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Miniere HJM, Lima EABF, Lorenzo G, Hormuth II DA, Ty S, Brock A, Yankeelov TE. A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin. Cancer Biol Ther 2024; 25:2321769. [PMID: 38411436 PMCID: PMC11057790 DOI: 10.1080/15384047.2024.2321769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 02/18/2024] [Indexed: 02/28/2024] Open
Abstract
Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential to develop tools capable of identifying and predicting intra- and inter-tumor heterogeneities. Biology-inspired mathematical models are capable of attacking this problem, but tumor heterogeneity is often overlooked in in-vivo modeling studies, while phenotypic considerations capturing spatial dynamics are not typically included in in-vitro modeling studies. We present a data assimilation-prediction pipeline with a two-phenotype model that includes a spatiotemporal component to characterize and predict the evolution of in-vitro breast cancer cells and their heterogeneous response to chemotherapy. Our model assumes that the cells can be divided into two subpopulations: surviving cells unaffected by the treatment, and irreversibly damaged cells undergoing treatment-induced death. MCF7 breast cancer cells were previously cultivated in wells for up to 1000 hours, treated with various concentrations of doxorubicin and imaged with time-resolved microscopy to record spatiotemporally-resolved cell count data. Images were used to generate cell density maps. Treatment response predictions were initialized by a training set and updated by weekly measurements. Our mathematical model successfully calibrated the spatiotemporal cell growth dynamics, achieving median [range] concordance correlation coefficients of > .99 [.88, >.99] and .73 [.58, .85] across the whole well and individual pixels, respectively. Our proposed data assimilation-prediction approach achieved values of .97 [.44, >.99] and .69 [.35, .79] for the whole well and individual pixels, respectively. Thus, our model can capture and predict the spatiotemporal dynamics of MCF7 cells treated with doxorubicin in an in-vitro setting.
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Affiliation(s)
- Hugo J. M. Miniere
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
| | - Ernesto A. B. F. Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
| | - Guillermo Lorenzo
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
- Department of Civil Engineering and Architecture, University of Pavia, Lombardy, Italy
| | - David A. Hormuth II
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, USA
| | - Sophia Ty
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
| | - Amy Brock
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, USA
| | - Thomas E. Yankeelov
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, USA
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, USA
- Department of Oncology, The University of Texas at Austin, Austin, USA
- Division of Diagnostic Imaging, The University of Texas M.D. Anderson Cancer Center, Houston, USA
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Marzban S, Srivastava S, Kartika S, Bravo R, Safriel R, Zarski A, Anderson A, Chung CH, Amelio AL, West J. Spatial interactions modulate tumor growth and immune infiltration. RESEARCH SQUARE 2024:rs.3.rs-3962451. [PMID: 38826398 PMCID: PMC11142313 DOI: 10.21203/rs.3.rs-3962451/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2024]
Abstract
Lenia, a cellular automata framework used in artificial life, provides a natural setting to implement mathematical models of cancer incorporating features such as morphogenesis, homeostasis, motility, reproduction, growth, stimuli response, evolvability, and adaptation. Historically, agent-based models of cancer progression have been constructed with rules that govern birth, death and migration, with attempts to map local rules to emergent global growth dynamics. In contrast, Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining an interaction kernel governing density-dependent growth dynamics. Lenia can recapitulate a range of cancer model classifications including local or global, deterministic or stochastic, non-spatial or spatial, single or multi-population, and off or on-lattice. Lenia is subsequently used to develop data-informed models of 1) single-population growth dynamics, 2) multi-population cell-cell competition models, and 3) cell migration or chemotaxis. Mathematical modeling provides important mechanistic insights. First, short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects. Next, we find that asymmetric interaction tumor-immune kernels lead to poor immune response. Finally, modeling recapitulates immune-ECM interactions where patterns of collagen formation provide immune protection, indicated by an emergent inverse relationship between disease stage and immune coverage.
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Affiliation(s)
- Sadegh Marzban
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sonal Srivastava
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sharon Kartika
- Dept. of Biological Sciences, Indian Institute of Science Education and Research Kolkata
| | - Rafael Bravo
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Rachel Safriel
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Aidan Zarski
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Alexander Anderson
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Christine H. Chung
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Antonio L. Amelio
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Jeffrey West
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
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Marzban S, Srivastava S, Kartika S, Bravo R, Safriel R, Zarski A, Anderson A, Chung CH, Amelio AL, West J. Spatial interactions modulate tumor growth and immune infiltration. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.01.10.575036. [PMID: 38370722 PMCID: PMC10871273 DOI: 10.1101/2024.01.10.575036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/20/2024]
Abstract
Direct observation of immune cell trafficking patterns and tumor-immune interactions is unlikely in human tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen formation evolve as a mechanism of immune escape, but the exact nature of the interaction between immune cells and collagen is poorly understood. Spatial data quantifying the degree of collagen fiber alignment in squamous cell carcinomas indicates that late stage disease is associated with highly aligned fibers. Here, we introduce a computational modeling framework (called Lenia) to discriminate between two hypotheses: immune cell migration that moves 1) parallel or 2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-ECM interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. We also illustrate the capabilities of Lenia to model the evolution of tumor progression and immune predation. Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining a kernel cell-cell interaction function that governs tumor growth dynamics under immune predation with immune cell migration. Mathematical modeling provides important mechanistic insights into cell interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interactions drives tumor growth and infiltration.
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Affiliation(s)
- Sadegh Marzban
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sonal Srivastava
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sharon Kartika
- Dept. of Biological Sciences, Indian Institute of Science Education and Research Kolkata
| | - Rafael Bravo
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Rachel Safriel
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Aidan Zarski
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Alexander Anderson
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Christine H. Chung
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Antonio L. Amelio
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Jeffrey West
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
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Schultz L, Gondim A, Ruan S. Gompertz models with periodical treatment and applications to prostate cancer. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:4104-4116. [PMID: 38549320 DOI: 10.3934/mbe.2024181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/02/2024]
Abstract
In this paper, Gompertz type models are proposed to understand the temporal tumor volume behavior of prostate cancer when a periodical treatment is provided. Existence, uniqueness, and stability of periodic solutions are established. The models are used to fit the data and to forecast the tumor growth behavior based on prostate cancer treatments using capsaicin and docetaxel anticancer drugs. Numerical simulations show that the combination of capsaicin and docetaxel is the most efficient treatment of prostate cancer.
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Affiliation(s)
- Leonardo Schultz
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL 33146, USA
| | - Antonio Gondim
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL 33146, USA
| | - Shigui Ruan
- Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL 33146, USA
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Kutuva AR, Caudell JJ, Yamoah K, Enderling H, Zahid MU. Mathematical modeling of radiotherapy: impact of model selection on estimating minimum radiation dose for tumor control. Front Oncol 2023; 13:1130966. [PMID: 37901317 PMCID: PMC10600389 DOI: 10.3389/fonc.2023.1130966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2022] [Accepted: 08/28/2023] [Indexed: 10/31/2023] Open
Abstract
Introduction Radiation therapy (RT) is one of the most common anticancer therapies. Yet, current radiation oncology practice does not adapt RT dose for individual patients, despite wide interpatient variability in radiosensitivity and accompanying treatment response. We have previously shown that mechanistic mathematical modeling of tumor volume dynamics can simulate volumetric response to RT for individual patients and estimation personalized RT dose for optimal tumor volume reduction. However, understanding the implications of the choice of the underlying RT response model is critical when calculating personalized RT dose. Methods In this study, we evaluate the mathematical implications and biological effects of 2 models of RT response on dose personalization: (1) cytotoxicity to cancer cells that lead to direct tumor volume reduction (DVR) and (2) radiation responses to the tumor microenvironment that lead to tumor carrying capacity reduction (CCR) and subsequent tumor shrinkage. Tumor growth was simulated as logistic growth with pre-treatment dynamics being described in the proliferation saturation index (PSI). The effect of RT was simulated according to each respective model for a standard schedule of fractionated RT with 2 Gy weekday fractions. Parameter sweeps were evaluated for the intrinsic tumor growth rate and the radiosensitivity parameter for both models to observe the qualitative impact of each model parameter. We then calculated the minimum RT dose required for locoregional tumor control (LRC) across all combinations of the full range of radiosensitvity and proliferation saturation values. Results Both models estimate that patients with higher radiosensitivity will require a lower RT dose to achieve LRC. However, the two models make opposite estimates on the impact of PSI on the minimum RT dose for LRC: the DVR model estimates that tumors with higher PSI values will require a higher RT dose to achieve LRC, while the CCR model estimates that higher PSI values will require a lower RT dose to achieve LRC. Discussion Ultimately, these results show the importance of understanding which model best describes tumor growth and treatment response in a particular setting, before using any such model to make estimates for personalized treatment recommendations.
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Affiliation(s)
- Achyudhan R. Kutuva
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, United States
- Department of Microbiology and Cell Science, University of Florida, Gainesville, FL, United States
| | - Jimmy J. Caudell
- Department of Radiation Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, United States
| | - Kosj Yamoah
- Department of Radiation Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, United States
| | - Heiko Enderling
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, United States
- Department of Radiation Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, United States
| | - Mohammad U. Zahid
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, United States
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Wagner A, Schlicke P, Fritz M, Kuttler C, Oden JT, Schumann C, Wohlmuth B. A phase-field model for non-small cell lung cancer under the effects of immunotherapy. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:18670-18694. [PMID: 38052574 DOI: 10.3934/mbe.2023828] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
Formulating mathematical models that estimate tumor growth under therapy is vital for improving patient-specific treatment plans. In this context, we present our recent work on simulating non-small-scale cell lung cancer (NSCLC) in a simple, deterministic setting for two different patients receiving an immunotherapeutic treatment. At its core, our model consists of a Cahn-Hilliard-based phase-field model describing the evolution of proliferative and necrotic tumor cells. These are coupled to a simplified nutrient model that drives the growth of the proliferative cells and their decay into necrotic cells. The applied immunotherapy decreases the proliferative cell concentration. Here, we model the immunotherapeutic agent concentration in the entire lung over time by an ordinary differential equation (ODE). Finally, reaction terms provide a coupling between all these equations. By assuming spherical, symmetric tumor growth and constant nutrient inflow, we simplify this full 3D cancer simulation model to a reduced 1D model. We can then resort to patient data gathered from computed tomography (CT) scans over several years to calibrate our model. Our model covers the case in which the immunotherapy is successful and limits the tumor size, as well as the case predicting a sudden relapse, leading to exponential tumor growth. Finally, we move from the reduced model back to the full 3D cancer simulation in the lung tissue. Thereby, we demonstrate the predictive benefits that a more detailed patient-specific simulation including spatial information as a possible generalization within our framework could yield in the future.
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Affiliation(s)
- Andreas Wagner
- School of Computation, Information and Technology, Technical University of Munich, Munich, Bavaria, Germany
| | - Pirmin Schlicke
- School of Computation, Information and Technology, Technical University of Munich, Munich, Bavaria, Germany
| | - Marvin Fritz
- Computational Methods for PDEs, Johann Radon Institute for Computational and Applied Mathematics, Linz, Upper Austria, Austria
| | - Christina Kuttler
- School of Computation, Information and Technology, Technical University of Munich, Munich, Bavaria, Germany
| | - J Tinsley Oden
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
| | - Christian Schumann
- Clinic of Pneumology, Thoracic Oncology, Sleep and Respiratory Critical Care, Klinikverbund Allgäu, Kempten, Bavaria, Germany
| | - Barbara Wohlmuth
- School of Computation, Information and Technology, Technical University of Munich, Munich, Bavaria, Germany
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Pasetto S, Harshe I, Brady-Nicholls R, Gatenby RA, Enderling H. Logistic tumor-population growth and ghost-points symmetry. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.30.555578. [PMID: 37693551 PMCID: PMC10491152 DOI: 10.1101/2023.08.30.555578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/12/2023]
Abstract
The observed time evolution of a population is well approximated by a logistic function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential at a constant rate and capped at a limit size, i.e., the carrying capacity. In mathematical oncology, the carrying capacity has been postulated to be co-evolving and thus patient-specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against a classic oncology database of logistic tumor growth, achieving a 30% to 40% reduction in the time necessary to correctly estimate the logistic growth rate and carrying capacity. Our results will improve tumor dynamics forecasting and augment the clinical decision-making process.
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8
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Du YK, Liang M, McAvan AS, Wilson RC, Ekstrom AD. Frontal-midline theta and posterior alpha oscillations index early processing of spatial representations during active navigation. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.04.22.537940. [PMID: 37131721 PMCID: PMC10153283 DOI: 10.1101/2023.04.22.537940] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Previous research has demonstrated that humans combine multiple sources of spatial information such as self-motion and landmark cues, while navigating through an environment. However, it is unclear whether this involves comparing multiple representations obtained from different sources during navigation (parallel hypothesis) or building a representation first based on self-motion cues and then combining with landmarks later (serial hypothesis). We tested these two hypotheses (parallel vs. serial) in an active navigation task using wireless mobile scalp EEG recordings. Participants walked through an immersive virtual hallway with or without conflicts between self-motion and landmarks (i.e., intersections) and pointed toward the starting position of the hallway. We employed the oscillatory signals recorded during mobile wireless scalp EEG as means of identifying when participant representations based on self-motion vs. landmark cues might have first emerged. We found that path segments, including intersections present early during navigation, were more strongly associated with later pointing error, regardless of when they appeared during encoding. We also found that there was sufficient information contained within the frontal-midline theta and posterior alpha oscillatory signals in the earliest segments of navigation involving intersections to decode condition (i.e., conflicting vs. not conflicting). Together, these findings suggest that intersections play a pivotal role in the early development of spatial representations, suggesting that memory representations for the geometry of walked paths likely develop early during navigation, in support of the parallel hypothesis.
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Affiliation(s)
- Yu Karen Du
- Department of Psychology, University of Arizona, 1503 E. University Blvd., Tucson, AZ 85719
- Department of Psychology & Brain and Mind Institute, University of Western Ontario, London, ON, Canada N6A 3K7
| | - Mingli Liang
- Department of Psychology, University of Arizona, 1503 E. University Blvd., Tucson, AZ 85719
| | - Andrew S McAvan
- Department of Psychology, University of Arizona, 1503 E. University Blvd., Tucson, AZ 85719
- Department of Psychology, Vanderbilt University, Vanderbilt University, Nashville, TN 37240
| | - Robert C Wilson
- Department of Psychology, University of Arizona, 1503 E. University Blvd., Tucson, AZ 85719
| | - Arne D Ekstrom
- Department of Psychology, University of Arizona, 1503 E. University Blvd., Tucson, AZ 85719
- Evelyn McKnight Brain Institute, University of Arizona, 1503 E. University Blvd., Tucson, AZ 85719
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Alinei-Poiana T, Dulf EH, Kovacs L. Fractional calculus in mathematical oncology. Sci Rep 2023; 13:10083. [PMID: 37344605 DOI: 10.1038/s41598-023-37196-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Accepted: 06/17/2023] [Indexed: 06/23/2023] Open
Abstract
Even though, nowadays, cancer is one of the leading causes of death, too little is known about the behavior of this disease due to its unpredictability from one patient to another. Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, improvements are still necessary on these models. The primary objective of the present research is to prove the efficiency of fractional order calculus in mathematical oncology, more specifically in tumor growth modeling. For this, a generalization of the four most used differential equation models in tumor volume measurements fitting is realized, using the corresponding fractional order equivalent. Are established the fractional order Exponential, Logistic, Gompertz, General Bertalanffy-Pütter and Classical Bertalanffy-Pütter models for a treated and untreated dataset. The obtained results are compared by Mean Squared Error (MSE) with the integer order correspondent of each model. The results prove the superiority of the fractional order models. The MSE of fractional order models are reduced at least at half in comparison with the MSE of the integer order equivalent. It is demonstrated in this way that fractional order deterministic models can offer a good starting point in finding a proper mathematical model for tumor evolution prediction. Fractional calculus is a suitable method in this case due to its memory property, aspect that particularly characterizes biological processes.
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Affiliation(s)
- Tudor Alinei-Poiana
- Department of Automation, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Memorandumului Str. 28, 400014, Cluj-Napoca, Romania
| | - Eva-H Dulf
- Department of Automation, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Memorandumului Str. 28, 400014, Cluj-Napoca, Romania.
- University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca, 3-5 Manastur Str., 400374, Cluj-Napoca, Romania.
| | - Levente Kovacs
- Physiological Controls Research Center, Óbuda University, Budapest, 1034, Hungary
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Wang H, Arulraj T, Kimko H, Popel AS. Generating immunogenomic data-guided virtual patients using a QSP model to predict response of advanced NSCLC to PD-L1 inhibition. NPJ Precis Oncol 2023; 7:55. [PMID: 37291190 DOI: 10.1038/s41698-023-00405-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Accepted: 05/25/2023] [Indexed: 06/10/2023] Open
Abstract
Generating realistic virtual patients from a limited amount of patient data is one of the major challenges for quantitative systems pharmacology modeling in immuno-oncology. Quantitative systems pharmacology (QSP) is a mathematical modeling methodology that integrates mechanistic knowledge of biological systems to investigate dynamics in a whole system during disease progression and drug treatment. In the present analysis, we parameterized our previously published QSP model of the cancer-immunity cycle to non-small cell lung cancer (NSCLC) and generated a virtual patient cohort to predict clinical response to PD-L1 inhibition in NSCLC. The virtual patient generation was guided by immunogenomic data from iAtlas portal and population pharmacokinetic data of durvalumab, a PD-L1 inhibitor. With virtual patients generated following the immunogenomic data distribution, our model predicted a response rate of 18.6% (95% bootstrap confidence interval: 13.3-24.2%) and identified CD8/Treg ratio as a potential predictive biomarker in addition to PD-L1 expression and tumor mutational burden. We demonstrated that omics data served as a reliable resource for virtual patient generation techniques in immuno-oncology using QSP models.
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Affiliation(s)
- Hanwen Wang
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, 21205, USA.
| | - Theinmozhi Arulraj
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, 21205, USA
| | - Holly Kimko
- Clinical Pharmacology & Quantitative Pharmacology, AstraZeneca, Gaithersburg, MD, USA
| | - Aleksander S Popel
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD, 21205, USA
- Department of Oncology, and the Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD, 21205, USA
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11
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Wang H, Arulraj T, Kimko H, Popel AS. Generating immunogenomic data-guided virtual patients using a QSP model to predict response of advanced NSCLC to PD-L1 inhibition. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.04.25.538191. [PMID: 37162938 PMCID: PMC10168221 DOI: 10.1101/2023.04.25.538191] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
Generating realistic virtual patients from a limited amount of patient data is one of the major challenges for quantitative systems pharmacology modeling in immuno-oncology. Quantitative systems pharmacology (QSP) is a mathematical modeling methodology that integrates mechanistic knowledge of biological systems to investigate dynamics in a whole system during disease progression and drug treatment. In the present analysis, we parameterized our previously published QSP model of the cancer-immunity cycle to non-small cell lung cancer (NSCLC) and generated a virtual patient cohort to predict clinical response to PD-L1 inhibition in NSCLC. The virtual patient generation was guided by immunogenomic data from iAtlas portal and population pharmacokinetic data of durvalumab, a PD-L1 inhibitor. With virtual patients generated following the immunogenomic data distribution, our model predicted a response rate of 18.6% (95% bootstrap confidence interval: 13.3-24.2%) and identified CD8/Treg ratio as a potential predictive biomarker in addition to PD-L1 expression and tumor mutational burden. We demonstrated that omics data served as a reliable resource for virtual patient generation techniques in immuno-oncology using QSP models.
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12
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Ghannoum S, Fantini D, Zahoor M, Reiterer V, Phuyal S, Leoncio Netto W, Sørensen Ø, Iyer A, Sengupta D, Prasmickaite L, Mælandsmo GM, Köhn-Luque A, Farhan H. A combined experimental-computational approach uncovers a role for the Golgi matrix protein Giantin in breast cancer progression. PLoS Comput Biol 2023; 19:e1010995. [PMID: 37068117 PMCID: PMC10159355 DOI: 10.1371/journal.pcbi.1010995] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Revised: 05/04/2023] [Accepted: 03/04/2023] [Indexed: 04/18/2023] Open
Abstract
Our understanding of how speed and persistence of cell migration affects the growth rate and size of tumors remains incomplete. To address this, we developed a mathematical model wherein cells migrate in two-dimensional space, divide, die or intravasate into the vasculature. Exploring a wide range of speed and persistence combinations, we find that tumor growth positively correlates with increasing speed and higher persistence. As a biologically relevant example, we focused on Golgi fragmentation, a phenomenon often linked to alterations of cell migration. Golgi fragmentation was induced by depletion of Giantin, a Golgi matrix protein, the downregulation of which correlates with poor patient survival. Applying the experimentally obtained migration and invasion traits of Giantin depleted breast cancer cells to our mathematical model, we predict that loss of Giantin increases the number of intravasating cells. This prediction was validated, by showing that circulating tumor cells express significantly less Giantin than primary tumor cells. Altogether, our computational model identifies cell migration traits that regulate tumor progression and uncovers a role of Giantin in breast cancer progression.
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Affiliation(s)
- Salim Ghannoum
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
| | - Damiano Fantini
- Department of Urology, Northwestern University, Chicago, Illinois, United States of America
| | - Muhammad Zahoor
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
| | - Veronika Reiterer
- Institute of Pathophysiology, Medical University of Innsbruck, Innsbruck, Austria
| | - Santosh Phuyal
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
| | - Waldir Leoncio Netto
- Oslo Centre for Biostatistics and Epidemiology, Faculty of Medicine, University of Oslo, Oslo, Norway
| | - Øystein Sørensen
- Center for Lifespan Changes in Brain and Cognition, Department of Psychology, University of Oslo, Oslo, Norway
| | - Arvind Iyer
- Department of Computational Biology, University of Lausanne (UNIL), Lausanne, Switzerland
| | - Debarka Sengupta
- Department of Computational Biology, Indraprastha Institute of Information Technology, New Delhi, India
- Centre for Artificial Intelligence, Indraprastha Institute of Information Technology, Delhi, India
| | - Lina Prasmickaite
- Department of Tumor Biology, Institute for Cancer Research, Oslo University Hospital, The Norwegian Radium Hospital, Oslo, Norway
| | - Gunhild Mari Mælandsmo
- Department of Tumor Biology, Institute for Cancer Research, Oslo University Hospital, The Norwegian Radium Hospital, Oslo, Norway
- Department of Medical Biology, UiT-The Arctic University of Norway, Tromsø, Norway
| | - Alvaro Köhn-Luque
- Oslo Centre for Biostatistics and Epidemiology, Faculty of Medicine, University of Oslo, Oslo, Norway
| | - Hesso Farhan
- Institute of Basic Medical Sciences, Department of Molecular Medicine, University of Oslo, Oslo, Norway
- Institute of Pathophysiology, Medical University of Innsbruck, Innsbruck, Austria
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13
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Browning AP, Simpson MJ. Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates. PLoS Comput Biol 2023; 19:e1010844. [PMID: 36662831 PMCID: PMC9891533 DOI: 10.1371/journal.pcbi.1010844] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2022] [Revised: 02/01/2023] [Accepted: 12/26/2022] [Indexed: 01/22/2023] Open
Abstract
An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth experiments. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, classify non-identifiable parameter spaces into identifiable parameter combinations that relate to features in the data characterised by parameters in a surrogate model, and overall provide additional biological insight from complex non-identifiable models.
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Affiliation(s)
- Alexander P. Browning
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- QUT Centre for Data Science, Queensland University of Technology, Brisbane, Australia
- * E-mail:
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14
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Grajek J, Kather JN, Poleszczuk J. An in silico model to study the impact of carbonic anhydrase IX expression on tumour growth and anti-PD-1 therapy. J R Soc Interface 2023; 20:20220654. [PMID: 36695125 PMCID: PMC9874981 DOI: 10.1098/rsif.2022.0654] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 01/04/2023] [Indexed: 01/26/2023] Open
Abstract
Immune checkpoint inhibitors (ICIs) are revolutionary cancer treatments. However, the mechanisms behind their effectiveness are not yet fully understood. Here, we aimed to investigate the role of the pH-regulatory enzyme carbonic anhydrase IX (CAIX) in ICI success. Consequently, we developed an in silico model of the tumour microenvironment. The hybrid model consists of an agent-based model of tumour-immune cell interactions, coupled with a set of diffusion-reaction equations describing substances in the environment. It is calibrated with data from the literature, enabling the study of its qualitative behaviour. In our model, CAIX-expressing tumours acidified their neighbourhood, thereby reducing immune infiltration by 90% (p < 0.001) and resulting in a 25% increase in tumour burden (p < 0.001). Moreover, suppression of CAIX improved the response to anti-PD-1 (23% tumour reduction in CAIX knockouts and 6% in CAIX-expressing tumours, p < 0.001), independently of initial PD-L1 expression. Our simulations suggest that patients with CAIX-expressing tumours could respond favourably to combining ICIs with CAIX suppression, even in the absence of pre-treatment PD-L1 expression. Furthermore, when calibrated with tumour-type-specific data, our model could serve as a high-throughput tool for testing the effectiveness of such a combinatorial approach.
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Affiliation(s)
- Julia Grajek
- Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw 02-109, Poland
| | - Jakob Nikolas Kather
- Else Kroener Fresenius Center for Digital Health, Technical University Dresden, Dresden 01309, Germany
| | - Jan Poleszczuk
- Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw 02-109, Poland
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15
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Jain HV, Norton KA, Prado BB, Jackson TL. SMoRe ParS: A novel methodology for bridging modeling modalities and experimental data applied to 3D vascular tumor growth. Front Mol Biosci 2022; 9:1056461. [PMID: 36619168 PMCID: PMC9816661 DOI: 10.3389/fmolb.2022.1056461] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/09/2022] [Indexed: 12/24/2022] Open
Abstract
Multiscale systems biology is having an increasingly powerful impact on our understanding of the interconnected molecular, cellular, and microenvironmental drivers of tumor growth and the effects of novel drugs and drug combinations for cancer therapy. Agent-based models (ABMs) that treat cells as autonomous decision-makers, each with their own intrinsic characteristics, are a natural platform for capturing intratumoral heterogeneity. Agent-based models are also useful for integrating the multiple time and spatial scales associated with vascular tumor growth and response to treatment. Despite all their benefits, the computational costs of solving agent-based models escalate and become prohibitive when simulating millions of cells, making parameter exploration and model parameterization from experimental data very challenging. Moreover, such data are typically limited, coarse-grained and may lack any spatial resolution, compounding these challenges. We address these issues by developing a first-of-its-kind method that leverages explicitly formulated surrogate models (SMs) to bridge the current computational divide between agent-based models and experimental data. In our approach, Surrogate Modeling for Reconstructing Parameter Surfaces (SMoRe ParS), we quantify the uncertainty in the relationship between agent-based model inputs and surrogate model parameters, and between surrogate model parameters and experimental data. In this way, surrogate model parameters serve as intermediaries between agent-based model input and data, making it possible to use them for calibration and uncertainty quantification of agent-based model parameters that map directly onto an experimental data set. We illustrate the functionality and novelty of Surrogate Modeling for Reconstructing Parameter Surfaces by applying it to an agent-based model of 3D vascular tumor growth, and experimental data in the form of tumor volume time-courses. Our method is broadly applicable to situations where preserving underlying mechanistic information is of interest, and where computational complexity and sparse, noisy calibration data hinder model parameterization.
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Affiliation(s)
- Harsh Vardhan Jain
- Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN, United States
| | - Kerri-Ann Norton
- Reem and Kayden Center for Science and Computation, Computational Biology Laboratory, Computer Science Program, Bard College, Annandale-on-Hudson, NY, United States
| | | | - Trachette L. Jackson
- Department of Mathematics, University of Michigan, Ann Arbor, MI, United States,*Correspondence: Trachette L. Jackson,
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16
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Lourenço D, Lopes R, Pestana C, Queirós AC, João C, Carneiro EA. Patient-Derived Multiple Myeloma 3D Models for Personalized Medicine-Are We There Yet? Int J Mol Sci 2022; 23:12888. [PMID: 36361677 PMCID: PMC9657251 DOI: 10.3390/ijms232112888] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Revised: 10/19/2022] [Accepted: 10/22/2022] [Indexed: 12/03/2023] Open
Abstract
Despite the wide variety of existing therapies, multiple myeloma (MM) remains a disease with dismal prognosis. Choosing the right treatment for each patient remains one of the major challenges. A new approach being explored is the use of ex vivo models for personalized medicine. Two-dimensional culture or animal models often fail to predict clinical outcomes. Three-dimensional ex vivo models using patients' bone marrow (BM) cells may better reproduce the complexity and heterogeneity of the BM microenvironment. Here, we review the strengths and limitations of currently existing patient-derived ex vivo three-dimensional MM models. We analyze their biochemical and biophysical properties, molecular and cellular characteristics, as well as their potential for drug testing and identification of disease biomarkers. Furthermore, we discuss the remaining challenges and give some insight on how to achieve a more biomimetic and accurate MM BM model. Overall, there is still a need for standardized culture methods and refined readout techniques. Including both myeloma and other cells of the BM microenvironment in a simple and reproducible three-dimensional scaffold is the key to faithfully mapping and examining the relationship between these players in MM. This will allow a patient-personalized profile, providing a powerful tool for clinical and research applications.
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Affiliation(s)
- Diana Lourenço
- Myeloma Lymphoma Research Group—Champalimaud Experimental Clinical Research Programme of Champalimaud Foundation, 1400-038 Lisbon, Portugal
- Faculty of Medicine, University of Coimbra, 3000-548 Coimbra, Portugal
| | - Raquel Lopes
- Myeloma Lymphoma Research Group—Champalimaud Experimental Clinical Research Programme of Champalimaud Foundation, 1400-038 Lisbon, Portugal
- Faculty of Medicine, University of Lisbon, 1649-028 Lisbon, Portugal
| | - Carolina Pestana
- Myeloma Lymphoma Research Group—Champalimaud Experimental Clinical Research Programme of Champalimaud Foundation, 1400-038 Lisbon, Portugal
- Centre of Statistics and Its Applications, Faculty of Sciences, University of Lisbon, 1749-016 Lisbon, Portugal
| | - Ana C. Queirós
- Myeloma Lymphoma Research Group—Champalimaud Experimental Clinical Research Programme of Champalimaud Foundation, 1400-038 Lisbon, Portugal
| | - Cristina João
- Myeloma Lymphoma Research Group—Champalimaud Experimental Clinical Research Programme of Champalimaud Foundation, 1400-038 Lisbon, Portugal
- Faculty of Medical Sciences, NOVA Medical School, 1169-056 Lisbon, Portugal
- Hemato-Oncology Department of Champalimaud Foundation, 1400-038 Lisbon, Portugal
| | - Emilie Arnault Carneiro
- Myeloma Lymphoma Research Group—Champalimaud Experimental Clinical Research Programme of Champalimaud Foundation, 1400-038 Lisbon, Portugal
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17
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Baumgartner C. The world's first digital cell twin in cancer electrophysiology: a digital revolution in cancer research? JOURNAL OF EXPERIMENTAL & CLINICAL CANCER RESEARCH : CR 2022; 41:298. [PMID: 36221111 PMCID: PMC9552501 DOI: 10.1186/s13046-022-02507-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 09/30/2022] [Indexed: 11/07/2022]
Abstract
Background The introduction of functional in-silico models, in addition to in-vivo tumor models, opens up new and unlimited possibilities in cancer research and drug development. The world's first digital twin of the A549 cell's electrophysiology in the human lung adenocarcinoma, unveiled in 2021, enables the investigation and evaluation of new research hypotheses about modulating the function of ion channels in the cell membrane, which are important for better understanding cancer development and progression, as well as for developing new drugs and predicting treatments. Main body The developed A549 in-silico model allows virtual simulations of the cell’s rhythmic oscillation of the membrane potential, which can trigger the transition between cell cycle phases. It is able to predict the promotion or interruption of cell cycle progression provoked by targeted activation and inactivation of ion channels, resulting in abnormal hyper- or depolarization of the membrane potential, a potential key signal for the known cancer hallmarks. For example, model simulations of blockade of transient receptor potential cation channels (TRPC6), which are highly expressed during S-G2/M transition, result in a strong hyperpolarization of the cell’s membrane potential that can suppress or bypass the depolarization required for the S-G2/M transition, allowing for possible cell cycle arrest and inhibition of mitosis. All simulated research hypotheses could be verified by experimental studies. Short conclusion Functional, non-phenomenological digital twins, ranging from single cells to cell–cell interactions to 3D tissue models, open new avenues for modern cancer research through "dry lab" approaches that optimally complement established in-vivo and in-vitro methods.
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Affiliation(s)
- Christian Baumgartner
- grid.410413.30000 0001 2294 748XInstitute of Health Care Engineering With European Testing Center of Medical Devices, Computational Cancer Electrophysiology Lab, Graz University of Technology, 8010 Graz, Austria
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18
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Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans? Bull Math Biol 2022; 84:130. [PMID: 36175705 PMCID: PMC9522842 DOI: 10.1007/s11538-022-01075-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2022] [Accepted: 08/29/2022] [Indexed: 11/17/2022]
Abstract
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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19
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Coggan H, Andres Terre H, Liò P. A novel interpretable machine learning algorithm to identify optimal parameter space for cancer growth. Front Big Data 2022; 5:941451. [PMID: 36172548 PMCID: PMC9510846 DOI: 10.3389/fdata.2022.941451] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 08/17/2022] [Indexed: 11/13/2022] Open
Abstract
Recent years have seen an increase in the application of machine learning to the analysis of physical and biological systems, including cancer progression. A fundamental downside to these tools is that their complexity and nonlinearity makes it almost impossible to establish a deterministic, a priori relationship between their input and output, and thus their predictions are not wholly accountable. We begin with a series of proofs establishing that this holds even for the simplest possible model of a neural network; the effects of specific loss functions are explored more fully in Appendices. We return to first principles and consider how to construct a physics-inspired model of tumor growth without resorting to stochastic gradient descent or artificial nonlinearities. We derive an algorithm which explores the space of possible parameters in a model of tumor growth and identifies candidate equations much faster than a simulated annealing approach. We test this algorithm on synthetic tumor-growth trajectories and show that it can efficiently and reliably narrow down the area of parameter space where the correct values are located. This approach has the potential to greatly improve the speed and reliability with which patient-specific models of cancer growth can be identified in a clinical setting.
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Affiliation(s)
- Helena Coggan
- Department of Mathematics, University College London, London, United Kingdom
- *Correspondence: Helena Coggan
| | - Helena Andres Terre
- Department of Computer Science and Technology, University of Cambridge, Cambridge, United Kingdom
| | - Pietro Liò
- Department of Computer Science and Technology, University of Cambridge, Cambridge, United Kingdom
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20
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Cárdenas SD, Reznik CJ, Ranaweera R, Song F, Chung CH, Fertig EJ, Gevertz JL. Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer. NPJ Syst Biol Appl 2022; 8:32. [PMID: 36075912 PMCID: PMC9458753 DOI: 10.1038/s41540-022-00244-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 08/05/2022] [Indexed: 11/09/2022] Open
Abstract
The promise of precision medicine has been limited by the pervasive resistance to many targeted therapies for cancer. Inferring the timing (i.e., pre-existing or acquired) and mechanism (i.e., drug-induced) of such resistance is crucial for designing effective new therapeutics. This paper studies cetuximab resistance in head and neck squamous cell carcinoma (HNSCC) using tumor volume data obtained from patient-derived tumor xenografts. We ask if resistance mechanisms can be determined from this data alone, and if not, what data would be needed to deduce the underlying mode(s) of resistance. To answer these questions, we propose a family of mathematical models, with each member of the family assuming a different timing and mechanism of resistance. We present a method for fitting these models to individual volumetric data, and utilize model selection and parameter sensitivity analyses to ask: which member(s) of the family of models best describes HNSCC response to cetuximab, and what does that tell us about the timing and mechanisms driving resistance? We find that along with time-course volumetric data to a single dose of cetuximab, the initial resistance fraction and, in some instances, dose escalation volumetric data are required to distinguish among the family of models and thereby infer the mechanisms of resistance. These findings can inform future experimental design so that we can best leverage the synergy of wet laboratory experimentation and mathematical modeling in the study of novel targeted cancer therapeutics.
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Affiliation(s)
- Santiago D Cárdenas
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, USA
| | - Constance J Reznik
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, USA.,Datacor, Inc., Florham Park, NJ, USA
| | - Ruchira Ranaweera
- Department of Head and Neck-Endocrine Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Feifei Song
- Department of Head and Neck-Endocrine Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Christine H Chung
- Department of Head and Neck-Endocrine Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Elana J Fertig
- Convergence Institute, Department of Oncology, Department of Biomedical Engineering, Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA.
| | - Jana L Gevertz
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, USA.
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21
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Nasim A, Yates J, Derks G, Dunlop C. A Spatially Resolved Mechanistic Growth Law for Cancer Drug Development Predicting Tumor Growing Fractions. CANCER RESEARCH COMMUNICATIONS 2022; 2:754-761. [PMID: 36923310 PMCID: PMC10010375 DOI: 10.1158/2767-9764.crc-22-0032] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Revised: 04/25/2022] [Accepted: 07/08/2022] [Indexed: 11/16/2022]
Abstract
Mathematical models used in preclinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumor volume; however, they typically have little connection with the underlying physiologic processes. This lack of a mechanistic underpinning restricts their flexibility and potentially inhibits their translation across studies including from animal to human. Here we present a mathematical model describing tumor growth for the evaluation of single-agent cytotoxic compounds that is based on mechanistic principles. The model can predict spatial distributions of cell subpopulations and account for spatial drug distribution effects within tumors. Importantly, we demonstrate that the model can be reduced to a growth law similar in form to the ones currently implemented in pharmaceutical drug development for preclinical trials so that it can integrated into the current workflow. We validate this approach for both cell-derived xenograft and patient-derived xenograft (PDX) data. This shows that our theoretical model fits as well as the best performing and most widely used models. However, in addition, the model is also able to accurately predict the observed growing fraction of tumours. Our work opens up current preclinical modeling studies to also incorporating spatially resolved and multimodal data without significant added complexity and creates the opportunity to improve translation and tumor response predictions. Significance This theoretical model has the same mathematical structure as that currently used for drug development. However, its mechanistic basis enables prediction of growing fraction and spatial variations in drug distribution.
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Affiliation(s)
- Adam Nasim
- Department of Mathematics, University of Surrey, Guildford, United Kingdom
| | - James Yates
- Oncology R&D, AstraZeneca, Cambridge, United Kingdom
| | - Gianne Derks
- Department of Mathematics, University of Surrey, Guildford, United Kingdom
| | - Carina Dunlop
- Department of Mathematics, University of Surrey, Guildford, United Kingdom
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