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O'Connor L, Lecoanet D, Anders EH, Augustson KC, Burns KJ, Vasil GM, Oishi JS, Brown BP. Iterative methods for Navier-Stokes inverse problems. Phys Rev E 2024; 109:045108. [PMID: 38755946 DOI: 10.1103/physreve.109.045108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 04/04/2024] [Indexed: 05/18/2024]
Abstract
Even when the partial differential equation underlying a physical process can be evolved forward in time, the retrospective (backward in time) inverse problem often has its own challenges and applications. Direct adjoint looping (DAL) is the defacto approach for solving retrospective inverse problems, but it has not been applied to deterministic retrospective Navier-Stokes inverse problems in 2D or 3D. In this paper, we demonstrate that DAL is ill-suited for solving retrospective 2D Navier-Stokes inverse problems. Alongside DAL, we study two other iterative methods: simple backward integration (SBI) and the quasireversible method (QRM). As far as we know, our iterative SBI approach is novel, while iterative QRM has previously been used. Using these three iterative methods, we solve two retrospective inverse problems: 1D Korteweg-de Vries-Burgers (decaying nonlinear wave) and 2D Navier-Stokes (unstratified Kelvin-Helmholtz vortex). In both cases, SBI and QRM reproduce the target final states more accurately and in fewer iterations than DAL. We attribute this performance gap to additional terms present in SBI and QRM's respective backward integrations which are absent in DAL.
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Affiliation(s)
- Liam O'Connor
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
- Center for Interdisciplinary Exploration and Research in Astrophysics, Northwestern University, Evanston, Illinois 60201, USA
| | - Daniel Lecoanet
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
- Center for Interdisciplinary Exploration and Research in Astrophysics, Northwestern University, Evanston, Illinois 60201, USA
| | - Evan H Anders
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - Kyle C Augustson
- Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA
- Center for Interdisciplinary Exploration and Research in Astrophysics, Northwestern University, Evanston, Illinois 60201, USA
| | - Keaton J Burns
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA
| | - Geoffrey M Vasil
- School of Mathematics, Edinburgh University, EH9 3FD, United Kingdom
| | - Jeffrey S Oishi
- Department of Physics and Astronomy, Bates College, Lewiston, Maine 04240, USA
| | - Benjamin P Brown
- Department of Astrophysical and Planetary Sciences, University of Colorado Boulder, Boulder, Colorado 80309, USA
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2
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Chaudhuri A, Pash G, Hormuth DA, Lorenzo G, Kapteyn M, Wu C, Lima EABF, Yankeelov TE, Willcox K. Predictive digital twin for optimizing patient-specific radiotherapy regimens under uncertainty in high-grade gliomas. Front Artif Intell 2023; 6:1222612. [PMID: 37886348 PMCID: PMC10598726 DOI: 10.3389/frai.2023.1222612] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2023] [Accepted: 09/07/2023] [Indexed: 10/28/2023] Open
Abstract
We develop a methodology to create data-driven predictive digital twins for optimal risk-aware clinical decision-making. We illustrate the methodology as an enabler for an anticipatory personalized treatment that accounts for uncertainties in the underlying tumor biology in high-grade gliomas, where heterogeneity in the response to standard-of-care (SOC) radiotherapy contributes to sub-optimal patient outcomes. The digital twin is initialized through prior distributions derived from population-level clinical data in the literature for a mechanistic model's parameters. Then the digital twin is personalized using Bayesian model calibration for assimilating patient-specific magnetic resonance imaging data. The calibrated digital twin is used to propose optimal radiotherapy treatment regimens by solving a multi-objective risk-based optimization under uncertainty problem. The solution leads to a suite of patient-specific optimal radiotherapy treatment regimens exhibiting varying levels of trade-off between the two competing clinical objectives: (i) maximizing tumor control (characterized by minimizing the risk of tumor volume growth) and (ii) minimizing the toxicity from radiotherapy. The proposed digital twin framework is illustrated by generating an in silico cohort of 100 patients with high-grade glioma growth and response properties typically observed in the literature. For the same total radiation dose as the SOC, the personalized treatment regimens lead to median increase in tumor time to progression of around six days. Alternatively, for the same level of tumor control as the SOC, the digital twin provides optimal treatment options that lead to a median reduction in radiation dose by 16.7% (10 Gy) compared to SOC total dose of 60 Gy. The range of optimal solutions also provide options with increased doses for patients with aggressive cancer, where SOC does not lead to sufficient tumor control.
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Affiliation(s)
- Anirban Chaudhuri
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
| | - Graham Pash
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
| | - David A. Hormuth
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX, United States
| | - Guillermo Lorenzo
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
- Department of Civil Engineering and Architecture, University of Pavia, Pavia, Italy
| | - Michael Kapteyn
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
| | - Chengyue Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
| | - Ernesto A. B. F. Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
- Texas Advanced Computing Center, The University of Texas at Austin, Austin, TX, United States
| | - Thomas E. Yankeelov
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, TX, United States
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX, United States
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, TX, United States
- Department of Oncology, The University of Texas at Austin, Austin, TX, United States
- Department of Imaging Physics, MD Anderson Cancer Center, Houston, TX, United States
| | - Karen Willcox
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, United States
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3
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Subramanian S, Ghafouri A, Scheufele KM, Himthani N, Davatzikos C, Biros G. Ensemble Inversion for Brain Tumor Growth Models With Mass Effect. IEEE TRANSACTIONS ON MEDICAL IMAGING 2023; 42:982-995. [PMID: 36378796 PMCID: PMC10201550 DOI: 10.1109/tmi.2022.3221913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We propose a method for extracting physics-based biomarkers from a single multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor. We account for mass effect, the deformation of brain parenchyma due to the growing tumor, which on its own is an important radiographic feature but its automatic quantification remains an open problem. In particular, we calibrate a partial differential equation (PDE) tumor growth model that captures mass effect, parameterized by a single scalar parameter, tumor proliferation, migration, while localizing the tumor initiation site. The single-scan calibration problem is severely ill-posed because the precancerous, healthy, brain anatomy is unknown. To address the ill-posedness, we introduce an ensemble inversion scheme that uses a number of normal subject brain templates as proxies for the healthy precancer subject anatomy. We verify our solver on a synthetic dataset and perform a retrospective analysis on a clinical dataset of 216 glioblastoma (GBM) patients. We analyze the reconstructions using our calibrated biophysical model and demonstrate that our solver provides both global and local quantitative measures of tumor biophysics and mass effect. We further highlight the improved performance in model calibration through the inclusion of mass effect in tumor growth models-including mass effect in the model leads to 10% increase in average dice coefficients for patients with significant mass effect. We further evaluate our model by introducing novel biophysics-based features and using them for survival analysis. Our preliminary analysis suggests that including such features can improve patient stratification and survival prediction.
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Phillips CM, Lima EABF, Gadde M, Jarrett AM, Rylander MN, Yankeelov TE. Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis. PLoS Comput Biol 2023; 19:e1009499. [PMID: 36652468 PMCID: PMC9886306 DOI: 10.1371/journal.pcbi.1009499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Revised: 01/30/2023] [Accepted: 12/13/2022] [Indexed: 01/19/2023] Open
Abstract
The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively. These parameters are then input into the multiscale tumor angiogenesis model, and the remaining model parameters are then calibrated to time resolved confocal microscopy images obtained within a 3D vascularized microfluidic platform. The microfluidic platform mimics a functional blood vessel with a surrounding collagen matrix seeded with inflammatory breast cancer cells, which induce tumor angiogenesis. Once the multi-scale model is fully parameterized, we forecast the spatiotemporal distribution of vascular sprouts at future time points and directly compare the predictions to experimentally measured data. We assess the ability of our model to globally recapitulate angiogenic vasculature density, resulting in an average relative calibration error of 17.7% ± 6.3% and an average prediction error of 20.2% ± 4% and 21.7% ± 3.6% using one and four calibrated parameters, respectively. We then assess the model's ability to predict local vessel morphology (individualized vessel structure as opposed to global vascular density), initialized with the first time point and calibrated with two intermediate time points. In this study, we have rigorously calibrated a mechanism-based, multiscale, mathematical model of angiogenic sprouting to multimodal experimental data to make specific, testable predictions.
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Affiliation(s)
- Caleb M. Phillips
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
| | - Ernesto A. B. F. Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Texas Advanced Computing Center, The University of Texas at Austin, Austin, Texas, United States of America
- * E-mail:
| | - Manasa Gadde
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
| | - Angela M. Jarrett
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, Texas, United States of America
| | - Marissa Nichole Rylander
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas, United States of America
| | - Thomas E. Yankeelov
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Diagnostic Medicine, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Oncology, The University of Texas at Austin, Austin, Texas, United States of America
- Livestrong Cancer Institutes, The University of Texas at Austin, Austin, Texas, United States of America
- Department of Imaging Physics, The University of Texas at Austin, MD Anderson Cancer Center, Houston, Texas, United States of America
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5
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Ezhov I, Scibilia K, Franitza K, Steinbauer F, Shit S, Zimmer L, Lipkova J, Kofler F, Paetzold JC, Canalini L, Waldmannstetter D, Menten MJ, Metz M, Wiestler B, Menze B. Learn-Morph-Infer: A new way of solving the inverse problem for brain tumor modeling. Med Image Anal 2023; 83:102672. [PMID: 36395623 DOI: 10.1016/j.media.2022.102672] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2021] [Revised: 07/18/2022] [Accepted: 10/20/2022] [Indexed: 11/06/2022]
Abstract
Current treatment planning of patients diagnosed with a brain tumor, such as glioma, could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, e.g. magnetic resonance imaging (MRI), contrast sufficiently well areas of high cell density. In gliomas, however, they do not portray areas of low cell concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. To estimate tumor cell densities beyond the visible boundaries of the lesion, numerical simulations of tumor growth could complement imaging information by providing estimates of full spatial distributions of tumor cells. Over recent years a corpus of literature on medical image-based tumor modeling was published. It includes different mathematical formalisms describing the forward tumor growth model. Alongside, various parametric inference schemes were developed to perform an efficient tumor model personalization, i.e. solving the inverse problem. However, the unifying drawback of all existing approaches is the time complexity of the model personalization which prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a deep learning based methodology for inferring the patient-specific spatial distribution of brain tumors from T1Gd and FLAIR MRI medical scans. Coined as Learn-Morph-Infer, the method achieves real-time performance in the order of minutes on widely available hardware and the compute time is stable across tumor models of different complexity, such as reaction-diffusion and reaction-advection-diffusion models. We believe the proposed inverse solution approach not only bridges the way for clinical translation of brain tumor personalization but can also be adopted to other scientific and engineering domains.
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Affiliation(s)
- Ivan Ezhov
- Department of Informatics, TUM, Munich, Germany; TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany.
| | | | | | | | - Suprosanna Shit
- Department of Informatics, TUM, Munich, Germany; TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany
| | - Lucas Zimmer
- TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany; Department of Quantitative Biomedicine, UZH, Zurich, Switzerland
| | - Jana Lipkova
- Department of Pathology, Brigham and Women's Hospital, Harvard Medical School, Boston, USA; Broad Institute of Harvard and MIT, Cambridge, USA; Data Science Program, Dana-Farber Cancer Institute, Boston, USA
| | - Florian Kofler
- Department of Informatics, TUM, Munich, Germany; TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany; Neuroradiology Department of Klinikum Rechts der Isar, TUM, Munich, Germany
| | - Johannes C Paetzold
- Department of Informatics, TUM, Munich, Germany; TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany
| | | | | | - Martin J Menten
- Department of Informatics, TUM, Munich, Germany; TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany
| | - Marie Metz
- TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany; Neuroradiology Department of Klinikum Rechts der Isar, TUM, Munich, Germany
| | - Benedikt Wiestler
- TranslaTUM - Central Institute for Translational Cancer Research, TUM, Munich, Germany; Neuroradiology Department of Klinikum Rechts der Isar, TUM, Munich, Germany
| | - Bjoern Menze
- Department of Quantitative Biomedicine, UZH, Zurich, Switzerland
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6
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Martens C, Rovai A, Bonatto D, Metens T, Debeir O, Decaestecker C, Goldman S, Van Simaeys G. Deep Learning for Reaction-Diffusion Glioma Growth Modeling: Towards a Fully Personalized Model? Cancers (Basel) 2022; 14:cancers14102530. [PMID: 35626134 PMCID: PMC9139770 DOI: 10.3390/cancers14102530] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Revised: 05/11/2022] [Accepted: 05/18/2022] [Indexed: 11/30/2022] Open
Abstract
Simple Summary Mathematical tumor growth models have been proposed for decades to capture the growth of gliomas, an aggressive form of brain tumor. However, the estimation of the tumor cell-density distribution at diagnosis and model parameters from partial observations provided by magnetic resonance imaging are ill-posed problems. In this work, we propose a deep learning-based approach to address these problems. 1200 synthetic tumors are first generated using the mathematical model over brain geometries of 6 volunteers. Two deep convolutional neural networks are then trained to (i) reconstruct a whole tumor cell-density distribution and (ii) evaluate the model parameters from partial observations provided in the form of threshold-like imaging contours, with state-of-the-art results. From the estimated cell-density distribution and parameter values, the spatio-temporal evolution of the tumor can ultimately be accurately captured by the mathematical model. Such an approach could be of great interest for glioma characterization and therapy planning. Abstract Reaction-diffusion models have been proposed for decades to capture the growth of gliomas, the most common primary brain tumors. However, ill-posedness of the initialization at diagnosis time and parameter estimation of such models have restrained their clinical use as a personalized predictive tool. In this work, we investigate the ability of deep convolutional neural networks (DCNNs) to address commonly encountered pitfalls in the field. Based on 1200 synthetic tumors grown over real brain geometries derived from magnetic resonance (MR) data of six healthy subjects, we demonstrate the ability of DCNNs to reconstruct a whole tumor cell-density distribution from only two imaging contours at a single time point. With an additional imaging contour extracted at a prior time point, we also demonstrate the ability of DCNNs to accurately estimate the individual diffusivity and proliferation parameters of the model. From this knowledge, the spatio-temporal evolution of the tumor cell-density distribution at later time points can ultimately be precisely captured using the model. We finally show the applicability of our approach to MR data of a real glioblastoma patient. This approach may open the perspective of a clinical application of reaction-diffusion growth models for tumor prognosis and treatment planning.
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Affiliation(s)
- Corentin Martens
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
- Correspondence:
| | - Antonin Rovai
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
| | - Daniele Bonatto
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
| | - Thierry Metens
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
- Department of Radiology, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium
| | - Olivier Debeir
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
| | - Christine Decaestecker
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
- Laboratory of Image Synthesis and Analysis (LISA), École Polytechnique de Bruxelles, Université libre de Bruxelles, Avenue Franklin Roosevelt 50, 1050 Brussels, Belgium; (D.B.); (T.M.)
| | - Serge Goldman
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
| | - Gaetan Van Simaeys
- Department of Nuclear Medicine, Hôpital Erasme, Université libre de Bruxelles, Route de Lennik 808, 1070 Brussels, Belgium; (A.R.); (S.G.); (G.V.S.)
- Center for Microscopy and Molecular Imaging (CMMI), Université libre de Bruxelles, Rue Adrienne Bolland 8, 6041 Charleroi, Belgium; (O.D.); (C.D.)
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Lipková J, Menze B, Wiestler B, Koumoutsakos P, Lowengrub JS. Modelling glioma progression, mass effect and intracranial pressure in patient anatomy. J R Soc Interface 2022; 19:20210922. [PMID: 35317645 PMCID: PMC8941421 DOI: 10.1098/rsif.2021.0922] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Accepted: 02/21/2022] [Indexed: 02/06/2023] Open
Abstract
Increased intracranial pressure is the source of most critical symptoms in patients with glioma, and often the main cause of death. Clinical interventions could benefit from non-invasive estimates of the pressure distribution in the patient's parenchyma provided by computational models. However, existing glioma models do not simulate the pressure distribution and they rely on a large number of model parameters, which complicates their calibration from available patient data. Here we present a novel model for glioma growth, pressure distribution and corresponding brain deformation. The distinct feature of our approach is that the pressure is directly derived from tumour dynamics and patient-specific anatomy, providing non-invasive insights into the patient's state. The model predictions allow estimation of critical conditions such as intracranial hypertension, brain midline shift or neurological and cognitive impairments. A diffuse-domain formalism is employed to allow for efficient numerical implementation of the model in the patient-specific brain anatomy. The model is tested on synthetic and clinical cases. To facilitate clinical deployment, a high-performance computing implementation of the model has been publicly released.
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Affiliation(s)
- Jana Lipková
- Department of Pathology, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, USA
- Dana-Farber Cancer Institute, Boston, MA, USA
- Broad Institute of Harvard and MIT, Cambridge, MA, USA
| | - Bjoern Menze
- Department of Informatics, Technical University of Munich, Munich, Germany
- Department of Quantitative Biomedicine, University of Zürich, Zürich, Switzerland
- Department of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
| | - Benedikt Wiestler
- Department of Neuroradiology, Klinikum Rechts der Isar, Technical University of Munich, Munich, Germany
| | - Petros Koumoutsakos
- Computational Science and Engineering Lab, ETH Zürich, Zürich, Switzerland
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | - John S. Lowengrub
- Department of Mathematics, University of California, Irvine, CA, USA
- Department of Biomedical Engineering, University of California, Irvine, CA, USA
- Center for Complex Biological Systems, Chao Family Comprehensive Cancer Center, University of California, Irvine, CA, USA
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8
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Alwuthaynani M, Eftimie R, Trucu D. Inverse problem approaches for mutation laws in heterogeneous tumours with local and nonlocal dynamics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:3720-3747. [PMID: 35341271 DOI: 10.3934/mbe.2022171] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study deals with the identification (or reconstruction) of the usually unknown cancer cell mutation law, which lead to the transformation of a primary tumour cell population into a secondary, more aggressive cell population. We focus on local and nonlocal mathematical models for cell dynamics and movement, and identify these mutation laws from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. In a local cancer invasion model, we first reconstruct the mutation law when we assume that the mutations depend only on the surrounding cancer cells (i.e., the ECM plays no role in mutations). Second, we assume that the mutations depend on the ECM only, and we reconstruct the mutation law in this case. Third, we reconstruct the mutation when we assume that there is no prior knowledge about the mutations. Finally, for the nonlocal cancer invasion model, we reconstruct the mutation law that depends on the cancer cells and on the ECM. For these numerical reconstructions, our approximations are based on the finite difference method combined with the finite elements method. As the inverse problem is ill-posed, we use the Tikhonov regularisation technique in order to regularise the solution. Stability of the solution is examined by adding additive noise into the measurements.
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Affiliation(s)
- Maher Alwuthaynani
- Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK
| | - Raluca Eftimie
- Laboratoire Mathématiques de Besançcon, UMR-CNRS 6623, Université de Bourgogne Franche-Comté, 16 Route de Gray, Besançcon 25000, France
| | - Dumitru Trucu
- Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK
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9
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Scheufele K, Subramanian S, Biros G. Fully Automatic Calibration of Tumor-Growth Models Using a Single mpMRI Scan. IEEE TRANSACTIONS ON MEDICAL IMAGING 2021; 40:193-204. [PMID: 32931431 PMCID: PMC8565678 DOI: 10.1109/tmi.2020.3024264] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
Our objective is the calibration of mathematical tumor growth models from a single multiparametric scan. The target problem is the analysis of preoperative Glioblastoma (GBM) scans. To this end, we present a fully automatic tumor-growth calibration methodology that integrates a single-species reaction-diffusion partial differential equation (PDE) model for tumor progression with multiparametric Magnetic Resonance Imaging (mpMRI) scans to robustly extract patient specific biomarkers i.e., estimates for (i) the tumor cell proliferation rate, (ii) the tumor cell migration rate, and (iii) the original, localized site(s) of tumor initiation. Our method is based on a sparse reconstruction algorithm for the tumor initial location (TIL). This problem is particularly challenging due to nonlinearity, ill-posedeness, and ill conditioning. We propose a coarse-to-fine multi-resolution continuation scheme with parameter decomposition to stabilize the inversion. We demonstrate robustness and practicality of our method by applying the proposed method to clinical data of 206 GBM patients. We analyze the extracted biomarkers and relate tumor origin with patient overall survival by mapping the former into a common atlas space. We present preliminary results that suggest improved accuracy for prediction of patient overall survival when a set of imaging features is augmented with estimated biophysical parameters. All extracted features, tumor initial positions, and biophysical growth parameters are made publicly available for further analysis. To our knowledge, this is the first fully automatic scheme that can handle multifocal tumors and can localize the TIL to a few millimeters.
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10
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Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect. MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION : MICCAI ... INTERNATIONAL CONFERENCE ON MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION 2020; 12262:551-560. [PMID: 34704089 DOI: 10.1007/978-3-030-59713-9_53] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We present a 3D fully-automatic method for the calibration of partial differential equation (PDE) models of glioblastoma (GBM) growth with "mass effect", the deformation of brain tissue due to the tumor. We quantify the mass effect, tumor proliferation, tumor migration, and the localized tumor initial condition from a single multiparameteric Magnetic Resonance Imaging (mpMRI) patient scan. The PDE is a reaction-advection-diffusion partial differential equation coupled with linear elasticity equations to capture mass effect. The single-scan calibration model is notoriously difficult because the precancerous (healthy) brain anatomy is unknown. To solve this inherently ill-posed and illconditioned optimization problem, we introduce a novel inversion scheme that uses multiple brain atlases as proxies for the healthy precancer patient brain resulting in robust and reliable parameter estimation. We apply our method on both synthetic and clinical datasets representative of the heterogeneous spatial landscape typically observed in glioblastomas to demonstrate the validity and performance of our methods. In the synthetic data, we report calibration errors (due to the ill-posedness and our solution scheme) in the 10%-20% range. In the clinical data, we report good quantitative agreement with the observed tumor and qualitative agreement with the mass effect (for which we do not have a ground truth). Our method uses a minimal set of parameters and provides both global and local quantitative measures of tumor infiltration and mass effect.
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Mang A, Bakas S, Subramanian S, Davatzikos C, Biros G. Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology. Annu Rev Biomed Eng 2020; 22:309-341. [PMID: 32501772 PMCID: PMC7520881 DOI: 10.1146/annurev-bioeng-062117-121105] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved (a) detection/segmentation of tumor subregions and (b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of (a) biophysical growth modeling and simulation,(b) inverse problems for model calibration, (c) these models' integration with imaging workflows, and (d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.
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Affiliation(s)
- Andreas Mang
- Department of Mathematics, University of Houston, Houston, Texas 77204, USA;
| | - Spyridon Bakas
- Department of Mathematics, University of Houston, Houston, Texas 77204, USA;
| | - Shashank Subramanian
- Oden Institute of Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA; ,
| | - Christos Davatzikos
- Center for Biomedical Image Computing and Analytics (CBICA); Department of Radiology; and Department of Pathology and Laboratory Medicine, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA; ,
| | - George Biros
- Oden Institute of Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, USA; ,
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