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Henscheid N, Clarkson E, Myers KJ, Barrett HH. Physiological random processes in precision cancer therapy. PLoS One 2018; 13:e0199823. [PMID: 29958271 PMCID: PMC6025881 DOI: 10.1371/journal.pone.0199823] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Accepted: 06/14/2018] [Indexed: 02/07/2023] Open
Abstract
Many different physiological processes affect the growth of malignant lesions and their response to therapy. Each of these processes is spatially and genetically heterogeneous; dynamically evolving in time; controlled by many other physiological processes, and intrinsically random and unpredictable. The objective of this paper is to show that all of these properties of cancer physiology can be treated in a unified, mathematically rigorous way via the theory of random processes. We treat each physiological process as a random function of position and time within a tumor, defining the joint statistics of such functions via the infinite-dimensional characteristic functional. The theory is illustrated by analyzing several models of drug delivery and response of a tumor to therapy. To apply the methodology to precision cancer therapy, we use maximum-likelihood estimation with Emission Computed Tomography (ECT) data to estimate unknown patient-specific physiological parameters, ultimately demonstrating how to predict the probability of tumor control for an individual patient undergoing a proposed therapeutic regimen.
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Affiliation(s)
- Nick Henscheid
- Center for Gamma-Ray Imaging, University of Arizona, Tucson, AZ, United States of America
- Program in Applied Mathematics, University of Arizona, Tucson, AZ, United States of America
| | - Eric Clarkson
- Center for Gamma-Ray Imaging, University of Arizona, Tucson, AZ, United States of America
- Program in Applied Mathematics, University of Arizona, Tucson, AZ, United States of America
- Department of Medical Imaging, University of Arizona, Tucson, AZ, United States of America
- College of Optical Sciences, University of Arizona, Tucson, AZ, United States of America
| | - Kyle J. Myers
- Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, MD, United States of America
| | - Harrison H. Barrett
- Center for Gamma-Ray Imaging, University of Arizona, Tucson, AZ, United States of America
- Program in Applied Mathematics, University of Arizona, Tucson, AZ, United States of America
- Department of Medical Imaging, University of Arizona, Tucson, AZ, United States of America
- College of Optical Sciences, University of Arizona, Tucson, AZ, United States of America
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Barrett HH, Alberts DS, Woolfenden JM, Caucci L, Hoppin JW. Therapy operating characteristic curves: tools for precision chemotherapy. J Med Imaging (Bellingham) 2016; 3:023502. [PMID: 27175376 PMCID: PMC4852214 DOI: 10.1117/1.jmi.3.2.023502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2015] [Accepted: 04/08/2016] [Indexed: 11/14/2022] Open
Abstract
The therapy operating characteristic (TOC) curve, developed in the context of radiation therapy, is a plot of the probability of tumor control versus the probability of normal-tissue complications as the overall radiation dose level is varied, e.g., by varying the beam current in external-beam radiotherapy or the total injected activity in radionuclide therapy. This paper shows how TOC can be applied to chemotherapy with the administered drug dosage as the variable. The area under a TOC curve (AUTOC) can be used as a figure of merit for therapeutic efficacy, analogous to the area under an ROC curve (AUROC), which is a figure of merit for diagnostic efficacy. In radiation therapy, AUTOC can be computed for a single patient by using image data along with radiobiological models for tumor response and adverse side effects. The mathematical analogy between response of observers to images and the response of tumors to distributions of a chemotherapy drug is exploited to obtain linear discriminant functions from which AUTOC can be calculated. Methods for using mathematical models of drug delivery and tumor response with imaging data to estimate patient-specific parameters that are needed for calculation of AUTOC are outlined. The implications of this viewpoint for clinical trials are discussed.
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Affiliation(s)
- Harrison H. Barrett
- University of Arizona, College of Optical Sciences, 1630 East University Boulevard, Tucson, Arizona 85721, United States
- University of Arizona, Center for Gamma-Ray Imaging, Department of Medical Imaging, Radiology Research Laboratory, Arizona Health Sciences Center, 1609 North Warren Avenue, Tucson, Arizona 85724, United States
- University of Arizona Cancer Center, 1515 North Campbell Avenue, Tucson, Arizona 85724, United States
| | - David S. Alberts
- University of Arizona Cancer Center, 1515 North Campbell Avenue, Tucson, Arizona 85724, United States
| | - James M. Woolfenden
- University of Arizona, Center for Gamma-Ray Imaging, Department of Medical Imaging, Radiology Research Laboratory, Arizona Health Sciences Center, 1609 North Warren Avenue, Tucson, Arizona 85724, United States
- University of Arizona Cancer Center, 1515 North Campbell Avenue, Tucson, Arizona 85724, United States
| | - Luca Caucci
- University of Arizona, Center for Gamma-Ray Imaging, Department of Medical Imaging, Radiology Research Laboratory, Arizona Health Sciences Center, 1609 North Warren Avenue, Tucson, Arizona 85724, United States
| | - John W. Hoppin
- inviCRO, 27 Drydock Avenue, Boston, Massachusetts 02210, United States
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