Workshop 5: Treatment, Clinical Trials, Resistance

(February 16,2015 - February 20,2015 )


Guido Marcucci
Comprehensive Cancer Center, The Ohio State University
Kristin Swanson
Department of Pathology, University of Washington
Jack Tuszynski
Oncology, University of Alberta

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

Zvia Agur
Institute for Medical Biomathematics
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
Helen Byrne
Centre for Mathematical Medicine and Biology, University of Nottingham
Arijit Chakravarty
Robert Gatenby
H. Lee Moffitt Cancer Center & Research Institute
Susan Geyer
Farzin Ghaffarizadeh
Andrea Hawkins-Daarud
Neurological Surgery, Northwestern University
Thomas Hillen
Mathematical and Statistical Sciences, University of Alberta
Pamela Jackson
Neurological Surgery, Northwestern University
Josh Jacobs
Robert Jeraj
Medical Physics, University of Wisconsin
Eugene Koay
Serge Koscielny
Biostatistics and Epidemiology, Gustave Roussy
Brenda Kurland
Biostatistics, University of Pittsburgh
Kevin Leder
Industrial and Systems Engineering, University of Minnesota
Alicia Martínez González
Mathematics, Universidad de Castilla-La Mancha
Bob Parker
Savannah Partridge
Radiology, University of Washington
Ami Radunskaya
Mathematics, Pomona College
Corbin Rayfield
Edward Rietman
pediatric oncology, tufts medical school, Newman Lakka Institute
Russell Rockne
Neurological Surgery, Northwestern University
Jacob Scott
Ariosto Silva
Cancer Imaging and Metabolism, H. Lee Moffitt Cancer Center
Andrew Trister
Cancer Biology, Sage Bionetworks
Jan Unkelbach
Radiation Oncology, Harvard Medical School
Jan Unkelbach
Radiation Oncology, Harvard Medical School
Jared Weis
Radiology and Radiological Sciences, Vanderbilt University
Thomas Yankeelov
Radiology, Vanderbilt University
Monday, February 16, 2015
Time Session
Tuesday, February 17, 2015
Time Session
Wednesday, February 18, 2015
Time Session
Thursday, February 19, 2015
Time Session
Friday, February 20, 2015
Time Session
Name Email Affiliation
Agur, Zvia Institute for Medical Biomathematics
Anderson, Alexander Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute
Badoual, Mathilde Physics, Paris Diderot University
Berry, Donald Biostatistics, University of Texas M.D. Anderson Cancer Center
Buetow, Kenneth
Byrne, Helen Centre for Mathematical Medicine and Biology, University of Nottingham
Chakravarty, Arijit
Durrett, Rick Department of Mathematics, Duke University
Gatenby, Robert H. Lee Moffitt Cancer Center & Research Institute
Geyer, Susan
Ghaffarizadeh, Farzin
Hawkins-Daarud, Andrea Neurological Surgery, Northwestern University
Hillen, Thomas Mathematical and Statistical Sciences, University of Alberta
Jackson, Pamela Neurological Surgery, Northwestern University
Jacobs, Josh
Jeraj, Robert Medical Physics, University of Wisconsin
Koay, Eugene
Koscielny, Serge Biostatistics and Epidemiology, Gustave Roussy
Kurland, Brenda Biostatistics, University of Pittsburgh
Leder, Kevin Industrial and Systems Engineering, University of Minnesota
Marcucci, Guido Comprehensive Cancer Center, The Ohio State University
Martínez González, Alicia Mathematics, Universidad de Castilla-La Mancha
Parker, Bob
Partridge, Savannah Radiology, University of Washington
Radunskaya, Ami Mathematics, Pomona College
Rayfield, Corbin
Rietman, Edward pediatric oncology, tufts medical school, Newman Lakka Institute
Rockne, Russell Neurological Surgery, Northwestern University
Scott, Jacob
Silva, Ariosto Cancer Imaging and Metabolism, H. Lee Moffitt Cancer Center
Swanson, Kristin Department of Pathology, University of Washington
Trister, Andrew Cancer Biology, Sage Bionetworks
Tuszynski, Jack Oncology, University of Alberta
Unkelbach, Jan Radiation Oncology, Harvard Medical School
Unkelbach, Jan Radiation Oncology, Harvard Medical School
Weis, Jared Radiology and Radiological Sciences, Vanderbilt University
Yankeelov, Thomas Radiology, Vanderbilt University
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.

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.

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.

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.

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.

Quantitative Imaging to Drive Biophysical Models of Tumor Growth

The ability to identify—early in the course of therapy—patients that are not responding to a given therapeutic regimen is highly significant. In addition to limiting patients’ exposure to the toxicities associated with unsuccessful therapies, it would allow patients the opportunity to switch to a potentially more efficacious treatment. In this presentation, we will discuss ongoing efforts at using data available from advanced imaging technologies to initialize and constrain predictive biophysical and biomathematical models of tumor growth and treatment response.


Radiotherapy target delineation for glioblastoma based on the Fisher-Kolmogorov model

Glioblastoma are known to infiltrate the healthy appearing brain parenchyma far beyond the tumor mass that is visible on current imaging modalities. In radiotherapy planning, this is currently accounted for by a 2-3 cm isotropic margin around the gross tumor volume. Radiotherapy planning can potentially be improved by accounting for the complex neuroanatomy that dominates the infiltrative spread of disease. The Fisher-Kolmogorov equation, a partial differential equation of reaction-diffusion type, represents one approach to model these growth patterns. In this work, the potential of this model to improve radiotherapy planning is characterized, and technical challenges in a practical application are described. It was found that tumors located close to the corpus callosum may benefit most from model based target delineation. In this case, the falx cerebri and the ventricles represent anatomical barriers, while the corpus callosum provides a route for contralateral spread of disease. This situation is difficult to account for in manual contouring. Reliable brain segmentation is the most important input to personalize the growth model to the patient at hand, and requires customized image processing algorithms.