BioModelsapplication/xmlhttps://www.ebi.ac.uk/biomodels/model/download/MODEL2003060001?filename=dePillis2007.xmlhttps://www.ebi.ac.uk/biomodels/model/download/MODEL2003060001?filename=dePillis2007.sedmlhttps://www.ebi.ac.uk/biomodels/model/download/MODEL2003060001?filename=dePillis2007.cpsprimaryOK200Mohammad Umer Sharif ShohanNon-curatedordinary differential equation modelL2V4https://www.ebi.ac.uk/biomodels/MODEL2003060001Immuno-oncologyfalseBioModelsSBMLModelsdePillis2007 Seeking Bang Bang Solutions of Mixed ImmunoChemotherapy of Tumors2007MODEL2003060001LISETTE G. DE PILLIS1, K. RENEE FISTER2, WEIQING GU1, CRAIG COLLINS2, MICHAEL DAUB3, DAVID GROSS1, JAMES MOORE1, BEN PRESKILL1*LISETTE G. DE PILLIS1, K. RENEE FISTER2, WEIQING GU1, CRAIG COLLINS2, MICHAEL DAUB3, DAVID GROSS1, JAMES MOORE1, BEN PRESKILL1*https://scholarship.claremont.edu/hmc_fac_pub/439/,
It is known that a beneficial cancer treatment approach for a single patient often involves the administration of more than one type of therapy. The question of how best to combine multiple cancer therapies, however, is still open. In this study, we investigate the theoretical interaction of three treatment types (two biological therapies and one chemotherapy) with a growing cancer, and present an analysis of an optimal control strategy for administering all three therapies in combination. In the situations with controls introduced linearly, we find that there are conditions on which the controls exist singularly. Although bang-bang controls (on-off) reflect the drug treatment approach that is often implemented clinically, we have demonstrated, in the context of our mathematical model, that there can exist regions on which this may not be the best strategy for minimizing a tumor burden. We characterize the controls in singular regions by taking time derivatives of the switching functions. We will examine these representations and the conditions necessary for the controls to be minimizing in the singular region. We begin by assuming only one of the controls is singular on a given interval. Then we analyze the conditions on which a pair and then all three controls are singular.. 171, 2007.
1 Harvey Mudd College
2 Murray State University
3 Williams Collegem.sharifshohan@gmail.comEMBL-EBIWe develop and analyze a mathematical model, in the form of a system of ordinary differential equations (ODEs), governing cancer growth on a cell population level with combination immune, vaccine and chemotherapy treatments. We characterize the ODE system dynamics by locating equilibrium points, determining stability properties, performing a bifurcation analysis, and identifying basins of attraction. These system characteristics are useful not only to gain a broad understanding of the specific system dynamics, but also to help guide the development of combination therapies. Numerical simulations of mixed chemo-immuno and vaccine therapy using both mouse and human parameters are presented. We illustrate situations for which neither chemotherapy nor immunotherapy alone are sufficient to control tumor growth, but in combination the therapies are able to eliminate the entire tumor.Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations.de Pillis L G LG, Gu W W, Radunskaya A E AEmalignant Growth, dmBest1, CG18319, determination, Burden, Effects, region or site annotation, Balkan Nephropathy, Tumor Weight, neoplasia, cell type cancer, RBAP2, 1700012P16Rik, A4, DEFN, DmelCG18319, Tumor, anon-WO0118547.380, TYPE, DmelCG6264, Long Term, Tumor Weights, aristolochic acid nephropathy, DAGA4, Load, period, Ubc13, Tg(Alb1-Myc)166.8Sst, X83320, AAN, ARB, Tumor Load, Volume, WBSCR12, WBSCR11, MAM, neoplasm, SCG3, Effect, MuSC, malignant tumour, treatment, study, hMusTRD1alpha1, positional, Bend, reference sample, Longterm, cell process disease, tumor disease, VMD2, neoplasm (disease), Loads, Weights, Chinese herb endemic nephropathy, present in organism, BMD, Long-Term, Solution, CA, drugs, Abstract, Ben, BEN, malignant neoplasm, medicine, disease management, site, Long-Term Effect, Tumor Volume, tumor, Tumor Loads, GTF3, Long-Term Effects, nj-262, Controlled, CD166, RP50, ESTM9, endemic nephropathy, anon-WO03040301.242, AI853494, malignancy, Controlling, Gtf2il, ubc13, Balkan nephropathy, CG6264, Danubian endemic familial nephropathy, malignant, nephropathia epidemica, drug, MUSTRD1, Longterm Effect, neoplastic disease, UbcD3, LGMD2C, neoplastic growth, DM-GRASP, MT, malignant neoplasm (disease), chemical analysis, Weight, Long Term Effects, organ system cancer, sequence, Chemotherapy, TU15B, region, dBest1, Dbest, Cream1, primary cancer, positional polypeptide feature, DMDA1, best, dbest1, patient, disease of cellular proliferation, malignant tumor, Longterm Effects, SC1, DMDA, WBS, malignant neoplastic disease, Balkan endemic nephropathy, SCARMD2, primary structure of sequence macromolecule., MusTRD1, assay, CREAM1, other neoplasm, cancer, BEST, timeneoplastic growth, neoplastic disease, tumor, other neoplasm, neoplasm, disease of cellular proliferation, cell process disease, tumor disease, neoplasm (disease)., Solution, neoplasiaChemotherapy, neoplastic growth, neoplastic disease, tumor, Immunotherapies, other neoplasm, neoplasm, disease of cellular proliferation, cell process disease, tumor disease, neoplasm (disease)., neoplasiaForms, malignant Growth, d230, human being, single-organism developmental process, determination, cell type cancer, postnatal development, dTAFII250, growth and development, broad, Tumor, EfW1, body system, dmTAF[[II]]230, School-Age, Readability, dmTAF1, Taf230, system, neoplasm, malignant tumour, TAF250, treatment, School-Age Populations, Taf200, anatomical systems, dTAF[[II]]250, TFIID TAF250, reference sample, cel, cell, neoplasm (disease), Taf1p, Population, man, CA, dTAF250, malignant neoplasm, disease management, Therapies, house mouse, School Age Population, TAF, Controlled, Therapy, malignancy, Controlling, dTAF[[II]]230, TAF[[II]]250, adequate, wide/broad, malignant, mouse, TAF200, l(3)84Ab, BG:DS00004.13, TAFII-250, TAF250/230, Cell, dTAF230, development, TAFII250, MT, Mus, p230, School Age, malignant neoplasm (disease), chemical analysis, organ system cancer, TAF[[II]]250/230, TFIID, Chemotherapy, connected anatomical system, Taf[[II]]250, Populations, Tumor., primary cancer, TAF[[II]]230, Immunotherapies, growth pattern, non-developmental growth, mice, postnatal growth, TAF[II]250, Understanding, CG17603, TAF[[II]], malignant tumor, School Age Populations, Treatments, human, organ system, wide, DmelCG17603, Taf250, Therapeutic, malignant neoplastic disease, Vaccine, SR3-5, Treatment, Mouse, School-Age Population, assay, cancer, growth, TAF230, TAF1falsedePillis2007 - Seeking Bang Bang Solutions of Mixed ImmunoChemotherapy of Tumors
SEEKING BANG-BANG SOLUTIONS OF MIXED IMMUNO-CHEMOTHERAPY OF TUMORS
LISETTE G. DE PILLIS, K. RENEE FISTER, WEIQING GU,
CRAIG COLLINS, MICHAEL DAUB, DAVID GROSS, JAMES MOORE, BEN PRESKILL*
Abstract.
It is known that a beneficial cancer treatment approach for a single patient often involves the administration of more than one type of therapy. The question of how best to combine multiple cancer therapies, however, is still open. In this study, we investigate the theoretical interaction of three treatment types (two biological therapies and one chemotherapy) with a growing cancer, and present an analysis of an optimal control strategy for administering all three therapies in combination. In the situations with controls introduced linearly, we find that there are conditions on which the controls exist singularly. Although bang-bang controls (on-off) reflect the drug treatment approach that is often implemented clinically, we have demonstrated, in the context of our mathematical model, that there can exist regions on which this may not be the best strategy for minimizing a tumor burden. We characterize the controls in singular regions by taking time derivatives of the switching functions. We will examine these representations and the conditions necessary for the controls to be minimizing in the singular region. We begin by assuming only one of the controls is singular on a given interval. Then we analyze the conditions on which a pair and then all three controls are singular
2020-03-062020-03-062020-03-06MODEL200306000116153659ISSN: 1072-669