Workshop 5: Treatment, Clinical Trials, Resistance

(February 16,2015 - February 20,2015 )

Organizers


Mariam Eljanne
Physical Sciences-Oncology, National Institutes of Health (NIH)
Larry Nagahara
Division of Cancer Biology, National Cancer Institute, NIH
Peter Shields
James Cancer Hospital and Comprehensive Cancer Center (CCC), The Ohio State University
Kristin Swanson
Neurological Surgery, Northwestern University
Jack Tuszynski
Oncology, University of Alberta

Co-sponsor: Physical Sciences-Oncology Program of the Division of Cancer Biology, National Cancer Institute, National Institutes of Health, U.S. Department of Health and Human Services.

While the primary forms of tumor treatment remain chemotherapy and radiation, generic cytotoxic therapies, the increasing understanding of the nature of the disease as being both heterogeneous and genetically unstable has induced a trend to design and create therapies tailored to the specific tumor (patient-specific) and to combat the many different subpopulations of cells with combination therapies. Despite these efforts, tumor resistance and recurrence remain an unfortunate challenge of clinical trials. However, the clinical focus has been primarily on the genetic heterogeneity in tumor cell populations, with minimal focus on the impacts of treatment on the subpopulations phenotypic interactions, either competitive or cooperative, the induced microenvironment, or the evolutionary pressures created. One likely reason is the inability of traditional clinical trials to quantify or meaningfully analyze these phenomena. Examining the impact of particular drug therapies and their scheduling on the local microenvironment and individual cellular behavior in both the long and short term is almost impossible in a clinical setting and extremely difficult in laboratory experiments. Limiting factors include inadequate observation tools, e.g. most imaging methodologies are too coarse to properly resolve the dynamics, changing the system by observing it, such as when resecting grown tumors in animals for closer observation, time for disease development and money. Mathematical models offer an approach to investigate many different types of therapies along with their impact on the microenvironment, and to explore optimal dosing combinations and schedules while bypassing the many limitations encountered in the clinic and laboratory. There are many different varieties of models, though they can generally be categorized into discrete, continuum, or statistical, each offering its own advantage for considering various scales or effects. They can be designed utilizing a basic understanding of the primary phenotypes and genotypes present in a tumor to investigate the likely induced microenvironment from various therapies and evolutionary selection pressures leading to resistance. It is even possible to use them to perform virtual clinical trials and compare different treatments on theoretical populations. This workshop will focus on two broad topics: Mathematical modeling of cancer treatment strategies and how to model resistance of cancers to drug treatments. Use of mathematical models to compare clinical trial arms and virtually simulate clinical trials outcomes. The workshop will highlight modeling applications that are as close as possible to direct clinical impact including design of multi-institutional clinical trials for patient-specific radiation dose strategies, quantification of patient-specific response to treatment that can be useful in predicting outcomes and treatment design, as well as include discussions of sequencing of drug treatments, optimal scheduling, and modeling of combination therapies which are useful in rapidly mutating diseases, such as cancer and HIV. The workshop will also discuss ways to implement the use of mathematical models in a clinical setting.

Accepted Speakers

Alexander Anderson
Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Mathilde Badoual
Physics, Paris Diderot University
Donald Berry
Biostatistics, University of Texas M.D. Anderson Cancer Center
Kenneth Buetow
Complex Adaptive Systems, Arizona State University
Arijit Chakravarty
Modeling and Simulation (DMPK), Takeda Pharmaceuticals Co.
Alex Fletcher
Wolfson Centre for Mathematical Biology, University of Oxford
Farzin Ghaffarizadeh
Center for Applied Molecular Medicine, University of Southern California
Thomas Hillen
Dept. of Mathematical & Statistical Sciences, University of Alberta
Pamela Jackson
Neurological Surgery, Northwestern University
Josh Jacobs
Neurosurguery, Northwestern University
Robert Jeraj
Medical Physics, University of Wisconsin
Eugene Koay
Radiation Oncology, MD Anderson Cancer Center
Serge Koscielny
Biostatistics and Epidemiology, Gustave Roussy
Kevin Leder
Industrial and Systems Engineering, University of Minnesota
Alicia Martínez González
Mathematics, Universidad de Castilla-La Mancha
Larry Nagahara
Division of Cancer Biology, National Cancer Institute, NIH
Bob Parker
Chemical and Petroleum Engineering, Bioengineering, and Critical Care Medicine, University of Pittsburgh
Ami Radunskaya
Mathematics, Pomona College
Corbin Rayfield
Department of Neurosurgery, Northwestern University
Edward Rietman
pediatric oncology, tufts medical school, Newman Lakka Institute
Russell Rockne
Neurological Surgery, Northwestern University
Jacob Scott
Department of Radiation Oncology, H. Lee Moffitt Cancer Center & Research Institute
Ariosto Silva
Cancer Imaging and Metabolism, H. Lee Moffitt Cancer Center
Jan Unkelbach
Radiation Oncology, Harvard Medical School
Jared Weis
Biomedical Engineering, Vanderbilt University
Monday, February 16, 2015
Time Session
07:45 AM

Shuttle to MBI

08:00 AM
08:30 AM

Breakfast

08:30 AM
09:00 AM

Opening remarks by Marty Golubitsky

09:00 AM
09:30 AM
Jack Tuszynski
09:30 AM
10:00 AM
Kenneth Buetow - Using Networks Models to Genetically Map Biologic Process to Complex Phenotypes

Much effort has been focused at the examination of molecular alterations occurring somatically in tumors. This somatic variation occurs against a highly polymorphic constitutional genetic background. Systems-wide molecular analysis of this constitutional variation has identified a cacophony of inherited variation associated with complex phenotypes. Coherence emerges from these data when evaluated using biologic networks as a modeling framework. These networks models account for the individual heterogeneity in underlying etiology as well as the diversity and interaction of events underpinning a complex phenotype such as cancer. We have previously described Pathways of Distinction Analysis (PoDA) as an approach that uses genome-wide data sets and established biologic networks as models. PoDA provides a means to map differences in genome-wide constitutional variation observed in networks to phenotypes of interest. PoDA and other network-based methods have identified networks important in cancer etiology not seen through single gene analysis. Enabled by a novel high performance computational capacity we have extended PoDA to include all measured inherited variability observed in the pathways and to search for the smallest collection of such variation with the network required to significantly classify alternative phenotypes.

10:00 AM
10:30 AM
Donald Berry - Platform Clinical Trials in Oncology and Neurology

Abstract not submitted.

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Kevin Leder - The Timing of Resistance Mediated Treatment Failure

A common problem for a wide range of treatment modalities is the development of resistance. One particular way by which resistance can arise is the development of mutant strains that are resistant to the relevant therapy. In this talk I will introduce a mathematical model for this phenomena, and then discuss what we can learn about the timing of treatment failure from this model. Time permitting I will also discuss optimization of combination therapy to minimize resistance risk.

11:30 AM
12:00 PM
Eugene Koay - Biophysical subtypes of pancreatic cancer

The dismal survival rate for patients with pancreatic cancer has been stagnant for decades. Personalized approaches to therapy may help accelerate progress, but requires establishment of robust biomarkers. Partly due to the complex biology of the disease and its significant heterogeneity between patients, the identification of molecular biomarkers has not been fruitful so far. To address this challenge, we have developed methods to characterize the physical properties of pancreatic cancer. Our work supports the notion that the multi-scale mass transport properties of this cancer influence the natural history of the disease and its sensitivity to cytotoxic therapies. Our ongoing efforts to further develop this approach and implement it in the clinic aim to achieve the goal of individualized treatments for this deadly disease.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Bob Parker - Personalizing Chemotherapy Treatment using Systems Engineering Tools and Model-Based Dynamic Optimization

Oncologists are challenged by the need to balance efficacy and toxicity for their patients. While models of drug pharmacokinetics (PK) and pharmacodynamic antitumor effect (PD) have been developed and studied in the search for optimal treatment schedules, data-driven mechanistic models of toxicity - which ultimately limit treatment to individual patients - are comparatively less-studied. We have developed a decision support system that combines PK and PD models, including drug-dependent toxicity, for the purpose of designing novel treatment regimens for chemotherapeutics using systems engineering dynamic optimization tools. As a case study, we employ docetaxel as the antitumor agent. A physiologically-based PK model is rigorously reduced for use within the algorithm. The neutropenia model is an extension of the well-known Friberg et al. model that includes the mechanistic insight necessary to incorporate the administration and effect of G-CSF as a neutropenia mitigating agent. Finally, efficacy is modeled using the power-law structure proposed by Norton and co-authors. The model-based mixed-integer dynamic optimization algorithm returns a dosing schedule that provides antitumor effect equivalent to the maximum docetaxel dose used in the clinic (100 mg/m^2 q3w), but with a toxicity profile that is controlled to be no greater than Grade 3 acutely, and not to exceed Grade 2 for more than 6 consecutive days. Furthermore, the algorithm can address combination therapy using drugs with overlapping toxicity (e.g., carboplatin) and can respond to patient-specific changes in drug efficacy and toxicity during cyclic chemotherapy.

03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM
Ami Radunskaya - Using mathematical models to design mixed treatment strategies

In many cases cancer is treated using a combination of treatments. Mathematical models can be used to design effective treatment strategies, answering the key questions: How Much? and How Often? In this talk I will review three mathematical models and optimization techniques that have been used to suggest treatment protocols using combinations of chemotherapy, monoclonal antibody treatments, and vaccine therapies. I will also discuss using mathematical models to simulate clinical trials.

04:00 PM
06:00 PM

Reception and Poster Session

06:00 PM

Shuttle pick-up from MBI

Tuesday, February 17, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Corbin Rayfield - Mathematical modeling as a tool to generate patient-specific radiotherapy dose plans

Due in large part to the difficulty in predicting tumor growth clinically, current treatment of Glioblastoma takes a blunt approach. Patients are stratified largely based on age, performance status, and other imprecise measurements. We have been unable to turn insights into the genetic, phenotypic, and growth rate diversity of different glioma cellsinto significant clinical gains. Rapid advances have been made, but this has not translated into tools for clinicians to differentiate patients. One such facet of glioma heterogeneity, hypoxia, presents an opportunity for modeling to aid in the selection of patient-specific treatment plans. As new techniques allow for better sculpting areas of dose across a tumor, the potential to target areas that are more radiosensitive while sparing dose to areas of resistance could mean significantly less dose to healthy tissue. This talk will focus on identifying areas of hypoxia and the implementation of a model of tumor hypoxia as a tool to compare modulating fractionation an optimized plan.

09:30 AM
10:00 AM
Alicia Martínez González - Targeting Hypoxia in Gliomas: From Mathematics to Bedside

This research explores the use of mathematical models as promising and powerful tools to understand the complexity of tumors and their environment. We focus on gliomas, which are primary brain tumors derived from glial cells, mainly astrocytes or oligodendrocytes. These tumors range from lower-grade astrocytomas, such as the diffuse astrocytoma with slow growth, to the highest grade, epitomized in the most malignant and prevalent one: the glioblastoma multiforme. A variety of mathematical models, based on ordinary differential equations and partial differential equations, have been developed both at the micro and macroscopic levels. Our aim is to describe key mechanisms relevant in tumors in a quantitative way and to design optimal therapeutical strategies. We consider both standard therapies such as radio and chemotherapy together with other novel therapies targeting oxidative stress, thromboembolic phenomena or the cell metabolism.

This study has been the basis of a multidisciplinary collaboration involving, among others, neuro-oncologists, radiation oncologists, pathologists, cancer biologists, surgeons and mathematicians with a common goal: to achieve a deeper understanding of the tumor evolution and to improve its therapeutical management.

10:00 AM
10:30 AM
Arijit Chakravarty - A bleaker view, more clearly: applying evolutionary dynamics modeling to the design and optimization of novel anticancer therapies

A slew of publications over the past decade has provided evidence for clonal selection and evolution in cancer. While this is generally not news to most practitioners in the field, the predictions (and the implications for anticancer drug development) that flow from Darwinian evolution as a theory differ dramatically from those made by other theories, such as Oncogene addiction or the Cancer Stem Cell hypothesis. What are the implications of an evolution-based view of cancer? How would one develop and evaluate therapies rationally if cancer progression is based on luck, response to therapy is stochastic, and all interventions eventually fail? In my talk I will review the practical application to drug discovery and development, of mathematical modeling frameworks based on evolutionary theory, population genetics and population biology.

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM

Discussion Session

11:30 AM
12:00 PM
Robert Jeraj - Interplay between molecular imaging and tumor modeling of anti-angiogenic therapies

Angiogenesis is one of the key tumor hallmarks. Use of anti-angiogenic therapies, particularly those targeting the VEGF pathway, is a common treatment strategy. However, clinical outcomes have been rather disappointing. One of the key phenomena in response to anti-angiogenic therapies is the so-called "angiogenic flare", rapid rebound of tumors after therapy cessation or during treatment breaks. In addition, prolonged exposure to anti-angiogenic agents leads to build-up of treatment resistance. A series of clinical trials using advanced molecular imaging techniques will be presented that has helped explaining the observed angiogenic flare, giving insights into potential treatment strategies. Furthermore, accompanying tumor modeling based on patient-specific molecular imaging input has been used to investigate potential mechanisms leading to treatment failures. Interplay between molecular imaging-driven clinical trials and tumor modeling will be presented as a role-model for better understanding of clinically observed phenomena and as a guiding tools to guide more successful future treatment strategies.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
03:00 PM
Kristin Swanson
03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM
Russell Rockne - Clinically targeted mathematical modeling to study response, resistance and recurrence of glioblastoma brain cancer.

Glioblastoma is a lethal primary brain tumor that often recurs after treatment. MRI is the principle means of monitoring the disease progress and response to treatment. Using an MRI-based, patient-specific mathematical model, we study the spatial-temporal evolution of glioblastoma through treatment to better understand how the phenotype and kinetics of the disease are changed by therapy. Specifically, we use patient-specific parameters to quantitatively study response, resistance and the dynamics of tumor recurrence on an individual basis using a macroscopic tumor cell density model. We find that the standard chemo-radiation therapy significantly changes the phenotype and growth kinetics of the disease in a way that may lead to the design of better, more individualized therapies.

04:00 PM
04:30 PM
Ariosto Silva - Personalized therapeutic regimens in multiple myeloma

We here describe how particular features of cancer, combined with flawed paradigms and bad habits widespread in cancer research, prevent us from curing cancer.

Next, we propose how one may overcome these challenges by combining biological models from biomedical sciences, clinical data, and evolutionary dynamics into a mechanistic framework capable of predicting clinical response.

Through this presentation we use our work in multiple myeloma, a treatable but incurable cancer of the bone marrow, as a proof of principle for adaptive personalized medicine. In other words:

The right drug combination at the right dose and schedule, for the right patient, at the right time, and for the right duration of time, adjusting any of these elements as needed, aiming to maximize survival and quality of life.

04:30 PM
05:30 PM

Discussion Session

05:30 PM

Shuttle pick-up from MBI

Wednesday, February 18, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Jared Weis - Predicting the Response of Breast Cancer to Neoadjuvant Chemotherapy Using a Mechanically Coupled Reaction-Diffusion Model

While there is considerable data on the use of mathematical modeling to describe tumor growth and response to therapy, they are often not of the form that can be easily applied to clinical data to generate testable predictions in individual patients. There is a clear need to develop and apply clinically-relevant oncological models that are amenable to available patient data and yet retain the most salient features of response prediction. We show how a biomechanical model of tumor growth can be initialized and constrained by patient-specific magnetic resonance imaging data, obtained early in the course of therapy, to predict the response for individual patients with breast cancer undergoing neoadjuvant chemotherapy. Using this mechanics-coupled modeling approach, we are able to predict, after the first cycle of therapy, breast cancer patients that would eventually achieve a complete pathological response and those who would not, with receiver operating characteristic area under the curve of 0.87. Our approach significantly outperformed standard (i.e., not mechanically coupled) reaction-diffusion predictive modeling, simple analysis of the tumor cellularity estimated from imaging data, and the Response Evaluation Criteria in Solid Tumors (RECIST). Thus, we show the potential for mathematical model prediction for use as a predictive indicator of response to therapy. The work indicates the considerable promise of image-driven biophysical modeling for predictive frameworks within therapeutic applications.

09:30 AM
10:00 AM
Zvia Agur - Virtual Talk: Predicting Response to Hormone Therapy in Advanced Prostate Cancer Patients by Integrating a Mathematical Mechanistic Model of Tumor Progression with Data from Clinical Trials

Abstract not submitted.

10:00 AM
10:30 AM
Alex Fletcher - Multiscale modelling of cell populations in a consistent computational framework: progress and challenges

Alongside experimental and clinical approaches, computational modelling offers a useful tool with which to unravel the complex interactions between processes at the intracellular, cellular and tissue scales that underlie the growth of tumours and their response to treatment. Avariety of different individual cell-based and multiscale modelling approaches have recently been developed for studying how processes at the level of a single cell affect tissue-level behaviour. While there are clear strengths and weaknesses with each modelling approach, and therefore cases in which it is clear which approach is valid, there are other cases in which it is not clear. When comparing different constitutive assumptions, a computational framework is required that allows one to easily change the fine details of a model and its implementation. A further barrier to the wider use of such models is the lack of standards or benchmarks; models and methods are often not reused effectively, because they are typically not available as rigorously tested, open-source simulation software. It is therefore difficult to guarantee the reproducibility of computational results. In this talk I describe work being done to address these issues through the C++ library, Chaste (http://www.cs.ox.ac.uk/chaste). I discuss its functionality and the approach we have taken to develop this code, and highlight some of the ongoing computational challenges associated with improving the reproducibility and re-use of individual cell-based and multiscale models.

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Edward Rietman - Design Principles for Cancer Therapy guided by changes in complexity of Protein-Protein Interaction Networks

The continuously increasing amount of molecular information on cancer dynamics has increased the need to understand the relationships and dependencies within protein interaction networks. Our early observation that network entropy, a complexity measure of cancer protein-protein interaction (PPI) networks, correlates with survival suggested that the organization of PPI networks could be explored with other complexity statistics, including topological measures and thermodynamic measures beyond network entropy.

We now show that a topological measure, the Betti number, correlates linearly with survival for different cancers, and that Betti numbers can be used to predict survival gains/losses produced by a targeted inhibition of specific proteins in the network. We propose that the interpolation of Betti numbers on cancer survival curves could potentially be explored with therapeutic intent and help clinicians in selecting therapies.

We also describe, and demonstrate, that Gibbs free energy for PPI networks of different cancer stages is linear correlated with stage as an ordinal number, and when combined with topological measures may provide additional new insights applicable to personalized medicine.

11:30 AM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Pamela Jackson - Predicting the differential localization of metastases to the brain

Brain metastases (mets) are a complication that occurs in about 40% of patients with systemic cancer and, when present, are typically the causes of mortality. Lung, breast, and melanoma cancers represent the highest incidence of brain metastases and demonstrate differential angiogenic tumor biology, raising the possibility for treatment using anti-angiogenics in select brain mets cases. Brain mets are typically treated the same regardless of the primary cancer; however, optimal treatment may vary with brain met histology and angiogenic tendency. Currently there are no adequate modeling strategies to assess spatial localization and differential growth tendencies within the brain based on tumor angiogenic biology. An enhanced understanding of the interplay between tumor angiogenic biology and spatial growth tendencies within the brain could have profound therapeutic impact. We are exploring a novel computational model that simulates a nexus between tumor angiogenic biology and spatial growth profiles seen on patient-specific MRI, thereby providing a personalized medicine paradigm for addressing brain mets.

02:30 PM
03:00 PM
Josh Jacobs - Evaluating Treatment Response in GBM: Improvement by incorporating Anatomical Boundaries

Abstract not submitted.

03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM
Farzin Ghaffarizadeh - Using bioengineered tissues to build computational models of tumor dynamics in human tissues

During the last decades, in vivo experiments have been a major tool for studying cancer treatments and developing clinical trials. However, these experiments are neither simple nor cheap. Simulated tissues could allow scientists to quickly test many therapeutic strategies simultaneously, allowing more rapid progress. However, such computational models must be built upon and validated against experimental measurements that represent patient tissues. In this talk, we will discuss our project to create a computational model of colon cancer metastases in the liver based upon imaging data from bioengineered liver tissues. We will show new techniques for quantifying liver organoid structure, assessing cancer cell phenotype in the orgnaoids, and applying these to create 3-D computational liver models for cancer simulations. We will show preliminary results for the cancer model, and discuss the possible implications for personalized medicine.

04:00 PM
05:00 PM

Discussion Session

05:00 PM

Shuttle pick-up from MBI

Thursday, February 19, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:30 AM
Jan Unkelbach - Radiotherapy planning based on the biologically equivalent dose model

Fractionation decisions in radiotherapy face a tradeoff between increasing the number of fractions to spare normal tissues and increasing the total dose to keep the same level of tumor control. The biologically equivalent dose (BED) model is the most common model to compare fractionation regimens in the clinic. The basic BED model assumes that the biological dose is given by a quadratic function of the physical dose. Despite its phenomenological nature and mathematical simplicity, the BED model yields surprising implications for fractionation decisions. In this presentation, two aspects of the BED model are discussed: 1) The interdependence of fractionation decisions and the spatial dose distribution, and 2) extensions of the BED model towards concurrent chemoradiation. It is demonstrated that, even in the absence of time dependencies in radiation response, the BED model suggests non-stationary treatment regimens, i.e. the delivery of different dose distributions in different fractions.

09:30 AM
10:00 AM
Thomas Hillen - A stochastic model for the normal tissue complication probability (NTCP) in radiation treatment

When radiation therapy is applied to a tumor, then inevitably, healthy tissue is exposed too. It is quite common that side effects arise or that organs fail. The normal tissue complication probability (NTCP) is an attempt to quantify the risks of side effects. So far, NTCP models have been based on statistical outcomes. In my talk I will develop a mechanistic model for tissue complication which is based on organ-specific and patient-specific model parameters. We get a surprisingly simple formulation of the NTCP, which only requires a few, obtainable, physiological characteristics.

10:00 AM
10:30 AM
Mathilde Badoual - Modeling the response of low-grade gliomas to radiotherapy

After years of slow growth, diffuse low-grade gliomas transform inexorably into more aggressive forms, jeopardizing the patient’s life. Mathematical modeling could help clinicians to have a better understanding of the natural history of these tumors, to optimize treatments, but also to predict their evolution. We present here a model for the effect of radiotherapy on these tumors. To build this model, we first analyzed histological samples from patients’ biopsies. The samples were prepared in Hospital Sainte-Anne (Paris, France). We were able to correlate the amount of edema in the samples with the MRI signal abnormalities. A mathematical model was then designed from these observations, involving the production and the draining of edema by tumor cells. The model is applied to clinical data consisting of the tumor radius along time, for a population of 28 patients. We show that the draining of edema accounts for the observed delay of tumor regrowth following radiotherapy, and we are able to fit the clinical data in a robust way. We argue that, within reasonable assumptions, it is possible to predict (with a precision around 20%) the regrowth delay after radiotherapy and the gain of lifetime due to radiotherapy.

10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Jacob Scott
11:30 AM
12:00 PM
Larry Nagahara - "I have a Ph.D. in mathematics and I'm here to help" Contributions to Cancer Research

More than 40 years ago, the U.S. government declared a “war on cancer” and committed to investing in laboratory and clinical research in order to understand the causes of cancer and thereby aid its diagnosis, treatment, and cure. Despite enormous advances and important improvements in the diagnosis and treatment of many cancers, the “war” has in significant ways progressed less than originally hoped. The complexity of the disease is clearly evident by the dynamic and evolving course the disease takes during its progression and response treatment. Building on progress in the molecular sciences and advanced technologies, the exploration of physical, engineering, and mathematical approaches may provide a complementary perspective to better elucidate the emergence and behavior of cancer at all scales. Initiatives from the National Cancer Institute (NCI) and other agencies are exploring opportunities to invigorate physical scientists/engineers/mathematicians and their approaches through improved integration with more traditional research effort in cancer biology and clinical oncology. In contrast to the well-worn and cynical phrase “I’m from the Government and I’m here to help,” examples of NCI’s effort to invoke the applied mathematics community and their perspectives into cancer research will be presented.

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Alexander Anderson - biPhase i trials in melanoma: a novel route to translate preclinical findings to the clinic

The combination of chemotherapy and an AKT inhibitor (MK2206) in patients with metastatic solid tumors including melanomas is associated with good treatment responses. Our experiments showed that treatments differentially induce autophagy in cells and that autophagy modulates treatment responses. Motivated by these experimental observations, we formulated a mathematical model comprising a system of ordinary differential equations that explains the dynamics of melanoma cells under different mono and combination therapies. Model parameters were estimated by utilizing an optimization algorithm that minimized the difference between predicted cell populations and experimentally measured cell numbers. We predict that the standard of care combination therapy is effective in short term tumor control but the treatment will eventually fail, although smarter schedules can be applied to extend response. To place these results in a more clinically relevant setting, we implemented a phase i trial (virtual/imaginary clinical trial). A genetic algorithm was employed to generate a cohort of over 3000 virtual patients that captured the diversity of disease response observed in a comparable clinical trial. We then simulated clinical trials with this cohort and performed a sensitivity analysis to determine key parameters that separate virtual patients with more favorable and less favorable outcomes on the basis of tumor volume changes. Our analysis shows the relevance of selecting patients based on autophagy transition rates and growth rates. Finally, we predict optimal therapeutic approaches across all virtual patients.

02:30 PM
03:00 PM
Cenny Taslim - Molecular Epidemiology and Breast Cancer Risk

Abstract not submitted.

03:00 PM
03:30 PM

Break

03:30 PM
04:30 PM
Serge Koscielny - Evaluation of tumor treatment efficacy: comparison of RECIST with the variation of tumor growth rate (TGR).

In drug development, many go/no-go decisions depend on results from phase I trials and evaluation of tumor response to therapy may be crucial. Tumor response is usually evaluated according to RECIST. However, RECIST takes into account only tumor growth during treatment, and it is impossible to distinguish the effect of treatment from the intrinsic characteristics of a tumor. For example, among the many tumors classified as stable according to RECIST, to discriminate those resulting from a real treatment effect from the indolent tumors remains challenging. We incorporated pretreatment data to measure treatment effect as the difference between the growth rate measured after and before treatment. We assumed an exponential growth for tumor lesions. We compared RECIST and TGR using data from patients treated mostly in phase I trials. We simulated the impact of the accuracy of tumor size measurement on both TGR and RECIST evaluations. Finally we discuss the feasibility of TGR evaluations.

04:30 PM
05:00 PM

Discussion Session

05:00 PM

Shuttle pick-up from MBI

06:30 PM
07:00 PM

Cash Bar at Crowne PLaza

07:00 PM
08:30 PM

Banquet at Crowne Plaza

Friday, February 20, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
11:00 AM

Discussion Session & Closing Remarks

11:00 AM

Shuttle pick-up from MBI (One to airport and one back to hotel)

Name Email Affiliation
Anderson, Alexander alexander.Anderson@moffitt.org Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Avendano, Alex avendano.8@osu.edu Mechanical and Aerospace Engineering, The Ohio State University
Badoual, Mathilde badoual@imnc.in2p3.fr Physics, Paris Diderot University
Bell, Erica erica.bell@osumc.edu Radiation Oncology, The Ohio State University
Berry, Donald dberry@mdanderson.org Biostatistics, University of Texas M.D. Anderson Cancer Center
Buetow, Kenneth Kenneth.Buetow@asu.edu Complex Adaptive Systems, Arizona State University
Carcillo, Christine cmc164@pitt.edu Chemical Engineering, University of Pittsburgh
Cebulla, Colleen colleen.cebulla@osumc.edu Ophthalmology and Visual Science, The Ohio State University
Chakravarty, Arijit Arijit.Chakravarty@takeda.com Modeling and Simulation (DMPK), Takeda Pharmaceuticals Co.
Durrett, Rick rtd@math.duke.edu Department of Mathematics, Duke University
Fessel, Kimberly fessel.6@mbi.osu.edu Mathematical Biosceinces Institute, The Ohio State University
Fletcher, Alex alexander.fletcher@maths.ox.ac.uk Wolfson Centre for Mathematical Biology, University of Oxford
Geyer, Susan susan.geyer@epi.usf.edu Health Informatics Institute, University of South Florida
Ghaffarizadeh, Ahmadreza aghaffar@usc.edu Center for Applied Molecular Medicine, University of Southern California
Han, Yang hanyang1122@gmail.com Medical School, University of Exeter
Hanson, Shalla shalladh@gmail.com Mathematics, Duke University
Hillen, Thomas thillen@ualberta.ca Dept. of Mathematical & Statistical Sciences, University of Alberta
Hsu, Jason jch@stat.ohio-state.edu Department of Statistics, The Ohio State University
Jackson, Pamela pamela.jackson@northwestern.edu Neurological Surgery, Northwestern University
Jacobs, Josh joshua.jacobs2@northwestern.edu Neurosurguery, Northwestern University
Jeraj, Robert rjeraj@wisc.edu Medical Physics, University of Wisconsin
Koay, Eugene EKoay@mdanderson.org Radiation Oncology, MD Anderson Cancer Center
Koscielny, Serge serge.koscielny@gustaveroussy.fr Biostatistics and Epidemiology, Gustave Roussy
Leder, Kevin kevin.leder@isye.umn.edu Industrial and Systems Engineering, University of Minnesota
Linder, Daniel dflinder@georgiasouthern.edu Biostatistics, Georgia Southern University
Martínez González, Alicia alicia.martinez@uclm.es Mathematics, Universidad de Castilla-La Mancha
Nagahara, Larry nagaharl@mail.nih.gov Division of Cancer Biology, National Cancer Institute, NIH
Parker, Robert rparker@pitt.edu Chemical and Petroleum Engineering, Bioengineering, and Critical Care Medicine, University of Pittsburgh
Radunskaya, Ami aradunskaya@pomona.edu Mathematics, Pomona College
Rambani, Komal rambani.1@osu.edu Biomedical Sciences, The Ohio State University
Rayfield, Corbin crayfi2@uic.edu Department of Neurosurgery, Northwestern University
Rietman, Edward erietman@gmail.com pediatric oncology, tufts medical school, Newman Lakka Institute
Rockne, Russell russell.rockne@northwestern.edu Neurological Surgery, Northwestern University
Scott, Jacob jacob.g.scott@gmail.com Department of Radiation Oncology, H. Lee Moffitt Cancer Center & Research Institute
Shields, Peter peter.shields@osumc.edu James Cancer Hospital and Comprehensive Cancer Center (CCC), The Ohio State University
Shivade, Chaitanya shivade.1@osu.edu Department of Computer Science and Engineering, The Ohio State University
Silva, Ariosto ariosto.silva@moffitt.org Cancer Imaging and Metabolism, H. Lee Moffitt Cancer Center
Swanson, Kristin kristin.swanson@northwestern.edu Neurological Surgery, Northwestern University
Taslim, Cenny taslim.2@osu.edu Biomedical Informatics, The Ohio State University
Tuszynski, Jack jackt@ualberta.ca Oncology, University of Alberta
Unkelbach, Jan junkelbach@partners.org Radiation Oncology, Harvard Medical School
Wei, Lai lai.wei@osumc.edu Center for Biostatistics, The Ohio State University
Weis, Jared jared.a.weis@vanderbilt.edu Biomedical Engineering, Vanderbilt University
Yu, Lianbo lianbo.yu@osumc.edu Center for Biostatistics, Biomedical Informatics, The Ohio State University
biPhase i trials in melanoma: a novel route to translate preclinical findings to the clinic

The combination of chemotherapy and an AKT inhibitor (MK2206) in patients with metastatic solid tumors including melanomas is associated with good treatment responses. Our experiments showed that treatments differentially induce autophagy in cells and that autophagy modulates treatment responses. Motivated by these experimental observations, we formulated a mathematical model comprising a system of ordinary differential equations that explains the dynamics of melanoma cells under different mono and combination therapies. Model parameters were estimated by utilizing an optimization algorithm that minimized the difference between predicted cell populations and experimentally measured cell numbers. We predict that the standard of care combination therapy is effective in short term tumor control but the treatment will eventually fail, although smarter schedules can be applied to extend response. To place these results in a more clinically relevant setting, we implemented a phase i trial (virtual/imaginary clinical trial). A genetic algorithm was employed to generate a cohort of over 3000 virtual patients that captured the diversity of disease response observed in a comparable clinical trial. We then simulated clinical trials with this cohort and performed a sensitivity analysis to determine key parameters that separate virtual patients with more favorable and less favorable outcomes on the basis of tumor volume changes. Our analysis shows the relevance of selecting patients based on autophagy transition rates and growth rates. Finally, we predict optimal therapeutic approaches across all virtual patients.

Modeling the response of low-grade gliomas to radiotherapy

After years of slow growth, diffuse low-grade gliomas transform inexorably into more aggressive forms, jeopardizing the patient’s life. Mathematical modeling could help clinicians to have a better understanding of the natural history of these tumors, to optimize treatments, but also to predict their evolution. We present here a model for the effect of radiotherapy on these tumors. To build this model, we first analyzed histological samples from patients’ biopsies. The samples were prepared in Hospital Sainte-Anne (Paris, France). We were able to correlate the amount of edema in the samples with the MRI signal abnormalities. A mathematical model was then designed from these observations, involving the production and the draining of edema by tumor cells. The model is applied to clinical data consisting of the tumor radius along time, for a population of 28 patients. We show that the draining of edema accounts for the observed delay of tumor regrowth following radiotherapy, and we are able to fit the clinical data in a robust way. We argue that, within reasonable assumptions, it is possible to predict (with a precision around 20%) the regrowth delay after radiotherapy and the gain of lifetime due to radiotherapy.

Platform Clinical Trials in Oncology and Neurology

Abstract not submitted.

Using Networks Models to Genetically Map Biologic Process to Complex Phenotypes

Much effort has been focused at the examination of molecular alterations occurring somatically in tumors. This somatic variation occurs against a highly polymorphic constitutional genetic background. Systems-wide molecular analysis of this constitutional variation has identified a cacophony of inherited variation associated with complex phenotypes. Coherence emerges from these data when evaluated using biologic networks as a modeling framework. These networks models account for the individual heterogeneity in underlying etiology as well as the diversity and interaction of events underpinning a complex phenotype such as cancer. We have previously described Pathways of Distinction Analysis (PoDA) as an approach that uses genome-wide data sets and established biologic networks as models. PoDA provides a means to map differences in genome-wide constitutional variation observed in networks to phenotypes of interest. PoDA and other network-based methods have identified networks important in cancer etiology not seen through single gene analysis. Enabled by a novel high performance computational capacity we have extended PoDA to include all measured inherited variability observed in the pathways and to search for the smallest collection of such variation with the network required to significantly classify alternative phenotypes.

A bleaker view, more clearly: applying evolutionary dynamics modeling to the design and optimization of novel anticancer therapies

A slew of publications over the past decade has provided evidence for clonal selection and evolution in cancer. While this is generally not news to most practitioners in the field, the predictions (and the implications for anticancer drug development) that flow from Darwinian evolution as a theory differ dramatically from those made by other theories, such as Oncogene addiction or the Cancer Stem Cell hypothesis. What are the implications of an evolution-based view of cancer? How would one develop and evaluate therapies rationally if cancer progression is based on luck, response to therapy is stochastic, and all interventions eventually fail? In my talk I will review the practical application to drug discovery and development, of mathematical modeling frameworks based on evolutionary theory, population genetics and population biology.

Multiscale modelling of cell populations in a consistent computational framework: progress and challenges

Alongside experimental and clinical approaches, computational modelling offers a useful tool with which to unravel the complex interactions between processes at the intracellular, cellular and tissue scales that underlie the growth of tumours and their response to treatment. Avariety of different individual cell-based and multiscale modelling approaches have recently been developed for studying how processes at the level of a single cell affect tissue-level behaviour. While there are clear strengths and weaknesses with each modelling approach, and therefore cases in which it is clear which approach is valid, there are other cases in which it is not clear. When comparing different constitutive assumptions, a computational framework is required that allows one to easily change the fine details of a model and its implementation. A further barrier to the wider use of such models is the lack of standards or benchmarks; models and methods are often not reused effectively, because they are typically not available as rigorously tested, open-source simulation software. It is therefore difficult to guarantee the reproducibility of computational results. In this talk I describe work being done to address these issues through the C++ library, Chaste (http://www.cs.ox.ac.uk/chaste). I discuss its functionality and the approach we have taken to develop this code, and highlight some of the ongoing computational challenges associated with improving the reproducibility and re-use of individual cell-based and multiscale models.

Using bioengineered tissues to build computational models of tumor dynamics in human tissues

During the last decades, in vivo experiments have been a major tool for studying cancer treatments and developing clinical trials. However, these experiments are neither simple nor cheap. Simulated tissues could allow scientists to quickly test many therapeutic strategies simultaneously, allowing more rapid progress. However, such computational models must be built upon and validated against experimental measurements that represent patient tissues. In this talk, we will discuss our project to create a computational model of colon cancer metastases in the liver based upon imaging data from bioengineered liver tissues. We will show new techniques for quantifying liver organoid structure, assessing cancer cell phenotype in the orgnaoids, and applying these to create 3-D computational liver models for cancer simulations. We will show preliminary results for the cancer model, and discuss the possible implications for personalized medicine.

A stochastic model for the normal tissue complication probability (NTCP) in radiation treatment

When radiation therapy is applied to a tumor, then inevitably, healthy tissue is exposed too. It is quite common that side effects arise or that organs fail. The normal tissue complication probability (NTCP) is an attempt to quantify the risks of side effects. So far, NTCP models have been based on statistical outcomes. In my talk I will develop a mechanistic model for tissue complication which is based on organ-specific and patient-specific model parameters. We get a surprisingly simple formulation of the NTCP, which only requires a few, obtainable, physiological characteristics.

Predicting the differential localization of metastases to the brain

Brain metastases (mets) are a complication that occurs in about 40% of patients with systemic cancer and, when present, are typically the causes of mortality. Lung, breast, and melanoma cancers represent the highest incidence of brain metastases and demonstrate differential angiogenic tumor biology, raising the possibility for treatment using anti-angiogenics in select brain mets cases. Brain mets are typically treated the same regardless of the primary cancer; however, optimal treatment may vary with brain met histology and angiogenic tendency. Currently there are no adequate modeling strategies to assess spatial localization and differential growth tendencies within the brain based on tumor angiogenic biology. An enhanced understanding of the interplay between tumor angiogenic biology and spatial growth tendencies within the brain could have profound therapeutic impact. We are exploring a novel computational model that simulates a nexus between tumor angiogenic biology and spatial growth profiles seen on patient-specific MRI, thereby providing a personalized medicine paradigm for addressing brain mets.

Evaluating Treatment Response in GBM: Improvement by incorporating Anatomical Boundaries

Abstract not submitted.

Interplay between molecular imaging and tumor modeling of anti-angiogenic therapies

Angiogenesis is one of the key tumor hallmarks. Use of anti-angiogenic therapies, particularly those targeting the VEGF pathway, is a common treatment strategy. However, clinical outcomes have been rather disappointing. One of the key phenomena in response to anti-angiogenic therapies is the so-called "angiogenic flare", rapid rebound of tumors after therapy cessation or during treatment breaks. In addition, prolonged exposure to anti-angiogenic agents leads to build-up of treatment resistance. A series of clinical trials using advanced molecular imaging techniques will be presented that has helped explaining the observed angiogenic flare, giving insights into potential treatment strategies. Furthermore, accompanying tumor modeling based on patient-specific molecular imaging input has been used to investigate potential mechanisms leading to treatment failures. Interplay between molecular imaging-driven clinical trials and tumor modeling will be presented as a role-model for better understanding of clinically observed phenomena and as a guiding tools to guide more successful future treatment strategies.

Biophysical subtypes of pancreatic cancer

The dismal survival rate for patients with pancreatic cancer has been stagnant for decades. Personalized approaches to therapy may help accelerate progress, but requires establishment of robust biomarkers. Partly due to the complex biology of the disease and its significant heterogeneity between patients, the identification of molecular biomarkers has not been fruitful so far. To address this challenge, we have developed methods to characterize the physical properties of pancreatic cancer. Our work supports the notion that the multi-scale mass transport properties of this cancer influence the natural history of the disease and its sensitivity to cytotoxic therapies. Our ongoing efforts to further develop this approach and implement it in the clinic aim to achieve the goal of individualized treatments for this deadly disease.

Evaluation of tumor treatment efficacy: comparison of RECIST with the variation of tumor growth rate (TGR).

In drug development, many go/no-go decisions depend on results from phase I trials and evaluation of tumor response to therapy may be crucial. Tumor response is usually evaluated according to RECIST. However, RECIST takes into account only tumor growth during treatment, and it is impossible to distinguish the effect of treatment from the intrinsic characteristics of a tumor. For example, among the many tumors classified as stable according to RECIST, to discriminate those resulting from a real treatment effect from the indolent tumors remains challenging. We incorporated pretreatment data to measure treatment effect as the difference between the growth rate measured after and before treatment. We assumed an exponential growth for tumor lesions. We compared RECIST and TGR using data from patients treated mostly in phase I trials. We simulated the impact of the accuracy of tumor size measurement on both TGR and RECIST evaluations. Finally we discuss the feasibility of TGR evaluations.

The Timing of Resistance Mediated Treatment Failure

A common problem for a wide range of treatment modalities is the development of resistance. One particular way by which resistance can arise is the development of mutant strains that are resistant to the relevant therapy. In this talk I will introduce a mathematical model for this phenomena, and then discuss what we can learn about the timing of treatment failure from this model. Time permitting I will also discuss optimization of combination therapy to minimize resistance risk.

Targeting Hypoxia in Gliomas: From Mathematics to Bedside

This research explores the use of mathematical models as promising and powerful tools to understand the complexity of tumors and their environment. We focus on gliomas, which are primary brain tumors derived from glial cells, mainly astrocytes or oligodendrocytes. These tumors range from lower-grade astrocytomas, such as the diffuse astrocytoma with slow growth, to the highest grade, epitomized in the most malignant and prevalent one: the glioblastoma multiforme. A variety of mathematical models, based on ordinary differential equations and partial differential equations, have been developed both at the micro and macroscopic levels. Our aim is to describe key mechanisms relevant in tumors in a quantitative way and to design optimal therapeutical strategies. We consider both standard therapies such as radio and chemotherapy together with other novel therapies targeting oxidative stress, thromboembolic phenomena or the cell metabolism.

This study has been the basis of a multidisciplinary collaboration involving, among others, neuro-oncologists, radiation oncologists, pathologists, cancer biologists, surgeons and mathematicians with a common goal: to achieve a deeper understanding of the tumor evolution and to improve its therapeutical management.

Personalizing Chemotherapy Treatment using Systems Engineering Tools and Model-Based Dynamic Optimization

Oncologists are challenged by the need to balance efficacy and toxicity for their patients. While models of drug pharmacokinetics (PK) and pharmacodynamic antitumor effect (PD) have been developed and studied in the search for optimal treatment schedules, data-driven mechanistic models of toxicity - which ultimately limit treatment to individual patients - are comparatively less-studied. We have developed a decision support system that combines PK and PD models, including drug-dependent toxicity, for the purpose of designing novel treatment regimens for chemotherapeutics using systems engineering dynamic optimization tools. As a case study, we employ docetaxel as the antitumor agent. A physiologically-based PK model is rigorously reduced for use within the algorithm. The neutropenia model is an extension of the well-known Friberg et al. model that includes the mechanistic insight necessary to incorporate the administration and effect of G-CSF as a neutropenia mitigating agent. Finally, efficacy is modeled using the power-law structure proposed by Norton and co-authors. The model-based mixed-integer dynamic optimization algorithm returns a dosing schedule that provides antitumor effect equivalent to the maximum docetaxel dose used in the clinic (100 mg/m^2 q3w), but with a toxicity profile that is controlled to be no greater than Grade 3 acutely, and not to exceed Grade 2 for more than 6 consecutive days. Furthermore, the algorithm can address combination therapy using drugs with overlapping toxicity (e.g., carboplatin) and can respond to patient-specific changes in drug efficacy and toxicity during cyclic chemotherapy.

Using mathematical models to design mixed treatment strategies

In many cases cancer is treated using a combination of treatments. Mathematical models can be used to design effective treatment strategies, answering the key questions: How Much? and How Often? In this talk I will review three mathematical models and optimization techniques that have been used to suggest treatment protocols using combinations of chemotherapy, monoclonal antibody treatments, and vaccine therapies. I will also discuss using mathematical models to simulate clinical trials.

Mathematical modeling as a tool to generate patient-specific radiotherapy dose plans

Due in large part to the difficulty in predicting tumor growth clinically, current treatment of Glioblastoma takes a blunt approach. Patients are stratified largely based on age, performance status, and other imprecise measurements. We have been unable to turn insights into the genetic, phenotypic, and growth rate diversity of different glioma cellsinto significant clinical gains. Rapid advances have been made, but this has not translated into tools for clinicians to differentiate patients. One such facet of glioma heterogeneity, hypoxia, presents an opportunity for modeling to aid in the selection of patient-specific treatment plans. As new techniques allow for better sculpting areas of dose across a tumor, the potential to target areas that are more radiosensitive while sparing dose to areas of resistance could mean significantly less dose to healthy tissue. This talk will focus on identifying areas of hypoxia and the implementation of a model of tumor hypoxia as a tool to compare modulating fractionation an optimized plan.

Design Principles for Cancer Therapy guided by changes in complexity of Protein-Protein Interaction Networks

The continuously increasing amount of molecular information on cancer dynamics has increased the need to understand the relationships and dependencies within protein interaction networks. Our early observation that network entropy, a complexity measure of cancer protein-protein interaction (PPI) networks, correlates with survival suggested that the organization of PPI networks could be explored with other complexity statistics, including topological measures and thermodynamic measures beyond network entropy.

We now show that a topological measure, the Betti number, correlates linearly with survival for different cancers, and that Betti numbers can be used to predict survival gains/losses produced by a targeted inhibition of specific proteins in the network. We propose that the interpolation of Betti numbers on cancer survival curves could potentially be explored with therapeutic intent and help clinicians in selecting therapies.

We also describe, and demonstrate, that Gibbs free energy for PPI networks of different cancer stages is linear correlated with stage as an ordinal number, and when combined with topological measures may provide additional new insights applicable to personalized medicine.

Personalized therapeutic regimens in multiple myeloma

We here describe how particular features of cancer, combined with flawed paradigms and bad habits widespread in cancer research, prevent us from curing cancer.

Next, we propose how one may overcome these challenges by combining biological models from biomedical sciences, clinical data, and evolutionary dynamics into a mechanistic framework capable of predicting clinical response.

Through this presentation we use our work in multiple myeloma, a treatable but incurable cancer of the bone marrow, as a proof of principle for adaptive personalized medicine. In other words:

The right drug combination at the right dose and schedule, for the right patient, at the right time, and for the right duration of time, adjusting any of these elements as needed, aiming to maximize survival and quality of life.

Molecular Epidemiology and Breast Cancer Risk

Abstract not submitted.

Radiotherapy planning based on the biologically equivalent dose model

Fractionation decisions in radiotherapy face a tradeoff between increasing the number of fractions to spare normal tissues and increasing the total dose to keep the same level of tumor control. The biologically equivalent dose (BED) model is the most common model to compare fractionation regimens in the clinic. The basic BED model assumes that the biological dose is given by a quadratic function of the physical dose. Despite its phenomenological nature and mathematical simplicity, the BED model yields surprising implications for fractionation decisions. In this presentation, two aspects of the BED model are discussed: 1) The interdependence of fractionation decisions and the spatial dose distribution, and 2) extensions of the BED model towards concurrent chemoradiation. It is demonstrated that, even in the absence of time dependencies in radiation response, the BED model suggests non-stationary treatment regimens, i.e. the delivery of different dose distributions in different fractions.

Predicting the Response of Breast Cancer to Neoadjuvant Chemotherapy Using a Mechanically Coupled Reaction-Diffusion Model

While there is considerable data on the use of mathematical modeling to describe tumor growth and response to therapy, they are often not of the form that can be easily applied to clinical data to generate testable predictions in individual patients. There is a clear need to develop and apply clinically-relevant oncological models that are amenable to available patient data and yet retain the most salient features of response prediction. We show how a biomechanical model of tumor growth can be initialized and constrained by patient-specific magnetic resonance imaging data, obtained early in the course of therapy, to predict the response for individual patients with breast cancer undergoing neoadjuvant chemotherapy. Using this mechanics-coupled modeling approach, we are able to predict, after the first cycle of therapy, breast cancer patients that would eventually achieve a complete pathological response and those who would not, with receiver operating characteristic area under the curve of 0.87. Our approach significantly outperformed standard (i.e., not mechanically coupled) reaction-diffusion predictive modeling, simple analysis of the tumor cellularity estimated from imaging data, and the Response Evaluation Criteria in Solid Tumors (RECIST). Thus, we show the potential for mathematical model prediction for use as a predictive indicator of response to therapy. The work indicates the considerable promise of image-driven biophysical modeling for predictive frameworks within therapeutic applications.

Posters

Simultaneous Confidence Bands for a Percentile Line in Linear Regression

Simultaneous confidence bands have been used to quantify unknown functions in various statistical problems. A common statistical problem is to make inference about a percentile line in linear regression.Construction of simultaneous confidence bands for a percentile line has been considered by several authors. But onlyconservative symmetric bands, whichuse critical constants over the whole covariate range(-∞,∞),are available in the literature.Methods given in this posterallow the construction of exact symmetric bands for a percentile lineover a finite interval of the covariate x. The exact symmetricbands can be substantially narrower than the corresponding conservative symmetric bands.Several exact symmetric confidence bands are compared under the average band width criterion.Furthermore, new asymmetric confidence bands for a percentile line areproposed. They are uniformly and can be verysubstantially narrower than the corresponding exact symmetric bands. Therefore, asymmetric bands shouldalways be used under the average band width criterion. The proposed methods areillustrated with real examples.

"I have a Ph.D. in mathematics and I'm here to help" Contributions to Cancer Research

More than 40 years ago, the U.S. government declared a “war on cancer” and committed to investing in laboratory and clinical research in order to understand the causes of cancer and thereby aid its diagnosis, treatment, and cure. Despite enormous advances and important improvements in the diagnosis and treatment of many cancers, the “war” has in significant ways progressed less than originally hoped. The complexity of the disease is clearly evident by the dynamic and evolving course the disease takes during its progression and response treatment. Building on progress in the molecular sciences and advanced technologies, the exploration of physical, engineering, and mathematical approaches may provide a complementary perspective to better elucidate the emergence and behavior of cancer at all scales. Initiatives from the National Cancer Institute (NCI) and other agencies are exploring opportunities to invigorate physical scientists/engineers/mathematicians and their approaches through improved integration with more traditional research effort in cancer biology and clinical oncology. In contrast to the well-worn and cynical phrase “I’m from the Government and I’m here to help,” examples of NCI’s effort to invoke the applied mathematics community and their perspectives into cancer research will be presented.

Clinically targeted mathematical modeling to study response, resistance and recurrence of glioblastoma brain cancer.

Glioblastoma is a lethal primary brain tumor that often recurs after treatment. MRI is the principle means of monitoring the disease progress and response to treatment. Using an MRI-based, patient-specific mathematical model, we study the spatial-temporal evolution of glioblastoma through treatment to better understand how the phenotype and kinetics of the disease are changed by therapy. Specifically, we use patient-specific parameters to quantitatively study response, resistance and the dynamics of tumor recurrence on an individual basis using a macroscopic tumor cell density model. We find that the standard chemo-radiation therapy significantly changes the phenotype and growth kinetics of the disease in a way that may lead to the design of better, more individualized therapies.

Conducting virtual clinical trials to evaluate hypo-fractionated radiotherapy for newly diagnosed glioblastoma

PURPOSE - Fractionated photon irradiation is an integral part of the standard-of-care for newly diagnosed glioblastoma (GBM). Radiotherapy (RT) remains an area of active research, as 42 of 56 open interventional clinical trials for newly diagnosed GBMs involve RT. Hingorani et al reviewed several studies involving hypo-fractionated radiotherapy (HFRT) that suggested improved outcomes with reduced treatment times and neurological complications. However, these studies, along with many others for GBM, suffer from having a small cohort of patients. In this setting, inter-tumoral heterogeneity presents a significant challenge to evaluating therapeutic response and the interpretation of trial outcomes.

METHODS - We present a method for conducting virtual clinical trials (VCT) for glioblastoma in the context of HFRT, although the method is applicable to a variety of therapies. For each VCT, we generate multiple virtual small cohorts of GBM patients by sampling tumor growth and response rates from a distribution created from a previously studied population of 63 GBM patients. The virtual cohorts are characterized by growth and response rates with mathematical models which can be determined through clinical imaging. These models are used to simulate four HFRT clinical trial protocols as well as the standard-of-care. Overall survival and dose to non-involved brain were compared for all protocols for each cohort while the standard-of-care is compared to a population-level control.

RESULTS - We found that this approach can be used to differentiate experimental treatments in silico. The ability to conduct repeated VCTs for a variety of cohorts is valuable with the limited availability of patients with newly diagnosed GBM for new trials. This method can be viewed as an additional layer to meta-analysis of published trials, or as a preclinical tool to test hypotheses regarding treatment protocols prior to the proposal of a phase II trial, with the goal of selecting more cost-and time-efficient trials.