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Pasetto S, Montejo M, Zahid MU, Rosa M, Gatenby R, Schlicke P, Diaz R, Enderling H. Calibrating tumor growth and invasion parameters with spectral spatial analysis of cancer biopsy tissues. NPJ Syst Biol Appl 2024; 10:112. [PMID: 39358360 PMCID: PMC11447233 DOI: 10.1038/s41540-024-00439-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 09/18/2024] [Indexed: 10/04/2024] Open
Abstract
The reaction-diffusion equation is widely used in mathematical models of cancer. The calibration of model parameters based on limited clinical data is critical to using reaction-diffusion equation simulations for reliable predictions on a per-patient basis. Here, we focus on cell-level data as routinely available from tissue biopsies used for clinical cancer diagnosis. We analyze the spatial architecture in biopsy tissues stained with multiplex immunofluorescence. We derive a two-point correlation function and the corresponding spatial power spectral distribution. We show that this data-deduced power spectral distribution can fit the power spectrum of the solution of reaction-diffusion equations that can then identify patient-specific tumor growth and invasion rates. This approach allows the measurement of patient-specific critical tumor dynamical properties from routinely available biopsy material at a single snapshot in time.
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Affiliation(s)
- Stefano Pasetto
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, USA.
| | - Michael Montejo
- Department of Radiation Oncology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, USA
| | - Mohammad U Zahid
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX, USA
| | - Marilin Rosa
- Department of Pathology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, USA
| | - Robert Gatenby
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, USA
- Department of Radiology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, USA
| | - Pirmin Schlicke
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX, USA
| | - Roberto Diaz
- Department of Radiation Oncology, H. Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, Tampa, FL, USA
| | - Heiko Enderling
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX, USA.
- Institute for Data Science in Oncology, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Blvd, Houston, TX, USA.
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Ocaña-Tienda B, Pérez-García VM. Mathematical modeling of brain metastases growth and response to therapies: A review. Math Biosci 2024; 373:109207. [PMID: 38759950 DOI: 10.1016/j.mbs.2024.109207] [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: 09/23/2023] [Revised: 04/04/2024] [Accepted: 05/10/2024] [Indexed: 05/19/2024]
Abstract
Brain metastases (BMs) are the most common intracranial tumor type and a significant health concern, affecting approximately 10% to 30% of all oncological patients. Although significant progress is being made, many aspects of the metastatic process to the brain and the growth of the resulting lesions are still not well understood. There is a need for an improved understanding of the growth dynamics and the response to treatment of these tumors. Mathematical models have been proven valuable for drawing inferences and making predictions in different fields of cancer research, but few mathematical works have considered BMs. This comprehensive review aims to establish a unified platform and contribute to fostering emerging efforts dedicated to enhancing our mathematical understanding of this intricate and challenging disease. We focus on the progress made in the initial stages of mathematical modeling research regarding BMs and the significant insights gained from such studies. We also explore the vital role of mathematical modeling in predicting treatment outcomes and enhancing the quality of clinical decision-making for patients facing BMs.
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Affiliation(s)
- Beatriz Ocaña-Tienda
- Mathematical Oncology Laboratory (MOLAB), University of Castilla-La Mancha, Avda. Camilo José Cela s/n, 13071, Ciudad Real, Spain.
| | - Víctor M Pérez-García
- Mathematical Oncology Laboratory (MOLAB), University of Castilla-La Mancha, Avda. Camilo José Cela s/n, 13071, Ciudad Real, Spain.
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Bond KM, Curtin L, Ranjbar S, Afshari AE, Hu LS, Rubin JB, Swanson KR. An image-based modeling framework for predicting spatiotemporal brain cancer biology within individual patients. Front Oncol 2023; 13:1185738. [PMID: 37849813 PMCID: PMC10578440 DOI: 10.3389/fonc.2023.1185738] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2023] [Accepted: 08/21/2023] [Indexed: 10/19/2023] Open
Abstract
Imaging is central to the clinical surveillance of brain tumors yet it provides limited insight into a tumor's underlying biology. Machine learning and other mathematical modeling approaches can leverage paired magnetic resonance images and image-localized tissue samples to predict almost any characteristic of a tumor. Image-based modeling takes advantage of the spatial resolution of routine clinical scans and can be applied to measure biological differences within a tumor, changes over time, as well as the variance between patients. This approach is non-invasive and circumvents the intrinsic challenges of inter- and intratumoral heterogeneity that have historically hindered the complete assessment of tumor biology and treatment responsiveness. It can also reveal tumor characteristics that may guide both surgical and medical decision-making in real-time. Here we describe a general framework for the acquisition of image-localized biopsies and the construction of spatiotemporal radiomics models, as well as case examples of how this approach may be used to address clinically relevant questions.
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Affiliation(s)
- Kamila M. Bond
- Mathematical Neuro-Oncology Lab, Department of Neurological Surgery, Mayo Clinic, Phoenix, AZ, United States
- Hospital of University of Pennsylvania, Department of Neurosurgery, Philadelphia, PA, United States
| | - Lee Curtin
- Mathematical Neuro-Oncology Lab, Department of Neurological Surgery, Mayo Clinic, Phoenix, AZ, United States
| | - Sara Ranjbar
- Mathematical Neuro-Oncology Lab, Department of Neurological Surgery, Mayo Clinic, Phoenix, AZ, United States
| | - Ariana E. Afshari
- Mathematical Neuro-Oncology Lab, Department of Neurological Surgery, Mayo Clinic, Phoenix, AZ, United States
| | - Leland S. Hu
- Mathematical Neuro-Oncology Lab, Department of Neurological Surgery, Mayo Clinic, Phoenix, AZ, United States
- Department of Radiology, Mayo Clinic, Phoenix, AZ, United States
| | - Joshua B. Rubin
- Departments of Neuroscience and Pediatrics, Washington University School of Medicine, St. Louis, MO, United States
| | - Kristin R. Swanson
- Mathematical Neuro-Oncology Lab, Department of Neurological Surgery, Mayo Clinic, Phoenix, AZ, United States
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The Next Frontier in Health Disparities—A Closer Look at Exploring Sex Differences in Glioma Data and Omics Analysis, from Bench to Bedside and Back. Biomolecules 2022; 12:biom12091203. [PMID: 36139042 PMCID: PMC9496358 DOI: 10.3390/biom12091203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Revised: 08/23/2022] [Accepted: 08/26/2022] [Indexed: 11/16/2022] Open
Abstract
Sex differences are increasingly being explored and reported in oncology, and glioma is no exception. As potentially meaningful sex differences are uncovered, existing gender-derived disparities mirror data generated in retrospective and prospective trials, real-world large-scale data sets, and bench work involving animals and cell lines. The resulting disparities at the data level are wide-ranging, potentially resulting in both adverse outcomes and failure to identify and exploit therapeutic benefits. We set out to analyze the literature on women’s data disparities in glioma by exploring the origins of data in this area to understand the representation of women in study samples and omics analyses. Given the current emphasis on inclusive study design and research, we wanted to explore if sex bias continues to exist in present-day data sets and how sex differences in data may impact conclusions derived from large-scale data sets, omics, biospecimen analysis, novel interventions, and standard of care management.
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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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A Deep Convolutional Neural Network for Annotation of Magnetic Resonance Imaging Sequence Type. J Digit Imaging 2021; 33:439-446. [PMID: 31654174 DOI: 10.1007/s10278-019-00282-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
The explosion of medical imaging data along with the advent of big data analytics has launched an exciting era for clinical research. One factor affecting the ability to aggregate large medical image collections for research is the lack of infrastructure for automated data annotation. Among all imaging modalities, annotation of magnetic resonance (MR) images is particularly challenging due to the non-standard labeling of MR image types. In this work, we aimed to train a deep neural network to annotate MR image sequence type for scans of brain tumor patients. We focused on the four most common MR sequence types within neuroimaging: T1-weighted (T1W), T1-weighted post-gadolinium contrast (T1Gd), T2-weighted (T2W), and T2-weighted fluid-attenuated inversion recovery (FLAIR). Our repository contains images acquired using a variety of pulse sequences, sequence parameters, field strengths, and scanner manufacturers. Image selection was agnostic to patient demographics, diagnosis, and the presence of tumor in the imaging field of view. We used a total of 14,400 two-dimensional images, each visualizing a different part of the brain. Data was split into train, validation, and test sets (9600, 2400, and 2400 images, respectively) and sets consisted of equal-sized groups of image types. Overall, the model reached an accuracy of 99% on the test set. Our results showed excellent performance of deep learning techniques in predicting sequence types for brain tumor MR images. We conclude deep learning models can serve as tools to support clinical research and facilitate efficient database management.
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Jiménez-Sánchez J, Bosque JJ, Jiménez Londoño GA, Molina-García D, Martínez Á, Pérez-Beteta J, Ortega-Sabater C, Honguero Martínez AF, García Vicente AM, Calvo GF, Pérez-García VM. Evolutionary dynamics at the tumor edge reveal metabolic imaging biomarkers. Proc Natl Acad Sci U S A 2021; 118:e2018110118. [PMID: 33536339 PMCID: PMC8017959 DOI: 10.1073/pnas.2018110118] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 01/04/2021] [Indexed: 01/09/2023] Open
Abstract
Human cancers are biologically and morphologically heterogeneous. A variety of clonal populations emerge within these neoplasms and their interaction leads to complex spatiotemporal dynamics during tumor growth. We studied the reshaping of metabolic activity in human cancers by means of continuous and discrete mathematical models and matched the results to positron emission tomography (PET) imaging data. Our models revealed that the location of increasingly active proliferative cellular spots progressively drifted from the center of the tumor to the periphery, as a result of the competition between gradually more aggressive phenotypes. This computational finding led to the development of a metric, normalized distance from 18F-fluorodeoxyglucose (18F-FDG) hotspot to centroid (NHOC), based on the separation from the location of the activity (proliferation) hotspot to the tumor centroid. The NHOC metric can be computed for patients using 18F-FDG PET-computed tomography (PET/CT) images where the voxel of maximum uptake (standardized uptake value [SUV]max) is taken as the activity hotspot. Two datasets of 18F-FDG PET/CT images were collected, one from 61 breast cancer patients and another from 161 non-small-cell lung cancer patients. In both cohorts, survival analyses were carried out for the NHOC and for other classical PET/CT-based biomarkers, finding that the former had a high prognostic value, outperforming the latter. In summary, our work offers additional insights into the evolutionary mechanisms behind tumor progression, provides a different PET/CT-based biomarker, and reveals that an activity hotspot closer to the tumor periphery is associated to a worst patient outcome.
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Affiliation(s)
- Juan Jiménez-Sánchez
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain
| | - Jesús J Bosque
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain
| | | | - David Molina-García
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain
| | - Álvaro Martínez
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain
- Nuclear Medicine Unit, Hospital General Universitario de Ciudad Real, Ciudad Real, 13005, Spain
| | - Julián Pérez-Beteta
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain
| | - Carmen Ortega-Sabater
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain
| | | | - Ana M García Vicente
- Thoracic Surgery Unit, Hospital General Universitario de Albacete, Albacete, 02006, Spain
| | - Gabriel F Calvo
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain;
| | - Víctor M Pérez-García
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Ciudad Real, 13071, Spain;
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Nardini JT, Lagergren JH, Hawkins-Daarud A, Curtin L, Morris B, Rutter EM, Swanson KR, Flores KB. Learning Equations from Biological Data with Limited Time Samples. Bull Math Biol 2020; 82:119. [PMID: 32909137 PMCID: PMC8409251 DOI: 10.1007/s11538-020-00794-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Accepted: 08/16/2020] [Indexed: 01/25/2023]
Abstract
Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.
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Affiliation(s)
- John T Nardini
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA.
- The Statistical and Applied Mathematical Sciences Institute, Durham, NC, USA.
| | - John H Lagergren
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
| | - Andrea Hawkins-Daarud
- Mathematical NeuroOncology Laboratory, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - Lee Curtin
- Mathematical NeuroOncology Laboratory, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - Bethan Morris
- Centre for Mathematical Medicine and Biology, University of Nottingham, Nottingham, UK
| | - Erica M Rutter
- Department of Applied Mathematics, University of California, Merced, Merced, CA, USA
| | - Kristin R Swanson
- Mathematical NeuroOncology Laboratory, Precision Neurotherapeutics Innovation Program, Mayo Clinic, Phoenix, AZ, USA
| | - Kevin B Flores
- Department of Mathematics, North Carolina State University, Raleigh, NC, USA
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