Characterizing the efficacy of anticancer drug treatment using mathematical models

POSTER

Abstract

\newcommand{\ic}{\ensuremath{\mathrm{IC}_{50}}\xspace} \newcommand{\emax}{\ensuremath{\epsilon_\mathrm{max}}\xspace} In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: \emax is the maximum possible effect from a drug, and \ic is the drug concentration where the effect diminishes by half. Currently, the technique used to measure these quantities gives estimates of the values that depend on the time at which the measurement is made. We use mathematical modeling to test a new method for measuring \emax and \ic that gives estimates independent of measurement time. We fit treatment data from the literature to determine values for \emax and \ic using mathematical models under two assumptions: that the drug reduces growth rate, or maximum number of cells. Our method produced \ic estimates similar to estimates derived using current techniques. This work is intended to characterize the efficacy of anticancer drug treatments and determine the correct doses before trying those in patients to get the most effective therapeutic treatment.

Authors

  • Hope Murphy

    Texas Christian University

  • Qiye Zheng

    Santa Fe Institute, Baylor University, University of Texas at Dallas, Department of Chemistry, The University of Texas at Austin, Jozef Stefan Institute, Texas A&M University-Commerce, Commerce, Texas 75429, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, Texas A&M University, Department of Physics, Texas State University, Department of Physics, Baylor University, University of Texas at El Paso, Univ of Texas, El Paso, University of Science and Technology of China, The University of Texas at Dallas, Faculty, None, Southwestern University, Texas State University, Texas A&M University - Commerce, UT Southwestern Medical Center, National High Magnetic Field Laboratory, The Cyclotron Institute at Texas A&M University, Department of Biological Sciences, Texas State Univ-San Marcos, The University of Texas at Dallas, Richardson, Texas 75080, King Abdullah University of Science and Technology, Univ of Texas, Dallas, N.Chiao Tung U., UT Dallas, Inorganic Chemistry and Catalysis Group, Utrecht University, Electrical & Computer Engineering, Baylor University, Department of Materials Science and NanoEngineering, Rice University, University of Texas at Arlington, University of Chicago, The University of Mississippi, Astronomical Observatory, Warsaw University, Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Rochester Institute of Technology, California Institute of Technology, University of Houston, NASA-GSFC and UMBC, MD, Virginia Tech, VA, Texas Christian University, The University of Texas at San Antonio, Department of Physics, Teivecca Nazarene University, Weatherford College, Air Force Research Laboratory, Sensors Directorate, WPAFB, OH, USA, Air Force Research Laboratory, Directed Energy Directorate, KAFB, NM, US, Department of Physics & Astronomy, University of Texas at San Antonio TX, USA, University of Arizona, University of North Carolina at Chapel Hill, Stanford University, Harvard Center for Astrophysics, Texas A\&M University, UTSW, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, Boston College, Chestnut Hill, Massachusetts 02467, Naval Research Laboratory, Washington, D.C. 20375

  • Qiye Zheng

    Santa Fe Institute, Baylor University, University of Texas at Dallas, Department of Chemistry, The University of Texas at Austin, Jozef Stefan Institute, Texas A&M University-Commerce, Commerce, Texas 75429, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, Texas A&M University, Department of Physics, Texas State University, Department of Physics, Baylor University, University of Texas at El Paso, Univ of Texas, El Paso, University of Science and Technology of China, The University of Texas at Dallas, Faculty, None, Southwestern University, Texas State University, Texas A&M University - Commerce, UT Southwestern Medical Center, National High Magnetic Field Laboratory, The Cyclotron Institute at Texas A&M University, Department of Biological Sciences, Texas State Univ-San Marcos, The University of Texas at Dallas, Richardson, Texas 75080, King Abdullah University of Science and Technology, Univ of Texas, Dallas, N.Chiao Tung U., UT Dallas, Inorganic Chemistry and Catalysis Group, Utrecht University, Electrical & Computer Engineering, Baylor University, Department of Materials Science and NanoEngineering, Rice University, University of Texas at Arlington, University of Chicago, The University of Mississippi, Astronomical Observatory, Warsaw University, Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Rochester Institute of Technology, California Institute of Technology, University of Houston, NASA-GSFC and UMBC, MD, Virginia Tech, VA, Texas Christian University, The University of Texas at San Antonio, Department of Physics, Teivecca Nazarene University, Weatherford College, Air Force Research Laboratory, Sensors Directorate, WPAFB, OH, USA, Air Force Research Laboratory, Directed Energy Directorate, KAFB, NM, US, Department of Physics & Astronomy, University of Texas at San Antonio TX, USA, University of Arizona, University of North Carolina at Chapel Hill, Stanford University, Harvard Center for Astrophysics, Texas A\&M University, UTSW, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, Boston College, Chestnut Hill, Massachusetts 02467, Naval Research Laboratory, Washington, D.C. 20375

  • Qiye Zheng

    Santa Fe Institute, Baylor University, University of Texas at Dallas, Department of Chemistry, The University of Texas at Austin, Jozef Stefan Institute, Texas A&M University-Commerce, Commerce, Texas 75429, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, Texas A&M University, Department of Physics, Texas State University, Department of Physics, Baylor University, University of Texas at El Paso, Univ of Texas, El Paso, University of Science and Technology of China, The University of Texas at Dallas, Faculty, None, Southwestern University, Texas State University, Texas A&M University - Commerce, UT Southwestern Medical Center, National High Magnetic Field Laboratory, The Cyclotron Institute at Texas A&M University, Department of Biological Sciences, Texas State Univ-San Marcos, The University of Texas at Dallas, Richardson, Texas 75080, King Abdullah University of Science and Technology, Univ of Texas, Dallas, N.Chiao Tung U., UT Dallas, Inorganic Chemistry and Catalysis Group, Utrecht University, Electrical & Computer Engineering, Baylor University, Department of Materials Science and NanoEngineering, Rice University, University of Texas at Arlington, University of Chicago, The University of Mississippi, Astronomical Observatory, Warsaw University, Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Rochester Institute of Technology, California Institute of Technology, University of Houston, NASA-GSFC and UMBC, MD, Virginia Tech, VA, Texas Christian University, The University of Texas at San Antonio, Department of Physics, Teivecca Nazarene University, Weatherford College, Air Force Research Laboratory, Sensors Directorate, WPAFB, OH, USA, Air Force Research Laboratory, Directed Energy Directorate, KAFB, NM, US, Department of Physics & Astronomy, University of Texas at San Antonio TX, USA, University of Arizona, University of North Carolina at Chapel Hill, Stanford University, Harvard Center for Astrophysics, Texas A\&M University, UTSW, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, Boston College, Chestnut Hill, Massachusetts 02467, Naval Research Laboratory, Washington, D.C. 20375