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Mahmoodi M, Pishevar A, Azargoshasbi F. Numerical investigation of the pharmacokinetics and pharmacodynamics of the chemotherapeutic drug in avascular and vascular stages of a brain tumor. J Theor Biol 2023; 575:111633. [PMID: 37839585 DOI: 10.1016/j.jtbi.2023.111633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 10/05/2023] [Indexed: 10/17/2023]
Abstract
One of the most commonly used approaches for treating solid tumors is the systemic delivery of chemotherapeutic drugs. However, our understanding of the factors influencing treatment efficacy through this method is still limited. This study presents a comprehensive and realistic mathematical model that incorporates the dynamics of tumor growth, capillary network extension, and drug delivery in a coupled and simultaneous manner. The model covers two stages of tumor growth: avascular and vascular. For tumor growth, a continuum model is employed using the phase field interface-capturing method. The neo-vascularization process is modeled using a hybrid discrete-continuum approach. Additionally, a multi-scale model is used to describe the pharmacokinetics of doxorubicin, considering various agents. The study investigates the effect of haptotaxis and reveals that a higher haptotaxis coefficient leads to faster tumor growth (up to 2.6 times) and a quicker progression to angiogenesis. The impact of tumor-related and drug-related parameters is also examined, including tumor size, tumor sensitivity to the drug, chemotherapy initialization, treatment cycle duration, drug affinity to cells, and drug dose. The findings indicate that chemotherapy is more effective during the angiogenesis stage when active loops have formed. Other clinical methods such as radiotherapy and surgery may be more appropriate during the avascular stage or the transition period between angiogenesis initialization and loop formation. The penetration depth of the drug decreases by approximately 50% with an increase in the drug binding rate to surface-cell receptors. As a result, high-associate-rate drugs are preferred for chemotherapy after active loops have formed, while low-associate-rate drugs are suitable for earlier stages.
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Affiliation(s)
- Mohammad Mahmoodi
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
| | - Ahmadreza Pishevar
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran.
| | - Farzaneh Azargoshasbi
- Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
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2
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Krolicki L, Kunikowska J, Cordier D, Slavova N, Koziara H, Bruchertseifer F, Maecke HR, Morgenstern A, Merlo A. Long-Term Tumor Control Following Targeted Alpha Therapy (TAT) of Low-Grade Gliomas (LGGs): A New Treatment Paradigm? Int J Mol Sci 2023; 24:15701. [PMID: 37958683 PMCID: PMC10650612 DOI: 10.3390/ijms242115701] [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: 09/14/2023] [Revised: 10/15/2023] [Accepted: 10/21/2023] [Indexed: 11/15/2023] Open
Abstract
The median survival time has been reported to vary between 5 and 8 years in low-grade (WHO grade 2) astrocytoma, and between 10 and 15 years for grade 2 oligodendroglioma. Targeted alpha therapy (TAT), using the modified peptide vector [213Bi]Bi/[225Ac]Ac-DOTA-substance P, has been developed to treat glioblastoma (GBM), a prevalent malignant brain tumor. In order to assess the risk of late neurotoxicity, assuming that reduced tumor cell proliferation and invasion should directly translate into good responses in low-grade gliomas (LGGs), a limited number of patients with diffuse invasive astrocytoma (n = 8) and oligodendroglioma (n = 3) were offered TAT. In two oligodendroglioma patients, TAT was applied as a second-line treatment for tumor progression, 10 years after targeted beta therapy using [90Y]Y-DOTA-substance P. The radiopharmaceutical was locally injected directly into the tumor via a stereotactic insertion of a capsule-catheter system. The activity used for radiolabeling was 2-2.5 GBq of Bismuth-213 and 17 to 35 MBq of Actinium-225, mostly applied in a single fraction. The recurrence-free survival times were in the range of 2 to 16 years (median 11 years) in low-grade astrocytoma (n = 8), in which TAT was administered following a biopsy or tumor debulking. Regarding oligodendroglioma, the recurrence-free survival time was 24 years in the first case treated, and 4 and 5 years in the two second-line cases. In conclusion, TAT leads to long-term tumor control in the majority of patients with LGG, and recurrence has so far not manifested in patients with low-grade (grade 2) astrocytomas who received TAT as a first-line therapy. We conclude that targeted alpha therapy has the potential to become a new treatment paradigm in LGG.
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Affiliation(s)
- Leszek Krolicki
- Nuclear Medicine Department, Medical University of Warsaw, 02-091 Warsaw, Poland; (L.K.); (J.K.)
| | - Jolanta Kunikowska
- Nuclear Medicine Department, Medical University of Warsaw, 02-091 Warsaw, Poland; (L.K.); (J.K.)
| | - Dominik Cordier
- Neurosurgery Department, University Hospital Basel, 4031 Basel, Switzerland;
| | - Nedelina Slavova
- Department of Neurology, Inselspital, University Hospital Bern, 3010 Bern, Switzerland;
| | - Henryk Koziara
- Department of Neurosurgery, Institute of Psychiatry and Neurology, 02-957 Warsaw, Poland;
| | - Frank Bruchertseifer
- European Commission, Joint Research Centre (JRC), 76125 Karlsruhe, Germany; (F.B.); (A.M.)
| | - Helmut R. Maecke
- Nuclear Medicine and Radiochemistry, University Hospital Basel, 4031 Basel, Switzerland
| | - Alfred Morgenstern
- European Commission, Joint Research Centre (JRC), 76125 Karlsruhe, Germany; (F.B.); (A.M.)
| | - Adrian Merlo
- Department of Neurosurgery, Bern and University of Basel, 4001 Basel, Switzerland
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3
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Flandoli F, Leocata M, Ricci C. The Mathematical modeling of Cancer growth and angiogenesis by an individual based interacting system. J Theor Biol 2023; 562:111432. [PMID: 36746298 DOI: 10.1016/j.jtbi.2023.111432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Revised: 01/23/2023] [Accepted: 01/26/2023] [Indexed: 02/07/2023]
Abstract
We present a mathematical model for the complex system for the growth of a solid tumor. The system embeds proliferation of cells depending on the surrounding oxygen field, hypoxia caused by insufficient oxygen when the tumor reaches a certain size, consequent VEGF release and angiogenic new vasculature growth, re-oxygenation of the tumor and subsequent tumor growth restart. Specifically cancerous cells are represented by individual units, interacting as proliferating particles of a solid body, oxygen, and VEGF are fields with a source and a sink, and new angiogenic vasculature is described by a network of growing curves. The model, as shown by numerical simulations, captures both the time-evolution of the tumor growth before and after angiogenesis and its spatial properties, with different distribution of proliferating and hypoxic cells in the external and deep layers of the tumor, and the spatial structure of the angiogenic network. The microscopic description of the growth opens the possibility of tuning the model to patient-specific scenarios.
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Affiliation(s)
- Franco Flandoli
- Scuola Normale Superiore, P.za dei Cavalieri, 7, Pisa, 56126, Italy.
| | - Marta Leocata
- Scuola Normale Superiore, P.za dei Cavalieri, 7, Pisa, 56126, Italy.
| | - Cristiano Ricci
- University of Pisa, Department of Economics and Management, Via Cosimo Ridolfi, 10, Pisa, 56124, Italy.
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4
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Narimani N, Dehghan M. Predicting the effect of a combination drug therapy on the prostate tumor growth via an improvement of a direct radial basis function partition of unity technique for a diffuse-interface model. Comput Biol Med 2023; 157:106708. [PMID: 36934535 DOI: 10.1016/j.compbiomed.2023.106708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Revised: 02/04/2023] [Accepted: 02/19/2023] [Indexed: 03/05/2023]
Abstract
Chemotherapy is usually applied to treat advanced prostate cancer that cancer cells spread outside the prostate gland. The treatment uses cytotoxic drugs to target cells that grow and divide quickly. On the other hand, the growth of such cancerous tumors depends on angiogenesis. In this paper, we numerically study a diffuse-interface model in a two-dimensional space related to the therapies of prostate cancer. The proposed model describes the tumor growth driven by a generic nutrient and producing the prostate-specific antigen. More precisely, the effect of cytotoxic chemotherapy in the model is evaluated by considering a time-dependent function in the tumor dynamics. Also, another function related to the antiangiogenic therapy is considered to show the reducing intratumoral nutrient supply in the nutrient dynamics. Here, a meshless approximation, i.e., a generalized form of the direct radial basis function partition of unity (D-RBF-PU) method is presented for finding the numerical simulations of this model utilizing in medical oncology. The method uses the lower number of trial points in each patch than the original D-RBF-PU scheme for approximating the trial function per test point. Hence, the time complexity of the method is less than the D-RBF-PU technique. Besides, a semi-implicit time discretization of order 1 has been used to deal with the time variable. Consequently, a linear system of algebraic equations could be solved iteratively per time step by the use of the biconjugate gradient stabilized method with zero-fill incomplete lower-upper preconditioner. Finally, the obtained results without using any adaptive algorithm demonstrate the response of the prostate tumor growth to the chemotherapy, antiangiogenic therapy and a combined therapy.
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Affiliation(s)
- Niusha Narimani
- Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424 , Hafez Ave., 15914, Tehran, Iran.
| | - Mehdi Dehghan
- Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424 , Hafez Ave., 15914, Tehran, Iran.
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5
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Jørgensen ACS, Hill CS, Sturrock M, Tang W, Karamched SR, Gorup D, Lythgoe MF, Parrinello S, Marguerat S, Shahrezaei V. Data-driven spatio-temporal modelling of glioblastoma. ROYAL SOCIETY OPEN SCIENCE 2023; 10:221444. [PMID: 36968241 PMCID: PMC10031411 DOI: 10.1098/rsos.221444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 02/23/2023] [Indexed: 06/18/2023]
Abstract
Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding glioblastoma, a malignant form of brain cancer. For each approach, we summarize the scope, drawbacks and assets. We highlight the potential clinical applications of each modelling technique and discuss the connections between the mathematical models and the molecular and imaging data used to inform them. By doing so, we aim to prime cancer researchers with current and emerging computational tools for understanding tumour progression. By providing an in-depth picture of the different modelling techniques, we also aim to assist researchers who seek to build and develop their own models and the associated inference frameworks. Our article thus strikes a unique balance. On the one hand, we provide a comprehensive overview of the available modelling techniques and their applications, including key mathematical expressions. On the other hand, the content is accessible to mathematicians and biomedical scientists alike to accommodate the interdisciplinary nature of cancer research.
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Affiliation(s)
| | - Ciaran Scott Hill
- Department of Neurosurgery, The National Hospital for Neurology and Neurosurgery, London WC1N 3BG, UK
- Samantha Dickson Brain Cancer Unit, UCL Cancer Institute, London WC1E 6DD, UK
| | - Marc Sturrock
- Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin D02 YN77, Ireland
| | - Wenhao Tang
- Department of Mathematics, Faculty of Natural Sciences, Imperial College London, London SW7 2AZ, UK
| | - Saketh R. Karamched
- Division of Medicine, Centre for Advanced Biomedical Imaging, University College London (UCL), London WC1E 6BT, UK
| | - Dunja Gorup
- Division of Medicine, Centre for Advanced Biomedical Imaging, University College London (UCL), London WC1E 6BT, UK
| | - Mark F. Lythgoe
- Division of Medicine, Centre for Advanced Biomedical Imaging, University College London (UCL), London WC1E 6BT, UK
| | - Simona Parrinello
- Samantha Dickson Brain Cancer Unit, UCL Cancer Institute, London WC1E 6DD, UK
| | - Samuel Marguerat
- Genomics Translational Technology Platform, UCL Cancer Institute, University College London, London WC1E 6DD, UK
| | - Vahid Shahrezaei
- Department of Mathematics, Faculty of Natural Sciences, Imperial College London, London SW7 2AZ, UK
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6
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Goodin DA, Frieboes HB. Evaluation of innate and adaptive immune system interactions in the tumor microenvironment via a 3D continuum model. J Theor Biol 2023; 559:111383. [PMID: 36539112 DOI: 10.1016/j.jtbi.2022.111383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2022] [Revised: 12/09/2022] [Accepted: 12/11/2022] [Indexed: 12/23/2022]
Abstract
Immune cells in the tumor microenvironment (TME) are known to affect tumor growth, vascularization, and extracellular matrix (ECM) deposition. Marked interest in system-scale analysis of immune species interactions within the TME has encouraged progress in modeling tumor-immune interactions in silico. Due to the computational cost of simulating these intricate interactions, models have typically been constrained to representing a limited number of immune species. To expand the capability for system-scale analysis, this study develops a three-dimensional continuum mixture model of tumor-immune interactions to simulate multiple immune species in the TME. Building upon a recent distributed computing implementation that enables efficient solution of such mixture models, major immune species including monocytes, macrophages, natural killer cells, dendritic cells, neutrophils, myeloid-derived suppressor cells (MDSC), cytotoxic, helper, regulatory T-cells, and effector and regulatory B-cells and their interactions are represented in this novel implementation. Immune species extravasate from blood vasculature, undergo chemotaxis toward regions of high chemokine concentration, and influence the TME in proportion to locally defined levels of stimulation. The immune species contribute to the production of angiogenic and tumor growth factors, promotion of myofibroblast deposition of ECM, upregulation of angiogenesis, and elimination of living and dead tumor species. The results show that this modeling approach offers the capability for quantitative insight into the modulation of tumor growth by diverse immune-tumor interactions and immune-driven TME effects. In particular, MDSC-mediated effects on tumor-associated immune species' activation levels, volume fraction, and influence on the TME are explored. Longer term, linking of the model parameters to particular patient tumor information could simulate cancer-specific immune responses and move toward a more comprehensive evaluation of immunotherapeutic strategies.
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Affiliation(s)
- Dylan A Goodin
- Department of Bioengineering, University of Louisville, KY, USA
| | - Hermann B Frieboes
- Department of Bioengineering, University of Louisville, KY, USA; James Graham Brown Cancer Center, University of Louisville, KY, USA; Center for Predictive Medicine, University of Louisville, KY, USA.
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7
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Coupling solid and fluid stresses with brain tumour growth and white matter tract deformations in a neuroimaging-informed model. Biomech Model Mechanobiol 2022; 21:1483-1509. [PMID: 35908096 PMCID: PMC9626445 DOI: 10.1007/s10237-022-01602-4] [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: 12/22/2021] [Accepted: 06/17/2022] [Indexed: 11/29/2022]
Abstract
Brain tumours are among the deadliest types of cancer, since they display a strong ability to invade the surrounding tissues and an extensive resistance to common therapeutic treatments. It is therefore important to reproduce the heterogeneity of brain microstructure through mathematical and computational models, that can provide powerful instruments to investigate cancer progression. However, only a few models include a proper mechanical and constitutive description of brain tissue, which instead may be relevant to predict the progression of the pathology and to analyse the reorganization of healthy tissues occurring during tumour growth and, possibly, after surgical resection. Motivated by the need to enrich the description of brain cancer growth through mechanics, in this paper we present a mathematical multiphase model that explicitly includes brain hyperelasticity. We find that our mechanical description allows to evaluate the impact of the growing tumour mass on the surrounding healthy tissue, quantifying the displacements, deformations, and stresses induced by its proliferation. At the same time, the knowledge of the mechanical variables may be used to model the stress-induced inhibition of growth, as well as to properly modify the preferential directions of white matter tracts as a consequence of deformations caused by the tumour. Finally, the simulations of our model are implemented in a personalized framework, which allows to incorporate the realistic brain geometry, the patient-specific diffusion and permeability tensors reconstructed from imaging data and to modify them as a consequence of the mechanical deformation due to cancer growth.
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8
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Wu C, Lorenzo G, Hormuth DA, Lima EABF, Slavkova KP, DiCarlo JC, Virostko J, Phillips CM, Patt D, Chung C, Yankeelov TE. Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology. BIOPHYSICS REVIEWS 2022; 3:021304. [PMID: 35602761 PMCID: PMC9119003 DOI: 10.1063/5.0086789] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 04/29/2022] [Indexed: 12/11/2022]
Abstract
Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.
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Affiliation(s)
- Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| | | | | | | | - Kalina P. Slavkova
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | | | | | - Caleb M. Phillips
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Debra Patt
- Texas Oncology, Austin, Texas 78731, USA
| | - Caroline Chung
- Department of Radiation Oncology, MD Anderson Cancer Center, University of Texas, Houston, Texas 77030, USA
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9
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Harkos C, Svensson SF, Emblem KE, Stylianopoulos T. Inducing Biomechanical Heterogeneity in Brain Tumor Modeling by MR Elastography: Effects on Tumor Growth, Vascular Density and Delivery of Therapeutics. Cancers (Basel) 2022; 14:cancers14040884. [PMID: 35205632 PMCID: PMC8870149 DOI: 10.3390/cancers14040884] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 02/07/2022] [Indexed: 02/01/2023] Open
Abstract
Simple Summary Biomechanical forces aggravate brain tumor progression. In this study, magnetic resonance elastography (MRE) is employed to extract tissue biomechanical properties from five glioblastoma patients and a healthy subject, and data are incorporated in a mathematical model that simulates tumor growth. Mathematical modeling enables further understanding of glioblastoma development and allows patient-specific predictions for tumor vascularity and delivery of drugs. Incorporating MRE data results in a more realistic intratumoral distribution of mechanical stress and anisotropic tumor growth and a better description of subsequent events that are closely related to the development of stresses, including heterogeneity of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs. Abstract The purpose of this study is to develop a methodology that incorporates a more accurate assessment of tissue mechanical properties compared to current mathematical modeling by use of biomechanical data from magnetic resonance elastography. The elastography data were derived from five glioblastoma patients and a healthy subject and used in a model that simulates tumor growth, vascular changes due to mechanical stresses and delivery of therapeutic agents. The model investigates the effect of tumor-specific biomechanical properties on tumor anisotropic growth, vascular density heterogeneity and chemotherapy delivery. The results showed that including elastography data provides a more realistic distribution of the mechanical stresses in the tumor and induces anisotropic tumor growth. Solid stress distribution differs among patients, which, in turn, induces a distinct functional vascular density distribution—owing to the compression of tumor vessels—and intratumoral drug distribution for each patient. In conclusion, incorporating elastography data results in a more accurate calculation of intratumoral mechanical stresses and enables a better mathematical description of subsequent events, such as the heterogeneous development of the tumor vasculature and intrapatient variations in tumor perfusion and delivery of drugs.
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Affiliation(s)
- Constantinos Harkos
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia 1678, Cyprus;
| | - Siri Fløgstad Svensson
- Division of Radiology and Nuclear Medicine, Department of Diagnostic Physics, Oslo University Hospital, 0372 Oslo, Norway; (S.F.S.); (K.E.E.)
- Department of Physics, The Faculty of Mathematics and Natural Sciences, University of Oslo, 0371 Oslo, Norway
| | - Kyrre E. Emblem
- Division of Radiology and Nuclear Medicine, Department of Diagnostic Physics, Oslo University Hospital, 0372 Oslo, Norway; (S.F.S.); (K.E.E.)
| | - Triantafyllos Stylianopoulos
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia 1678, Cyprus;
- Correspondence:
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10
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Almeida L, Estrada-Rodriguez G, Oliver L, Peurichard D, Poulain A, Vallette F. Treatment-induced shrinking of tumour aggregates: a nonlinear volume-filling chemotactic approach. J Math Biol 2021; 83:29. [PMID: 34427771 DOI: 10.1007/s00285-021-01642-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Revised: 03/24/2021] [Accepted: 07/18/2021] [Indexed: 11/24/2022]
Abstract
Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we propose a novel mechano-transduction mechanism where the introduction of a chemotherapeutic treatment induces mechanical changes at the cell level. We analyse the influence of these individual mechanical changes on the properties of the aggregates obtained at the population level. We employ a nonlinear volume-filling chemotactic system of partial differential equations, where the elastic properties of the cells are taken into account through the so-called squeezing probability, which depends on the concentration of the treatment in the extracellular microenvironment. We explore two scenarios for the effect of the treatment: first, we suppose that the treatment acts only on the mechanical properties of the cells and, in the second one, we assume it also prevents cell proliferation. We perform a linear stability analysis which enables us to identify the ability of the system to create patterns and fully characterize their size. Moreover, we provide numerical simulations in 1D and 2D that illustrate the shrinking of the aggregates due to the presence of the treatment.
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Affiliation(s)
- Luis Almeida
- Laboratoire Jacques-Louis Lions, UMR7598, Sorbonne Université, CNRS, Inria, Université de Paris, 75005, Paris, France
| | - Gissell Estrada-Rodriguez
- Laboratoire Jacques-Louis Lions, UMR7598, Sorbonne Université, CNRS, Inria, Université de Paris, 75005, Paris, France.
| | - Lisa Oliver
- UMR 1232, Centre de Recherche en Cancérologie et Immunologie Nantes-Angers, Université de Nantes, Nantes, France
| | - Diane Peurichard
- Sorbonne Université, Inria, Université de Paris, CNRS, Laboratoire Jacques-Louis Lions, 75005, Paris, France
| | - Alexandre Poulain
- Laboratoire Jacques-Louis Lions, UMR7598, Sorbonne Université, CNRS, Inria, Université de Paris, 75005, Paris, France
| | - Francois Vallette
- UMR 1232, Centre de Recherche en Cancérologie et Immunologie Nantes-Angers, Université de Nantes, Nantes, France
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11
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Falco J, Agosti A, Vetrano IG, Bizzi A, Restelli F, Broggi M, Schiariti M, DiMeco F, Ferroli P, Ciarletta P, Acerbi F. In Silico Mathematical Modelling for Glioblastoma: A Critical Review and a Patient-Specific Case. J Clin Med 2021; 10:2169. [PMID: 34067871 PMCID: PMC8156762 DOI: 10.3390/jcm10102169] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 04/24/2021] [Accepted: 05/14/2021] [Indexed: 01/28/2023] Open
Abstract
Glioblastoma extensively infiltrates the brain; despite surgery and aggressive therapies, the prognosis is poor. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of glioblastoma evolution in every single patient, with the aim of tailoring therapeutic weapons. In particular, the ultimate goal of biomathematics for cancer is the identification of the most suitable theoretical models and simulation tools, both to describe the biological complexity of carcinogenesis and to predict tumor evolution. In this report, we describe the results of a critical review about different mathematical models in neuro-oncology with their clinical implications. A comprehensive literature search and review for English-language articles concerning mathematical modelling in glioblastoma has been conducted. The review explored the different proposed models, classifying them and indicating the significative advances of each one. Furthermore, we present a specific case of a glioblastoma patient in which our recently proposed innovative mechanical model has been applied. The results of the mathematical models have the potential to provide a relevant benefit for clinicians and, more importantly, they might drive progress towards improving tumor control and patient's prognosis. Further prospective comparative trials, however, are still necessary to prove the impact of mathematical neuro-oncology in clinical practice.
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Affiliation(s)
- Jacopo Falco
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Abramo Agosti
- MOX, Department of Mathematics, Politecnico di Milano, 20133 Milan, Italy; (A.A.); (P.C.)
| | - Ignazio G. Vetrano
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Alberto Bizzi
- Department of Neuroradiology, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy;
| | - Francesco Restelli
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Morgan Broggi
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Marco Schiariti
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Francesco DiMeco
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
- Department of Pathophysiology and Transplantation, Università degli Studi di Milano, 20122 Milan, Italy
- Department of Neurological Surgery, Johns Hopkins Medical School, Baltimora, MD 21205, USA
| | - Paolo Ferroli
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
| | - Pasquale Ciarletta
- MOX, Department of Mathematics, Politecnico di Milano, 20133 Milan, Italy; (A.A.); (P.C.)
| | - Francesco Acerbi
- Department of Neurosurgery, Fondazione IRCCS Istituto Neurologico Carlo Besta, 20133 Milan, Italy; (J.F.); (I.G.V.); (F.R.); (M.B.); (M.S.); (F.D.); (P.F.)
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12
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Ayensa-Jiménez J, Pérez-Aliacar M, Randelovic T, Oliván S, Fernández L, Sanz-Herrera JA, Ochoa I, Doweidar MH, Doblaré M. Mathematical formulation and parametric analysis of in vitro cell models in microfluidic devices: application to different stages of glioblastoma evolution. Sci Rep 2020; 10:21193. [PMID: 33273574 PMCID: PMC7713081 DOI: 10.1038/s41598-020-78215-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2020] [Accepted: 10/26/2020] [Indexed: 12/31/2022] Open
Abstract
In silico models and computer simulation are invaluable tools to better understand complex biological processes such as cancer evolution. However, the complexity of the biological environment, with many cell mechanisms in response to changing physical and chemical external stimuli, makes the associated mathematical models highly non-linear and multiparametric. One of the main problems of these models is the determination of the parameters’ values, which are usually fitted for specific conditions, making the conclusions drawn difficult to generalise. We analyse here an important biological problem: the evolution of hypoxia-driven migratory structures in Glioblastoma Multiforme (GBM), the most aggressive and lethal primary brain tumour. We establish a mathematical model considering the interaction of the tumour cells with oxygen concentration in what is called the go or grow paradigm. We reproduce in this work three different experiments, showing the main GBM structures (pseudopalisade and necrotic core formation), only changing the initial and boundary conditions. We prove that it is possible to obtain versatile mathematical tools which, together with a sound parametric analysis, allow to explain complex biological phenomena. We show the utility of this hybrid “biomimetic in vitro-in silico” platform to help to elucidate the mechanisms involved in cancer processes, to better understand the role of the different phenomena, to test new scientific hypotheses and to design new data-driven experiments.
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Affiliation(s)
- Jacobo Ayensa-Jiménez
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain.,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain
| | - Marina Pérez-Aliacar
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain.,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain
| | - Teodora Randelovic
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain.,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain
| | - Sara Oliván
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain.,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain
| | - Luis Fernández
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain.,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), C/ Monforte de Lemos 3-5, Pabellón 11. Planta 0, 28029, Madrid, Spain
| | - José Antonio Sanz-Herrera
- School of Engineering, Department of Mechanics of Continuous Media and Theory of Structures, University of Seville, Camino de los descubrimientos, s/n, 41092, Sevilla, Spain
| | - Ignacio Ochoa
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain.,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), C/ Monforte de Lemos 3-5, Pabellón 11. Planta 0, 28029, Madrid, Spain
| | - Mohamed H Doweidar
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain.,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), C/ Monforte de Lemos 3-5, Pabellón 11. Planta 0, 28029, Madrid, Spain
| | - Manuel Doblaré
- Aragón Institute of Engineering Research (I3A), University of Zaragoza, Mariano Esquillor s/n, 50018, Zaragoza, Spain. .,Institute for Health Research Aragón (IIS Aragón), Avda. San Juan Bosco, 13, 50009, Zaragoza, Spain. .,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), C/ Monforte de Lemos 3-5, Pabellón 11. Planta 0, 28029, Madrid, Spain.
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13
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Giannakakis E, Han CE, Weber B, Hutchings F, Kaiser M. Towards simulations of long-term behavior of neural networks: Modeling synaptic plasticity of connections within and between human brain regions. Neurocomputing 2020; 416:38-44. [PMID: 33250573 PMCID: PMC7598092 DOI: 10.1016/j.neucom.2020.01.050] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Simulations of neural networks can be used to study the direct effect of internal or external changes on brain dynamics. However, some changes are not immediate but occur on the timescale of weeks, months, or years. Examples include effects of strokes, surgical tissue removal, or traumatic brain injury but also gradual changes during brain development. Simulating network activity over a long time, even for a small number of nodes, is a computational challenge. Here, we model a coupled network of human brain regions with a modified Wilson-Cowan model representing dynamics for each region and with synaptic plasticity adjusting connection weights within and between regions. Using strategies ranging from different models for plasticity, vectorization and a different differential equation solver setup, we achieved one second runtime for one second biological time.
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Affiliation(s)
- Emmanouil Giannakakis
- Interdisciplinary Computing and Complex BioSystems (ICOS) research group, School of Computing, Newcastle University, Newcastle upon Tyne NE4 5TG, United Kingdom
| | - Cheol E Han
- Department of Electronics and Information Engineering, Korea University, Sejong, Republic of Korea
| | - Bernd Weber
- Institute of Experimental Epileptology and Cognition Research, University of Bonn, Germany
| | - Frances Hutchings
- Interdisciplinary Computing and Complex BioSystems (ICOS) research group, School of Computing, Newcastle University, Newcastle upon Tyne NE4 5TG, United Kingdom
| | - Marcus Kaiser
- Interdisciplinary Computing and Complex BioSystems (ICOS) research group, School of Computing, Newcastle University, Newcastle upon Tyne NE4 5TG, United Kingdom.,Institute of Neuroscience, Newcastle University, the Henry Wellcome Building, Newcastle upon Tyne NE2 4HH, United Kingdom.,Department of Functional Neurosurgery, Ruijin Hospital, School of Medicine, Shanghai Jiao Tong University, Shanghai 200025, China
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14
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A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma. Bull Math Biol 2020; 82:143. [PMID: 33159592 DOI: 10.1007/s11538-020-00814-y] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 09/25/2020] [Indexed: 10/23/2022]
Abstract
Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence.
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15
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Mohammadi V, Dehghan M. Generalized moving least squares approximation for the solution of local and non-local models of cancer cell invasion of tissue under the effect of adhesion in one- and two-dimensional spaces. Comput Biol Med 2020; 124:103803. [PMID: 32738629 DOI: 10.1016/j.compbiomed.2020.103803] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Revised: 05/02/2020] [Accepted: 05/02/2020] [Indexed: 11/17/2022]
Abstract
The main aim of this study is to solve numerically the mathematical models showing cancer cell invasion of tissue with/without considering the effect of cell-cell and cell-matrix adhesion. The mathematical models studied here are the systems of time-dependent reaction-diffusion-taxis equations in one- and two-dimensional spaces, which are formulated in the local and non-local forms. There are some difficulties in finding their solutions via numerical methods. The main difficulty is to compute the non-local term appearing in one of the studied models, which causes more CPU time during simulations. The current paper aims to overcome this problem, where a new meshless method, namely generalized moving least squares (GMLS) approximation in space and a semi-implicit backward differential formula of first-order (SBDF1) in time have been applied. Based on GMLS theory, the non-local term is approximated without any difficulties. Moreover, a simple method based on the GMLS technique is presented to implement the boundary conditions. The obtained discrete scheme for both mathematical models is a linear system of algebraic equations per time step. The biconjugate gradient stabilized (BiCGSTAB) algorithm with zero-fill incomplete lower-upper (ILU) preconditioner is used to solve the obtained linear system at each time step. At the end of this paper, some simulation results are reported to show the behavior of cancer cell invasion in the local model, and the non-local model due to reduction of cell-cell adhesion and increasing cell-matrix adhesion in one- and two-dimensional spaces, where two different types of distribution points have been considered in the square domain. The computational algorithms of the GMLS approximation and the developed numerical method for solving the non-local (local) model are included in the Appendix.
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Affiliation(s)
- Vahid Mohammadi
- Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran.
| | - Mehdi Dehghan
- Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran.
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16
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Faghihi D, Feng X, Lima EABF, Oden JT, Yankeelov TE. A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2020; 139:103936. [PMID: 32394987 PMCID: PMC7213200 DOI: 10.1016/j.jmps.2020.103936] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
We develop a general class of thermodynamically consistent, continuum models based on mixture theory with phase effects that describe the behavior of a mass of multiple interacting constituents. The constituents consist of solid species undergoing large elastic deformations and compressible viscous fluids. The fundamental building blocks framing the mixture theories consist of the mass balance law of diffusing species and microscopic (cellular scale) and macroscopic (tissue scale) force balances, as well as energy balance and the entropy production inequality derived from the first and second laws of thermodynamics. A general phase-field framework is developed by closing the system through postulating constitutive equations (i.e., specific forms of free energy and rate of dissipation potentials) to depict the growth of tumors in a microenvironment. A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.
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Affiliation(s)
- Danial Faghihi
- Department of Mechanical and Aerospace Engineering, University at Buffalo
| | - Xinzeng Feng
- Oden Institute for Computational Engineering and Sciences
| | | | - J. Tinsley Oden
- Oden Institute for Computational Engineering and Sciences
- Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin
- Department of Mathematics, The University of Texas at Austin
- Department of Computer Science, The University of Texas at Austin
- Livestrong Cancer Institutes, The University of Texas at Austin
| | - Thomas E. Yankeelov
- Oden Institute for Computational Engineering and Sciences
- Department of Biomedical Engineering, The University of Texas at Austin
- Department of Diagnostic Medicine, The University of Texas at Austin
- Department of Oncology, The University of Texas at Austin
- Livestrong Cancer Institutes, The University of Texas at Austin
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17
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Glioma invasion and its interplay with nervous tissue and therapy: A multiscale model. J Theor Biol 2020; 486:110088. [DOI: 10.1016/j.jtbi.2019.110088] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Revised: 09/23/2019] [Accepted: 11/18/2019] [Indexed: 01/05/2023]
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18
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Gallaher JA, Massey SC, Hawkins-Daarud A, Noticewala SS, Rockne RC, Johnston SK, Gonzalez-Cuyar L, Juliano J, Gil O, Swanson KR, Canoll P, Anderson ARA. From cells to tissue: How cell scale heterogeneity impacts glioblastoma growth and treatment response. PLoS Comput Biol 2020; 16:e1007672. [PMID: 32101537 PMCID: PMC7062288 DOI: 10.1371/journal.pcbi.1007672] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2019] [Revised: 03/09/2020] [Accepted: 01/21/2020] [Indexed: 11/18/2022] Open
Abstract
Glioblastomas are aggressive primary brain tumors known for their inter- and intratumor heterogeneity. This disease is uniformly fatal, with intratumor heterogeneity the major reason for treatment failure and recurrence. Just like the nature vs nurture debate, heterogeneity can arise from intrinsic or environmental influences. Whilst it is impossible to clinically separate observed behavior of cells from their environmental context, using a mathematical framework combined with multiscale data gives us insight into the relative roles of variation from different sources. To better understand the implications of intratumor heterogeneity on therapeutic outcomes, we created a hybrid agent-based mathematical model that captures both the overall tumor kinetics and the individual cellular behavior. We track single cells as agents, cell density on a coarser scale, and growth factor diffusion and dynamics on a finer scale over time and space. Our model parameters were fit utilizing serial MRI imaging and cell tracking data from ex vivo tissue slices acquired from a growth-factor driven glioblastoma murine model. When fitting our model to serial imaging only, there was a spectrum of equally-good parameter fits corresponding to a wide range of phenotypic behaviors. When fitting our model using imaging and cell scale data, we determined that environmental heterogeneity alone is insufficient to match the single cell data, and intrinsic heterogeneity is required to fully capture the migration behavior. The wide spectrum of in silico tumors also had a wide variety of responses to an application of an anti-proliferative treatment. Recurrent tumors were generally less proliferative than pre-treatment tumors as measured via the model simulations and validated from human GBM patient histology. Further, we found that all tumors continued to grow with an anti-migratory treatment alone, but the anti-proliferative/anti-migratory combination generally showed improvement over an anti-proliferative treatment alone. Together our results emphasize the need to better understand the underlying phenotypes and tumor heterogeneity present in a tumor when designing therapeutic regimens.
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Affiliation(s)
- Jill A. Gallaher
- Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America
| | - Susan C. Massey
- Precision NeuroTherapeutics Innovation Program, Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurological Surgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Andrea Hawkins-Daarud
- Precision NeuroTherapeutics Innovation Program, Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurological Surgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Sonal S. Noticewala
- Department of Pathology and Cell Biology, Columbia University Medical Center, New York, New York, United States of America
- Department of Radiation Oncology, University of Texas MD Anderson Cancer Center, Houston, Texas, United States of America
| | - Russell C. Rockne
- Division of Mathematical Oncology, City of Hope National Medical Center, Duarte, California, United States of America
| | - Sandra K. Johnston
- Precision NeuroTherapeutics Innovation Program, Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurological Surgery, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Radiology, University of Washington, Seattle, Washington, United States of America
| | - Luis Gonzalez-Cuyar
- Department of Pathology, University of Washington, Seattle, Washington, United States of America
| | - Joseph Juliano
- Keck School of Medicine, University of Southern California, Los Angeles, California, United States of America
| | - Orlando Gil
- Department of Pathology and Cell Biology, Columbia University Medical Center, New York, New York, United States of America
- Department of Biology, Hunter College, City University of New York, New York, New York, United States of America
| | - Kristin R. Swanson
- Precision NeuroTherapeutics Innovation Program, Mathematical NeuroOncology Lab, Mayo Clinic, Phoenix, Arizona, United States of America
- Department of Neurological Surgery, Mayo Clinic, Phoenix, Arizona, United States of America
| | - Peter Canoll
- Department of Pathology and Cell Biology, Columbia University Medical Center, New York, New York, United States of America
| | - Alexander R. A. Anderson
- Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida, United States of America
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19
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Sorribes IC, Handelman SK, Jain HV. Mitigating temozolomide resistance in glioblastoma via DNA damage-repair inhibition. J R Soc Interface 2020; 17:20190722. [PMID: 31964274 DOI: 10.1098/rsif.2019.0722] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Glioblastomas are among the most lethal cancers, with a 5 year survival rate below 25%. Temozolomide is typically used in glioblastoma treatment; however, the enzymes alkylpurine-DNA-N-glycosylase (APNG) and methylguanine-DNA-methyltransferase (MGMT) efficiently mediate the repair of DNA damage caused by temozolomide, reducing treatment efficacy. Consequently, APNG and MGMT inhibition has been proposed as a way of overcoming chemotherapy resistance. Here, we develop a mechanistic mathematical model that explicitly incorporates the effects of chemotherapy on tumour cells, including the processes of DNA damage induction, cell arrest and DNA repair. Our model is carefully parametrized and validated, and then used to virtually recreate the response of heteroclonal glioblastomas to dual treatment with temozolomide and inhibitors of APNG/MGMT. Using our mechanistic model, we identify four combination treatment strategies optimized by tumour cell phenotype, and isolate the strategy most likely to succeed in a pre-clinical and clinical setting. If confirmed in clinical trials, these strategies have the potential to offset chemotherapy resistance in patients with glioblastoma and improve overall survival.
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Affiliation(s)
| | - Samuel K Handelman
- Department of Internal Medicine, University of Michigan, Ann Arbor, MI 48109, USA
| | - Harsh V Jain
- Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA
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20
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Chamseddine IM, Frieboes HB, Kokkolaras M. Design Optimization of Tumor Vasculature-Bound Nanoparticles. Sci Rep 2018; 8:17768. [PMID: 30538267 PMCID: PMC6290012 DOI: 10.1038/s41598-018-35675-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2018] [Accepted: 10/26/2018] [Indexed: 01/07/2023] Open
Abstract
Nanotherapy may constitute a promising approach to target tumors with anticancer drugs while minimizing systemic toxicity. Computational modeling can enable rapid evaluation of nanoparticle (NP) designs and numerical optimization. Here, an optimization study was performed using an existing tumor model to find NP size and ligand density that maximize tumoral NP accumulation while minimizing tumor size. Optimal NP avidity lies at lower bound of feasible values, suggesting reduced ligand density to prolong NP circulation. For the given set of tumor parameters, optimal NP diameters were 288 nm to maximize NP accumulation and 334 nm to minimize tumor diameter, leading to uniform NP distribution and adequate drug load. Results further show higher dependence of NP biodistribution on the NP design than on tumor morphological parameters. A parametric study with respect to drug potency was performed. The lower the potency of the drug, the bigger the difference is between the maximizer of NP accumulation and the minimizer of tumor size, indicating the existence of a specific drug potency that minimizes the differential between the two optimal solutions. This study shows the feasibility of applying optimization to NP designs to achieve efficacious cancer nanotherapy, and offers a first step towards a quantitative tool to support clinical decision making.
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Affiliation(s)
| | - Hermann B Frieboes
- Department of Bioengineering, University of Louisville, Louisville, KY, USA
- James Graham Brown Cancer Center, University of Louisville, Louisville, KY, USA
| | - Michael Kokkolaras
- Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada.
- GERAD - Group for Research in Decision Analysis, Montreal, Quebec, Canada.
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21
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Koay EJ, Lee Y, Cristini V, Lowengrub JS, Kang Y, Lucas FAS, Hobbs BP, Ye R, Elganainy D, Almahariq M, Amer AM, Chatterjee D, Yan H, Park PC, Rios Perez MV, Li D, Garg N, Reiss KA, Yu S, Chauhan A, Zaid M, Nikzad N, Wolff RA, Javle M, Varadhachary GR, Shroff RT, Das P, Lee JE, Ferrari M, Maitra A, Taniguchi CM, Kim MP, Crane CH, Katz MH, Wang H, Bhosale P, Tamm EP, Fleming JB. A Visually Apparent and Quantifiable CT Imaging Feature Identifies Biophysical Subtypes of Pancreatic Ductal Adenocarcinoma. Clin Cancer Res 2018; 24:5883-5894. [PMID: 30082477 PMCID: PMC6279613 DOI: 10.1158/1078-0432.ccr-17-3668] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Revised: 05/14/2018] [Accepted: 07/30/2018] [Indexed: 12/12/2022]
Abstract
PURPOSE Pancreatic ductal adenocarcinoma (PDAC) is a heterogeneous disease with variable presentations and natural histories of disease. We hypothesized that different morphologic characteristics of PDAC tumors on diagnostic computed tomography (CT) scans would reflect their underlying biology. EXPERIMENTAL DESIGN We developed a quantitative method to categorize the PDAC morphology on pretherapy CT scans from multiple datasets of patients with resectable and metastatic disease and correlated these patterns with clinical/pathologic measurements. We modeled macroscopic lesion growth computationally to test the effects of stroma on morphologic patterns, hypothesizing that the balance of proliferation and local migration rates of the cancer cells would determine tumor morphology. RESULTS In localized and metastatic PDAC, quantifying the change in enhancement on CT scans at the interface between tumor and parenchyma (delta) demonstrated that patients with conspicuous (high-delta) tumors had significantly less stroma, higher likelihood of multiple common pathway mutations, more mesenchymal features, higher likelihood of early distant metastasis, and shorter survival times compared with those with inconspicuous (low-delta) tumors. Pathologic measurements of stromal and mesenchymal features of the tumors supported the mathematical model's underlying theory for PDAC growth. CONCLUSIONS At baseline diagnosis, a visually striking and quantifiable CT imaging feature reflects the molecular and pathological heterogeneity of PDAC, and may be used to stratify patients into distinct subtypes. Moreover, growth patterns of PDAC may be described using physical principles, enabling new insights into diagnosis and treatment of this deadly disease.
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Affiliation(s)
- Eugene J Koay
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas.
| | - Yeonju Lee
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Vittorio Cristini
- Center for Precision Biomedicine, The University of Texas Health Science Center, Houston, Texas
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, Texas
- Department of Imaging Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - John S Lowengrub
- Department of Mathematics, University of California, Irvine, California
- Department of Biomedical Engineering, University of California, Irvine, California
- Chao Family Comprehensive Cancer Center, University of California, Irvine, California
- Center for Complex Biological Systems, University of California, Irvine, California
| | - Ya'an Kang
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - F Anthony San Lucas
- Sheikh Ahmed Center for Pancreatic Cancer Research, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Brian P Hobbs
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Rong Ye
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Dalia Elganainy
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Muayad Almahariq
- Deparment of Pharmacology and Toxicology, University of Texas Medical Branch, Galveston, Texas
| | - Ahmed M Amer
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Deyali Chatterjee
- Department of Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Huaming Yan
- Department of Mathematics, University of California, Irvine, California
| | - Peter C Park
- Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Mayrim V Rios Perez
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Dali Li
- Sheikh Ahmed Center for Pancreatic Cancer Research, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Naveen Garg
- Department of Diagnostic Radiology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Kim A Reiss
- Department of Medical Oncology, The University of Pennsylvania Abramson Cancer Center, Philadelphia, Pennsylvania
| | - Shun Yu
- Department of Internal Medicine, The University of Pennsylvania, Philadelphia, Pennsylvania
| | - Anil Chauhan
- Department of Radiology, The University of Pennsylvania, Philadelphia, Pennsylvania
| | - Mohamed Zaid
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Newsha Nikzad
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Robert A Wolff
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Milind Javle
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Gauri R Varadhachary
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Rachna T Shroff
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Prajnan Das
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Jeffrey E Lee
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Mauro Ferrari
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, Texas
| | - Anirban Maitra
- Sheikh Ahmed Center for Pancreatic Cancer Research, The University of Texas MD Anderson Cancer Center, Houston, Texas
- Department of Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Cullen M Taniguchi
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Michael P Kim
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Christopher H Crane
- Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Matthew H Katz
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Huamin Wang
- Department of Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Priya Bhosale
- Department of Diagnostic Radiology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Eric P Tamm
- Department of Diagnostic Radiology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Jason B Fleming
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
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22
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A mathematical model of angiogenesis and tumor growth: analysis and application in anti-angiogenesis therapy. J Math Biol 2018; 77:1589-1622. [DOI: 10.1007/s00285-018-1264-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Revised: 05/23/2018] [Indexed: 12/14/2022]
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23
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Ng CF, Frieboes HB. Simulation of Multispecies Desmoplastic Cancer Growth via a Fully Adaptive Non-linear Full Multigrid Algorithm. Front Physiol 2018; 9:821. [PMID: 30050447 PMCID: PMC6052761 DOI: 10.3389/fphys.2018.00821] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2018] [Accepted: 06/12/2018] [Indexed: 12/28/2022] Open
Abstract
A fully adaptive non-linear full multigrid (FMG) algorithm is implemented to computationally simulate a model of multispecies desmoplastic tumor growth in three spatial dimensions. The algorithm solves a thermodynamic mixture model employing a diffuse interface approach with Cahn-Hilliard-type fourth-order equations that are coupled, non-linear, and numerically stiff. The tumor model includes extracellular matrix (ECM) as a major component with elastic energy contribution in its chemical potential term. Blood and lymphatic vasculatures are simulated via continuum representations. The model employs advection-reaction-diffusion partial differential equations (PDEs) for the cell, ECM, and vascular components, and reaction-diffusion PDEs for the elements diffusing from the vessels. This study provides the details of the numerical solution obtained by applying the fully adaptive non-linear FMG algorithm with finite difference method to solve this complex system of PDEs. The results indicate that this type of computational model can simulate the extracellular matrix-rich desmoplastic tumor microenvironment typical of fibrotic tumors, such as pancreatic adenocarcinoma.
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Affiliation(s)
- Chin F. Ng
- Department of Bioengineering, University of Louisville, Louisville, KY, United States
| | - Hermann B. Frieboes
- Department of Bioengineering, University of Louisville, Louisville, KY, United States
- James Graham Brown Cancer Center, University of Louisville, Louisville, KY, United States
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24
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Alfonso JCL, Talkenberger K, Seifert M, Klink B, Hawkins-Daarud A, Swanson KR, Hatzikirou H, Deutsch A. The biology and mathematical modelling of glioma invasion: a review. J R Soc Interface 2018; 14:rsif.2017.0490. [PMID: 29118112 DOI: 10.1098/rsif.2017.0490] [Citation(s) in RCA: 112] [Impact Index Per Article: 18.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Accepted: 10/17/2017] [Indexed: 12/13/2022] Open
Abstract
Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion.
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Affiliation(s)
- J C L Alfonso
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany.,Centre for Information Services and High Performance Computing, Technische Universität Dresden, Germany
| | - K Talkenberger
- Centre for Information Services and High Performance Computing, Technische Universität Dresden, Germany
| | - M Seifert
- Institute for Medical Informatics and Biometry, Technische Universität Dresden, Germany.,National Center for Tumor Diseases (NCT), Dresden, Germany
| | - B Klink
- Institute for Clinical Genetics, Faculty of Medicine Carl Gustav Carus, Technische Universität Dresden, Germany.,National Center for Tumor Diseases (NCT), Dresden, Germany.,German Cancer Consortium (DKTK), partner site, Dresden, Germany.,German Cancer Research Center (DKFZ), Heidelberg, Germany
| | - A Hawkins-Daarud
- Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - K R Swanson
- Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - H Hatzikirou
- Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany.,Centre for Information Services and High Performance Computing, Technische Universität Dresden, Germany
| | - A Deutsch
- Centre for Information Services and High Performance Computing, Technische Universität Dresden, Germany
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25
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Immunohistochemical Characterization of Immune Cell Infiltration in Feline Glioma. J Comp Pathol 2018; 160:15-22. [DOI: 10.1016/j.jcpa.2018.02.003] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2017] [Revised: 01/16/2018] [Accepted: 02/22/2018] [Indexed: 12/15/2022]
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26
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Ozdemir-Kaynak E, Qutub AA, Yesil-Celiktas O. Advances in Glioblastoma Multiforme Treatment: New Models for Nanoparticle Therapy. Front Physiol 2018; 9:170. [PMID: 29615917 PMCID: PMC5868458 DOI: 10.3389/fphys.2018.00170] [Citation(s) in RCA: 92] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 02/20/2018] [Indexed: 11/30/2022] Open
Abstract
The most lethal form of brain cancer, glioblastoma multiforme, is characterized by rapid growth and invasion facilitated by cell migration and degradation of the extracellular matrix. Despite technological advances in surgery and radio-chemotherapy, glioblastoma remains largely resistant to treatment. New approaches to study glioblastoma and to design optimized therapies are greatly needed. One such approach harnesses computational modeling to support the design and delivery of glioblastoma treatment. In this paper, we critically summarize current glioblastoma therapy, with a focus on emerging nanomedicine and therapies that capitalize on cell-specific signaling in glioblastoma. We follow this summary by discussing computational modeling approaches focused on optimizing these emerging nanotherapeutics for brain cancer. We conclude by illustrating how mathematical analysis can be used to compare the delivery of a high potential anticancer molecule, delphinidin, in both free and nanoparticle loaded forms across the blood-brain barrier for glioblastoma.
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Affiliation(s)
- Elif Ozdemir-Kaynak
- Department of Bioengineering, Faculty of Engineering, Ege University, Bornova-Izmir, Turkey
| | - Amina A Qutub
- Department of Bioengineering, Rice University, Houston, TX, United States
| | - Ozlem Yesil-Celiktas
- Department of Bioengineering, Faculty of Engineering, Ege University, Bornova-Izmir, Turkey.,Biomaterials Innovation Research Center, Division of Biomedical Engineering, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States.,Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA, United States
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27
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Grogan JA, Connor AJ, Pitt-Francis JM, Maini PK, Byrne HM. The importance of geometry in the corneal micropocket angiogenesis assay. PLoS Comput Biol 2018; 14:e1006049. [PMID: 29522527 PMCID: PMC5862519 DOI: 10.1371/journal.pcbi.1006049] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2017] [Revised: 03/21/2018] [Accepted: 02/22/2018] [Indexed: 11/19/2022] Open
Abstract
The corneal micropocket angiogenesis assay is an experimental protocol for studying vessel network formation, or neovascularization, in vivo. The assay is attractive due to the ease with which the developing vessel network can be observed in the same animal over time. Measurements from the assay have been used in combination with mathematical modeling to gain insights into the mechanisms of angiogenesis. While previous modeling studies have adopted planar domains to represent the assay, the hemispherical shape of the cornea and asymmetric positioning of the angiogenic source can be seen to affect vascular patterning in experimental images. As such, we aim to better understand: i) how the geometry of the assay influences vessel network formation and ii) how to relate observations from planar domains to those in the hemispherical cornea. To do so, we develop a three-dimensional, off-lattice mathematical model of neovascularization in the cornea, using a spatially resolved representation of the assay for the first time. Relative to the detailed model, we predict that the adoption of planar geometries has a noticeable impact on vascular patterning, leading to increased vessel 'merging', or anastomosis, in particular when circular geometries are adopted. Significant differences in the dynamics of diffusible aniogenesis simulators are also predicted between different domains. In terms of comparing predictions across domains, the 'distance of the vascular front to the limbus' metric is found to have low sensitivity to domain choice, while metrics such as densities of tip cells and vessels and 'vascularized fraction' are sensitive to domain choice. Given the widespread adoption and attractive simplicity of planar tissue domains, both in silico and in vitro, the differences identified in the present study should prove useful in relating the results of previous and future theoretical studies of neovascularization to in vivo observations in the cornea.
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Affiliation(s)
- James A. Grogan
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Anthony J. Connor
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Joe M. Pitt-Francis
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Philip K. Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Helen M. Byrne
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
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28
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The Evolution of Tumour Composition During Fractionated Radiotherapy: Implications for Outcome. Bull Math Biol 2018; 80:1207-1235. [PMID: 29488054 DOI: 10.1007/s11538-018-0391-9] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Accepted: 01/08/2018] [Indexed: 01/29/2023]
Abstract
Current protocols for delivering radiotherapy are based primarily on tumour stage and nodal and metastases status, even though it is well known that tumours and their microenvironments are highly heterogeneous. It is well established that the local oxygen tension plays an important role in radiation-induced cell death, with hypoxic tumour regions responding poorly to irradiation. Therefore, to improve radiation response, it is important to understand more fully the spatiotemporal distribution of oxygen within a growing tumour before and during fractionated radiation. To this end, we have extended a spatially resolved mathematical model of tumour growth, first proposed by Greenspan (Stud Appl Math 51:317-340, 1972), to investigate the effects of oxygen heterogeneity on radiation-induced cell death. In more detail, cell death due to radiation at each location in the tumour, as determined by the well-known linear-quadratic model, is assumed also to depend on the local oxygen concentration. The oxygen concentration is governed by a reaction-diffusion equation that is coupled to an integro-differential equation that determines the size of the assumed spherically symmetric tumour. We combine numerical and analytical techniques to investigate radiation response of tumours with different intratumoral oxygen distribution profiles. Model simulations reveal a rapid transient increase in hypoxia upon regrowth of the tumour spheroid post-irradiation. We investigate the response to different radiation fractionation schedules and identify a tumour-specific relationship between inter-fraction time and dose per fraction to achieve cure. The rich dynamics exhibited by the model suggest that spatial heterogeneity may be important for predicting tumour response to radiotherapy for clinical applications.
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29
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Nargis NN, Aldredge RC, Guy RD. The influence of soluble fragments of extracellular matrix (ECM) on tumor growth and morphology. Math Biosci 2017; 296:1-16. [PMID: 29208360 DOI: 10.1016/j.mbs.2017.11.014] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Revised: 11/22/2017] [Accepted: 11/30/2017] [Indexed: 01/27/2023]
Abstract
A major challenge in matrix-metalloproteinase (MMP) target validation and MMP-inhibitor-drug development for anti-cancer clinical trials is to better understand their complex roles (often competing with each other) in tumor progression. While there is extensive research on the growth-promoting effects of MMPs, the growth-inhibiting effects of MMPs has not been investigated thoroughly. So we develop a continuum model of tumor growth and invasion including chemotaxis and haptotaxis in order to examine the complex interaction between the tumor and its host microenvironment and to explore the inhibiting influence of the gradients of soluble fragments of extracellular matrix (ECM) density on tumor growth and morphology. Previously, it was shown both computationally (in one spatial dimension) and experimentally that the chemotactic pull due to soluble ECM gradients is anti-invasive, contrary to the traditional view of the role of chemotaxis in malignant invasion [1]. With two-dimensional numerical simulation and using a level set based tumor-host interface capturing method, we examine the effects of chemotaxis on the progression and morphology of a tumor growing in nutrient-rich and nutrient-poor microenvironments which was not investigated before. In particular we examine how the geometry of the growing tumor is affected when placed in different environments. We also investigate the effects of varying ECM degradation rate, the production rate of matrix degrading enzymes (MDE), and the conversion of ECM into soluble ECM. We find that chemotaxis due to ECM-fragment gradients strongly influences tumor growth and morphology, and that the instabilities caused by tumor cell proliferation and haptotactic movements can be prevented if chemotaxis is sufficiently strong. The influence of chemotaxis and the above factors on tumor growth and morphology are found to be more prominent in nutrient-poor environments than in nutrient-rich environments. So we extend our investigations of these antinvasive chemotactic influences by examining the effects of cell-cell and cell-ECM adhesion and low proliferation rate for tumors growing in low-nutrient environments. We find that as the extent of chemotaxis increases, the effects of adhesion on tumor growth and shape become negligible. Under conditions of low cell mitosis, chemotaxis may cause the tumor to shrink, as the extent of chemotaxis increases. Both stable and unstable tumor shrinkage are predicted by our model. Unexpectedly, in some cases chemotaxis may contribute toward developing instability where haptotaxis alone induces stable growth.
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Affiliation(s)
- Nurun N Nargis
- Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA
| | - Ralph C Aldredge
- Department of Mechanical and Aerospace Engineering, University of California, Davis, CA 95616, USA.
| | - Robert D Guy
- Department of Mathematics, University of California, Davis, CA 95616, USA
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30
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Ng CF, Frieboes HB. Model of vascular desmoplastic multispecies tumor growth. J Theor Biol 2017; 430:245-282. [PMID: 28529153 PMCID: PMC5614902 DOI: 10.1016/j.jtbi.2017.05.013] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2016] [Revised: 03/07/2017] [Accepted: 05/09/2017] [Indexed: 12/21/2022]
Abstract
We present a three-dimensional nonlinear tumor growth model composed of heterogeneous cell types in a multicomponent-multispecies system, including viable, dead, healthy host, and extra-cellular matrix (ECM) tissue species. The model includes the capability for abnormal ECM dynamics noted in tumor development, as exemplified by pancreatic ductal adenocarcinoma, including dense desmoplasia typically characterized by a significant increase of interstitial connective tissue. An elastic energy is implemented to provide elasticity to the connective tissue. Cancer-associated fibroblasts (myofibroblasts) are modeled as key contributors to this ECM remodeling. The tumor growth is driven by growth factors released by these stromal cells as well as by oxygen and glucose provided by blood vasculature which along with lymphatics are stimulated to proliferate in and around the tumor based on pro-angiogenic factors released by hypoxic tissue regions. Cellular metabolic processes are simulated, including respiration and glycolysis with lactate fermentation. The bicarbonate buffering system is included for cellular pH regulation. This model system may be of use to simulate the complex interactions between tumor and stromal cells as well as the associated ECM and vascular remodeling that typically characterize malignant cancers notorious for poor therapeutic response.
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Affiliation(s)
- Chin F Ng
- Department of Bioengineering, University of Louisville, Lutz Hall 419, KY 40208, USA
| | - Hermann B Frieboes
- Department of Bioengineering, University of Louisville, Lutz Hall 419, KY 40208, USA; James Graham Brown Cancer Center, University of Louisville, KY, USA.
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31
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Sultana S, Blatt JE, Gilles B, Rashid T, Audette MA. MRI-Based Medial Axis Extraction and Boundary Segmentation of Cranial Nerves Through Discrete Deformable 3D Contour and Surface Models. IEEE TRANSACTIONS ON MEDICAL IMAGING 2017; 36:1711-1721. [PMID: 28422682 DOI: 10.1109/tmi.2017.2693182] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This paper presents a segmentation technique to identify the medial axis and the boundary of cranial nerves. We utilize a 3-D deformable one-simplex discrete contour model to extract the medial axis of each cranial nerve. This contour model represents a collection of two-connected vertices linked by edges, where vertex position is determined by a Newtonian expression for vertex kinematics featuring internal and external forces, the latter of which include attractive forces toward the nerve medial axis. We exploit multiscale vesselness filtering and minimal path techniques in the medial axis extraction method, which also computes a radius estimate along the path. Once we have the medial axis and the radius function of a nerve, we identify the nerve surface using a two-simplex deformable model, which expands radially and can accommodate any nerve shape. As a result, the method proposed here combines the benefits of explicit contour and surface models, while also achieving a cornerstone for future work that will emphasize shape statistics, static collision with other critical structures, and tree-shape analysis.
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32
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Macklin P, Frieboes HB, Sparks JL, Ghaffarizadeh A, Friedman SH, Juarez EF, Jonckheere E, Mumenthaler SM. Progress Towards Computational 3-D Multicellular Systems Biology. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2017; 936:225-246. [PMID: 27739051 DOI: 10.1007/978-3-319-42023-3_12] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Tumors cannot be understood in isolation from their microenvironment. Tumor and stromal cells change phenotype based upon biochemical and biophysical inputs from their surroundings, even as they interact with and remodel the microenvironment. Cancer should be investigated as an adaptive, multicellular system in a dynamical microenvironment. Computational modeling offers the potential to detangle this complex system, but the modeling platform must ideally account for tumor heterogeneity, substrate and signaling factor biotransport, cell and tissue biophysics, tissue and vascular remodeling, microvascular and interstitial flow, and links between all these sub-systems. Such a platform should leverage high-throughput experimental data, while using open data standards for reproducibility. In this chapter, we review advances by our groups in these key areas, particularly in advanced models of tissue mechanics and interstitial flow, open source simulation software, high-throughput phenotypic screening, and multicellular data standards. In the future, we expect a transformation of computational cancer biology from individual groups modeling isolated parts of cancer, to coalitions of groups combining compatible tools to simulate the 3-D multicellular systems biology of cancer tissues.
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Affiliation(s)
- Paul Macklin
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, CA, USA.
| | - Hermann B Frieboes
- Department of Bioengineering, University of Louisville, Louisville, KY, USA
| | - Jessica L Sparks
- Department of Chemical, Paper, and Biomedical Engineering, Miami University, Oxford, OH, USA
| | - Ahmadreza Ghaffarizadeh
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, CA, USA
| | - Samuel H Friedman
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, CA, USA
| | - Edwin F Juarez
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, CA, USA.,Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA
| | - Edmond Jonckheere
- Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA
| | - Shannon M Mumenthaler
- Lawrence J. Ellison Institute for Transformative Medicine, University of Southern California, Los Angeles, CA, USA
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33
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Henares-Molina A, Benzekry S, Lara PC, García-Rojo M, Pérez-García VM, Martínez-González A. Non-standard radiotherapy fractionations delay the time to malignant transformation of low-grade gliomas. PLoS One 2017; 12:e0178552. [PMID: 28570587 PMCID: PMC5453550 DOI: 10.1371/journal.pone.0178552] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2017] [Accepted: 05/15/2017] [Indexed: 12/15/2022] Open
Abstract
Grade II gliomas are slowly growing primary brain tumors that affect mostly young patients. Cytotoxic therapies (radiotherapy and/or chemotherapy) are used initially only for patients having a bad prognosis. These therapies are planned following the “maximum dose in minimum time” principle, i. e. the same schedule used for high-grade brain tumors in spite of their very different behavior. These tumors transform after a variable time into high-grade gliomas, which significantly decreases the patient’s life expectancy. In this paper we study mathematical models describing the growth of grade II gliomas in response to radiotherapy. We find that protracted metronomic fractionations, i.e. therapeutical schedules enlarging the time interval between low-dose radiotherapy fractions, may lead to a better tumor control without an increase in toxicity. Other non-standard fractionations such as protracted or hypoprotracted schemes may also be beneficial. The potential survival improvement depends on the tumor’s proliferation rate and can be even of the order of years. A conservative metronomic scheme, still being a suboptimal treatment, delays the time to malignant progression by at least one year when compared to the standard scheme.
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Affiliation(s)
- Araceli Henares-Molina
- Department of Mathematics, University of Castilla-La Mancha, Ciudad Real, Castilla-La Mancha, Spain
| | - Sebastien Benzekry
- INRIA Bordeaux Sud-Ouest, team MONC, Institut de Mathematiques de Bordeaux, Bordeaux, Nouvelle-Aquitaine, France
| | - Pedro C Lara
- Department of Radiation Oncology, Negrín Las Palmas University Hospital, Las Palmas GC, Canarias, Spain
| | - Marcial García-Rojo
- Department of Pathology, Hospital de Jerez de la Frontera, Jerez de la Frontera, Cádiz, Spain
| | - Víctor M Pérez-García
- Department of Mathematics, University of Castilla-La Mancha, Ciudad Real, Castilla-La Mancha, Spain
| | - Alicia Martínez-González
- Department of Mathematics, University of Castilla-La Mancha, Ciudad Real, Castilla-La Mancha, Spain
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34
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Rutter EM, Stepien TL, Anderies BJ, Plasencia JD, Woolf EC, Scheck AC, Turner GH, Liu Q, Frakes D, Kodibagkar V, Kuang Y, Preul MC, Kostelich EJ. Mathematical Analysis of Glioma Growth in a Murine Model. Sci Rep 2017; 7:2508. [PMID: 28566701 PMCID: PMC5451439 DOI: 10.1038/s41598-017-02462-0] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Accepted: 03/13/2017] [Indexed: 11/21/2022] Open
Abstract
Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm3 to 62 mm3, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.
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Affiliation(s)
- Erica M Rutter
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA. .,Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, 27695, USA.
| | - Tracy L Stepien
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA.,Department of Mathematics, Univeristy of Arizona, Tucson, AZ, 85721, USA
| | - Barrett J Anderies
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA.,School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, 85287, USA
| | - Jonathan D Plasencia
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, 85287, USA
| | - Eric C Woolf
- School of Life Sciences, Arizona State University, Tempe, AZ, 85287, USA.,Neuro-Oncology Research, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, USA
| | - Adrienne C Scheck
- School of Life Sciences, Arizona State University, Tempe, AZ, 85287, USA.,Neuro-Oncology Research, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, USA.,Department of Neurosurgery, Neurosurgery Research Lab, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, USA
| | - Gregory H Turner
- BNI-ASU Center for Preclinical Imaging, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, USA
| | - Qingwei Liu
- BNI-ASU Center for Preclinical Imaging, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, USA
| | - David Frakes
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, 85287, USA
| | - Vikram Kodibagkar
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, 85287, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
| | - Mark C Preul
- Department of Neurosurgery, Neurosurgery Research Lab, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ, USA
| | - Eric J Kostelich
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA
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35
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Tennill TA, Gross ME, Frieboes HB. Automated analysis of co-localized protein expression in histologic sections of prostate cancer. PLoS One 2017; 12:e0178362. [PMID: 28552967 PMCID: PMC5446169 DOI: 10.1371/journal.pone.0178362] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2017] [Accepted: 05/11/2017] [Indexed: 12/13/2022] Open
Abstract
An automated approach based on routinely-processed, whole-slide immunohistochemistry (IHC) was implemented to study co-localized protein expression in tissue samples. Expression of two markers was chosen to represent stromal (CD31) and epithelial (Ki-67) compartments in prostate cancer. IHC was performed on whole-slide sections representing low-, intermediate-, and high-grade disease from 15 patients. The automated workflow was developed using a training set of regions-of-interest in sequential tissue sections. Protein expression was studied on digital representations of IHC images across entire slides representing formalin-fixed paraffin embedded blocks. Using the training-set, the known association between Ki-67 and Gleason grade was confirmed. CD31 expression was more heterogeneous across samples and remained invariant with grade in this cohort. Interestingly, the Ki-67/CD31 ratio was significantly increased in high (Gleason ≥ 8) versus low/intermediate (Gleason ≤7) samples when assessed in the training-set and the whole-tissue block images. Further, the feasibility of the automated approach to process Tissue Microarray (TMA) samples in high throughput was evaluated. This work establishes an initial framework for automated analysis of co-localized protein expression and distribution in high-resolution digital microscopy images based on standard IHC techniques. Applied to a larger sample population, the approach may help to elucidate the biologic basis for the Gleason grade, which is the strongest, single factor distinguishing clinically aggressive from indolent prostate cancer.
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Affiliation(s)
- Thomas A. Tennill
- Department of Bioengineering, University of Louisville, Louisville, KY, United States of America
| | - Mitchell E. Gross
- Lawrence J. Elliston Institute for Transformational Medicine, University of Southern California, Los Angeles, CA, United States of America
| | - Hermann B. Frieboes
- Department of Bioengineering, University of Louisville, Louisville, KY, United States of America
- James Graham Brown Cancer Center, University of Louisville, Louisville, KY, United States of America
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36
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Grogan JA, Connor AJ, Markelc B, Muschel RJ, Maini PK, Byrne HM, Pitt-Francis JM. Microvessel Chaste: An Open Library for Spatial Modeling of Vascularized Tissues. Biophys J 2017; 112:1767-1772. [PMID: 28494948 PMCID: PMC5425404 DOI: 10.1016/j.bpj.2017.03.036] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2016] [Revised: 02/22/2017] [Accepted: 03/27/2017] [Indexed: 11/29/2022] Open
Abstract
Spatial models of vascularized tissues are widely used in computational physiology. We introduce a software library for composing multiscale, multiphysics models for applications including tumor growth, angiogenesis, osteogenesis, coronary perfusion, and oxygen delivery. Composition of such models is time consuming, with many researchers writing custom software. Recent advances in imaging have produced detailed three-dimensional (3D) datasets of vascularized tissues at the scale of individual cells. To fully exploit such data there is an increasing need for software that allows user-friendly composition of efficient, 3D models of vascularized tissues, and comparison of predictions with in vivo or in vitro experiments and alternative computational formulations. Microvessel Chaste can be used to build simulations of vessel growth and adaptation in response to mechanical and chemical stimuli; intra- and extravascular transport of nutrients, growth factors and drugs; and cell proliferation in complex 3D geometries. In addition, it can be used to develop custom software for integrating modeling with experimental data processing workflows, facilitated by a comprehensive Python interface to solvers implemented in C++. This article links to two reproducible example problems, showing how the library can be used to build simulations of tumor growth and angiogenesis with realistic vessel networks.
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Affiliation(s)
- James A Grogan
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom.
| | - Anthony J Connor
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom; Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Bostjan Markelc
- CRUK/MRC Oxford Institute for Radiation Oncology, University of Oxford, Oxford, United Kingdom
| | - Ruth J Muschel
- CRUK/MRC Oxford Institute for Radiation Oncology, University of Oxford, Oxford, United Kingdom
| | - Philip K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Helen M Byrne
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Joe M Pitt-Francis
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
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Stamatakos GS, Giatili SG. A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects. Cancer Inform 2017; 16:1176935116684824. [PMID: 28469383 PMCID: PMC5392020 DOI: 10.1177/1176935116684824] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2016] [Accepted: 11/24/2016] [Indexed: 12/22/2022] Open
Abstract
A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient's multiscale data and experimenting in silico (ie, on the computer).
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Affiliation(s)
- Georgios S Stamatakos
- In Silico Oncology and In Silico Medicine Group, Institute of Communication and Computer Systems, National Technical University of Athens, Zografou, Greece
| | - Stavroula G Giatili
- In Silico Oncology and In Silico Medicine Group, Institute of Communication and Computer Systems, National Technical University of Athens, Zografou, Greece
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38
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A Multiscale Mathematical Model of Tumour Invasive Growth. Bull Math Biol 2017; 79:389-429. [DOI: 10.1007/s11538-016-0237-2] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2015] [Accepted: 12/02/2016] [Indexed: 10/20/2022]
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39
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Modeling tumor growth with peridynamics. Biomech Model Mechanobiol 2017; 16:1141-1157. [DOI: 10.1007/s10237-017-0876-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2016] [Accepted: 01/11/2017] [Indexed: 12/30/2022]
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40
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Alfonso JCL, Köhn-Luque A, Stylianopoulos T, Feuerhake F, Deutsch A, Hatzikirou H. Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights. Sci Rep 2016; 6:37283. [PMID: 27876890 PMCID: PMC5120360 DOI: 10.1038/srep37283] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Accepted: 10/26/2016] [Indexed: 12/18/2022] Open
Abstract
Gliomas are highly invasive brain tumours characterised by poor prognosis and limited response to therapy. There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve tumour blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation induced by blood vessel occlusion/collapse. In contrast, the therapeutic intention of normalising the abnormal tumour vasculature is to improve the efficacy of conventional treatment modalities. Although these strategies have shown therapeutic potential, it remains unclear why they both often fail to control glioma growth. To shed some light on this issue, we propose a mathematical model based on the migration/proliferation dichotomy of glioma cells in order to investigate why vaso-modulatory interventions have shown limited success in terms of tumour clearance. We found the existence of a critical cell proliferation/diffusion ratio that separates glioma responses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the front speed and increase the infiltration width, for those in the other regime, the invasion speed increases and infiltration width decreases. We discuss how these in silico findings can be used to guide individualised vaso-modulatory approaches to improve treatment success rates.
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Affiliation(s)
- J C L Alfonso
- Braunschweig Integrated Centre of Systems Biology and Helmholtz Center for Infectious Research, Braunschweig, Germany.,Center for Information Services and High Performance Computing, Technische Universität Dresden, Germany
| | - A Köhn-Luque
- Department of Biostatistics, Faculty of Medicine, University of Oslo, Norway.,BigInsight, Centre for Research-based Innovation (SFI), Oslo, Norway
| | - T Stylianopoulos
- Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
| | - F Feuerhake
- Institute of Pathology, Medical School of Hannover, Germany.,Institute of Neuropathology, University Clinic Freiburg, Germany
| | - A Deutsch
- Center for Information Services and High Performance Computing, Technische Universität Dresden, Germany
| | - H Hatzikirou
- Braunschweig Integrated Centre of Systems Biology and Helmholtz Center for Infectious Research, Braunschweig, Germany
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41
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Tissue-scale, personalized modeling and simulation of prostate cancer growth. Proc Natl Acad Sci U S A 2016; 113:E7663-E7671. [PMID: 27856758 DOI: 10.1073/pnas.1615791113] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Recently, mathematical modeling and simulation of diseases and their treatments have enabled the prediction of clinical outcomes and the design of optimal therapies on a personalized (i.e., patient-specific) basis. This new trend in medical research has been termed "predictive medicine." Prostate cancer (PCa) is a major health problem and an ideal candidate to explore tissue-scale, personalized modeling of cancer growth for two main reasons: First, it is a small organ, and, second, tumor growth can be estimated by measuring serum prostate-specific antigen (PSA, a PCa biomarker in blood), which may enable in vivo validation. In this paper, we present a simple continuous model that reproduces the growth patterns of PCa. We use the phase-field method to account for the transformation of healthy cells to cancer cells and use diffusion-reaction equations to compute nutrient consumption and PSA production. To accurately and efficiently compute tumor growth, our simulations leverage isogeometric analysis (IGA). Our model is shown to reproduce a known shape instability from a spheroidal pattern to fingered growth. Results of our computations indicate that such shift is a tumor response to escape starvation, hypoxia, and, eventually, necrosis. Thus, branching enables the tumor to minimize the distance from inner cells to external nutrients, contributing to cancer survival and further development. We have also used our model to perform tissue-scale, personalized simulation of a PCa patient, based on prostatic anatomy extracted from computed tomography images. This simulation shows tumor progression similar to that seen in clinical practice.
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Chaddad A, Desrosiers C, Hassan L, Tanougast C. A quantitative study of shape descriptors from glioblastoma multiforme phenotypes for predicting survival outcome. Br J Radiol 2016; 89:20160575. [PMID: 27781499 DOI: 10.1259/bjr.20160575] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
OBJECTIVE Predicting the survival outcome of patients with glioblastoma multiforme (GBM) is of key importance to clinicians for selecting the optimal course of treatment. The goal of this study was to evaluate the usefulness of geometric shape features, extracted from MR images, as a potential non-invasive way to characterize GBM tumours and predict the overall survival times of patients with GBM. METHODS The data of 40 patients with GBM were obtained from the Cancer Genome Atlas and Cancer Imaging Archive. The T1 weighted post-contrast and fluid-attenuated inversion-recovery volumes of patients were co-registered and segmented into delineate regions corresponding to three GBM phenotypes: necrosis, active tumour and oedema/invasion. A set of two-dimensional shape features were then extracted slicewise from each phenotype region and combined over slices to describe the three-dimensional shape of these phenotypes. Thereafter, a Kruskal-Wallis test was employed to identify shape features with significantly different distributions across phenotypes. Moreover, a Kaplan-Meier analysis was performed to find features strongly associated with GBM survival. Finally, a multivariate analysis based on the random forest model was used for predicting the survival group of patients with GBM. RESULTS Our analysis using the Kruskal-Wallis test showed that all but one shape feature had statistically significant differences across phenotypes, with p-value < 0.05, following Holm-Bonferroni correction, justifying the analysis of GBM tumour shapes on a per-phenotype basis. Furthermore, the survival analysis based on the Kaplan-Meier estimator identified three features derived from necrotic regions (i.e. Eccentricity, Extent and Solidity) that were significantly correlated with overall survival (corrected p-value < 0.05; hazard ratios between 1.68 and 1.87). In the multivariate analysis, features from necrotic regions gave the highest accuracy in predicting the survival group of patients, with a mean area under the receiver-operating characteristic curve (AUC) of 63.85%. Combining the features of all three phenotypes increased the mean AUC to 66.99%, suggesting that shape features from different phenotypes can be used in a synergic manner to predict GBM survival. CONCLUSION Results show that shape features, in particular those extracted from necrotic regions, can be used effectively to characterize GBM tumours and predict the overall survival of patients with GBM. Advances in knowledge: Simple volumetric features have been largely used to characterize the different phenotypes of a GBM tumour (i.e. active tumour, oedema and necrosis). This study extends previous work by considering a wide range of shape features, extracted in different phenotypes, for the prediction of survival in patients with GBM.
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Affiliation(s)
- Ahmad Chaddad
- 1 Laboratory for Imagery, Vision and Artificial Intelligence, University of Québec, École de Technologie Supérieure, Montréal, QC, Canada.,2 Laboratory of Conception, Optimization and Modeling of Systems, University of Lorraine, Metz, Lorraine, France
| | - Christian Desrosiers
- 1 Laboratory for Imagery, Vision and Artificial Intelligence, University of Québec, École de Technologie Supérieure, Montréal, QC, Canada
| | - Lama Hassan
- 1 Laboratory for Imagery, Vision and Artificial Intelligence, University of Québec, École de Technologie Supérieure, Montréal, QC, Canada.,2 Laboratory of Conception, Optimization and Modeling of Systems, University of Lorraine, Metz, Lorraine, France
| | - Camel Tanougast
- 2 Laboratory of Conception, Optimization and Modeling of Systems, University of Lorraine, Metz, Lorraine, France
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43
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Yan H, Romero-Lopez M, Frieboes HB, Hughes CCW, Lowengrub JS. Multiscale Modeling of Glioblastoma Suggests that the Partial Disruption of Vessel/Cancer Stem Cell Crosstalk Can Promote Tumor Regression Without Increasing Invasiveness. IEEE Trans Biomed Eng 2016; 64:538-548. [PMID: 27723576 DOI: 10.1109/tbme.2016.2615566] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
OBJECTIVE In glioblastoma, the crosstalk between vascular endothelial cells (VECs) and glioma stem cells (GSCs) has been shown to enhance tumor growth. We propose a multiscale mathematical model to study this mechanism, explore tumor growth under various initial and microenvironmental conditions, and investigate the effects of blocking this crosstalk. METHODS We develop a hybrid continuum-discrete model of highly organized vascularized tumors. VEC-GSC crosstalk is modeled via vascular endothelial growth factor (VEGF) production by tumor cells and by secretion of soluble factors by VECs that promote GSC self-renewal and proliferation. RESULTS VEC-GSC crosstalk increases both tumor size and GSC fraction by enhancing GSC activity and neovascular development. VEGF promotes vessel formation, and larger VEGF sources typically increase vessel numbers, which enhances tumor growth and stabilizes the tumor shape. Increasing the initial GSC fraction has a similar effect. Partially disrupting the crosstalk by blocking VEC secretion of GSC promoters reduces tumor size but does not increase invasiveness, which is in contrast to antiangiogenic therapies, which reduce tumor size but may significantly increase tumor invasiveness. SIGNIFICANCE Multiscale modeling supports the targeting of VEC-GSC crosstalk as a promising approach for cancer therapy.
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44
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Lyu J, Cao J, Zhang P, Liu Y, Cheng H. Coupled Hybrid Continuum-Discrete Model of Tumor Angiogenesis and Growth. PLoS One 2016; 11:e0163173. [PMID: 27701426 PMCID: PMC5049767 DOI: 10.1371/journal.pone.0163173] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Accepted: 08/04/2016] [Indexed: 11/18/2022] Open
Abstract
The processes governing tumor growth and angiogenesis are codependent. To study the relationship between them, we proposed a coupled hybrid continuum-discrete model. In this model, tumor cells, their microenvironment (extracellular matrixes, matrix-degrading enzymes, and tumor angiogenic factors), and their network of blood vessels, described by a series of discrete points, were considered. The results of numerical simulation reveal the process of tumor growth and the change in microenvironment from avascular to vascular stage, indicating that the network of blood vessels develops gradually as the tumor grows. Our findings also reveal that a tumor is divided into three regions: necrotic, semi-necrotic, and well-vascularized. The results agree well with the previous relevant studies and physiological facts, and this model represents a platform for further investigations of tumor therapy.
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Affiliation(s)
- Jie Lyu
- Medical Instrumentation School, Shanghai University of Medicine and Health Sciences, Shanghai, 201318, China
| | - Jinfeng Cao
- Periodicals Agency, Shanghai University, Shanghai, 200444, China
- * E-mail:
| | - Peiming Zhang
- Medical Instrumentation School, Shanghai University of Medicine and Health Sciences, Shanghai, 201318, China
| | - Yang Liu
- Medical Instrumentation School, Shanghai University of Medicine and Health Sciences, Shanghai, 201318, China
| | - Hongtao Cheng
- Medical Instrumentation School, Shanghai University of Medicine and Health Sciences, Shanghai, 201318, China
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45
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Xu J, Vilanova G, Gomez H. A Mathematical Model Coupling Tumor Growth and Angiogenesis. PLoS One 2016; 11:e0149422. [PMID: 26891163 PMCID: PMC4758654 DOI: 10.1371/journal.pone.0149422] [Citation(s) in RCA: 58] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2015] [Accepted: 01/31/2016] [Indexed: 11/21/2022] Open
Abstract
We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments.
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Affiliation(s)
- Jiangping Xu
- Applied Mathematics, University of A Coruña, A Coruña, Spain
| | | | - Hector Gomez
- Applied Mathematics, University of A Coruña, A Coruña, Spain
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46
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Raman F, Scribner E, Saut O, Wenger C, Colin T, Fathallah-Shaykh HM. Computational Trials: Unraveling Motility Phenotypes, Progression Patterns, and Treatment Options for Glioblastoma Multiforme. PLoS One 2016; 11:e0146617. [PMID: 26756205 PMCID: PMC4710507 DOI: 10.1371/journal.pone.0146617] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2015] [Accepted: 12/18/2015] [Indexed: 12/02/2022] Open
Abstract
Glioblastoma multiforme is a malignant brain tumor with poor prognosis and high morbidity due to its invasiveness. Hypoxia-driven motility and concentration-driven motility are two mechanisms of glioblastoma multiforme invasion in the brain. The use of anti-angiogenic drugs has uncovered new progression patterns of glioblastoma multiforme associated with significant differences in overall survival. Here, we apply a mathematical model of glioblastoma multiforme growth and invasion in humans and design computational trials using agents that target angiogenesis, tumor replication rates, or motility. The findings link highly-dispersive, moderately-dispersive, and hypoxia-driven tumors to the patterns observed in glioblastoma multiforme treated by anti-angiogenesis, consisting of progression by Expanding FLAIR, Expanding FLAIR + Necrosis, and Expanding Necrosis, respectively. Furthermore, replication rate-reducing strategies (e.g. Tumor Treating Fields) appear to be effective in highly-dispersive and moderately-dispersive tumors but not in hypoxia-driven tumors. The latter may respond to motility-reducing agents. In a population computational trial, with all three phenotypes, a correlation was observed between the efficacy of the rate-reducing agent and the prolongation of overall survival times. This research highlights the potential applications of computational trials and supports new hypotheses on glioblastoma multiforme phenotypes and treatment options.
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Affiliation(s)
- Fabio Raman
- The University of Alabama, Birmingham, Department of Biomedical Engineering, Birmingham, Alabama, United States of America
| | - Elizabeth Scribner
- The University of Alabama, Birmingham, Department of Mathematics, Birmingham, Alabama, United States of America
| | - Olivier Saut
- The University of Bordeaux, Department of Mathematics, Talence, France
| | - Cornelia Wenger
- Universidade de Lisboa, Faculdade de Ciências da Universidade de Lisboa, Institute of Biophysics and Biomedical Engineering, Lisboa, Portugal
| | - Thierry Colin
- The University of Bordeaux, Department of Mathematics, Talence, France
| | - Hassan M. Fathallah-Shaykh
- The University of Alabama, Birmingham, Department of Biomedical Engineering, Birmingham, Alabama, United States of America
- The University of Alabama, Birmingham, Department of Mathematics, Birmingham, Alabama, United States of America
- The University of Alabama, Birmingham, Department of Neurology, Birmingham, Alabama, United States of America
- * E-mail:
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47
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Frieboes HB, Curtis LT, Wu M, Kani K, Mallick P. Simulation of the Protein-Shedding Kinetics of a Fully Vascularized Tumor. Cancer Inform 2015; 14:163-75. [PMID: 26715830 PMCID: PMC4687979 DOI: 10.4137/cin.s35374] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2015] [Revised: 11/09/2015] [Accepted: 11/15/2015] [Indexed: 12/12/2022] Open
Abstract
Circulating biomarkers are of significant interest for cancer detection and treatment personalization. However, the biophysical processes that determine how proteins are shed from cancer cells or their microenvironment, diffuse through tissue, enter blood vasculature, and persist in circulation remain poorly understood. Since approaches primarily focused on experimental evaluation are incapable of measuring the shedding and persistence for every possible marker candidate, we propose an interdisciplinary computational/experimental approach that includes computational modeling of tumor tissue heterogeneity. The model implements protein production, transport, and shedding based on tumor vascularization, cell proliferation, hypoxia, and necrosis, thus quantitatively relating the tumor and circulating proteomes. The results highlight the dynamics of shedding as a function of protein diffusivity and production. Linking the simulated tumor parameters to clinical tumor and vascularization measurements could potentially enable this approach to reveal the tumor-specific conditions based on the protein detected in circulation and thus help to more accurately manage cancer diagnosis and treatment.
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Affiliation(s)
- Hermann B Frieboes
- Department of Bioengineering, University of Louisville, Louisville, KY, USA. ; James Graham Brown Cancer Center, University of Louisville, Louisville, KY, USA
| | - Louis T Curtis
- Department of Bioengineering, University of Louisville, Louisville, KY, USA
| | - Min Wu
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Chicago, IL, USA
| | - Kian Kani
- Center for Applied Molecular Medicine, University of Southern California, Los Angeles, CA, USA
| | - Parag Mallick
- Canary Center at Stanford for Cancer Early Detection, Stanford University, Stanford, CA, USA
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48
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Sallemi L, Njeh I, Lehericy S. Towards a Computer Aided Prognosis for Brain Glioblastomas Tumor Growth Estimation. IEEE Trans Nanobioscience 2015; 14:727-33. [DOI: 10.1109/tnb.2015.2450365] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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49
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Martirosyan NL, Rutter EM, Ramey WL, Kostelich EJ, Kuang Y, Preul MC. Mathematically modeling the biological properties of gliomas: A review. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2015; 12:879-905. [PMID: 25974347 DOI: 10.3934/mbe.2015.12.879] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be difficult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the infiltrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their influence on the surrounding anatomical structures in the brain.
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50
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Colombo MC, Giverso C, Faggiano E, Boffano C, Acerbi F, Ciarletta P. Towards the Personalized Treatment of Glioblastoma: Integrating Patient-Specific Clinical Data in a Continuous Mechanical Model. PLoS One 2015; 10:e0132887. [PMID: 26186462 PMCID: PMC4505854 DOI: 10.1371/journal.pone.0132887] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2015] [Accepted: 06/22/2015] [Indexed: 12/31/2022] Open
Abstract
Glioblastoma multiforme (GBM) is the most aggressive and malignant among brain tumors. In addition to uncontrolled proliferation and genetic instability, GBM is characterized by a diffuse infiltration, developing long protrusions that penetrate deeply along the fibers of the white matter. These features, combined with the underestimation of the invading GBM area by available imaging techniques, make a definitive treatment of GBM particularly difficult. A multidisciplinary approach combining mathematical, clinical and radiological data has the potential to foster our understanding of GBM evolution in every single patient throughout his/her oncological history, in order to target therapeutic weapons in a patient-specific manner. In this work, we propose a continuous mechanical model and we perform numerical simulations of GBM invasion combining the main mechano-biological characteristics of GBM with the micro-structural information extracted from radiological images, i.e. by elaborating patient-specific Diffusion Tensor Imaging (DTI) data. The numerical simulations highlight the influence of the different biological parameters on tumor progression and they demonstrate the fundamental importance of including anisotropic and heterogeneous patient-specific DTI data in order to obtain a more accurate prediction of GBM evolution. The results of the proposed mathematical model have the potential to provide a relevant benefit for clinicians involved in the treatment of this particularly aggressive disease and, more importantly, they might drive progress towards improving tumor control and patient’s prognosis.
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Affiliation(s)
- Maria Cristina Colombo
- MOX-Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; Fondazione CEN, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Chiara Giverso
- MOX-Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; Fondazione CEN, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Elena Faggiano
- MOX-Department of Mathematics, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy; Labs-Department of Chemistry, Materials and Chemical Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Carlo Boffano
- Neuroradiology-Fondazione I.R.C.C.S. Istituto Neurologico Carlo Besta, Via Celoria 11, 20133 Milano, Italy
| | - Francesco Acerbi
- Department of Neurosurgery-Fondazione I.R.C.C.S. Istituto Neurologico Carlo Besta, Via Celoria 11, 20133 Milano, Italy
| | - Pasquale Ciarletta
- Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France
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