Mathematics of cancer models
Mathematical models based on differential equations, individual-based or partial differential equations are built to describe different processes of relevance in cancer research. We study their theoretical properties (existence of traveling wave solutions, asymptotic behavior, etc.) to understand their potential utility and applicability to the description of the processes involved. We also use the models as in-silico test-bench systems mimicking real tumor behavior.
Publications
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Mathematical model of CAR-T-cell therapy for a B-cell Lymphoma lymph nodeS. Sabir, O. León-Triana, S, Serrano, R, Barrio, V. M. Pérez-Garcíaarxiv.org/abs/2409.01164
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Understanding the role of B cells in CAR T-cell therapy in leukemia through a mathematical modelS. Serrano, R. Barrio, A. Martínez-Rubio, J. Belmonte-Beitia, V. M. Pérez-GarcíaChaos 34, 083142 (2024)
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Breaking Down Cell-Free DNA Fragmentation: A Markov Model ApproachTerence H.L. Tsui, Phil F. Xie, Salvador Chulián, Víctor M. Pérez-Garcíabiorxiv (doi:10.1101/2023.07.06.547953)
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Mean first-passage time of cell migration in confined domainsH. Serrano, R.F. Álvarez-Estrada, G.F. CalvoMathematical Methods in the Applied Sciences 46, 7435-7453 (2023)
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Stochastic Fluctuations Drive Non-genetic Evolution of Proliferation in Clonal Cancer Cell PopulationsC Ortega-Sabater, GF Calvo, Jelena Dinic, Ana Podolski, Milica Pesic, VM Perez-GarciaBulletin of Mathematical Biology 85(1) 8 (2023)
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Dynamics and analysis of a mathematical model of neuroblastoma treated with CelyvirJ. García Otero, A. Alvarez Arenas, J. Belmonte BeitiaApplied Mathematical Modelling 110 (2022) 131-148
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Mathematical models of leukaemia and its treatment: a reviewS. Chulián, Á. Martínez-Rubio, M. Rosa, V. M. Pérez-GarcíaSEMA Journal 79, 441-486 (2022)
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Modelling the effect of vascular status on tumour evolution and outcome after thermal therapyJesús J. Bosque, Gabriel F. Calvo, María Cruz NavarroApplied Mathematical Modelling 110 (2022) 207–240
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Patient-specific forecasting of post-radiotherapy prostate-specific antigen kinetics enables early prediction of biochemical relapseG. Lorenzo, N. di Muzio, C. L. Deantoni, C. Cozzarini, A. Fodor, A. Briganti, F. Montorsi, V. M. Pérez-García, H. Gómez, A. RealiiScience 25, 105430 (2022)
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A mesoscopic simulator to uncover heterogeneity and evolutionary dynamics in tumorsJ. Jiménez-Sánchez, A. Martínez-Rubio, A. Popov, J. Pérez-Beteta, Y. Azimzade, D. Molina-García, J. Belmonte-Beitia, G.F. Calvo, V.M. Pérez-GarcíaPLoS Computational Biology 17(2) e1008266 (2021).
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Brain Metastasis Response to Stereotactic Radio Surgery: A Mathematical ApproachO. León-Triana, J. Pérez-Beteta, D. Albillo, A. Ortiz de Mendivil, L.A. Pérez-Romasanta, E. González del Portillo, M. Llorente, N. Carballo, E. Arana, V.M. Pérez-GarcíaMathematics 9(7) 716 (2021)
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CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathematical modelsO. León-Triana, S. Sabir, G.F. Calvo, J. Belmonte-Beitia, S. Chulian, A. Martínez-Rubio, M. Rosa, A. Pérez-Martínez, M. Ramírez-Orellana, V.M. Pérez-GarcíaComm Nonlin Sci Numer Simul 94, 105570 (2021)
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CAR T cells for T-cell leukemias: Insights from mathematical modelsV.M. Pérez-García, O. León-Triana, M. Rosa, A. Pérez-MartínezComm Nonlin Sci Numer Simul, 96, 105684 (2021)
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Dynamical properties of feedback signalling in B lymphopoiesis: A mathematical modelling approachS. Chulián, A. Martínez-Rubio, A. Marciniak-Czochra, T. Stiehl, C.B. Goñi, J.F. Rodríguez Gutiérrez, M.R. Orellana, A.C. Robleda, V.M. Pérez-García, M. RosaJournal of Theoretical Biology 110685 (2021)
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The interplay of blood flow and temperature in regional hyperthermia: a mathematical approachJ.J. Bosque, G.F. Calvo, V.M Pérez-García, M.C. NavarroRoyal Society Open Science 8, 201234 (2021)
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Modelling the role of flux density and coating on nanoparticle internalization by tumor cells under centrifugationG.F. Calvo, B. Cortes-Llanos, J. Belmonte-Beitia, Gorka Salas, A. Ayuso-SacidoApplied Mathematical Modelling, 78 (2020) 98-116
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Tumor width on T1-weighted MRI images of glioblastoma as a prognostic biomarker: A mathematical modelJ. Pérez Beteta, J. Belmonte-Beitia, V.M. Pérez-GarcíaMathematical Modelling of Natural Phenomena 15, 10 (2020)
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Universal scaling laws rule explosive growth in human cancersV.M. Pérez-García, G.F. Calvo, J.J. Bosque, O. León-Triana, J. Jiménez-Sánchez, J. Pérez-Beteta, J. Belmonte-Beitia, M. Valiente, L. Zhu, P. García-Gómez, P. Sánchez-Gómez, E. Hernández, R. Hortigüela, Y. Azimzade, D. Molina-García, A.Martínez-Rubio, A. Acosta, A. Ortiz de Mendivil, F. Vallette, P. Schucht, M. Murek, M.Pérez-Cano, D.Albillo, AF Honguero, G.A. Jiménez, E. Arana, AM García-VicenteNature Physics 16, 1232-1237 (2020)
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Applied Mathematics in Oncology. How can we help cancer patients?V.M. Pérez-García, S. Fitzpatrick, M. Pesic, P. Schucht, J.M. Sepúlveda, F.M. ValletteICIAM Valencia Intelligencer (2019) 72-82
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Radiation protraction schedules for low-grade gliomas: A comparison between different mathematical modelsI. Budia, A. Álvarez-Arenas, T.E. Wooley, G.F. Calvo, J. Belmonte-BeitiaJournal of the Royal Society of Interface 16, 20190665 (2019)
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Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas.V.M. Pérez-García, L.E. Ayala-Hernández, J. Belmonte-Beitia, P. Schucht, M. Murek, A. RaabePLOS Computational Biology 15(7) (2019) e1006778
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Ultimate dynamics and optimal control of a multi-compartment model of tumor resistance to chemotherapyA. Alvarez-Arenas, K.E. Starkov, G.F. Calvo, J. Belmonte-BeitiaDiscrete and Continuous Dynamical Systems B 24(5) 2017-2038 (2019)
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Symmetry analysis for a Fisher equation with exponential diffusionM.L. Gandarias, M. Rosa, R. TracinaMathematical Methods in the Applied Sciences 41, 7214-7226 (2018)
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Optimizing the delivery of combination therapy for tumors: A mathematical modelC. Rojas Rodríguez and J. Belmonte-BeitiaInternational Journal of Biomathematics 10 (2017) 1750039
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Stochastic modelling of slow-progressing tumors: analysis and applications to the cell interplay and control of low grade gliomasC. Rojas-Rodríguez, G. Fernández Calvo, I. Ramis-Conde, J. Belmonte-BeitiaCommunications in Nonlinear Science and Numerical Simulation 49 (2017) 63-80
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Applied mathematics and nonlinear sciences in the war on cancerV.M. Pérez-García, S. Fitzpatrick, L.A. Pérez-Romasanta, M. Pesic, P. Schucht, E. Arana, P. Sánchez-GómezApplied Mathematics and Nonlinear Sciences 1(2) (2016) 423-436
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Classical and potential symmetries for a generalized Fisher equationM. Rosa, J.C. Camacho, M.S. Bruzón, M.L. GandariasJournal of Computational and Applied Mathematics 318, 181-188 (2016)
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Dynamics and optimal control of chemotherapy for low grade gliomas: insights from a mathematical modelC. Rojas-Rodriguez, J. Belmonte-Beitia, V.M. Pérez-García, H. MaurerDiscrete and Continuous Dynamical Systems B, 21, 1895-1915 (2016)
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Existence of travelling wave solutions for a Fisher-Kolmogorov system with biomedical applicationsJ. Belmonte-BeitiaCommunications in Nonlinear Science and Numerical Simulation 36, 14-20 (2016)
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Nonlinear ghost waves accelerate the progression of high-grade brain tumorsR. Pardo, A. Martínez-González, V.M. Pérez-GarcíaCommunications in Nonlinear Science and Numerical Simulation 39, 360-380 (2016)
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Nonlinear waves in a simple model of high-grade gliomaA. Álvarez-Arenas, J. Belmonte-Beitia and G.F. CalvoApplied Mathematics and Nonlinear Sciences 1(2) (2016) 405-422
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Symmetry analysis and exact solutions for a generalized Fisher equation in cylindrical coordinates.M. Rosa, M.S Bruzón, M.L GandariasCommun Nonlinear Sci Numer Simulat, 25, 74-83 (2015)
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Effective particle methods for the Fisher-Kolmogorov equations: Theory and applications to brain tumor dynamicsJ. Belmonte-Beitia, G.F. Calvo, V.M. Pérez-GarcíaCommunications in Nonlinear Science and Numerical Simulation. 19, 3267-3283 (2014)
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Enabling multiscale modeling in systems medicineO. Wolkenhauer, C. Auffray, O. Brass, J. Clairambault, A. Deutsch, D. Drasdo, F. Gervasio, L. Preziosi, I. Ramís-Conde, P. Maini, A. Marciniak-Czochra, C. Kossow, L. KuepGenome Medicine. 6, 21 (2014)
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On the existence of traveling wave solutions and upper and lower bounds for some Fisher–Kolmogorov type equationsJ. Belmonte-BeitiaInternational Journal of Biomathematics 07, 1450050 (2014)
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Modeling the connection between primary and metastatic tumorsD. Diego, G.F. Calvo, V.M. Pérez-GarcíaJournal of Mathematical Biology 67, 657-692 (2013)
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Modelling biological invasions: Individual to population scales at interfacesJ. Belmonte-Beitia, T. Wooley, J. Scott, P.K. Maini, E. GaffneyJournal of Theoretical Biology, 334, 1-12 (2013).
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A Mathematical model for the glucose-lactate metabolism of in-vitro cancer cellsB. Mendoza-Juez, A. Martínez-González, G.F. Calvo, V.M. Pérez-GarcíaBulletin of Mathematical Biology, 74(5), 1125-1142 (2012).
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Computational modeling of single-cell migration: the leading role of extracellular matrix fibersD.K. Schlüter, I. Ramis-Conde, M.A. J. ChaplainBiophysical Journal. 103, 1141-1151 (2012)
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Bright solitary waves in malignant gliomas.V.M. Pérez-García, G.F. Calvo, J. Belmonte-Beitia, D. Diego, L.A. Pérez-RomasantaPhysical Review E 84, 021921 (2011)
Projects
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Ministerio de Economía y Competitividad (2013 - 2015)
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Ministerio de Economía y Competitividad (2016 - 2019)
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Junta de Comunidades de Castilla-La Mancha (2018 - 2021)
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Ministerio de Ciencia e Innovación (Spain) (2020 - 2023)
Collaborators
This research line is being carried out in collaboration with Marek Bodnar, Monika Piotrowska, Urszula Forys, from Warsaw University, Poland, Warsaw Biomat Team , and Mariusz Bodzioch, from University of Warmia and Mazury in Olsztyn, Poland. Milica Pešić (Head of the Department of Neurobiology, Institute for Biological Research “Siniša Stanković”, University of Belgrade, Serbia). François Vallette and Lisa Oliver (Centre de Recherche en Cancérologie et Immunologie Intégrée Nantes Angers, University of Nantes, France). Ángel Ayuso Sacido (Vithas Hospital and Universidad Francisco de Vitoria, Madrid, Spain).
