Physiological Random Processes in Precision Cancer Therapy

Overview

Journal PLoS One

Specialties General Medicine
Science

Date 2018 Jun 30

PMID 29958271

Citations 5

Authors

Nick Henscheid

Eric Clarkson

Kyle J Myers

Harrison H Barrett

Affiliations

Soon will be listed here.

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.

Citing Articles

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References

Michor F, Liphardt J, Ferrari M, Widom J . What does physics have to do with cancer?. Nat Rev Cancer. 2011; 11(9):657-70. PMC: 3711102. DOI: 10.1038/nrc3092. View

Kansal A, Torquato S, Harsh GR I, Chiocca E, Deisboeck T . Simulated brain tumor growth dynamics using a three-dimensional cellular automaton. J Theor Biol. 2000; 203(4):367-82. DOI: 10.1006/jtbi.2000.2000. View

Weinstein J, van Osdol W . Early intervention in cancer using monoclonal antibodies and other biological ligands: micropharmacology and the "binding site barrier". Cancer Res. 1992; 52(9 Suppl):2747s-2751s. View

Hanahan D, Weinberg R . The hallmarks of cancer. Cell. 2000; 100(1):57-70. DOI: 10.1016/s0092-8674(00)81683-9. View

Mintun M, Raichle M, Kilbourn M, Wooten G, Welch M . A quantitative model for the in vivo assessment of drug binding sites with positron emission tomography. Ann Neurol. 1984; 15(3):217-27. DOI: 10.1002/ana.410150302. View

Sanga S, Sinek J, Frieboes H, Ferrari M, Fruehauf J, Cristini V . Mathematical modeling of cancer progression and response to chemotherapy. Expert Rev Anticancer Ther. 2006; 6(10):1361-76. DOI: 10.1586/14737140.6.10.1361. View

Ding Y, Caucci L, Barrett H . Charged-particle emission tomography. Med Phys. 2017; 44(6):2478-2489. PMC: 5903440. DOI: 10.1002/mp.12245. View

Minchinton A, Tannock I . Drug penetration in solid tumours. Nat Rev Cancer. 2006; 6(8):583-92. DOI: 10.1038/nrc1893. View

Araujo R, McElwain D . A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull Math Biol. 2004; 66(5):1039-91. DOI: 10.1016/j.bulm.2003.11.002. View

10.

Clarkson E, Barrett H . Characteristic functionals in imaging and image-quality assessment: tutorial. J Opt Soc Am A Opt Image Sci Vis. 2016; 33(8):1464-75. PMC: 5683092. DOI: 10.1364/JOSAA.33.001464. View

11.

Mellman I, Yarden Y . Endocytosis and cancer. Cold Spring Harb Perspect Biol. 2013; 5(12):a016949. PMC: 3839607. DOI: 10.1101/cshperspect.a016949. View

12.

Anderson A, Chaplain M . Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol. 1998; 60(5):857-99. DOI: 10.1006/bulm.1998.0042. View

13.

Norton L . A Gompertzian model of human breast cancer growth. Cancer Res. 1988; 48(24 Pt 1):7067-71. View

14.

Hanahan D, Weinberg R . Hallmarks of cancer: the next generation. Cell. 2011; 144(5):646-74. DOI: 10.1016/j.cell.2011.02.013. View

15.

Wiley H, Cunningham D . The endocytotic rate constant. A cellular parameter for quantitating receptor-mediated endocytosis. J Biol Chem. 1982; 257(8):4222-9. View

16.

Barrett H, Alberts D, Woolfenden J, Liu Z, Caucci L, Hoppin J . Quantifying and Reducing Uncertainties in Cancer Therapy. Proc SPIE Int Soc Opt Eng. 2015; 9412. PMC: 4497821. DOI: 10.1117/12.2189093. View

17.

Klauschen F, Andreeff M, Keilholz U, Dietel M, Stenzinger A . The combinatorial complexity of cancer precision medicine. Oncoscience. 2015; 1(7):504-9. PMC: 4278319. DOI: 10.18632/oncoscience.66. View

18.

Gatenby R, Gillies R . Why do cancers have high aerobic glycolysis?. Nat Rev Cancer. 2004; 4(11):891-9. DOI: 10.1038/nrc1478. View

19.

Barrett H, Furenlid L, Freed M, Hesterman J, Kupinski M, Clarkson E . Adaptive SPECT. IEEE Trans Med Imaging. 2008; 27(6):775-88. PMC: 2575754. DOI: 10.1109/TMI.2007.913241. View

20.

Doherty G, McMahon H . Mechanisms of endocytosis. Annu Rev Biochem. 2009; 78:857-902. DOI: 10.1146/annurev.biochem.78.081307.110540. View