Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?
Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of t...
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description | Several mathematical models to predict tumor growth over time have been developed in the last decades. A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of these models and has been used as a basis for many other related models and theoretical studies. However, none of these models have been validated with large-scale real-world data of human patients treated with cancer immunotherapy. In addition, parameter estimation of these models remains a major bottleneck on the way to model-based and data-driven medical treatment. In this study, we quantitatively fit Kuznetsov’s model to a large dataset of 1472 patients, of which 210 patients have more than six data points, by estimating the model parameters of each patient individually. We also conduct a global practical identifiability analysis for the estimated parameters. We thus demonstrate that several combinations of parameter values could lead to accurate data fitting. This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions. |
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A central aspect of such models is the interaction of tumor cells with immune effector cells. The Kuznetsov model (Kuznetsov et al. in Bull Math Biol 56(2):295–321, 1994) is the most prominent of these models and has been used as a basis for many other related models and theoretical studies. However, none of these models have been validated with large-scale real-world data of human patients treated with cancer immunotherapy. In addition, parameter estimation of these models remains a major bottleneck on the way to model-based and data-driven medical treatment. In this study, we quantitatively fit Kuznetsov’s model to a large dataset of 1472 patients, of which 210 patients have more than six data points, by estimating the model parameters of each patient individually. We also conduct a global practical identifiability analysis for the estimated parameters. We thus demonstrate that several combinations of parameter values could lead to accurate data fitting. This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions.</description><identifier>ISSN: 0092-8240</identifier><identifier>EISSN: 1522-9602</identifier><identifier>DOI: 10.1007/s11538-022-01075-7</identifier><identifier>PMID: 36175705</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Cancer ; Cancer immunotherapy ; Cell Biology ; Cell Count ; Data points ; Effector cells ; Humans ; Immunotherapy ; Life Sciences ; Mathematical and Computational Biology ; Mathematical Concepts ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Medical treatment ; Models, Biological ; Neoplasms - therapy ; Original ; Original Article ; Parameter estimation ; Parameter identification ; Patients ; Tumor cells ; Tumors</subject><ispartof>Bulletin of mathematical biology, 2022, Vol.84 (11), p.130-130, Article 130</ispartof><rights>The Author(s) 2022. corrected publication 2023</rights><rights>2022. The Author(s).</rights><rights>The Author(s) 2022. corrected publication 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). 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This opens the potential for global parameter estimation of the model, in which the values of all or some parameters are fixed for all patients. Furthermore, by omitting the last two or three data points, we show that the model can be extrapolated and predict future tumor dynamics. This paves the way for a more clinically relevant application of mathematical tumor modeling, in which the treatment strategy could be adjusted in advance according to the model’s future predictions.</description><subject>Cancer</subject><subject>Cancer immunotherapy</subject><subject>Cell Biology</subject><subject>Cell Count</subject><subject>Data points</subject><subject>Effector cells</subject><subject>Humans</subject><subject>Immunotherapy</subject><subject>Life Sciences</subject><subject>Mathematical and Computational Biology</subject><subject>Mathematical Concepts</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Medical treatment</subject><subject>Models, Biological</subject><subject>Neoplasms - therapy</subject><subject>Original</subject><subject>Original Article</subject><subject>Parameter estimation</subject><subject>Parameter identification</subject><subject>Patients</subject><subject>Tumor cells</subject><subject>Tumors</subject><issn>0092-8240</issn><issn>1522-9602</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>EIF</sourceid><recordid>eNp9kUFPFTEUhRuigQfyB1iYJm7cjN7bdqbtRkNeBIwQjJF10-l0eEPmtc92BiO_3uJDUBd20zT3O-fe20PIEcIbBJBvM2LNVQWMVYAg60rukAXW5akbYM_IAkCzSjEBe2Q_5xsoIs31LtnjDcpaQr0gJ0sb6LTy9NN8F_yU4y29iJ0f6Re_GQdnJ09t6Ojn5LvBTbTQzid6muL3aUWHQM_mtQ35_QvyvLdj9ocP9wG5OvnwdXlWnV-eflwen1eO1_VUdYhN1_u-FdxpLRxayblWEtAxVIp5aKDFXrTQssZxoSTvUCETiLocxQ_Iu63vZm7XvnM-TMmOZpOGtU0_TLSD-bsShpW5jrdGl29RghWD1w8GKX6bfZ7MesjOj6MNPs7ZMMlAsAYUFPTVP-hNnFMo6xUKtaiVZPeGbEu5FHNOvn8cBsHcx2S2MZkSk_kVk5FF9PLPNR4lv3MpAN8CuZTCtU9Pvf9j-xOnOZtW</recordid><startdate>2022</startdate><enddate>2022</enddate><creator>El Wajeh, Mohammad</creator><creator>Jung, Falco</creator><creator>Bongartz, Dominik</creator><creator>Kappatou, Chrysoula Dimitra</creator><creator>Ghaffari Laleh, Narmin</creator><creator>Mitsos, Alexander</creator><creator>Kather, Jakob Nikolas</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SS</scope><scope>7TK</scope><scope>JQ2</scope><scope>K9.</scope><scope>7X8</scope><scope>5PM</scope><orcidid>https://orcid.org/0000-0002-3730-5348</orcidid></search><sort><creationdate>2022</creationdate><title>Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?</title><author>El Wajeh, Mohammad ; 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subjects | Cancer Cancer immunotherapy Cell Biology Cell Count Data points Effector cells Humans Immunotherapy Life Sciences Mathematical and Computational Biology Mathematical Concepts Mathematical models Mathematics Mathematics and Statistics Medical treatment Models, Biological Neoplasms - therapy Original Original Article Parameter estimation Parameter identification Patients Tumor cells Tumors |
title | Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans? |
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