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
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

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
Arijit Chakravarty
Susan Geyer
Health Informatics Institute, University of South Florida
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
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
Ariosto Silva
Cancer Imaging and Metabolism, H. Lee Moffitt Cancer Center
Andrew Trister
Cancer Biology, Sage Bionetworks
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
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
Josh Jacobs
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
10:30 AM
11:00 AM

Break

11:00 AM
11:30 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.

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

TBD

03:00 PM
03:30 PM

Break

03:30 PM
04:00 PM
Corbin Rayfield
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

TBD

10:00 AM
10:30 AM
Kristin Swanson
10:30 AM
11:00 AM

Break

11:00 AM
11:30 AM
Edward Rietman
11:30 AM
12:00 PM

TBD

12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Pamela Jackson
02:30 PM
03:00 PM
Zvia Agur - 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.

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
04:30 PM
Susan Geyer
04:30 PM
05:30 PM

Discussion Session

05:30 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
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.

09:30 AM
10:00 AM
Savannah Partridge, 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

TBD

11:30 AM
12:00 PM
Larry Nagahara
12:00 PM
02:00 PM

Lunch Break

02:00 PM
02:30 PM
Alexander Anderson
02:30 PM
03:00 PM
Andrew Trister
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
09:30 AM
Jacob Scott
09:30 AM
10:00 AM

Break

10:00 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
Agur, Zvia agur@imbm.org Institute for Medical Biomathematics
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
Butuci, Melina butuci@usc.edu Molecular and Computational Biology, USC
Byrne, Helen byrneh@maths.ox.ac.uk Centre for Mathematical Medicine and Biology, University of Nottingham
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
Durrett, Rick rtd@math.duke.edu Department of Mathematics, Duke University
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
Hillen, Thomas thillen@ualberta.ca Dept. of Mathematical & Statistical Sciences, University of Alberta
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
Kanwal, Madiha madiha_k14@hotmail.com Laboratory of Molecular and Experimental Pathology, Kunming Institute of Zoology, CAS, China
Kheibarshekan, Leila leila.kheibarshekan.asl@umontreal.ca pharmacy, Universite de Montreal
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
Martínez González, Alicia alicia.martinez@uclm.es Mathematics, Universidad de Castilla-La Mancha
Nagahara, Larry nagaharl@mail.nih.gov
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
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
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
Trister, Andrew trister@u.washington.edu Cancer Biology, Sage Bionetworks
Tuszynski, Jack jackt@ualberta.ca Oncology, University of Alberta
Unkelbach, Jan junkelbach@partners.org Radiation Oncology, Harvard Medical School
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
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.

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.

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.

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.

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.

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.