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Modeling tumor growth accurately is essential for understanding cancer progression and informing treatment strategies. To estimate the parameters in the tumor growth model described by a nonlinear PDE, we adopt Physics-Informed Neural…

Analysis of PDEs · Mathematics 2025-11-21 Liu Liu , Yifei Wang , Qinyu Xu , Xiaoqian Xu

Existing approaches to modeling the dynamics of brain tumor growth, specifically glioma, employ biologically inspired models of cell diffusion, using image data to estimate the associated parameters. In this work, we propose an alternative…

The brain is a complex organ controlling cognitive process and physical functions. Tumors in the brain are accelerated cell growths affecting the normal function and processes in the brain. MRI scans provides detailed images of the body…

Image and Video Processing · Electrical Eng. & Systems 2020-03-20 Miriam Zulema Jacobo , Jose Mejia

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue.…

Computational Engineering, Finance, and Science · Computer Science 2022-09-27 Baoshan Liang , Jingye Tan , Luke Lozenski , David A. Hormuth , Thomas E. Yankeelov , Umberto Villa , Danial Faghihi

Brain tumor is a life-threatening problem and hampers the normal functioning of the human body. The average five-year relative survival rate for malignant brain tumors is 35.6 percent. For proper diagnosis and efficient treatment planning,…

Image and Video Processing · Electrical Eng. & Systems 2024-07-16 Vidhyapriya Ranganathan , Celshiya Udaiyar , Jaisree Jayanth , Meghaa P , Srija B , Uthra S

Brain tumors are abnormal cell growths in the central nervous system (CNS), and their timely detection is critical for improving patient outcomes. This paper proposes an automatic and efficient deep-learning framework for brain tumor…

Computer Vision and Pattern Recognition · Computer Science 2025-09-30 Ahta-Shamul Hoque Emran , Hafija Akter , Abdullah Al Shiam , Abu Saleh Musa Miah , Anichur Rahman , Fahmid Al Farid , Hezerul Abdul Karim

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…

Medical Physics · Physics 2020-01-28 Klaudius Scheufele , Shashank Subramanian , George Biros

Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…

Populations and Evolution · Quantitative Biology 2020-03-23 Yuri Kozitsky , Krzysztof Pilorz

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…

We propose a curve-based Riemannian-geometric approach for general shape-based statistical analyses of tumors obtained from radiologic images. A key component of the framework is a suitable metric that (1) enables comparisons of tumor…

Applications · Statistics 2017-02-07 Karthik Bharath , Sebastian Kurtek , Arvind Rao , Veerabhadran Baladandayuthapani

Central nervous system (CNS) tumors come with the vastly heterogeneous histologic, molecular and radiographic landscape, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics…

Quantitative Methods · Quantitative Biology 2020-06-30 Andreas Mang , Spyridon Bakas , Shashank Subramanian , Christos Davatzikos , George Biros

We present a novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, MRI scan of a glioblastoma patient. Tumor growth models are typically nonlinear parabolic partial differential equations…

Quantitative Methods · Quantitative Biology 2020-06-30 Klaudius Scheufele , Shashank Subramanian , Andreas Mang , George Biros , Miriam Mehl

Glioblastoma is among the most aggressive brain tumors in adults, characterized by patient-specific invasion patterns driven by the underlying brain microstructure. In this work, we present a proof-of-concept for a mathematical model of GBL…

Image and Video Processing · Electrical Eng. & Systems 2025-06-23 D. Cerrone , D. Riccobelli , S. Gazzoni , P. Vitullo , F. Ballarin , J. Falco , F. Acerbi , A. Manzoni , P. Zunino , P. Ciarletta

Diagnosing Brain Tumor with the aid of Magnetic Resonance Imaging (MRI) has gained enormous prominence over the years, primarily in the field of medical science. Detection and/or partitioning of brain tumors solely with the aid of MR…

Image and Video Processing · Electrical Eng. & Systems 2020-11-19 Md. Abu Bakr Siddique , Shadman Sakib , Mohammad Mahmudur Rahman Khan , Abyaz Kader Tanzeem , Madiha Chowdhury , Nowrin Yasmin

Uncontrolled cell division in the brain is what gives rise to brain tumors. If the tumor size increases by more than half, there is little hope for the patient's recovery. This emphasizes the need of rapid and precise brain tumor diagnosis.…

Image and Video Processing · Electrical Eng. & Systems 2025-03-11 Plabon Paul , Md. Nazmul Islam , Fazle Rafsani , Pegah Khorasani , Shovito Barua Soumma

Brain tumor analysis in MRI images is a significant and challenging issue because misdiagnosis can lead to death. Diagnosis and evaluation of brain tumors in the early stages increase the probability of successful treatment. However, the…

Image and Video Processing · Electrical Eng. & Systems 2021-12-30 Zahra Sobhaninia , Nader Karimi , Pejman Khadivi , Shadrokh Samavi

Surgery planning in patients diagnosed with brain tumor is dependent on their survival prognosis. A poor prognosis might demand for a more aggressive treatment and therapy plan, while a favorable prognosis might enable a less risky surgery…

Image and Video Processing · Electrical Eng. & Systems 2020-09-08 Sobia Yousaf , Syed Muhammad Anwar , Harish RaviPrakash , Ulas Bagci

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.Mathematical models of GBM growth can complement the data in…

Machine Learning · Computer Science 2024-08-19 Ray Zirui Zhang , Ivan Ezhov , Michal Balcerak , Andy Zhu , Benedikt Wiestler , Bjoern Menze , John S. Lowengrub

In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…

Biological Physics · Physics 2023-02-07 Maxim V. Polyakov , Valeria V. Ten

Tumor growth is a complex process characterized by uncontrolled cell proliferation and invasion of neighboring tissues. The understanding of these phenomena is of vital importance to establish appropriate diagnosis and therapeutic strategy…

Tissues and Organs · Quantitative Biology 2019-10-23 Miguel Martín-Landrove , Francisco Torres-Hoyos , Antonio Rueda-Toicen
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