the 6 h mark of the higher dose infusion, arterial samples for blood gas analysis were also obtained. All venous blood collection was performed via a Cavafix® (B Braun Medical Inc., Breinigsville, PA) sampling catheter placed in either the left or right lateral saphenous vein, to the level of the caudal vena cava, following manufacturer recommendations [25]. At each time point, 2 mL whole blood samples were drawn into a Vacutainer® PST™ Lithium Heparin
(Becton Dickinson, Franklin Lakes, NJ) green top tube and promptly stored on ice until centrifugation. Blood was centrifuged for 20 min at 4°C and 2,000 rpm (671 g). Plasma was collected and stored at −80°C until analysis [26]. Arterial samples for blood gas analysis were obtained via an AirLifeTM Reduced Heparin Arterial Blood Sampler
(CareFusion).
Plasma ascorbate quantification was conducted at The University of Iowa using two different assay systems as previously described [27,28]. Briefly, a plate reader
(SpectraMax® M3, Molecular Devices, Sunnyvale, CA) was used to measure baseline and physiological levels of ascorbate present in the plasma samples [28]. To quantify the high pharmacological levels of ascorbate a second assay using an Implen
Nanophotometer (Implen GmbH, Munich, Germany) microvolume UV-Vis spectrometer was used. With little required sample processing, this assay, developed at The
University of Iowa [27], allows rapid assessment of ascorbate concentrations in plasma ranging from 2.9 to 35 mM. 26
Arterial blood gas samples were processed by the Iowa State University Clinical
Pathology Lab using a RAPIDPoint® 500 Blood Gas Analyzer (Siemens Medical
Solutions USA, Inc., Malvern, PA). Additional complete blood counts, chemistries, and urinalyses were performed in conjunction with another study taking place during the same time period.
Pharmacokinetic Modeling
Time-courses for the concentration of ascorbate in blood plasma following low- dose and high-dose IV infusion were analyzed simultaneously using the stochastic approximation expectation maximization (SAEM) algorithm implemented in the Monolix
Suite 2018R2 (Lixoft, France). Data below the lower limit of quantification (LLOQ) were modeled by adding to the likelihood function a term describing the probability that the true observation lies between zero and the LLOQ. Individual model parameters were obtained post-hoc using the mean of the full posterior distribution, as previously described for nonlinear mixed-effects (NLME) models in animal health [29].
Convergence of the SAEM algorithm was evaluated by inspection of the stability of the fixed and random effect parameter search and the log-likelihood estimate after the exploratory period of the algorithm (i.e., after 1,000 iterations of SAEM). Standard goodness-of-fit diagnostics, including individual predictions vs. observations, the distributions of weighted residuals, and normalized prediction distribution errors were used to assess the performances of the candidate models [30–32]. Prediction distributions from 1,000 Monte Carlo simulations were used to evaluate the ability of the final model to reproduce the variability in the observed pharmacokinetic data. Residual error estimates from the mathematical models were used as supportive information for evaluation of lack of fit. Normality and independence of residuals were assessed using 27 histograms, quantile-quantile plots, and autocorrelation of conditional weighted residuals. For converging models with satisfactory goodness-of-fit diagnostics, model selection was based on the Bayesian information criteria (BIC) and the precision of the model parameter estimates.
For completeness, non-compartmental analysis (NCA) of ascorbate PK was performed using PKanalix (Monolix Suite 2019R1, Lixoft, France). Standard PK parameters were generated for individual dogs, as follows:
;Area under concentration-time curve, AUCINF ־
A linear trapezoidal linear rule was used to estimate the area under the
ascorbate time-curves
;Maximum concentration, CMAX ־
;Steady state concentration, CSS ־
;Steady state volume, VSS ־
;Clearance, Cl ־
;Time of maximum concentration, TMAX ־
;Half-life, T1/2 ־
;Elimination rate constant, λz ־
Computed by linear regression of the logarithmic concentration vs. time
curve during the elimination phase
In Vitro Ascorbate Analysis – Cell Lines and Reagents
Two canine osteosarcoma cell lines were obtained, D-17 (American Type Culture
Collection, Rockville, MD, USA) and OSCA-8 (Kerafast, Inc., Boston, MA), and grown in pyruvate free DMEM 10% fetal bovine serum (FBS). Canine primary dermal fibroblasts were obtained as a normal tissue control (Cell Biologics, Chicago, IL). Cell lines were 28 grown in proprietor complete fibroblast media (M2267 for dermal fibroblasts) containing
1 mM pyruvate. Cells were kept in either 21 or 4% O2 at 37°C, 5% CO2, in a humidified atmosphere.
For cell culture studies, ascorbate stock solutions, 1 M in water, with the pH adjusted to 7.0 with NaOH were prepared from L-ascorbic acid (Macron Fine
Chemicals, Avantor Performance Materials, Inc., Center Valley, PA) and stored in the dark at 5°C in sealed glass test tubes until use [11]. The ascorbate stock concentration was verified spectrophotometrically. Appropriate volumes of the stock to achieve 50 pmole/cell (5 mM) and 75 pmol/cell (7.5 mM) were added to culture media for 1 h as previously described [7,11].
In Vitro Ascorbate Analysis – Clonogenic Survival Assay
To determine the effect of P-AscH− on the reproductive integrity, D-17 and
OSCA-8 canine osteosarcoma cells were plated at 80,000 cells per 60-mm dish.
Seventy-two hours after plating, one dish was counted to determine the number of cells on the plate. The volume of media in the dishes was adjusted so that cells were treated with a range of stock ascorbate, 2.5 pmoles/cell (0.25 mM)−50 pmoles/cell (5 mM).
Ascorbate was dosed per cell as previous literature has demonstrated that H2O2 and ascorbate toxicity depends on cell number/density [15,33,34]. After 1 h of P-
AscH− treatment both floating and attached cells from control and treated dishes were collected using 0.25% trypsin (GIBCO). Trypsin was inactivated with media containing any floating cells, centrifuged at 1,200 rpm (335 g) for 5 min and resuspended in fresh media. Cell counts were made with a Coulter Counter (Beckman Coulter Z1) and the cells were plated at various densities and allowed to grow for 10–12 days in complete media at 21% O2. Subsequently, the cells were stained with Coomassie Blue dye, and 29 colonies of >50 cells on each plate were counted and recorded. Surviving fraction was determined as the number of colonies per plate divided by the number of cells initially added to that plate. Normalized surviving fraction was determined as the surviving fraction of any given clonogenic plate from a treatment group divided by the average surviving fraction of the control (untreated) plates within a given experiment.
The clonogenic experiment comparing osteosarcoma cells to canine fibroblast cells were performed similarly with the following exceptions. Optimal conditions for normal fibroblasts is 4% O2 (normal physiologic condition) and proprietary media
(complete fibroblast media M2267) which contains sodium pyruvate, known to scavenge
H2O2 [15]. In addition, normal canine fibroblasts will only form clones when plated on lethally irradiated feeder cells (see below). Therefore, in experiments comparing the reproductive viability of P-AscH− on cancer cells vs. fibroblasts, the dose of P-
AscH− was increased to 75 pmol/cell (7.5 mM) and all cultures, including the sarcoma lines, were treated in identical fibroblast media at 4% O2 and plated onto feeder cells.
In Vitro Ascorbate Analysis – B1 Feeder Layer Cells
Chinese hamster fibroblasts designated as B1 (passages 20–40) were maintained at 21% oxygen in high glucose DMEM 1× media containing L-glutamine and sodium pyruvate and supplemented with 10% FBS, 20 mmol/L HEPES, pH 7.3, 1×
MEM non-essential amino acids. The feeder layer was prepared 24 h prior to any clonogenic survival assay by irradiating the cells with 30 Gy of X-rays at a dose rate of
27 Gy/min then plating in the cloning dishes at 100,000 cells per dish. During clonogenic survival assays comparing P-AscH− treatment of cancer cell lines to normal canine fibroblasts, all cloning plates were grown using a feeder layer and each 30 clonogenic experiment had two extra dishes plated with feeder cells alone to ensure no colony growth at the end of the 10- to 12-day incubation.
Statistical Analysis
The clonogenic survival analysis was done using a minimum of three cloning dishes per experimental condition, and the experiments were repeated a minimum of three times on separate occasions. Statistical analyses were done using the GraphPad
Prism software. Statistical significance was determined using one-way ANOVA and
Dunnett's multiple comparisons test was performed. Error bars represent ± standard error of the mean, and statistical significance was defined as P < 0.05.
The Wilcoxon signed rank test was used to examine the difference between the pre- and post-ascorbate administration for each of nine safety parameters evaluated by blood gas. A P-value < 0.05 was considered significant. Statistical analysis was performed using R (version 3.5.2) (R Foundation for Statistical Computing, Vienna,
Austria).
Results
Safety
The ascorbate infusion was well-tolerated by all dogs, with one dog experiencing a grade I veterinary cooperative oncology group-common terminology criteria for adverse events (VCOG-CTCAE) vomiting during the higher dose infusion, and another showing VCOG-CTCAE grade I nausea/ptyalism [35]. No changes on complete blood count or chemistry panels were noted during the course of the study for any dog. Blood gas analysis revealed statistically significant changes in pre- and post-ascorbate calcium, sodium, potassium, chloride, bicarbonate, partial pressure of carbon dioxide, 31 anion gap, lactate, and glucose measurements (table 2.1). The pH was not significantly different pre- and post-ascorbate administration.
In Vivo Pharmacokinetics
The mean initial plasma ascorbate concentration for the eight dogs at the 550 mg/kg P-AscH− dose (≈4 g) was 0.02 mM (± 0.01 mM). Over the course of the 6-h infusion, this peaked to 2.14 mM (± 0.54 mM). Once the infusion was completed, ascorbate levels fell sharply below therapeutic levels, and returned to near baseline by
6 h post infusion (figure 2.1). The mean initial plasma ascorbate concentration for the eight dogs at the 2,200 mg/kg dose of P-AscH− (≈15–21 g) was 0.02 mM (± 0.01 mM).
Over the course of the 6-h infusion, this peaked to 8.6 ± 2.1 mM. Once the infusion was completed, ascorbate levels fell sharply below proposed therapeutic levels, and returned to near baseline by 6 h post infusion (figure 2.1).
A two-compartment mammillary disposition model with first-order elimination and zero-order absorption following IV infusion best described the PK of ascorbate in plasma (figure 2.2). A combined error model with an additive and a proportional error term was used to account for the residual noise in ascorbate measurement. The robustness and predictive performances of the final model were supported by the inspection of the standard goodness-of-fit diagnostics (supplemental figure 2.S1).
Overall, the model was able to reproduce the individual experimental data for the two dosing schedules with excellent accuracy, as shown by the quality of the individual fits
(figure 2.3).
Using standard mathematical equations for a two-compartment PK model [38], the elimination half-life of ascorbate in canine plasma can be estimated at ~3.5 h. 32
Population PK parameter estimates and their related variances are summarized in table
2.2. For all model parameters, the precision of the final estimates was considered satisfactory (RSE ≤ 25%). The systemic total body clearance (CL) of ascorbate was estimated to be low to moderate (2.0 L/h, or 0.24 L/kg/h), according to previous definition [39], while the steady-state volume of distribution was estimated to be relatively small (2.69 L or 0.32 L/kg), with the central compartment occupying most of the distribution of ascorbate in dogs. The global extraction ratio of ascorbate (E) calculated as CL/Q [with cardiac output Q (mL/kg/min)] approximated by the formula: Q
= 180 × BW−0.19 [39], was estimated to be low (E = 0.03).
Prediction distributions (from the 2.5th to 97.5th percentile) derived from 1,000
Monte Carlo simulations confirmed the good performances of the final selected model which was able to reproduce the variability in the observed disposition kinetic data of circulating ascorbate following IV infusion dosing (figure 2.4).
The NCA PK parameters are collated in table 2.3. The mean maximum ascorbate plasma concentration was estimated as 9.23 ± 1.33 mM for beagles administered 2,200 mg/kg P-AscH− and 2.26 ± 0.61 mM for beagles administered 550 mg/kg P-AscH−. Peak plasma concentrations were observed around a median value of
5.5 ± 1.0 h. Mean clearance and steady state volume estimates were unremarkable
(2.05 ± 0.35 L/h and 3.52 ± 1.54 L respectively). The median elimination half-life was estimated at 3.73 ± 1.47 h. All NCA PK parameters agree well with their NLME counterparts.
Clonogenic Assay
To test the hypothesis that treatment with P-AscH− decreases clonogenic survival in canine osteosarcoma cancer cells, D-17 and OSCA-8 were treated with 0.25–50 33 pmol/cell ascorbate for 1 h. In both cell lines, P-AscH− treatment resulted in significant
(P < 0.001), dose-dependent decreases in clonogenic cell survival compared to untreated controls (figure 2.5, A). To test the hypothesis that P-AscH− causes differential susceptibility in osteosarcoma cells vs. normal canine dermal fibroblast, again clonogenic survival assay was performed. Optimal growing conditions for dermal fibroblast include proprietary media containing 1 mmol pyruvate and 4% O2. Both
O2 and pyruvate have been demonstrated to affect the production and removal of
H2O2 with ascorbate treatment [15], therefore clonogenic assay was done using 75 pmol/cell P-AscH− for 1 h and optimal fibroblast growing conditions for both the cancer cell lines and normal fibroblast cells. Treatment with P-AscH− demonstrated significant differential susceptibility in osteosarcoma cells vs. normal fibroblast by decreasing clonogenic survival in both osteosarcoma cell lines (D-17 63%, SD = 0.010, P = 0.005;
OSCA-8 50%, SD = 0.086, P = 0.026), more than normal fibroblasts (27%, SD = 0.056)
(figure 2.5, B).
Discussion
Based on the plasma ascorbate concentration analysis reported herein, it has been determined that it is safe to administer P-AscH− (2,200 mg/kg) to healthy dogs.
Using an infusion rate of 50 mL/h of a solution containing 500 mg ascorbate per mL, in vivo peak plasma ascorbate concentrations reached up to 10 mM and were found to be dose-dependent. To our knowledge, this is the first comprehensive characterization of ascorbate PK in dogs. A two-compartmental mammillary disposition model with first- order elimination and zero-order absorption after IV infusion dosing best described the available PK data. Parameter estimates of the final NLME model suggest that ascorbate has a rather low extraction ratio (0.03) but a small volume of distribution, resulting in a 34 short elimination half-life in dogs, in agreement with previous findings from the human literature [19].
Adverse effects that were previously noted in human studies, including vomiting, diarrhea, and weight loss, were minimal in our canine subjects [21]. During the infusion of both doses, and for at least 24 h post infusion, only one dog vomited. All dogs remained bright, alert, and responsive, had a good appetite following the infusion, and maintained their body condition. This suggests that P-AscH− will be well-tolerated in healthy dogs, even at elevated doses.
It is worth noting that in the present study, mild changes on blood gas analysis were noted after administration of 2,200 mg/kg P-AscH− (table 2.1). There are several possible explanations for these findings, the first of which is analytical interference. A significant elevation in anion gap and hyperlactatemia were observed 6 h into the infusion of the higher dose P-AscH− (2,200 mg/kg) in all eight dogs. Ascorbic acid has been shown to interfere with blood gas electrodes that use oxidase for amperometric methods of detection (namely lactate and glucose) [40,41], including the Siemens analyzer used in this study [42]. Additionally, when a comparable solution of ascorbate and sterile water was run alone, elevations in lactate were detected (table 2.1), suggesting the apparent hyperlactatemia is most likely due to an electrode analytical interference and may not be clinically relevant.
Alternatively, hyperlactatemia is a reported side effect of multiple drugs, the mechanism of which is varied but does include interference with the Cori cycle, inhibition of mitochondrial protein synthesis, inhibition of the electron transport chain
(ETC), and uncoupling of oxidative phosphorylation [43]. Recent research with P- 35
AscH− in humans revealed that several of the mitochondrial ETC complexes may be inhibited during treatment [7], possibly contributing to the hyperlactatemia. The true cause of the hyperlactaemia in the Beagles is unknown and may be a combination of analytical interference and more insidious causes. Awareness of this possible elevation is extremely important as use of ascorbate becomes prevalent in clinically ill dogs and humans. Future studies are needed to determine if hyperlactatemia is truly due to analytical interference or if it might be more clinically relevant.
Elevated bicarbonate and hypernatremia were noted and expected, as the formulation of P-AscH− is buffered by sodium and bicarbonate. Expected compensatory hypochloremia and high pCO2 were also observed. The elevation of sodium and decreased chloride may also be attributed to analytical inference, as erroneous hypernatremia and hypochloremia have been noted previously following the use of P-
AscH− [40]. Glucose, although expected to be high [44], was found to be decreased in all 8 Beagles. This was attributed to the fast prior to and during the infusion of P-AscH−.
Hypokalemia was likely due to increased diffusion of ascorbate into cells, followed by secondary increase in Na/K-ATPase activity and rapid intracellular potassium uptake (dogs synthesize ascorbate from glucose via the glucuronic pathway and absorb it via passive diffusion, while in people ascorbate requires facilitated diffusion or active transport) [45,46]. This is contrary to an expected hyperkalemia that has been noted in humans and has been attributed to an analytical interference [40].
This discrepancy may be attributed to the different mechanisms by which ascorbate is taken into cells in dogs compared to humans. 36
Calcium at the upper end of the reference interval post-treatment was an unexpected finding, as in people ascorbate acts as a weak calcium chelator, possibly leading to hypocalcemia [47]. However, ascorbate has been shown to interfere with calcium analysis, much like lactate, usually resulting in false elevations [40], which may have occurred in our study. In addition, high doses of oral ascorbate have previously been found to cause hypercalcemia in broiler chickens and hens, likely due to altered calcium metabolism (either enhancement of intestinal absorption or resorption of bone)
[48], which may be a phenomenon unique to species that can synthesize ascorbate, such as dogs.
Most of the blood gas analysis changes, although mathematically significant, were considered to be mild and are likely due to analytical interference caused by high concentrations of ascorbate in the plasma. Knowledge of these possible alterations, however, are important so that overzealous correction of these temporary, and likely clinically insignificant, changes does not occur to the detriment of the patient. Further analysis is necessary to make conclusions about the causes of these observed changes.
The two assays for the determination of plasma ascorbate concentrations used in this study have not previously been reported in a canine trial setting. The plate reader assay has been validated with canine, porcine and human plasma [28]. The 0 h results
(≈20 μM) from this study fall within the established detection range for the assay and correspond with values that were found in the validation study [28]. To date, the Implen
Nanophotometer has not been used to quantify plasma ascorbate in canines [49]. A recent study confirmed the ability to use UV spectroscopy to rapidly quantify high 37 concentrations (up to 35 mM) of human plasma ascorbate, with minimal processing
[27]. Using this same assay on our canine plasma samples detected ascorbate concentrations that corresponded with those found in human and murine studies
[7,17,21]. The novel use of these quantification methods in this study provides proof of concept for future studies.
In vitro, following treatment with P-AscH− ranging from 0.25 to 50 pmole/cell, the clonogenic cell survival of both OSA cell lines (D-17 and OSCA-8) was significantly decreased compared to untreated controls in a dose-dependent manner (figure 2.5, A).
Similarly, the clonogenic survival of both cell lines after treatment with 75 pmole/cell (7.5 mM) of P-AscH− was significantly decreased compared to normal canine fibroblasts
(figure 2.5, B). This is similar to human OSA in vitro studies, which showed a dose- dependent decrease in cell growth following exposure to P-AscH− (range of doses up to
1 mM) and a sparing of normal control cells; the most significant growth effects were found at the 1 mM concentration [50,51]. Similar findings have been confirmed for a variety of human tumors [7]. Recently, the in vitro effects of P-AscH− on canine melanoma cell lines have also been investigated, and show similar, dose-dependent findings with IC50 values (those that reduce the survival of each cell line by 50%) between 3.6 and 9.9 mM [52].
Utilizing human cell lines, ascorbate concentrations of 1–7 mM are required for cytotoxicity and additional cell kill is achieved with higher doses [10]. However, the suggested target level of plasma ascorbate that is believed to be most effective for humans is ≈20 mM [7]. When the Beagles received a dose of 2,200 mg/kg over 6 h, plasma levels peaked at approximately 10 mM around the 6 h mark. Although this is 38 above the in vitro cytotoxic threshold of 7.5 mM, it is below the target dose in humans.
However, it is not known if the human target level of 20 mM is required, or if lower plasma concentrations may be equally successful. In addition, in vitro data cannot be directly correlated with an expected cytotoxic dose in vivo, as conditions in these two situations are different [15]. Specifically, for in vitro P-AscH− treatment, the cell cultures contain 1 mM of pyruvate which is known to remove cytotoxic H2O2, potentially interfering with the main mechanism of action of P-AscH−, and decreasing the observed effects of P-AscH− in vitro [53].
The level of intracellular labile iron also influences the cytotoxicity of P-
AscH− [7,14]. In general, normal cells have a lower labile iron pool compared to cancerous cells, potentially explaining the sparing effects of P-AscH− on normal cells.
The level of labile iron in the OSA cells is unknown, but it is possible that they have a relatively decreased amount of iron, impacting the cytotoxicity of P-AscH− in vitro.
Similarly, this would impact cytotoxic levels in vivo should a particular patient have a tumor with inherently less labile iron, be anemic [54], have endogenous or exogenous exposure to glucocorticoids [55], or have circadian drops in iron [56], complicating administration and assessment of an expected cytotoxic dose. In vivo tumor analysis of
P-AscH− levels are required to fully assess the concentrations of P-AscH− achievable and if these levels are clinically effective.
In vitro analysis also fails to replicate the in vivo microenvironment that exerts a significant influence on the achievable intracellular levels of therapeutics. Thus, direct correlations between the cytotoxic in vitro dose of P-AscH− and that which will be cytotoxic in vivo is not possible. The in vitro information can guide in vivo experiments 39 and the interpretation of results. Our in vitro data suggest that P-AscH− is cytotoxic to canine OSA cell lines, providing proof of concept for additional investigations in tumor- bearing dogs.
Interestingly, it has been determined that pancreatic cancer, NSCLC, and GBM cells treated with ascorbate are more sensitive to concurrent or subsequent treatment with ionizing radiation and chemotherapy, while normal cells were spared [7,57]. In a murine model, it has been shown that pharmacologic ascorbate enhances pancreatic tumor cell radiation cytotoxicity while offering potential protection from radiation damage to normal surrounding tissue [57]. This indicates that adjuvant ascorbate combined with other cancer therapies, may be more advantageous than ascorbate alone, or that synergism between treatments may imply a lower dose of P-AscH− would still be effective [58]. Further research into this area is needed to determine the best use of ascorbate in our canine patients.
The most advantageous dosing strategy for P-AscH− is also unknown [20].
Recent literature report that the clearance of P-AscH− in humans following a 60-g dose was 6.0 L/h [19]. In light of this fast elimination from the body, a bolus loading dose followed by a maintenance infusion of P-AscH− was recommended to maintain P-
AscH− concentrations in the potential cytotoxic range (>20 mM) [19], but this dosing was not studied further. In the current Beagle study, a clearance of 2.0 L/h was identified.
This slower clearance may indicate that an in vivo cytotoxic dose is achievable in dogs.
This study evaluated the use of P-AscH− in healthy Beagle dogs. It is acknowledged that oncology patients may have significantly different plasma dispositions of P-AscH− due to their disease that may influence dosing, PK parameters, 40 toxicity, and efficacy of this treatment in the clinical setting. Clinical patients will be of a variety of breeds, who may process P-AscH− differently from Beagles due to genetic differences. In addition, clinical patients will be on a variety of medications, including chemotherapy, which may cause unintended drug-drug interactions, or alter the PK parameters, toxicity, and efficacy of P-AscH−. Additional studies in tumor-bearing dogs are needed to fully evaluate the PK parameters and impact of P-AscH− in canine oncology patients.
In summary, the findings presented here give a biological basis for the efficacy of ascorbate in vitro and an understanding of the pharmacokinetics of P-AscH− in healthy dogs. Together, they provide compelling evidence to investigate the concurrent use of ascorbate with standard of care chemotherapy and radiation therapy in tumor-bearing dogs. The combined in vitro and in vivo results suggest that P-AscH− may be a safe, reasonable adjuvant therapeutic option for dogs diagnosed with cancer, specifically osteosarcoma, and that cytotoxic doses of ascorbate may be achievable in vivo. Further studies are necessary to determine the optimal dose to achieve cytotoxic levels in tumor tissue, ideal dosing strategies, and to confirm the safety profile when combined with traditional oncologic therapies.
Data Availability Statement
The datasets generated for this study are available on request to the corresponding author.
Ethics Statement
The animal study was reviewed and approved by the Iowa State University
Institutional Animal Care and Use Committee. Compliance with the US National 41
Research Council's Guide for the Care and Use of Laboratory Animals was maintained throughout the study.
Conflict of Interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Author Contributions
MM, AM, MF, GB, BW, JM, and CJ were involved with experimental design, data analysis, and manuscript writing. MM and AM obtained all in vivo experimental data. GB and BW analyzed all blood samples for vitamin C levels. MF designed, executed, and analyzed the data of the in vitro cell culture experiments. BS, Y-JS, and JM interpreted the pharmacological data and prepared the PK model. BS and Y-JS assisted with manuscript writing and peer review.
Funding
This work was funded by a generous grant from the University of Iowa Sarcoma
Group; NIH R01 CA169046; and P01CA217797.
42
Tables and Figures
Table 3.1 Arterial Blood Gas and Electrolyte Abnormalities Observed in 8 Beagle Dogs After Receiving Pharmacological Ascorbate (2200 mg/kg) a) Blood was drawn at the 6-h mark immediately following cessation of pharmacological ascorbate infusion. b) IQR: interquartile range. c) P-values for differences were obtained from the Wilcoxon signed-rank test (significance level = .05). d) Canine Normal displays a generally accepted normal range for healthy dogs for each parameter for the RAPIDPoint 500 analyzer [57,58].
Parameter Median Median Median IQR P-valuec Canine Ascorbate Pre- Post- Difference Differenceb Normald and Sterile Ascorbate Ascorbatea (Post - Pre) Water Blank Ca (mmol/L) 1.37 1.40 .030 .030 .034 1.23 - 1.40 Decreased out of range Na (mmol/L) 146 152 6.00 4.25 .007 143 - 151 224x K (mmol/L) 3.56 3.39 - .170 .170 .015 3.60 - 4.70 < 1 Cl (mmol/L) 114 107 - 7.00 1.50 .013 109 - 117 N/A
HCO3 21.3 22.7 1.40 .900 .015 19.0 – 25.0 N/A (mmol/L) pCO2 37.1 39.9 2.80 3.15 .023 29.0 – 45.0 N/A (mmHg) Anion Gap 15.6 28.4 12.8 4.10 .007 12.0 – 21.0 N/A (mmol/L) Lactate .640 8.64 8.00 2.10 .007 .430 - 2.10 Increased (mmol/L) out of range Glucose 107 51.5 - 55.5 23.0 .014 62.0 - 115 246 (mg/dL) pH 7.37 7.37 0.00 .040 1.00 7.34 - 7.45 N/A
Table 3.2 Model Pharmacokinetic Parameter Estimates as Determined by the Stochastic Approximation Expectation-Maximization Algorithm
Parameter Symbol Unit Point Estimate RSE (%) IIV (%) Clearance CL L/h 2.04 3.18 6.86
Central Volume V1 L 1.96 5.99 11.9 Inter-compartmental Q L/h 0.16 15.0 - Clearance Peripheral Volume V2 L 0.76 24.7 46.6
RSE: Relative Standard Error of the Estimate; IIV: Inter-individual Variability
43
Table 3.3 Noncompartmental Analysis Pharmacokinetic Parameters
Median PK Parameters
Group AUCINF CMAX CSS VSS Cl TMAX T1/2 λz
Unit mM*h mM mM L L/h h h 1/h
All 12.7 2.17 5.08 2.53 1.84 5.0 3.73 0.138
2.2 g/kg 49.0 8.26 8.88 2.23 1.83 4.0 3.87 0.149
0.55 g/kg 11.1 1.94 2.11 3.18 1.85 5.0 3.73 0.124
Figure 3.1 In Vivo Pharmacokinetics of Two Doses of Pharmacological Ascorbate in Eight Healthy Beagle Dogs Distribution of individual ascorbate concentrations (small open circles) are plotted alongside the mean ascorbate concentrations (dashed line) and standard error (bars) for all observations at each time point following ascorbate infusions (550 and 2,200 mg/kg).
44
Figure 3.2 Pharmacokinetic Schematic Representation of the Two-Compartment Model Developed in this Study Ascorbate was administered intravenously (I.V.) with an infusion time denoted by tinf. The transfer between the two compartments is governed by intercompartmental transfer parameter Q, and the drug's elimination was determined by the clearance from the central compartment (CL).
Figure 3.3 Individual Predicted Concentration of Ascorbate in Plasma Individual predicted curves (blue) are plotted against the individual measurements of ascorbate (gray circles) over time. There are two individual fits for each animal dependent on dose. The difference between the individual predictions and observations defines the residual error in the model, which is low in these cases. 45
Figure 3.4 Prediction of Ascorbate Distribution These figures were produced by Monte Carlo simulation from the model fit. Briefly, a population of 2,000 individuals were simulated. Half were virtually administered a dose equal to 2,200 mg/kg and the other half were administered a dose equal to 550 mg/kg. Then, at each time point from 0 to 16 h in steps of 0.05 h, i.e., (0, 0.05, 0.1, 0.15, …,15.95, 16), the quantiles of the resulting simulations were calculated and plotted along with observations for comparison (gray dots).
Figure 3.5 Pharmacological Ascorbate Treatment Results in Selective Clonogenic Cell Death in Canine Osteosarcoma Cell Lines (A) Significant dose dependent decreases in clonogenic survival for two osteosarcoma cell lines (D-17 and OSCA-8) following treatment with 0.25–50 pmol/cell ascorbate at 21% O2 DMEM no pyruvate 10% FBS media. (B) Significant survival differences between two osteosarcoma cell lines (D-17 and OSCA-8) vs. primary canine fibroblasts after treatment with 75 pmol/cell ascorbate in fibroblast media 4% O2. *Denotes statistical significance. 46
Figure 3.S1 Assessment of Quality of Model Fit Individual observations and individual predictions are plotted against each other to analyze the quality of model fit. Points have semi-transparent grey fill to reduce visual distortions due to over-plotting. The dashed cyan line is the spline best-fit for the data and the solid black line is the line of perfect fit (i.e. observation exactly equals prediction). The difference between the dashed and solid line indicates the degree to which the model is misspecified. Here, the misspecification is very low. Predictions are displayed in log10 scale to allow analysis of model fit across the full range of observations (min = 0.03, max = 11.64).
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CHAPTER 4. OPTIMAL SCHEDULING OF BEVACIZUMAB AND PEMETREXED/CISPLATIN DOSING IN NON‐SMALL CELL LUNG CANCER
Authors and Affiliations
Benjamin K Schneider1, Arnaud Boyer2,3, Joseph Ciccolini2, Fabrice Barlesi3,
Kenneth Wang4, Sebastien Benzekry1,5* and Jonathan P Mochel1*
1Iowa State University College of Veterinary Medicine, Ames, IA, U.S.A,
2SMARTc Unit, Centre de Recherche en Cancérologie de Marseille UMR Inserm
U1068, Aix Marseille University, Marseille, France 3Multidisciplinary Oncology and
Therapeutic Innovations Department, Assistance Publique Hôpitaux de Marseille,
Marseille, France, 4Mayo Clinic, Rochester, MS, U.S.A, 5Team MONC, Inria Bordeaux
Sud-Ouest, Institut de Mathématiques de Bordeaux, France. *: co-last authors.
Modified from a manuscript published in Clinical Pharmacology and
Therapeutics: Pharmacometrics & Systems Pharmacology.
Abstract
Bevacizumab-pemetrexed/cisplatin (BEV-PEM/CIS) is a first line therapeutic for advanced non-squamous non-small cell lung cancer (NSCLC). Bevacizumab potentiates PEM/CIS cytotoxicity by inducing transient tumor vasculature normalization.
BEV-PEM/CIS has a narrow therapeutic window. Therefore, it is an attractive target for administration schedule optimization. The present study leverages our previous work on
BEV-PEM/CIS pharmacodynamic modeling in NSCLC-bearing mice to estimate the optimal gap in the scheduling of sequential BEV-PEM/CIS. We predicted the optimal gap in BEV-PEM/CIS dosing to be 2.0 days in mice and 1.2 days in humans. Our simulations suggest that the efficacy loss in scheduling BEV-PEM/CIS at too great of a 54 gap is much less than the efficacy loss in scheduling BEV-PEM/CIS at too short of a gap.
Introduction
Bevacizumab-pemetrexed/cisplatin (BEV-PEM/CIS) combination therapy has been shown to be an effective first line and maintenance therapy for non-small cell lung cancer (NSCLC) in Phase II and Phase III clinical trials [1,2]. Pemetrexed inhibits enzymes necessary for pyrimidine and purine synthesis – primarily thymidylate synthase, which is necessary for thymidine synthesis and tumor cell replication [3].
Cisplatin is an alkylating agent which crosslinks adjacent N7 centers on purine residues, damaging DNA, disrupting repair, and disrupting purine synthesis [4–6]. Disrupting DNA substrate supply results in S-phase arrest, DNA repair disruption, and eventually apoptosis [7,8]. Cisplatin also significantly disrupts calcium and reactive oxygen species
(ROS) regulation, inducing cellular lesions which further sensitizes cancer cells to apoptosis [6].
In contrast to the effect of PEM/CIS, i.e. DNA damage, bevacizumab is an anti-
VEGF (vascular endothelial growth factor) humanized monoclonal antibody. VEGF is an angiogenic potentiator which promotes the growth of endothelial tissue necessary for arteries, veins, and lymphatics. By limiting neovascular growth, and therefore blood delivery to neoplasms, bevacizumab exhibits limited antiproliferative properties [9].
More importantly, bevacizumab transiently induces a pruning effect on neovascular beds, which normalizes blood supply to neovascularly dense tissues (i.e. tumors) [10–12]. By normalizing blood supply, bevacizumab enhances chemotherapeutic (i.e. PEM/CIS) delivery to neoplasms [13,14]. 55
The effects of BEV-PEM/CIS are generalized i.e. any cell capable of uptaking the drugs are susceptible to their effects, especially rapidly-dividing cells such as myeloid cells [15]. Accordingly, BEV-PEM/CIS has a narrow therapeutic window and generalized side-effects [16]. Previous studies on BEV-PEM/CIS suggest that sequential administration of BEV-PEM/CIS (i.e. BEV before PEM/CIS) outperforms concomitant scheduling of BEV-PEM/CIS in treating NSCLC [11,17–19]. This makes
BEV-PEM/CIS an attractive target for scheduling optimization via modeling and simulation, as a range of practical predictions – such as optimal scheduling in humans – can be made without the considerable time and resource investment required to conduct in vivo experiments. These predictions can be used to guide future studies, greatly accelerating drug development [20].
In our previous work on BEV-PEM/CIS published in Imbs et al. 2017 [17], mice with NSCLC tumor xenografts were administered bevacizumab with PEM/CIS combination therapy (CT) in either concomitant, or delayed (i.e. bevacizumab before
PEM/CIS) scheduling. The NSCLC tumors had been modified such that tumor growth could be tracked over time via either bioluminescence or fluorescence. Following previous theoretical investigations, the dataset generated from the mice with bioluminescent tumors was used to develop a semi-mechanistic PK/PD model for tumor dynamics in response to BEV-PEM/CIS [21,22]. The model was then used to predict the optimal scheduling gap between bevacizumab and PEM/CIS administration.
The aim of this follow-up modeling work was to both refine and expand upon previous results on BEV-PEM/CIS CT using the much larger fluorescence dataset generated in Imbs et al. 2017 [17]. We first showed that the semi-mechanistic model 56 previously developed better explained the data than comparable models (i.e. we validated the previously developed structural model). Then, we refined the parameter estimates of the model, and used it to predict the optimal scheduling gap between bevacizumab and PEM/CIS administration. Next, we used stochastic simulations to explore the marginal loss in therapeutic efficacy when BEV-PEM/CIS was administered at a sub-optimal gap, the effect of bevacizumab dose scaling on population optimal gap, as well as the inter-individual variability (IIV) of optimal gap. Here, marginal loss in therapeutic efficacy refers to the loss in treatment efficacy from either scheduling the drugs with a gap shorter or longer than the optimal gap e.g. 1 day earlier or later than the optimal gap. Lastly, using literature human PK/PD models and parameter estimates, we were able to scale the model to estimate the optimal scheduling of BEV-PEM/CIS in humans.
Methods
Experimental Procedure
Comprehensive details on animals and the experimental procedure are available in Imbs et al. 2017 [17]. Briefly, on Day 0 of the experiment, tumors (ca 120,000 cells) consisting of H460 human NSCLC transfected with luciferase and the tdTomato gene
(H460 Luc+ tdTomato+, Perkin Elmer France) were injected ectopically into the left flank of 90 mice. Animals were pathogen-free, immunocompromised, 6-week-old, female
Swiss nude mice (Charles River, France). The mice were randomized into one of five treatment groups. The first study group (Control) received no treatment. The second treatment group (PEM/CIS) was administered both 100 mg/kg of pemetrexed IP and 3 mg/kg of cisplatin IP on Days 14, 28, and 42 of the experiment. The third, fourth, and 57 fifth treatment groups (BEV-PEM/CIS) received the same PEM/CIS treatment as the second experimental group.
In addition, the BEV-PEM/CIS treatment groups were administered 20 mg/kg IP of bevacizumab either concomitantly with the PEM/CIS administrations (group 3), 3 days prior to each PEM/CIS administration (group 4), or 8 days prior to each PEM/CIS administration (group 5) – see table 4.S1 for administration tabulation.
Tumor growth was monitored on a minimum bi-weekly basis using Ivis Spectrum imager (Perkin Elmer France) and images were acquired and analyzed using the Living
Image 6.0. software (Perkin Elmer France).
Mice were supplied with paracetamol supplemented water (e.g. 80 mg/kg/day) to prevent disease-related pain. Animals showing signs of distress, pain, cachexia (i.e. loss of 10% of body mass), or extensive tumor proliferation (i.e. within 2-3 cm) were euthanized. All animals were euthanized on Day 87 of the experiment. All experiments were approved by the local ethical committee at French Ministère de l’Education
Nationale, de l’Enseignement Supérieur et de la Recherche, and registered as
#2015110616255292.
PK/PD Structural Model Building and Evaluation
The PK models for bevacizumab, pemetrexed, and cisplatin were derived from previously published PK models in mice [23–25]. The parameters for these models were fixed to the typical values from those studies and assumed no IIV.
The PD model was selected from a series of sequentially fit tumor growth and drug effect models. First – using only the control dataset – the exponential, linear- exponential, and Gompertz growth model were cross-evaluated as models of unperturbed tumor growth [26]. Then, incorporating the full dataset into the fit, the log- 58 kill effect of bevacizumab, log-kill effect of pemetrexed, and log-kill effect of cisplatin were each considered. The interaction effect between bevacizumab and PEM/CIS was included to represent the synergistic effect of bevacizumab. Following previous work for the effect of cytotoxic drugs, three cellular death compartments were included in the PD portion of the model to represent the delay between cellular damage due to PEM/CIS and cell death [27].
Competing models were evaluated numerically using Bayesian information criteria (BIC) and the precision of parameter estimates – defined as the relative standard error of the estimate (RSE). Observed vs. predicted plots, individual fit plots, and Visual Predictive Checks (VPCs) were produced to graphically assist model evaluation (as automated in Monolix 2018R2). VPCs were produced using the default estimation process for VPCs as of Monolix 2018R2 i.e. to create the 90% prediction intervals for the 10th, 50th, and 90th percentiles, 500 simulations are performed using random individual parameters and the design structure of the experiment.
After model selection, the statistical correlations between random-effects were explored via visual inspection. Correlations plots between random effects were
produced, defined as 휂푖,푡,휙1 vs 휂푖,푡,휙2 i.e. the random effect 휂, of individual 푖, at time 푡, of parameter 1, i.e. 휙1, vs the random effect 휂, of individual 푖, at time 푡, of parameter 2, i.e.
휙2. The full posterior distribution of the parameters were used in place of EBEs to avoid visual artifacts due to shrinkage as suggested by Lavielle, et al, 2016 [28] and Pelligand
L, et al, 2016 [29]. Statistical correlations between random effects were also numerically assessed using a Pearson correlation test at a P < .05 threshold. 59
SAEM convergence and final model parameterization were graphically assessed by inspection of search stability, distribution of the individual parameters, distribution of the random effects, individual prediction vs. observation, individual fits, distributions of the weighted residuals, as well as VPCs.
The precision of parameter estimates was numerically assessed using RSE. The normality of random effects distributions, the normality of individual parameter distributions, and the normality of the distribution of residuals were each numerically assessed using a Shapiro-Wilk test (P < .05). The centering of the distribution of residuals (i.e. centered on 0) was numerically assessed using a Van Der Waerden test
(P < .05).
Parameter stability was assessed by comparing parameterizations resulting from random-initial starting value selection – as implemented in the Monolix assessment suite. The assessment suite performs 5 SAEM parameterizations in series using random initial parameter values uniformly drawn from the interval from approximately
60% to 160% of final parameter estimates. The SAEM of the individual parameterizations was then tracked between runs - giving a range of parameter value estimates, RSEs, and log-likelihoods to compare. This assessment was used to ensure that the algorithm did not converge to a log-likelihood local minimum during the process of producing final parameter estimates. The settings described are the default as of
Monolix 2018R2.
Simulations
Simulations were performed in R 3.4.4 using Simulx 3.3.0 [30] to simulate from
Monolix run files. First, a function was built which accepted treatment schedule, parameter substitutions, dose, and number of individuals as input and produced a 60 simulated population as an output. This function was simply a convenience wrapper of
Simulx for automation purposes and was verified by reproducing VPCs per treatment group. Simulation set 1 was used to predict the optimal gap between administration of bevacizumab and PEM/CIS. Simulation set 2 produced an estimate of the IIV of the optimal gap. Simulation set 3 examined the anticipated effect of varying the dose of bevacizumab on the optimal gap. Simulation set 4 scaled predictions of BEV-PEM/CIS efficacy to humans. All simulations were of population level response (i.e. simulated without RSE or IIV) except for simulation set 2 (simulated without RSE and with IIV) which used 1000 Monte Carlo samples. Further details are provided in the supplementary methods.
Quality Assessment
All mlxtran and R codes were assessed for quality control by an independent evaluator. Results
Error Model
Measurement error was best described using a log-normal constant-error model
(equation 1). The natural-log of each individual measurement, 푙푛(푦푖푗) with individual i and repetition j, was modeled as a measurement centered on the natural-log mean of
푦푖푗 over j, i.e. 푙푛(𝑥̄ 푖), in addition to some residual error, 휖푖푗, normally distributed, centered on zero, and with standard deviation 푎.
휖푖푗 푦푖푗 = 𝑥̄ 푖 ⋅ 푒 푤ℎ푒푟푒 푙푛(푦푖푗) = 푙푛(𝑥̄ 푖) + 휖푖푗 | 휖 ∼ 푁(0, 푎) (equation 1) The sGOF graphics and numerical analyses supported that a log-constant error model best fit the data. The log-constant error model was not rejected for both the Kolmogorov-Smirnov test for normality (P = .22) nor the Pearson chi-square normality test (P = .0509). In contrast, a constant error model was rejected by these two tests (see figure 4.S1 for further details). 61
PKPD Structural Model Building
No outliers were identified during initial data exploration. Therefore, no collected data were excluded from model building. The pharmacokinetics of bevacizumab, pemetrexed, and cisplatin were each modeled using one-compartment models with first order IP absorption and first order elimination based on literature descriptions and PK parameter estimates (table 4.S3)
[23–25]. Random effects (i.e. 휂푝푘) were set to 0 as individual PK was not reported in these experiments. A Gompertz function (equation 2) was found to best describe the unperturbed tumor growth 푉(푡), based on its fit performance over competing models, low RSE on parameter estimates, and literature-established descriptive quality.
(α − β ∙ ln(푉⁄푉푐)) ∙ 푉 (equation 2) Due to relative sparseness in sampling, fitting more complex semi-mechanistic models of growth incorporating cellular quiescence, biphasic growth, and cell-type heterogeneity did not produce model fits with lower BIC or comparable precision in parameter estimates (RSE) to the simpler Gompertz model of tumor growth. Parameters 훼 and 훽 represent the proliferation rate of the tumor cells and rate of exponential decrease of the tumor relative growth rate, respectively. 푉퐶 is the unit value of relative fluorescence units (RFU) corresponding to one cell, i.e. the proportionality constant between RFU and the number of cancer cells in the fluorescent volume.
푉퐶 was estimated externally from Monolix by conducting a naive-pooled, linear- regression on the natural-log of the full dataset. The regression gave a rough estimate of 푉0 which was then scaled by the approximate number of cells injected at time 0 (ca. −4 120,000 cells) to derive 푉퐶 = 5.064 × 10 RFU. After selecting an appropriate growth model, the log-kill effects of pemetrexed, cisplatin, and bevacizumab were each considered in parallel. The log-kill effect of bevacizumab was estimated as insignificant and removed from the model. The estimation of the log-kill effect of pemetrexed and cisplatin were found to be highly correlated. To reduce model complexity, only their combined concentration, 퐶(푡), and a corresponding log-kill parameter, 훾, were considered in the final model (equation 3). 62
휏 휏푏표푢푛푑 ∙ 10 ‐
푄(푡) 1 + 훿 ∙ 퐴(푡 − 휏) ‐
V̇ (α − β ∙ ln(푉⁄푉 )) ∙ 푉 − γ푄퐶푉 푉(0) = 푉 푐 0 푍1̇ = 훾푄퐶푉 − 푘 ∙ 푍1 , 푍1(0) = 0 (equation 3)
̇ 푍2 푘 ∙ (푍1 − 푍2) 푍2(0) = 0
푍̇ 푘 ∙ (푍 − 푍 ) 푍 (0) = 0 3 2 3 3 [ ] [ 푁 ] [ 푉 + 푍1 + 푍2 + 푍3 ] ‐
퐴(푡) represents the plasma concentration of bevacizumab. 푄(푡) represents the synergistic effect of improved vascular quality. In brief, the increase in neoplasm vascular quality due to bevacizumab typically occurs within a period of a few days after administration. To represent this delay in effect, time (푡) was delayed by 휏. Parameter 훿 represents the proportional increase in PEM/CIS efficacy due to vascular quality improvement under bevacizumab therapy. The estimation of 휏 was bounded between 0 and 10 using the link function
휏 = 휏푏표푢푛푑 ⋅ 10, where 푙표푔푖푡(휏푏표푢푛푑) ∼ 푁(0,1). All other parameters were best estimated as log-normally distributed. The full statistical representation of individual parameters,
휙푖, estimated via SAEM is shown in equation 4, where the full structural model is denoted by 퐹. (equation 4)
푎 휀푖푗 푦푖푗 = 퐹(훷푖, 푡푖푗) ∙ 푒 , 푗 휖 {1, … , 푛푖}
훼 = 훼 ∙ 푒휂훼,푖 푖 푝표푝 휂훽,푖 훽푖 = 훽푝표푝 ∙ 푒
훾 = 훾 ∙ 푒휂훾,푖 푖 푝표푝 휂훿,푖 휙푖 = 훿푖 = 훿푝표푝 ∙ 푒 , 푖 휖 {1, … , 푁}
푙표푔푖푡(휏 ) = 푙표푔푖푡(휏 ) + 휂 푏표푢푛푑푖 푏표푢푛푑푝표푝 휏푏표푢푛푑,푖 휂 푉 = 푉 ∙ 푒 푉0,푖 0푖 0푝표푝 [ 푘푖 = 푘푝표푝 ]
Cellular death due to chemotherapeutic treatment was modeled as a three- compartment transition from the growth compartment to death [27]. The compartments 63
are labeled 푍1, 푍2, and 푍3 (numbering respective to their order) and transition between compartments is governed by intercompartmental clearance parameter 푘. After a period of manual exploration, 푘 was set to the value of 0.3. This choice is consistent with the parameterization made in Imbs et al [17]. This choice also limits the total transition time from the tumor mass compartment to cellular death to the order of a day which is consistent with upper limits of cellular death clearance [31]. The full tumor size, 푁, was the sum of the size of unperturbed cells, 푉, as well as the size of damaged cells undergoing cellular death i.e. 푍1 + 푍2 + 푍3. No correlations between random effects were statistically significant enough to be included in the final model (figure 4.S2). Full parameter estimates and model diagram are provided in table 4.1 and figure 4.1 respectively. Model diagnostics are collected in figure 4.2 through figure 4.4. Simulations
Mouse simulations
Simulating the experimental treatments with a range of administration gaps from 0 to 10 days (step-size = 0.1 day) suggested that the optimal time delay between scheduling bevacizumab and PEM/CIS in mice is 2.0 days (simulation set 1). The simulated IIV of the optimal gap was relatively small. Only three values of individual optimal gap were produced. 96.5% of the virtual animals had an individual optimal gap of 2.0 days, 1.0% of the virtual animals had an individual optimal gap of 2.1 days, and 2.5% of virtual animals had an individual gap of 1.9 days (simulation set 2). Scaling the dosage of bevacizumab to either 30 mg/kg or 10 mg/kg produced no effect in the estimated optimal gap and produced no effect in the IIV of the optimal gap (simulation set 3). Human simulations
Simulations of the typical human response to chemotherapy and bevacizumab were performed using IV administration, two-compartment absorption, and first order elimination models and parameters [32–34]. Dosage, infusion time, and frequency of administration for BEV-PEM/CIS were adapted from the induction phase of the AVAPERL phase III clinical trial in BEV-PEM/CIS [2]. Average adult weight and BSA 64 were obtained from Center for Disease Control and literature estimates respectively [35,36]. Except for the proliferation rate of the tumor cells and rate of exponential decrease of the tumor relative growth rate (i.e. 훼 and 훽), the PD model and parameterization (훾, 훿, 휏, 푘) were reused exactly as they were determined in the mouse portion of the model. 훼 and 훽 estimates were obtained from Bilous et al. 2018 [37], where clinical NSCLC doubling times reported in Friberg and Mattson, 1998 [38] were used to estimate population 훼 and 훽 for NSCLC in humans. The value of VC came from the classical assumption that a 1 mm3 volume of tumor cells is approximately 106 cells 3 [39]. V0 was arbitrarily set to 3 cm . This scaling procedure resulted in an adapted model primarily constructed to predict optimal gap in humans. In contrast, the model relies on several implicit assumptions for scaling tumor response (see the supplementary methods). The full PK/PD model was then used to simulate the typical cancer growth under various administration schedules with a starting tumor volume of 3 cm3. Parameter estimates are reported in table 4.2, simulation administration schedule is reported in table 4.S2, and simulation summaries are depicted in figure 4.5. The estimated optimal gap between bevacizumab and PEM/CIS administration in humans was 1.2 days. Discussion
By normalizing tumor vasculature, bevacizumab improves delivery of PEM/CIS to tumors and consequently PEM/CIS efficacy. Pemetrexed and cisplatin each have a narrow therapeutic window, and high toxicity. It is therefore critical that BEV-PEM/CIS doses are administered as efficiently as possible. This makes BEV-PEM/CIS a natural fit for modeling and simulation studies, as the drug scheduling can be optimized without the need for multiple time and resource intensive in vivo studies. In this analysis we conducted an in-silico study of the optimal administration of BEV-PEM/CIS in a xenograft, and human, model of NSCLC by constructing a mathematical model of tumor dynamics in response to BEV-PEM/CIS. In constructing that model, we were able to validate and refine previous modeling in BEV-PEM/CIS. Greater precision in parameter estimates was achieved through external estimation of 푉푐, external validation of the residual error model, as well as using the larger fluorescence dataset to obtain final 65 parameter estimates. Then, after exploring a range of predictions in mice, we scaled our model to predict optimal scheduling in humans. In the error modeling portion of the experiment, we demonstrated a strategy through which the choice of the error model can be validated externally to the primary dataset by including supplementary data collection in the experimental design. This simplified the error modeling step in the model building process. The next stage of this study consisted of determining whether the semi- mechanistic model of tumor dynamics in response to BEV-PEM/CIS developed in Imbs et al. 2017 [17] best fit the unfit fluorescence data from the same study. During model building, we attempted to balance our model building procedure between model performance (empirical fit) and the underlying biology, an approach often referred to as the middle-out approach [40,41]. In selecting potential PD models of tumor growth, several semi-mechanistic models were fit to the experimental data. The Gompertz model and linear-exponential model performed comparably. The parameters of the Gompertz model were estimated with greater precision than the parameters of the linear-exponential model (RSE) where the linear-exponential model was fit with a lower BIC than the Gompertz model. Ultimately, the Gompertz model was chosen over the linear exponential model due to the physiological relevance of its construction. The parameterization of the final model was slightly unstable due to modest overparameterization. To compensate for this, 푘 was fixed to a reasonable physiological estimate to improve precision of parameter estimates, and the search for 휏 was bounded to reduce spurious individual parameter estimates. During structural model building, we confirmed the validity of the model previously published in Imbs et al. 2017 [17] We also reconfirmed the efficacy improvement of BEV-PEM/CIS dosing over PEM/CIS or control. We observed that a 3 day gap in scheduling is superior to both concomitant scheduling and an 8 day gap in scheduling. We were also able to build on previous work by identifying with greater precision the parameters underlying the mathematical model of BEV-PEM/CIS in NSCLC-tumor bearing mice. 66
In our mouse simulations, the final tumor volume (after 67 days) in the optimal scheduling group with BEV-PEM/CIS (gap = 2.0 days) was 88.5% of the size of final tumor volume in the concomitant scheduling group. This is consistent with our experimental results i.e. that mice administered bevacizumab approximately 2.0 days before PEM/CIS have a moderately better response (i.e. greater tumor size reduction) to BEV-PEM/CIS than mice who are administered BEV-PEM/CIS concomitantly. We also found, through simulation, that scaling the dose of bevacizumab had no effect on the optimal gap and that IIV on gap is low. Predictions made by our model agree with previous findings in BEV-PEM/CIS scheduling. The order of the optimal scheduling delay (2.0 days) is within the 1 to 5 day gap predictions of previous studies [11,18,19]. Studies in tumor perfusion and bevacizumab showed Day 1 and Day 4 decrease in tumor perfusion which is consistent with the marginal predictions in our study i.e. optimal perfusion should be on the order of 2 days with comparable marginal losses on either side of that minimum [42]. After adapting our model to make simulations in humans, we predicted a robust response to both sequential and concomitant BEV-PEM/CIS scheduling. The final tumor volume (after 85 days) in the optimal scheduling group (gap = 1.2 days) was 52% of the size of the final tumor volume in the concomitant scheduling group. If these predictions are accurate, scheduling optimization could result in significant improvement in BEV- PEM/CIS CT efficacy with no increase in toxicity. Since the dose of the therapeutics, their pharmacokinetics, administration method, and dosing schedules are different in humans vs. tumor-bearing mice, a shift in the optimal gap is expected between species. In this study, the discrepancy between the optimal gap in humans vs. NSCLC tumor-bearing mice is driven by the slow IP absorption of bevacizumab in mice (table 4.S3). When exploring marginal efficacy loss in sub-optimal administration schedules, we consistently found that the marginal cost of scheduling bevacizumab and PEM/CIS too close together in time was greater than the marginal cost of scheduling bevacizumab and PEM/CIS with too great of a gap in administration - in both mice and humans. This indicates that any potential clinical studies in antiangiogenics and 67 cytotoxics should weight scheduling recommendations toward scheduling at slightly too large of gap. Lastly, we would like to acknowledge some limitations of this study. The tumor microenvironment is known to be complex and varied. Tumor tissues contain necrotic pockets, heterogenous and dynamic microvasculature, and various sub-mutations which result in differential local growth rates and drug sensitivities. Furthermore, bevacizumab efficacy is potentially disease state dependent. Considering this biological heterogeneity and identifying biomarkers for measuring individual response would greatly improve future model predictions, model scalability between species, as well as modeling-based individualized therapy development. In summary, our analysis confirms previous findings in BEV-PEM/CIS scheduling while improving precision of parameter estimates, improving prediction quality and detail, and scaling the model to predict the optimal scheduling of BEV-PEM/CIS in humans. Antiangiogenics will continue to be useful agents in oncology. There are currently several other antiangiogenics regularly used in combination with cytotoxics which could potentially benefit from sequential administration (i.e. antiangiogenic then cytotoxic) [43]. Of note, bevacizumab is currently only approved for concomitant administration with chemotherapy in all of its indications e.g. lung cancer, breast cancer, gastric cancer, etc. This contrasts with the optimized sequential scheduling that model simulations suggest. There is a recent trend to develop model-informed drug development to optimize anticancer therapy. Our work highlights how mathematical modeling could help to refine clinical treatment modalities. The semi-mechanistic nature of this model allows it to be modularly reconfigured to extend predictions to other antiangiogenics as well as novel therapeutic paradigms such as the immune checkpoint inhibitor, monoclonal antibody pembrolizumab [44]. This work continues to lay the foundation for building systems pharmacology models of the effect of antiangiogenic and antiproliferative combination therapy in advanced NSCLC. Tortuous vasculature is a phenotype exhibited by many solid tumors, and predicting optimal antiangiogenic scheduling could greatly increase the efficacy of future oncology therapeutics and combination therapies [45]. 68
Acknowledgements
We would like to thank Yeon-Jung Seo of Iowa State University College of Veterinary Medicine, Ames, IA, U.S.A, for performing the quality control assessment on code written to produce this study. We thank Dr Valerie Le Morvan and Professor Jacques Robert from the Institut Bergonié, France, for their kind assistance. Conflicts of Interest
The authors declared no conflicts of interest.
Author Contributions
B.K.S., S.B., and J.M. wrote the article. J.C., F.B., and S.B. designed the previous research. A.B. and J.C. performed the previous research. B.K.S., S.B., and J.M. analyzed the data. Supplementary Methods
Simulation Details
In simulation set 1, population response was simulated with no IIV and without
RSE. The simulated treatment schedule consisted of 100 mg/kg of pemetrexed IP and 3 mg/kg of cisplatin IP on Day 14, 28, and 42. 20 mg/kg IP of bevacizumab was virtually administered anywhere from 0 to 10 days (in steps of .1) before Day 14, 28, and 42.
See table 4.S2 for details.
The simulation was stopped after 67 virtual days. These simulations allowed the prediction of the optimal gap between administering bevacizumab and PEM-CIS.
Efficacy of the drugs was assessed using AUC of the tumor growth over time as calculated by the spline method implemented in the R package DescTools 0.99.25 [1].
The optimal gap was defined as the administration scheduling gap which resulted in the lowest AUC of tumor growth vs. time over the simulated time period (t = 0 to t = 67). 69
In simulation set 2 the inter-individual variability of optimal gap was meticulously calculated using a virtual population of 1000 simulated mice. First, a set of parameters representing 1000 virtual mice was generated without RSE from the parameter distributions determined in the structural modeling phase. Then, the procedure from simulation set 1 was replicated per individual to estimate each individual optimal gap.
Finally, the distribution of individual optimal gaps was assessed using the mode, standard deviation, and range as well as graphical methods such as a violin plot of count density.
To produce simulation set 3, the procedure which generated simulation set 1 was repeated with scaled doses of bevacizumab. First, 10 mg/kg IP of bevacizumab was substituted for 20 mg/kg IP of bevacizumab. Second, 30 mg/kg IP of bevacizumab substituted for 20 mg/kg IP of bevacizumab. This was done to assess the effect of bevacizumab dosage on the estimated optimal gap.
In simulation set 4 an analogous treatment regimen to simulation set 1 was simulated in a virtual NSCLC tumor-bearing human population using adapted human dosing recommendations (see table 4.S2). The random effects were set to zero and population response was simulated without RSE. Therefore, our simulations represent the average effect of varied administration schedule.
The model used in simulation set 4 was a scaling of the model fit obtained from the xenograft mouse model. The PK portion of the model was built and parameterized using previously published PK models and typical parameter values. The PD parameter estimates were obtained from both the xenograft mouse model and from literature values. 70
Tumor dynamics in response to PEM-CIS-BEV were simulated using a scheduling gap of 0 days to 10 days in steps of 0.1. A graphical representation of the
AUC vs. administration gap was generated to determine the optimal gap between bevacizumab and PEM-CIS dosing.
Further Justification and Limitations of Scaling Procedure
Xenografts were grown after subcutaneous implantation in the mice flank, and not directly in the lungs. This is because monitoring tumor growth of lung orthotopic xenografts with non-invasive techniques is limitingly difficult due to both the rapid movements of the chest in mice during imaging, and photon emission attenuation by the high amount of water in lung tissues. Consequently, ectopic xenografts were considered as the more robust experimental model for data collection. The molecular profile of xenografts has a high degree of similarity with the molecular profile of the primary tumors from which the xenograft was derived [2]. This indicates that there is a compositional heterogeneity between xenografts and primary tumors. In addition, human NSCLC H460 cells are an experimentally established paradigm for modeling
NSCLC tumors [3–5].
As mentioned in the manuscript, dosage, administration route (IV), frequency of administration, and infusion time were adapted from the induction phase of the
AVAPERL phase III clinical trial in BEV-PEM/CIS [6] and are summarized in a table
4.S2.
The human PK portion of the model was re-parameterized using IV administration, two compartment absorption, and first order elimination models and parameters from Lu et al. 2008 [7] (bevacizumab), Latz et al. 2006 [8] (pemetrexed), 71 and Urien et al. 2005 [9] (cisplatin). These PK studies were all performed in diverse populations of cancer patients i.e. not all patients were NSCLC patients.
Human 휶 and 휷 estimates came from Bilous et al. 2018 [10], where human 훼 and
휷 parameter values were estimated from clinical NSCLC data. In contrast, 휸, 휹, and 풌 were reused exactly as they were determined in the mouse portion of the model, as human parameter values and efficacy data for BEV-PEM/CIS are not available in the current literature. Theoretically, these parameters should not affect the predicted optimal gap, but they could affect the scale of efficacy in our simulations.
흉 was reused as determined in the mouse portion of the model for both physiological and literature value availability reasons. With respect to mechanism of action, bevacizumab acts by inhibiting VEGF-A produced by NSCLC cells [11]. Previous work has established that bevacizumab’s effect is asymptotic [12,13]. In other words, if bevacizumab is maintained at some minimum inhibitory plasma concentration, its effects on VEGF-A signaling should remain consistent between xenograft and primary tumors. This was the physiological basis for reusing 흉 when scaling the model to make predictions in humans as VEGF-A signaling should remain relatively constant between primary and xenograft tumors [2].
Using this adapted parameterization, we estimated both optimal schedule of administration of BEV-PEM/CIS in humans and the marginal effects of a sub-optimal administration schedule of BEV-PEM/CIS in humans (i.e. bevacizumab administered too many or too few days before PEM/CIS). Full parameter estimates are available in
Table 2. 72
Several limiting assumptions were made in our simulations of BEV-PEM/CIS pharmacodynamics in humans. First and foremost, we have assumed that the immune system of the immunocompromised mice is comparable to that of a cancer patient, which is highly unlikely. Second, we have implicitly assumed that the combination effect of BEV-PEM/CIS on tumor growth is similar in humans vs. mice. This assumption further holds for the prediction of BEV-PEM/CIS adverse effects and sensitivity to chemotherapeutics, such as thymidylate synthase inhibition with PEM. Lastly, we chose to model tumor response with respect to total concentrations of bevacizumab, pemetrexed, and cisplatin. Although unbound concentrations are undoubtedly more relevant than total drug levels, detailed PK parameter values for bevacizumab, pemetrexed, and cisplatin unbound concentrations are not available in the current literature. However, differences in protein binding typically do not affect the time-course of drug effect, and hence should have negligible impact on the estimated optimal gap between bevacizumab, pemetrexed, and cisplatin.
In summary, the predictions of efficacy in humans produced in this study are not meant to be substituted for clinical testing. Indeed, this model was primarily adapted to scale the optimal scheduling gap from the xenograft model to humans. Both the predicted optimal gap and predicted efficacy require further validation with clinical data.
However, our scaled model of BEV-PEM/CIS in human NSCLC and prediction of optimal gap should help guide clinical testing conditions for optimal sequential scheduling in humans.
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Tables and Figures
Table 4.1 PD Model Parameters for Tumor Proliferation in NSCLC-Xenografted Mice Model parameter estimates (fixed and random-effects) as well as standard errors as determined by the Stochastic Approximation Expectation-Maximization algorithm as implemented in Monolix 2018R2. α and β represent the proliferation rate of the tumor cells and rate of exponential decrease of the tumor relative growth rate, respectively. γ was used to model the log-kill effect of pemetrexed and cisplatin’s combined concentration. δ represents the proportional increase in pemetrexed/cisplatin efficacy due to vascular quality improvement under bevacizumab therapy. τ was the time delay in bevacizumab effect. 푉0 represents the volume of cells at time 0. 푘 governs intercompartmentalTable 1 clearance between cellular death compartments.
Model Parameter Estimate SE RSE (%) IIV IIV (CV%)
-1 휶 0.77 day 0.0081 1.06 0.037 4.76
-1 휷 0.04 day 0.0005 1.16 0.015 33.55
-1 휸 35.74 (mg·day) 6.36 17.79 0.46 1.28
-1 휹 3.73 (mg·day) 0.92 24.70 0.35 9.51
흉 1.19 days 0.017 1.50 0.17 14.50
푽0 3.4 RFU* 0.27 22.55 1.73 143.03
-1 풌 0.30 day - - - -
Residual Error Variance 0.43 0.01 2.55 - -
*RFU: Relative Fluorescence Unit
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Table 4.2 Parameterization for Simulations of NSCLC treated with BEV-PEM/CIS in Humans Except for the proliferation rate of the tumor cells and rate of exponential decrease of the tumor relative growth rate (i.e. α and β), the PD model and parameterization were reused exactly as they were determined in the mouse portion of the model. α and β estimates were obtained from Bilous et al. 2018 [37], where clinical NSCLC doubling times reported in Friberg and Mattson, 1998 [38] were used to estimate population α and βfor NSCLC in humans. The value of VC came from the classical assumption that a 1 mm3 volume of tumor cells is approximately 106 cells [39]. V0 was arbitrarily set to 3.0 3 cm . 푉1, 푉2, 푄, and 퐶푙 represent volume of compartment 1 and peripheral compartment 2, intercompartmental clearance, and clearance from compartment 1 respectively. Table 2
Pharmacokinetics Pharmacodynamics
-1 Drug Pemetrexed Cisplatin Bevacizumab 휶 0.0284 day
-1 푽1 (L) 12.9 22.3 2.8 휷 1.03E-3 day
-1 푽2 (L) 3.38 77.0 2.9 휸 35.7 (mg·day)
-1 푸 (L/day) 20.7 456.0 0.6 휹 3.73 (mg·day)
푪푳 (L/day) 131.9 6.5 0.2 흉 1.19 days
3 Infusion Time (min) 10.0 120.0 60.0 푽ퟎ 3 cm
풌 0.3 days
3 -1 푽풄 10E-3 mm ·cell
Table 4.S1 Administration (adm) Schedule for the Five Experimental Groups The cytotoxics consisted of an administration of both 100 mg/kg of pemetrexed IP and 3 mg/kg of cisplatin IP. Bevacizumab was administered in doses of 20 mg/kg IP.
75
Table 4.S2 Administration (adm) schedule for the simulated human individual Drugs were administered on three separate occasions, the 17th, 38th, and 59th experimental day, via IV administration. Bevacizumab administration (adm) was varied between simulation run i.e. it was administered anywhere between 0 and 10 days before Pemetrexed-Cisplatin. The simulation was stopped on virtual experimental day 85.
Table 4.S3 Pharmacokinetic parameters for pemetrexed, cisplatin, and bevacizumab in mice 풌풂, 푽, and 푪풍 represent first-order absorption constant, volume of distribution, and clearance, respectively.
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Figure 4.1 Structural Model Diagram The scheme of the structural model is depicted to the right. Unperturbed cells grow at rate governed by 훼 and 훽. When a cytotoxic is introduced into the system, the cytotoxic impairs the growth of the tumor by sending cells into a death succession. The parameter which determines the cytotoxic efficacy, 훾, is scaled by both the concentration of cytotoxics, 퐶(푡), and the volume of the tumor, 푉(푡). Bevacizumab improves vascular quality, 푄(푡), after time delay, 휏, which scales the cytotoxic effect by parameter 훿. When a cell is damaged by cytotoxics it begins a progression from unperturbed growth – compartment 푉(푡) – to damage compartments 푍1 through 푍1. Eventually the cell exits the tumor volume as it dies. The rate of transfer between damage compartments is governed by intercompartmental clearance parameter 푘.
Figure 4.2 Standard Goodness-of-Fit Diagnostic Plots. On the left is individual predictions vs. observations and on the right are the individualized weighted residuals (IWRES) vs time. During model fitting, observations were natural-log-transformed to stabilize predictions. Therefore, residuals, predictions, and observations are natural-log-transformed in these figures. The predictions are approximately normally distributed. On the left, the one-to-one prediction line is the center solid black line, the spline (average agreement between individual prediction and observation) is solid orange, the dashed black lines are the borders of the 90% prediction interval. On the right, the zero residual error line is the center dashed black line, the spline is solid orange. The dashed black lines are the borders of the 90% prediction interval.
77
Figure 4.3 Sample of Individual Fits The blue dots represent individual observations while the solid violet line represents individual fits. Some mice – e.g. mice in the control group – were not tracked for the full course of the study. These animals experienced complications due to the experiment and either spontaneously passed or were euthanized to prevent excessive suffering.
Figure 4.4 Combined and Stratified Visual Predictive Checks The blue lines are the 10th, 50th, and 90th empirical percentiles calculated for each unique value of time. Blue and pink areas represent 90% prediction intervals for the 10th (blue), 50th (pink), and 90th (blue) percentiles. Prediction intervals are calculated by Monte Carlo simulation. To create prediction intervals for each unique value of time, 500 simulations are performed using random individual parameters. The red areas and red- circled points represent areas where empirical measurements fall outside of the bounds of the 90% prediction intervals.
78
Figure 4.5 Human Pharmacodynamic and Pharmacodynamic Simulations Summary To produce these figures, bevacizumab (BEV) was administered anywhere from 0 to 10 days (in steps of 0.1) before pemetrexed/cisplatin (PEM/CIS) was administered. Tumor growth was simulated from 0 to 67 days with no IIV and no RSE. In the top figure, AUC of tumor growth vs gap (0 to 10 days) is depicted. In the middle figure, tumor dynamics over time, with gap indicated by color, are depicted. In the bottom panel, the PK of BEV- PEM/CIS is depicted with gap indicated by color. The top figure indicates that the optimal scheduling gap is 1.2 days and the middle figure depicts the difference in tumor volume between administration gaps. The patient with optimal scheduling had a final tumor volume approx. 30% the size of the concomitant scheduling. 79
Figure 4.S1 Comparison of Error Models In the left column are the probability density distributions (red) vs. theoretical normal distributions (blue) for each error group. On the right are the quantile-quantile plots which compare the quantiles between the theoretical and observed distributions of points. Below each set of sGOF graphics are the scores for the Kolomogorov-Smirnov normality test as well as the Pearson chi-square normality test. Graphically, the log- constant error model outperformed the constant error model. Numerically, the log- constant error model outperformed the constant error model in both the Kolmogorov- Smirnov normality test and the Pearson-Chi square test.
80
Figure 4.S2 Correlation Between Parameter Estimates The Pearson’s Correlation Coefficient is displayed in each correlation and the red line is the linear regression of the conditional distribution.
Figure 4.S3 SAEM Convergence Diagnosis Above are various SAEM convergence results produced by Monolix’s assessment suite. The best performing (defined as lowest -2 loglikelihood) parameterization (in yellow) closely matches our final parameter estimates. The assessment indicates that there is some degree of instability in parameter estimates. But, variance in parameter estimates is relatively low and RSE on final parameter estimates is low, indicating that we’ve achieved a reasonable balance between the empirical fit and underlying biology. Especially important to our analysis is the relatively low variability in Tau parameter estimates. 81
Figure 4.S4 Simulated Tumor Growth and Response – Mouse Model Above is the 3D surface of simulated tumor growth response (dimension 1) with respect to gap (dimension 2) and time (dimension 3) in mice. This 3D surface allowed us to more intuitively understand the effect of varied administration schedules. It is available for manipulation at https://plot.ly/~Benjamin-PKPD/15/#/. 82
Figure 4.S5 Simulated Tumor Growth and Response – Humans Above is the 3D surface of simulated tumor growth response (dimension 1) with respect to gap (dimension 2) and time (dimension 3) in humans. This 3D surface allowed us to more intuitively understand the effect of varied administration schedules. It is available for manipulation at https://plot.ly/~Benjamin-PKPD/17/#/.
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CHAPTER 5. COMPREHENSIVE JOINT MODELING OF FIRST-LINE THERAPEUTICS IN NON-SMALL CELL LUNG CANCER
Authors and Affiliations
Benjamin K Schneider1, Sebastien Benzekry1,2* and Jonathan P Mochel1*
1Iowa State University College of Veterinary Medicine, Ames, IA, U.S.A, 2Team
MONC, Inria Bordeaux Sud-Ouest, Institut de Mathématiques de Bordeaux, France. *: co-last authors.
Abstract
First-line antiproliferatives for non-small cell lung cancer (NSCLC) have a relatively high failure rate due to high intrinsic resistance rates and acquired resistance rates to therapy. 57% patients are diagnosed in late-stage disease due to the tendency of early-stage NSCLC to be asymptomatic. For patients first diagnosed with metastatic disease the 5-year survival rate is approximately 5%. To help accelerate the development of novel therapeutics and computer-based tools for optimizing individual therapy, we have collated data from 11 different clinical trials in NSCLC and developed a semi-mechanistic, clinical model of NSCLC growth and pharmacodynamics relative to the various therapeutics represented in the study. In this study, we have produced extremely precise estimates of clinical parameters fundamental to cancer modeling such as the rate of acquired resistance to various pharmaceuticals, the relationship between drug concentration and rate of cancer cell death, as well as the fine temporal dynamics of anti-VEGF therapy. In the simulation sets documented in this study, we have used the model to make meaningful descriptions of efficacy gain in making bevacizumab-antiproliferative combination therapy sequential, over a series of days, rather than concurrent. 90
Reference Nomenclature and Abbreviations for Equations afolate The antifolate action of a cytotoxic drug i.e. pemetrexed apo Apomab aka DAB4, its chimeric derivative chDAB4, or PRO95780 auc The area under the curve of drug concentration over time, usually
interpreted as a measure of exposure bev Bevacizumab car Carboplatin cc Concentration, usually concentration as a function of time cis Cisplatin doc Docetaxel dr5 The mechanism of action of Apomab, a monoclonal antibody
against death receptor 5 eff Effect egfr The egfr-based (endothelial growth factor receptor) mechanism of
erlotinib erl Erlotinib gem Gemcitabine kk Rate of passage between compartments microt The microtubule-inhibition mechanisms of paclitaxel and docetaxel n Sum of primary all tumor volumes i.e. v + vi + z1 + z2 + z3 dnasub The mechanism of action of gemcitabine whereby it masquerades
as a functional nucleoside only to cause masked chain termination
when incorporated into DNA pac Paclitaxel 91
pem Pemetrexed
plat The class of cytotoxics whose mechanism involves platinum i.e.
cisplatin, carboplatin, etc.
Qα, Qρ The effects whereby certain drugs limit the rate of growth of the
tumor e.g. cell cycle arrest, nutrient supply disruption, etc.
Qγ The effect whereby certain drugs kill tumor cells directly
t Time in days
v Primary tumor volume in cm3
vi Volume of tumor cells which are injured by vegf and microt drugs
vegf The anti-vegf (vascular endothelial growth factor) mechanism of
bevacizumab
z1–3 Irreversible cell death compartments
wd A scaling factor between drug concentration and cytotoxic effect
λd Scaling factor between drug exposure and resistance
Introduction
With an estimated 135,000 deaths per year in the United States, lung cancer has the highest mortality rate of any cancer type (1). Approximately 85% of those deaths are attributable to non-small cell lung cancer (NSCLC). Often, NSCLC is not detected until late-stage disease as the early progression produces relatively few symptoms. First-line therapeutics for the management of metastatic or recurrent NSCLC (i.e. late-stage
NSCLC) include combination chemotherapies (including platinum-based doublets) alone, or associated with immune checkpoint inhibitors (i.e. PD-1/PD-L1 or CTLA4 inhibitors) or antiangiogenics (e.g. bevacizumab, BEV). However, first- and second-line therapies have a relatively high failure rate. As an example, in the recent ARIES 92 observational cohort study of first-line treatment involving bevacizumab the failure rate was approximately 51%.
Acquired or intrinsic drug resistance is a major cause for therapeutic failure in
NSCLC. In a previous study of resected NSCLC by d’Amato et al., intermediate to extreme resistance to carboplatin was found in 68% of NSCLC cultures (vs. 63% and
40% for cisplatin and paclitaxel, respectively). Likewise, in the KEYNOTE-001 study completed last fall, NSCLC patients receiving pembrolizumab had an objective response rate of 19.4%, indicating that a vast majority of individuals did not significantly respond to therapy. Patients are also sometimes forced to cycle off chemotherapy due to excessive side-effects. Chemotherapeutics are notorious for broad and severe off- target effects that exacerbate underlying vulnerabilities – e.g. chronic kidney disease.
After initial therapeutic options fail, many patients choose to enroll in clinical trials to receive experimental therapies (2). Though the prognosis for NSCLC patients is improving, at this time the 5-year survival rate in non-small cell lung cancer (NSCLC) is only approximately 20%. For the 57% of lung cancer patients first diagnosed with metastatic disease the 5-year survival rate is approximately 5% (3). Therefore, there is a critical need to improve the efficacy of existing therapeutics, to develop a better understanding of individualized NSCLC therapy, and to accelerate experimental therapeutic development. Mathematical modeling is a key strategy for addressing these needs, as its use in cancer is a proven method for solving problems in optimization and precision medicine (4–7).
Mathematical modeling of drug pharmacokinetics and pharmacodynamics is an extremely efficient method for optimization of therapeutic dosing schedules, without the 93 considerable time and resource investment required to conduct a suite of in vivo clinical trials. Using this computational platform, one can leverage data from multiple studies, involving diverse patient populations, varying drug combinations and administration schedules, to build a series of “what if” scenarios and derive the best scheduling and dosing of therapeutic drug intervention in a given set of patients.
Bevacizumab is an important targeted therapy in treating NSCLC that has performed strongly when used in combination with a broad spectrum of antiproliferatives. Bevacizumab is an anti-angiogenic, and therefore inhibits the development of the neovascular architecture supporting tumor proliferation.
Neovascular growth disruption is directly cytotoxic. Bevacizumab has also been shown to induce a transient period of perfusion normalization. This perfusion normalization improves the delivery of cytotoxics to the tumor resulting in improved efficacy of the cytotoxic. Because efficacy is improved, prescribing cytotoxics in combination with bevacizumab often allows clinicians to reduce the dosage of primary cytotoxics, thereby reducing the side-effect burden on the patient (8).
Previously, we have shown experimentally and described mathematically the time-course of this transient perfusion-normalization in a xenograft-murine model of
NSCLC (9). In that experiment, pemetrexed-cisplatin (PEM/CIS) was administered sequentially with bevacizumab (BEV). By varying the gap between bevacizumab and cytotoxic administration, we were able to estimate the time-course of vascular normalization, as well as several other parameters used to build a pharmacokinetic- pharmacodynamic (PKPD) description of NSCLC growth and response to BEV-
PEM/CIS. 94
In our previous model description, we could predict that administering BEV and
PEM/CIS sequentially with a gap of 1 day, rather than concurrently, would improve the efficacy of this combination (quantified as final tumor volume) by more than 50% without the need for increasing therapeutic doses. However, optimal scheduling of this combination in humans has yet to be verified with large sets of clinical data, and the model needs to be generalized to other combination therapies, including immune checkpoint inhibitors.
Our previous preclinical study is a demonstration of a proven paradigm of therapeutic development that could become especially impactful in NSCLC. In this paradigm, scientists develop novel and individualized therapeutic strategies from existing and approved therapeutics (2,10). Additionally, there is a wealth of data currently available from clinical data-sharing services such as Vivli, CSDR, Project
Datasphere, YODA and others. When using previously produced data, researchers obviate the need for human or animal participants. The cost and time required to clean and organize the data, build the model, evaluate the model, and simulate clinical trials is drastically less than that required when designing and performing new clinical trials.
Clinical trials are usually only designed to test a sparse number of medications and scheduling strategies over the course of the study. Via simulation, we can trial a vast number of medication combinations and scheduling strategies simultaneously.
Data from clinical trials will not always be directly comparable due to, for example, variations in experimental design, differences in operating procedure, and differences in patient cohort characteristics. This variation can be an advantage of pooling datasets from separate trials if the statistical framework for analysis is able to 95 account for and elucidate any potential sources of variation. Non-linear mixed effects
(NLME) modeling of tumor proliferation and response is a proven framework for pooling data to model-build (9,11,12)
In this study, we have implemented these principles to build a unified, semi- mechanistic model and platform for scheduling bevacizumab in combination with several approved therapeutics in NSCLC. Specifically, we have collated individual tumor progression data from 11 different clinical trials (> 8000 stage II through stage IV, metastatic, and non-metastatic patients) involving BEV and multiple chemotherapies such as PEM, CIS, apomab, paclitaxel, carboplatin, gemcitabine, and erlotinib. These data were made available to us through a data sharing agreement with vivli.org. Our overall objectives in this study are to (1) generalize our model of NSCLC growth and response to BEV-PEM/CIS to the greater set of combination therapies and modes of action represented in our large clinical database, and (2) characterize the time-course of resistance for those registered therapeutics in humans.
Methods
Literature Search and Review
To build our model, we sought access to data using very broad criteria. Briefly, we were interested in requesting access to data from clinical trials where bevacizumab had been used in combination with other therapeutics to treat NSCLC. To build on previous modeling efforts, it was necessary for most studies to include records of individual patient tumor sizes over time. After reviewing several potential data access providers with which we could partner, we applied for data access through the Clinical
Study Data Request (CSDR) portal. We were able to identify 11 different studies available through CSDR’s platform which met our requirements (Table 1) and were 96 permitted access to a secure server containing the datasets beginning on January 6th,
2020.
Due to contractual obligations between the data owners (Roche, Eli Lilly) and data access provider (CSDR), our project and access to the datasets were moved to a secure server managed by Vivli on September 22nd, 2020. During this transfer process, we requested access to, and were granted access to, 5 additional datasets involving immune-checkpoint inhibitors and NSCLC which were not available at the time we first applied for access through CSDR.
Data Processing and Collation
Data annotation, units, organization, and shorthand is highly variable between datasets. This variability makes collating and preparing large datasets for mathematical modeling a challenging, and highly error-prone task.
To reduce the possibility of introducing mistakes into the datasets during collation, we systematized the iterative collation of datasets. First, we identified the comma separated value files containing the most relevant base information. The information we were interested in for initial model-building was individual, tumor identifier, tumor type, tumor size, and drug administration details all organized longitudinally. Data were then imported into R (version 3.5.2) to be normalized for import into our NLME parameter estimation software (Monolix Suite version 2020R1,
Lixoft). Normalization consisted of formatting the data as recommend by Lixoft (15), as well as matching units to an internal dictionary of standards – tumor measurements in cm, amount administered in mg, etc.
After each dataset was produced, the data was explored visually with a combination of R as well as Datxplore (Monolix Suite version 2020R1) to check for 97 inconsistencies. Finally, the individual datasets produced in analyzing each individual study were bound into one single comma separated value file. As a final quality check, the final dataset was re-imported in R, and subset down to individual studies. Then, the processed studies were compared with the raw files from the clinical trials for consistency. Data were both received and maintained in a fully anonymized format to protect patient privacy.
Non-Linear Mixed Effects Modeling and Characterizing Individual Variation
The recorded data (yij) were pooled and used to estimate model parameters via the stochastic approximation expectation maximization algorithm (SAEM) as implemented in Monolix. After estimating population parameters (μ) and variance, individual parameters (ϕi) were estimated using the modes of the individual estimated posterior distributions. The posterior distributions were estimated using a Markov-Chain
Monte-Carlo (MCMC) procedure. NLME models were written as previously described
(Pelligand et al., 2016; Sheiner & Ludden, 1992) (Equation 1).
Equation 1:
2 푦푖푗 = 퐹(흓푖, 휷푖, 푡푖푗) + 퐺(흓푖, 푡푖푗) ∙ 휀푖푗 | 휺푖푗~풩(ퟎ, 휎 )
2 흓푖 = ℎ(흁, 휼푖, 휷푖) | 휼푖푗~풩(ퟎ, 훀, 휔 )
푗 ∈ 1, … , 푛푖, 푖 ∈ 1, … , 푁
th th Model predictions (F(ϕi, βi, tij)) for the i individual at the j timepoint were written as a function of individual parameters, individual covariates (βi), and time (tij).
The residuals were modeled as G(ϕi, tij) ∙ εij.
Individual parameters are modeled with function h(μ, ηi, βi). Interindividual variability, ηi, are distributed normally with mean 0, variance-covariance matrix Ω, and 98
2 variance ω . Typically, h(μ, ηi, βi) is a lognormal link function (Equation 2). In cases where ϕi is bounded, h(μ, ηi, βi) was typically a lognormal link function (Equation 3).
Equation 2:
ηi + βi ϕi = 휇 ∙ e
Equation 3:
ϕi 휇 푙표푔 ( ) = 푙표푔 ( ) + 휂푖 + 훽푖 1 − ϕi 1 − 휇
Model Building
PKPD models were built in multiple development phases. First, we reproduced previously established models of therapeutic PK within our modeling project using
Mlxtran. Then, we created several sample sets with between 5% and 10% of the complete dataset for initial model building. This shortened calculation time and reduced computational complexity. Next, we identified our preferred base candidate models for
PD and implemented them in Mlxtran. Finally, using manual exploration and cursory
SAEM parameterizations, we were able to determine reasonable parameter estimates with which to initialize our parameter search.
The PK portion of our PKPD model was implemented using previously published human PK models and parameter values. PK models were written in Mlxtran. We verified PK model integrity by simulating trivial scenarios with known outcomes using
Mlxplore. If outcomes simulated deviated from expectations, the code was reviewed for inconsistencies.
To begin building our model of NSCLC PKPD, we used exploration to parameterize two base models of NSCLC PD. The first model parameterized was the traditionally used Claret model of tumor growth and response to anti-proliferatives. The 99 second base model implemented was built on our previous Gompertzian model of BEV-
PEM/CIS published elsewhere.
To initially parameterize these candidate models, we visually explored potential initial parameter spaces using smaller sample subsets. Once we had a set of potential initial parameter values, we ran the SAEM algorithm on these sample sets to determine numerical stability of these parameter values. This process would result in loops of exploration and parameterization leading to further exploration and parameterization.
Once we had implemented a PKPD model in Mlxtran and had reasonable initial parameter estimates, we were able to fit the model to the full dataset using the SAEM method. After fitting base models of PKPD, we were able to evaluate and iteratively improve on the deficiencies in fit using numerical experimentation, model exploration, goodness-of-fit metrics, traditional analysis, as well as reviewing previously published theories of NSCLC response to various therapeutics. For example, using simulation engines like Simulx and Mlxplore, we were able to test whether known biological phenomena were reliably reproduced by the model. Using model evaluation tools
(below), we were able to test whether our fit appropriately met the assumptions made for NLME modeling. If the model did not produce individual fits which closely matched measurements, we used fundamental compartmental modeling concepts to add parameters, and therefore flexibility, to the model.
Our primary structural concerns were modeling individual tumor growth and response, modeling both acquired and intrinsic resistance, modeling individual drug effects and interactions, as well as modeling the timescale of perfusion enhancement via bevacizumab. Modeling perfusion enhancement via bevacizumab was especially 100 important as it was the primary structure that would allow us to determine the optimal predicted scheduling of sequential bevacizumab and various anti-proliferatives.
Model Evaluation
We employed state-of-the-art model building techniques to develop our model into a meaningfully complete description of the variation in the dataset and evaluate the quality of model. This broadly required us to evaluate quality of fit, validate assumptions made about variance, test correlation between individual parameters with both other individual parameters as well as covariates, consider various statistical formulations of individual parameters, determine precision of individual parameter estimates, and finally measure models against one another.
Quality of fit was determined using both goodness-of-fit plots and summary statistics. Stability of parameter estimates was assessed by both inspection of SAEM search, attainment of auto-stop criteria as implemented in Monolix, and whether randomized (but still local) initial starting parameters converge to the same set of parameter estimates. Accuracy of individual fits was assessed using a sample of individual plots, an observations-vs-predictions plot using the full conditional distribution, a scatter plot of the residuals, as well as the corrected Bayesian information criteria
(BIC) – estimated via importance sampling).
Assumptions of variance were validated by plotting the conditional distribution against theoretical distributions as well as standard statistical tests. Within the NLME framework, random effects and residuals are assumed to be predictably distributed – usually normally or functionally-linked to normal. We used the Shapiro-Wilk test of normality to determine normality, and Van Der Waerden test to determine symmetry of distributions about 0. 101
Correlation between individual parameters and other individual parameters or covariates were tested with a Pearson’s correlation test and ANOVA, respectively.
Plotting these relationships assisted in determining the nature of these correlations.
Precision and accuracy of the final model was assessed to evaluate models against one another. Precision of parameter estimates was made using relative standard error (RSE). Overall model quality of fit was evaluated BICc. Diagnostic plots assisted in comparing models with similar overall performance.
Clinical Trial Simulations
In our clinical trial simulations, we hoped to determine what benefit (if any) sequentially administering therapy with bevacizumab produced. To do this, we took the individual fits from the experimental arms of the trials and simulated them with various gaps between bevacizumab and treatment using Simulx (Monolix Suite version 2020R1,
Lixoft). The highest performing gap was then compared with the experimental standard.
Study Details
Randomized, Open-Label, Phase 3 Study of Pemetrexed Plus Carboplatin and
Bevacizumab Followed by Maintenance Pemetrexed and Bevacizumab Versus
Paclitaxel Plus Carboplatin and Bevacizumab Followed by Maintenance Bevacizumab in Patients With Stage IIIB or IV Nonsquamous Non-Small Cell Lung Cancer
Between 2008 and 2014, 939 patients were administered either bevacizumab + pemetrexed + carboplatin (experimental arm) or bevacizumab + paclitaxel + carboplatin
(comparator arm) to treat phase 3 NSCLC. Primary outcome was overall survival time from baseline to date of death (any cause). ClinicalTrials.gov Identifier: NCT00762034
A Study of Pemetrexed and Bevacizumab for Participants With Advanced Non-
Small Cell Cancer 102
Between 2009 and 2013, 109 patients were administered bevacizumab + pemetrexed + carboplatin (single treatment arm) to treat stage IIIB or stage IV NSCLC that was not amenable to curative therapy. Primary outcome was progression free survival from baseline. Progression was scored using response evaluation criteria in solid tumors (RECIST criteria). ClinicalTrials.gov Identifier: NCT01004250
A Study of PRO95780 in Patients With Previously Untreated, Advanced-Stage
Non-Small Cell Lung Cancer (APM4074g)
Between 2007 and 2010, 128 patients were administered either bevacizumab + carboplatin + paclitaxel + PRO95780 (experimental arm), or bevacizumab- pemetrexed/carboplatin (single treatment arm) to treat stage IIIB or stage IV NSCLC that was not amenable to curative therapy. Primary outcome was progression free survival from baseline. Progression was scored using response evaluation criteria in solid tumors (RECIST criteria). ClinicalTrials.gov Identifier: NCT00480831
A Study of Avastin (Bevacizumab) in Patients With Non-Squamous Non-Small
Cell Lung Cancer (NSCLC)
Over a period of 6 years starting in 2005, 1044 patients with advanced or recurrent non-squamous NSCLC were randomized to any of three experimental arms.
The first two arms were cisplatin + gemcitabine + bevacizumab combination therapy with bevacizumab administered at either a high dosage or low dosage. The third arm was a placebo comparator where patients were administered cisplatin + gemcitabine + placebo. The primary outcome measured was progression-free survival. Efficacy and safety were tracked as secondary outcomes. Efficacy was defined as a combination of survival duration, time to treatment failure, response rate, and duration of response. 103
Safety was measured through a state-of-the art panel of laboratory values.
ClinicalTrials.gov Identifier: NCT00806923
A Study of Avastin (Bevacizumab) in Combination With Carboplatin-Based
Chemotherapy in Patients With Advanced or Recurrent Non-Squamous Non-Small Cell
Lung Cancer
From 2008 to 2012, 303 patients were administered a combination of bevacizumab and carboplatin with either 7.5 mg/kg bevacizumab or 15.0 mg/kg bevacizumab. The treatments were being used to treat patients with advanced or recurrent non-squamous NSCLC. The primary outcome measured was the percentage of patients with either a complete response or partial response. Progression-free survival and duration of response were the secondary outcomes measured.
ClinicalTrials.gov Identifier: NCT00700180
A Study of Bevacizumab in Combination With First- or Second-Line Therapy in
Subjects With Treated Brain Metastases Due to Non-Squamous NSCLC (PASSPORT)
Starting in 2006, 115 participants with metastatic non-squamous NSCLC with previously treated central nervous system metastases were administered an experimental combination of bevacizumab with either first-line or second-line chemotherapy. The trial lasted for 3 years. The primary outcome measured was the percentage of participants with symptomatic NCI CTCAE (16) Grade ≥ 2 CNS hemorrhage. Secondary outcomes measured included patient overall survival and adverse effects. ClinicalTrials.gov Identifier: NCT00312728
A Study of Avastin (Bevacizumab) in Patients With Non-Squamous Non-Small
Cell Lung Cancer With Asymptomatic Untreated Brain Metastasis 104
Between 2009 and 2012, 91 patients with stage IV NSCLC were sorted into one of two experimental groups. The first group received bevacizumab + carboplatin + paclitaxel combination therapy and the second group received bevacizumab + erlotinib combination therapy. The primary outcomes measured were progression-free survival at 6 months, percentage of participants with disease progression, and time to disease progression or death. Secondary outcomes included percentage of patients achieving complete response and percentage of patients achieving partial response.
ClinicalTrials.gov Identifier: NCT00800202
Effects of Two Doses of rhuMAB-VEGF Antibody in Combination w/Chemotherapy in Subjects With Locally Advanced or Metastatic Lung Cancer
The details and results from this clinical trial were published in 2004
[https://doi.org/10.1200/JCO.2004.11.022]. In this phase II trial, 99 patients were randomly assigned either to bevacizumab + carboplatin + paclitaxel (experimental arm) or carboplatin + paclitaxel alone (comparator arm). The primary efficacy measures were time to disease progression and best confirmed response rate. ClinicalTrials.gov
Identifier: N/A
Safety and Efficacy Study of Avastin in Locally Advanced Metastatic or Recurrent
Non-small Lung Cancer (NSLC) Participants
996 participants were enrolled in this study between its start and finish, 2007 and
2013. Patients were administered several cycles of bevacizumab before beginning chemotherapy. After chemotherapy, patients were cycled back to bevacizumab as a maintenance therapy. The primary outcome measurement was the percentage of patients with adverse effects. Among the secondary outcomes measured were the 105 number of cycles of therapy tolerated, percentage of patients with complete or partial response, eastern cooperative group (ECOG) performance status grades, and progression free survival. ClinicalTrials.gov Identifier: NCT02596958
A Study of Bevacizumab Versus Placebo in Combination With
Carboplatin/Paclitaxel in Participants With Advanced or Recurrent Non-Squamous Non-
Small Cell Lung Cancer Who Have Not Received Previous Chemotherapy
This randomized, double-blind, placebo-controlled study was conducted between
2011 and 2017. 276 participants were distributed to either a group receiving bevacizumab + carboplatin + paclitaxel (experimental arm) or carboplatin + paclitaxel + placebo (active comparator arm). Progression free survival was the primary outcome measured, and several survival and lab-value related secondary outcomes were also measured. ClinicalTrials.gov Identifier: NCT01364012
A Study of Avastin in Combination With Chemotherapy for Treatment of
Colorectal Cancer and Non-Small Cell Lung Cancer (ARIES)
In the ARIES study, approximately 4,000 patients with locally advanced or metastatic NSCLC (or a similar colorectal cancer – CRC), who were also receiving a combination bevacizumab therapy, were observed between 2006 and 2012 for disease progression. Several data-points were collected over the period to measure safety and efficacy of bevacizumab for NSCLC or CRC. The collected data include progression- free survival and physical tumor biopsies. This study was largely ignored for semi- mechanistic modeling purposes as it included few tumor measurements.
ClinicalTrials.gov Identifier: NCT00388206 106
Results
Data Summary
Data were received in directories of fully anonymized dataframes (e.g. excel files,
SAS files, .csvs) organized by general category of data. For initial data processing, data were explored for bulk trends, standardized, and unsuitable data were removed. Studies were then collated in a single dataframe designed for use with the Monolix suite.
Between the 11 studies, 3686 patients’ data were determined to be potentially suitable for analysis. After exploring the datasets in greater detail, we determined that only 2586 patients (between the studies) had all the data necessary to create models of tumor growth and response – unique patient IDs, a time recorded for each dosing and measurement event, tumor measurements, and therapeutic administration details for each patient. Data that were unsuitable for analysis were either missing proper documentation detailing the contents of the dataframe – e.g. dictionary for column ids – or were missing data necessary for longitudinal modeling – e.g. unique patient ids or dosing events.
We chose to model individual tumor longest diameter time-course as our independent variable, as the sum of the longest diameter (SLD) typically do not perform as well as individual tumor diameter in semi-mechanistic models of tumor growth, and individual tumor longest diameter is truer to the biology of the disease {cite}. We were not able to separate inter-individual variability (IIV) and inter-occasion variability (IOV) resulting from patients with more than 1 tumor being measured. Statistically, all patient- tumor combinations were treated as unique subject-occasions. This is a biological oversimplification, as multiple tumors within a single individual most likely have related individual parameters, but this compromise provided a good balance between modeling 107 systems biology and model identifiability. Among the subject-occasions, we had data from 6197 unique tumors belonging to 2586 patients.
After a short period of testing, we imposed several further restrictions on the dataset to better facilitate modeling. The first condition was that tumors were required to have been measured 3 or more times to qualify for inclusion. This reduced the number of unique tumor ids to 4701 and unique individuals to 2036. Then we removed monotonic non-responders from the dataset. If for each sample yi,t, for individual i at time t, yi,t was greater than or equal to yi,t-1 we labeled the tumor as a monotonic non- responder and excluded it from the dataset. This reduced the number of individual tumors to 4473 and individual ids to 1977. After removing these data, we were left with
4450 tumors and 1963 individuals. These restrictions imposed on the initial dataset representing 2586 patients reduced the number of samples from 29885 to 26515. This is an approximate 11% reduction in data. Lastly, because of our limited CPU resources, we chose to only work with approximately 5% of the data from each study (randomly allocated by subject-tumor pairs). The final dataset used for model building detailed tumor growth time-course for 250 individual tumors from 221 patients.
We also imposed an artificial condition on the lower limit of quantification to reduce the chance that noisy measurements would produce numerical instabilities in the
SAEM search. As an example, in some of the datasets, clinicians would record size = 0 if they could not find a tumor. If during the next visit, the clinician would find the tumor again, the clinician would log a size greater than 0 for the tumor. Records like these would occasionally cause convergence issues with the SAEM algorithm. To remedy this, we set the lower limit of quantification as 1 mm in diameter. 108
PKPD Model Building
Individual PK parameters and models were estimated in few of the clinical trials used in this study. Therefore, population PK models were collated from various publications involving the relevant therapeutics, and IIV was not included in the final PK model as it led to structural unidentifiability (Table 5.1).
As a first step, we wrote our previous model of bevacizumab- pemetrexed/cisplatin therapy in Mlxtran and validated the model against the dataset produced in various treatments receiving any combination of the medications. The units of the previous publication were relative to fluorescence, so results were not directly translatable. Also, our previous model only dealt with combination bevacizumab- pemetrexed/cisplatin and we used a simple scaling factor against concentration to evaluate effect. This prevented us from being able to validate against other medications.
We only simulated over short periods in our previous work which made the effects of acquired resistance relatively inconsequential, however this effect was readily available in various patients within the Vivli dataset. Taken together, this suggested that we first start by modifying the Gompertzian growth and cytotoxic kill effect equations to account for an expanded set of medications and new units, and later attempt to capture the dynamics of resistance.
To create initial parameterizations for our pharmacodynamic modeling, we subsetted to small samples of the full dataset to perform short experiments as well as visual exploration. Two primary models were evaluated for the basic description of tumor growth and response; (1) the Gompertzian model of tumor growth and (2) the
Claret model of tumor growth (6,13). As both models are relative to tumor volumes, we modeled the tumors as spherical – an oversimplification as tumors are often oblong. 109
Using the Bayesian information criteria as a parsimonious method of cross-evaluating models, we found that the Gompertzian model outperformed the Claret model of tumor growth at several layers of structural model-building. In the Gompertz model of tumor growth (Equation 4), the unperturbed tumor grows at rate α and is exponentially limited in growth by parameter β. vc is a scaling factor relating individual tumor cell turnover to volume. It was set to 106 cells/mm3 which is the classical assumption of approximate number of cells per unit volume (14).
Equation 4
(4a)
푑푣 푣 = (α ∙ 푄α − β ∙ 푙표푔 ( )) ∙ 푣 − 푄γ ∙ 푣 푑푡 푣푐
푙표푔(푄훼) = − (1 + 푤푏푒푣훼 ∙ 푐푐푏푒푣(푡 − τ)) ∙ (푒푓푓푚푖푐푟표푡 + 푒푓푓푣푒푔푓)
푄훾 = (1 + 푤푏푒푣γ ∙ 푐푐푏푒푣(푡 − τ)) ∙ (푒푓푓푝푙푎푡 + 푒푓푓푎푓표푙푎푡푒 + 푒푓푓푑푟5 + 푒푓푓푒푔푓푟 + 푒푓푓푑푛푎푠푢푏)
(4b)
푑푣 푣 = (α − β ∙ 푙표푔 ( )) ∙ 푣 − 푄γ ∙ 푣 − 푄ρ ∙ v + kki ∙ vi ∙ 푝 푑푡 푣푐
푑푣 푖 = 푄 ∙ 푣 − 푘푘 ∙ 푣 − 푄 ∙ 푣 푑푡 휌 푖 푖 훾 푖
( ) 푄훿 = (1 + 푤푏푒푣훿 ∙ 푐푐푏푒푣 푡 − 휏 ) ∙ (푒푓푓푚푖푐푟표푡 + 푒푓푓푣푒푔푓)
푄훾 = (1 + 푤푏푒푣γ ∙ 푐푐푏푒푣(푡 − τ)) ∙ (푒푓푓푝푙푎푡 + 푒푓푓푎푓표푙푎푡푒 + 푒푓푓푑푟5 + 푒푓푓푒푔푓푟 + 푒푓푓푑푛푎푠푢푏)
In Equation 4a, Qα and Qγ are the antiproliferative effects resulting in growth reduction and irreversible cell death, respectively. Chemotherapeutics which acted on the microtubules – docetaxel and paclitaxel – along with the direct effect of 110
bevacizumab were included in Qα. All other drugs were treated as drugs resulting in irreversible cell death. Transient enhancement in efficacy via perfusion normalization by bevacizumab was modeled as occurring at time (t – τ) to account for the time delay between administration and efficacy enhancement i.e. τ. We found Equation 4a to heavily exaggerate the effect of bevacizumab in limiting cell growth rates. To account for this, we used a second compartment which represented reversible cell injury, vi, from which cells could return from (Equation 4b). Return rate is governed by intercompartmental transfer rate kki as well as proportion of repaired cells returned to the unperturbed cycle of proliferation, p. We found this better represented the growth limiting effects of bevacizumab, paclitaxel, and docetaxel without being as exaggerated of an effect as modeled in Equation 4a.
Irreversible cell death was modeled as occurring over a series of transitions between several compartments with intercompartmental transfer rate kk. The final tumor volume, a summation of the primary tumor volume and death compartments (z1, z2, and z3,) as well as injured cell volume vi, was then transformed to a tumor diameter to match the independent variable in the dataset (equation 5).
Equation 5
푑푧 1 = 푄 ∙ 푣 − 푘푘 ∙ 푧 푑푡 훾 1
푑푧 2 = 푘푘 ∙ 푧 − 푘푘 ∙ 푧 푑푡 1 2
푑푧 3 = 푘푘 ∙ 푧 − 푘푘 ∙ 푧 푑푡 2 3
푛 = 푣 + 푧1 + 푧2 + 푧3 + 푣푖
1 3푛 ⁄3 푇푢푚표푟 퐷푖푎푚푒푡푒푟 = 2 ∙ ( ⁄4휋) 111
For the pharmacodynamic effect on the tumor growth, we started with a simple version of our previous model whereby each drug’s concentration was scaled by a single parameter (represented by w for weighting) and the sum of those concentrations determined cytotoxic effect (Equation 6a). That proved slightly unstable, so we eventually grouped the sum of those effects under an inverse logit function so that their sum would be limited. However, this also resulted in parameter instability as there was no upper cap on estimates (Equation 6b). After several more iterations of the model, we settled on a pharmacodynamic model that individualized drug effects relative to those that shared their mechanism of action. We also implemented a model of resistance. In this model, the cancer became increasingly more resistant (rate governed by parameter
λ) to treatment as a function of exposure (AUC) – Equation 6c. A whole diagram of the model is available for review in Figure 5.1.
Equation 6
(6a)
푒푓푓푑 = (푤푑 ∙ 푐푐푑)
푒푓푓푡표푡푎푙 = ∑ 푤푑 ∙ 푐푐푑
푑 ∈ 푐푖푠, 푐푎푟, 푝푒푚, 푎푝표, 푒푟푙, 푔푒푚, 푝푎푐, 푑표푐, 푏푒푣
(6b)
푒푓푓푑 = (푤푑 ∙ 푐푐푑)
푒푓푓푡표푡푎푙 = γ ∙ (푖푛푣푙표푔푖푡 (∑ 푤푑 ∙ 푐푐푑) − 0.5)
푑 ∈ 푐푖푠, 푐푎푟, 푝푒푚, 푎푝표, 푒푟푙, 푔푒푚, 푝푎푐, 푑표푐, 푏푒푣
112
(6c)
퐴푈퐶푑 = ∫ 푐푐푑(푡)
푠푖푛푔푙푒 푑푟푢푔 푒푓푓 ≡ 푙표푔(푒푓푓푚) = 푙표푔(푤푑 ∙ 푐푐푑) − (λ푑 ∙ 퐴푈퐶푑) [ ] ( ) 푝푎푖푟푒푑 푑푟푢푔 푒푓푓 ≡ 푙표푔 푒푓푓푚 = 푙표푔 (푤푑1−푟푒푙−2(푐푐푑1 + 푤푑2푐푐푑2)) − λ푑1−푟푒푙−2(퐴푈퐶푑1 + λ푑2퐴푈퐶푑2)
푑 ∈ 푐푖푠, 푐푎푟, 푝푒푚, 푎푝표, 푒푟푙, 푔푒푚, 푝푎푐, 푑표푐, 푏푒푣
푚 ∈ 푝푙푎푡, 푎푓표푙푎푡푒, 푑푟5, 푒푔푓푟, 푑푛푎푠푢푏, 푚푖푐푟표푡, 푣푒푔푓
Individual variability was modeled using the standard log-link formulation and initial tumor volumes were fixed to the measurement of the tumor at time 0, relative for each individual. The only except was parameter p which was fixed between 0 and 1 using a logit-link function (Equation 7). Measurement error was modeled using the equation titled combined 1 in Monolix, i.e. a single additive term (a) added with a single proportional term (b).
Equation 7
휂푖 log-link: 휙푖 = 휙푝표푝 ∙ 푒
logit-link: 푙표푔푖푡(휙푖) = 푙표푔푖푡(휙푝표푝) + η_푖
푣(푡 = 0) = 푦(푡 = 0)
Model Diagnostics
Our model diagnostics suggest a stable and precise fit that largely fits the assumptions necessary to draw conclusions. We observed that the SAEM search was stable and reliable when estimating our final set of parameter estimates (Figure 5.2).
We were not able to perform a full convergence assessment because of computational constraints, but our experiments in subsets of the data suggest that results are stable regardless of relative initial parameter estimates. Individual fits were reasonably 113 descriptive with both a well described response and rebound after treatment cessation
(Figure 5.3). After seeing evidence of correlations (via Pearson’s test) between individual effects, we inspected those correlations using the full posterior plot of individual effects in parameter ηL vs ηK where L is not equal to K. We found that though correlations existed, the slope of the correlations was nearly zero and they were likely just natural artifacts that appear when working with large datasets (increased statistical power). An even spread of observations vs. individual predictions suggests that our model has no major structural misspecifications and that our error model was well specified (Figure 5.4). However, formal tests for residual normality and centering on zero failed. This is likely because of our use of the initial measured tumor volume as a covariate (residual is equal to 0) and the artificial implementation of a universal lower limit of quantification (observations fixed to 0.1). Once removing the censored points and the points measured at time 0, our residual error model aligns much more closely with the theoretical model. Precision of parameter estimates is extremely high with low dependency between estimates. Full parameter estimates, IIV, and RSEs are reported in Table 2. The visual predictive check (VPC) was informative as to wholistic model performance. Although the clinical trials were not matched, the VPC still indicates overall high-quality fit (Figure 5.4). Spread of individual parameters meets the
Kolmogorov-Smirnov test for normality.
Clinical Trial Simulations
In our clinical trial simulations, we found an unexpected result. When we simulated the exact conditions of the clinical trial, but with a gap that was varied between administering bevacizumab 5 days earlier than scheduled and 5 days later than scheduled (at steps of 1 days), we found almost no difference between treatment 114 groups. Put another way, administering bevacizumab before cytotoxics did not increase efficacy as expected (Figure 5.5 and Table 5.3).
We wanted to further investigate this outcome, so we simulated a human analog of our 2018 trial in mice using the full posterior distribution as estimated in Monolix as a virtual population pool. We largely found the same result (Figure 5.6 and Table 5.4).
As one last test, we began simulating individual IDs and comparing the outcome at various gaps from administering bevacizumab 5 days earlier to administering bevacizumab 5 days later. Explored in this way, it became clear that administering bevacizumab before pemetrexed/cisplatin did produce a significant effect in some patients, but not in all (Figure 5.7).
Discussion
Our primary goal for this project was building a comprehensive semi-mechanistic model of NSCLC growth and response to various clinical anti-proliferatives. To that end, we have largely been successful in developing a model to explain the variation we see in the data. Our model captures the antiproliferative effects of the 11 different therapeutics used across the clinical trials as well as intrinsic and acquired resistance.
We have pooled the best available and published pharmacokinetic models of the therapeutics involved, and we have used population estimates for each individual patient. This compromise likely slightly inflates the estimates of pharmacodynamic variation. Guided by our previous findings, we were also able to capture the transient enhancement of perfusion resulting from anti-VEGF therapy (bevacizumab). Individual predictions are relatively precise and our model captures the well-described rebound in growth after treatment cessation in non-small cell lung cancer. 115
We have also built that model with several innovations from our previous efforts.
We have used AUC as a measure of exposure to model acquired resistance. Intrinsic resistance has been folded into the distribution of wd (i.e. weighting) terms in our system of equations. We also found that having a second cytotoxic effect for reversible cellular injury allowed us to capture direct effects of bevacizumab as well as capture the effect of medications known to cause reversible cell injury (i.e. paclitaxel and docetaxel). Our largely modular form of differential equations also provides a natural avenue for adding more drugs to the model. We have also provided a robust set of parameter estimates and have made our model code freely available for future research in non-small cell lung cancer.
When evaluating our model, we found robust evidence to support our choice of model structure. Parameter estimates and individual predictions were made with relatively high precision. This is likely due to the largeness of the dataset included.
Model structure was based on biological mechanisms making interpretation of parameters relatively natural – e.g. λ parameters define the rate of acquired resistance vs. exposure – and lending the model the longevity afforded by mechanistic modeling.
On parameter estimate interpretation, we have used relatively simple naming heuristics to aid in interpretation. As stated above, λ parameters define the rate of acquired resistance vs. exposure. wd parameters weight drug action against the tumor i.e. the larger the wd parameter, the larger the action the drug takes proportional to both the tumor size and concentration of the drug in plasma. The parameter titled imv_r_perc indicates the proportion of cells in the injured volume which return to unperturbed tumor growth. Unperturbed tumor growth is governed by parameters α, exponential rate of 116 growth of tumor, and β, exponential rate of decrease in growth rate due to nutrient supply limitations.
We acknowledge several weaknesses in our approach which must be addressed in future studies. Due to limited computing resources and poor documentation, we were unable to work with larger (approaching 95%) portions of the dataset. The model was not validated against data not used in training the fit. In the future, we will use individualized Bayesian predictions based on initial measurements of tumor growth and response to test if our model can make accurate predictions of the observed late stages of response. We also have a large amount of data on cutting-edge first-line therapies i.e. pembrolizumab and other immune-checkpoint inhibitors. This data was granted to us through a sub-request, and has not been able to be included in this modeling project.
There are also several covariates which have not been included or tested in the model.
To make individual predictions meaningful, they must be matched against patient characteristics and lab values.
One of the primary features we hoped to capture with our model was the transient enhancement of drug delivery after bevacizumab administration. Theoretically, this transient enhancement would drive the synergism between bevacizumab and other antiproliferatives. A natural conclusion, and a conclusion supported by previously published clinical papers, is that administering bevacizumab before other antiproliferatives should result in the greatest reduction in tumor size. Unexpectedly, we found through simulation that this result is only true in some cases. Moreover, in some individuals, delaying the bevacizumab until after other therapeutics provided the greatest reduction in tumor volume. Why this is so is not readily suggested by the model 117 developed in this study. To solve this problem, our research group will simulate more clinical trials to determine if there is parameter clustering or some covariate which might predict what the optimal gap in any given patient might be.
Making individual predictions is the long-term goal for this modeling project. This first phase of research was meant to establish a robust preliminary model structure which explained a great deal of variation in the data. Expanding our dataset past 5% of the cleanest data, including covariates and individual patient characteristics, using simulation to find what might predict ultimate gap between bevacizumab and combination antiproliferatives, and refining the structure of our model will give us the full set of tools to develop tools to take individual patient data, and from that data individualize therapy.
Tables and Figures
Table 5.1 Pharmacokinetic Parameters
Therapeutic V1 V2 V3 Q1 Q2 k12 k21 Cl Source Units mL mL mL mL/day mL/day day–1 day–1 mL/day - bevacizumab 2804.12 - - - - 0.223 0.215 216.291 (17) cisplatin 22300 77000 - 456000 - - - 6480 (18) pemetrexed 12900 3380 - 20736 - - - 131904 (19) apomab* 3970 3840 - 793 - - - 328 (20) paclitaxel 229000 856000 30300 3216000 5112000 - - 10296000 (21) carboplatin 11900 8230 - 2172000 - - - 177120 (22) gemcitabine 15000 15000 - 1008000 - - - 3888000 (23) docetaxel 7900 - - - - 27.12 3.6 723120 (24) erlotinib† 210000 ------102960 (25) *see supplementary methods 1; †bioavailability estimated at 60%, ka estimated at 21.36 day–1 (25,26)
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Table 5.2 Pharmacodynamic Parameters
Parameter Value Stoch. Approx. Units S.E R.S.E.(%) Fixed Effects alpha_pop 0.17 0.0045 2.65 beta_pop 0.024 0.00047 1.95 tau_pop 0.37 0.013 3.39 kk_pop 0.0069 0.0013 19.4 w_cis_rel_pop 0.52 0.059 11.3 w_car_pop 0.82 0.054 6.53 w_pem_pop 0.87 0.063 7.32 w_apo_pop 0.78 0.022 2.87 w_erl_pop 0.66 0.025 3.77 w_gem_pop 0.95 0.05 5.27 w_pac_rel_pop 0.85 0.043 5.09 w_doc_pop 0.93 0.019 2 w_bev_pop 1.78 0.29 16.6 lambda_cis_rel_pop 0.001 0.000023 2.23 lambda_car_pop 0.0013 0.000092 7.14 lambda_pem_pop 0.0009 0.000039 4.37 lambda_apo_pop 0.00072 0.000014 1.9 lambda_erl_pop 0.0012 0.00011 8.99 lambda_gem_pop 0.0014 0.00005 3.69 lambda_pac_rel_pop 0.00088 0.000048 5.49 lambda_doc_pop 0.0011 0.000051 4.74 lambda_bev_pop 0.0039 0.00068 17.2 w_bev_gamma_pop 1.03 0.051 4.94 w_bev_rho_pop 2.05 0.26 12.7 kk_i_pop 0.0099 0.0025 25.2 imv_r_perc_pop 0.3 0.058 19.5
Standard Deviation of the Random Effects omega_alpha 0.32 0.02 6.38 omega_beta 0.23 0.016 7.11 omega_tau 0.35 0.033 9.48 omega_kk 2.06 0.16 7.55 omega_w_cis_rel 1.12 0.11 9.87 omega_w_car 0.61 0.059 9.65 omega_w_pem 0.7 0.061 8.79 omega_w_apo 0.27 0.026 9.47 omega_w_erl 0.36 0.32 8.96 omega_w_gem 0.51 0.042 8.29 omega_w_pac_rel 0.47 0.055 11.8 omega_w_doc 0.2 0.016 7.89 119
Table 5.2 continued Parameter Value Stoch. Approx. Units S.E R.S.E.(%) Fixed Effects omega_w_bev 1.95 0.14 7.32 omega_lambda_cis_rel 0.22 0.02 8.99 omega_lambda_erl 0.9 0.087 9.66 omega_lambda_gem 0.37 0.035 9.51 omega_lambda_pack_rel 0.49 0.05 10.2 omega_lambda_doc 0.48 0.043 9.07 omega_lambda_bev 1.8 0.12 6.6 omega_w_bev_gamma 0.47 0.044 9.36 omega_w_bev_rho 1.17 0.12 9.98 omega_kk_i 3.1 0.26 8.29 omega_imv_r_perc 2.85 0.24 8.52
Error Model Parameters a 0.11 0.008 7.57 b 0.088 0.0054 6.13
Table 5.3 Summary of Simulation Outcomes 1 In this simulated experiment, all patients fit during the course of the study were simulated again, except this time bevacizumab was administered between 5 and 0 days before the primary medication (m5 through c0) or between 0 and 5 days after the primary medication (c0 through p5). Below are the minimum, 5th percentile, median, 95th percentile, and maximum of the minimum tumor volume relative to baseline, e.g. in the c0 group, the median tumor reduction was by 69%.
min P05 Median P95 Max m5 0 0.00081 0.3 0.88 1.12 m4 0 0.00014 0.3 0.88 1.12 m3 0 0.000028 0.29 0.88 1.12 m2 0 0.00084 0.29 0.88 1.16 m1 0 0.0012 0.3 0.88 1.21 c0 0 0 0.31 0.88 1.25 p1 0 0.0011 0.31 0.88 1.3 p2 0 0.0017 0.31 0.88 0.135 p3 0 0.0017 0.3 0.89 1.39 p4 0 0.0019 0.3 0.89 1.44 p5 0 0.0015 0.29 0.89 1.49
120
Table 5.4 Summary of Simulation Outcomes 2 In this simulated experiment, bevacizumab pemetrexed and cisplatin were administered at recommended dosages to virtual patients every 21 days for 4 cycles. The gap between bevacizumab and pemetrexed/cisplatin administration was set at either 5 days (m5), 3 days (m3), 1 day (m1), 0 days (c0), or pemetrexed/cisplatin was administered either 1 day (p1) or 2 days (p2) before bevacizumab. Below are the minimum, 5th percentile, median, 95th percentile, and maximum of the minimum tumor volume relative to baseline, e.g. in the c0 group, the median tumor reduction was by 39%
min P05 Median P95 Max m5 0 0.11 0.65 1 1.07 m3 0 0.13 0.63 1 1.07 m1 0 0.15 0.61 1 1.09 c0 0 0.16 0.6 1 1.09 p1 0 0.16 0.59 1 1.09 p2 0 0.16 0.59 1 1.09
Figure 5.1 Model Diagram 121
Figure 5.2 SAEM Search Stochastic approximation expectation maximization search for most likely estimates of parameter values. Exploratory search in black and smoothing search in red.
Figure 5.3 Sample of Individual Fits Several individual fits (black) vs observations (blue) and population prediction (purple). 122
Figure 5.4 Observations vs. Predictions by Patients Receiving Therapeutic In these figures the observations vs predictions (black points) are plotted along with censored data (red points). Blue line is where observations meet predictions i.e. ratio is 1. Error model 95% prediction boundaries at dotted red lines. Points are semitransparent to reduce visual overcrowding of points.
123
Figure 5.5 Visual Predictive Check 124
Figure 5.6 Summary of Simulation Outcomes with Box and Whiskers Plots 1 In this simulated experiment, all patients fit during the course of the study were simulated again, except this time bevacizumab was administered between 5 and 0 days before the primary medication (m5 through c0) or between 0 and 5 days after the primary medication (c0 through p5). The horizontal red lines are reference lines to the 1st, 2nd, and 3rd quartile for the simulated trial where gap was equal to zero. 125
Figure 5.7 Summary of Simulation Outcomes with Box and Wiskers Plots 2 In this simulated experiment, bevacizumab pemetrexed and cisplatin were administered at recommended dosages to virtual patients every 21 days for 4 cycles. The gap between bevacizumab and pemetrexed/cisplatin administration was set at either 5 days (m5), 3 days (m3), 1 day (m1), 0 days (c0), or pemetrexed/cisplatin was administered either 1 day (p1) or 2 days (p2) before bevacizumab. The horizontal red lines are reference lines to the 1st, 2nd, and 3rd quartile for the simulated trial where gap was equal to zero. 126
Figure 5.8 A Pair of Illustrative Examples In this simulated experiment, bevacizumab pemetrexed and cisplatin were administered at recommended dosages to virtual patients every 21 days for 4 cycles. The gap between bevacizumab and pemetrexed/cisplatin administration was set at either 5 days (m5), 3 days (m3), 1 day (m1), 0 days (c0), or pemetrexed/cisplatin was administered either 1 day (p1) or 2 days (p2) before bevacizumab. For the virtual patient with a larger final tumor volume, administering bevacizumab after pemetrexed/cisplatin produces the maximum tumor volume reduction. However, the opposite is true of the virtual patient with the greater response.
127
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CHAPTER 6. GENERAL CONCLUSION
Developing clinical therapeutics that are broadly effective in NSCLC is extremely challenging due to the idiosyncrasies of individualizing therapies which are often developed in small and noisy sample sets which are unrepresentative of the general population. Therapeutics that are approved for use in NSCLC are usually only effective in a small subset of the population – at their approved dosage and recommended scheduling. Individual patient characteristics and the patients’ cancer characteristics determine the viability of various treatments. And Although a therapeutic might initially be helpful, there is always the eventuality that the drug becomes intolerable to the patient or that their cancer develops resistance. As of yet, medical doctors cannot reliably individualize cancer therapy to meet the needs of every patient. Instead, doctors use insight gained from their clinical experience, in combination with formal recommendations from accredited institutions, to guide their choices when treating individual patients. The greatest aspiration of mathematical modelers in NSCLC is to create robust tools that clinicians can use in their daily practice to assist them in selecting the right therapeutics at the right dosages in the right patient populations. To build those tools, a thorough mathematical and biological understanding of NSCLC growth and response to anti-proliferatives will be necessary.
Throughout these research projects we have been attempting to create comprehensive, semi-mechanistic mathematical descriptions of various anti-NSCLC therapies. We have built these models using a variety of heuristics. A common starting place in pharmaceutical modeling projects is to reference the literature for previous efforts. Hopefully, one can use a previously published model as a base structure or gain 131 an understanding of the most prominent biological features. If the modeling project is novel, simple mammillary compartmental models and exponential-family functions can be arranged to produce a rough empirical fit. The base model structure is used as a platform for developing a more sophisticated description, but the model must be informed with data. This data can either be produced experimentally in a preclinical or clinical environment, it can be collated from previously published studies and clinical trials, or it can be simulated directly if the biology is sufficiently well understood. After fitting a base model, the structure can be refined systematically until the model sufficiently explains the variation in the data. Then, final parameter estimates are derived from the dataset and the model is said to be fit or parameterized. A fit model can then be used to simulate various clinical trials to answer questions of interest to the research group. After publishing results and the data used to derive them, other members of the research community can structurally improve the NLME model or use the final parameterization for simulation.
Those heuristics have been implemented throughout the publications collated in this document. In Chapter 2, we outline a perspective for solving problems in PKPD modeling which emphasizes the development of spontaneous-disease animal models.
In Chapter 3, we detail the PKPD of pharmacological ascorbate for cancer and build a modeling framework based on mamillary compartmental models which will be reusable in future studies in either preclinical, clinical, or veterinary environments. In Chapter 4, we built a translational model of bevacizumab-pemetrexed/cisplatin for NSCLC. We used the structure of a previously published NLME model in the study. We fit the model using data from a xenograft model of NSCLC. Lastly, in Chapter 5, we took preliminary 132 findings from Chapter 4 and used them to build a clinical model of anti-NSCLC therapy.
Our final model developed in Chapter 5 was a combination of various biological mechanisms of the therapeutics, and previously published pharmacokinetics and pharmacodynamics models, as well as our previous work in bevacizumab- pemetrexed/cisplatin. The data used to fit the model was collated from several large clinical trials in anti-NSCLC therapy.
NLME modeling is a natural framework for solving problems in pharmacokinetics.
When a patient is administered a medication, researchers cannot take samples at frequent time intervals without significantly perturbing the system, or worse, endangering the health of the patient. NLME modeling excels in sparse sampling regimens when the inter-individual variation and error from measurements are relatively regular. NLME modeling also gives a logical structure to analyze the variation in the estimates you derive when the model is fit. The researcher describes individual variation in terms of some theoretical population center relative to various covariates. In most diseases, the NLME approach is also well-suited to the pharmacodynamics modeling for much the same reasons.
There is a necessary deductive aspect of modeling anti-NSCLC therapy. As of yet, there is no method for reliably and frequently measuring the volume of NSCLC tumors. Contrarily, a unique facet of NSCLC modeling is that direct samples of the tumor are taken at exceptionally long intervals relative to almost any other disease. And, the samples that are produced are usually heavily affected by measurement error.
Clinicians use a great variety of techniques – from physical calipers to CT scans – to measure tumor volumes. In many studies, tumor volumes are not even recorded. Often, 133 clinicians simply approximate the tumor burden by working with the longest diameters of the largest tumors. And, the time-of-day of measurement is usually considered irrelevant and left out of records. Trials in clinical therapeutics are also typically coordinated between many different treatment centers and research groups. These various groups tend to have minor variations in laboratory protocols, further adding to the total error in the dataset. Lastly, because cancer usually develops as a cascade of mutations, there is high variability between patients in cancer pathology. Consequently, modelers in NSCLC, and in cancer generally, use a combination of sparse samples, biomarkers of tumor growth and response, and time-to-death to develop an empirical semi-mechanistic understanding of the largely latent process that is cancer progression.
The logic underlying this modeling strategy is that when variability is relatively regular, each datapoint puts constraints on the possible solutions to the structural model describing the latent process. With enough datapoints and a simple enough model, the modeler should theoretically be able to identify a set of parameters which largely accounts for the variability in the data.
Perspectives and Next Steps
In the final study reproduced in this document, Chapter 5, we collated several datasets from 11 intensively-sampled clinical trials in NSCLC to develop a generalized platform for modeling in NSCLC. The basic motivation behind this study was that with a big enough dataset, and the model structure developed in Chapter 4, we believed that it might be possible for us to produce a robust and reusable description of NSCLC growth and response to various antiproliferative therapies. In the course of fitting that model, we found the population variability quite difficult to describe and the datapoints following inexplicable time-courses. This is, at least in part, because the datasets contained many 134 clear errors and physiologically improbable events –as a hypothetical example: tumor diameter fluctuating from 1.0 cm in January, to 2.0 cm in June, and 0.0 cm in July, before climbing to 4.0 cm in August. Patients also commonly miss or must reschedule visits, making measurement intervals erratic. And as a final note, tumor measurements with CT scans, ultrasounds, calipers, etc. require the involvement of a medical doctor.
This puts a large cost burden on the study sponsors as well as patients. That cost burden perversely incentivizes a minimal sampling schedule with rudimentary methods.
If, in the future, we want to fully leverage the potential of mathematical modeling to solve problems in NSCLC, it seems clear to me that the best place to innovate is not in intelligently designed statistics or clever computer algorithms, but in developing more robust procedures for measurement.