Neural Parameters Estimation for Brain Tumor Growth Modeling (original) (raw)
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Geometry-Aware Neural Solver for Fast Bayesian Calibration of Brain Tumor Models
IEEE Transactions on Medical Imaging, 2021
Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using highly-efficient numerical solvers, a single forward simulation takes up to a few minutes of compute. At the same time, clinical applications of tumor modeling often imply solving an inverse problem, requiring up to tens of thousands of forward model evaluations when used for a Bayesian model personalization via sampling. This results in a total inference time prohibitively expensive for clinical translation. While recent data-driven approaches become capable of emulating physics simulation, they tend to fail in generalizing over the variability of the boundary conditions imposed by the patient-specific anatomy. In this paper, we propose a learnable surrogate for simulating tumor growth which maps the biophysical model parameters directly to simulation outputs, i.e. the local tumor cell densities, whilst respecting patient geometry. We test the neural solver in a Bayesian model personalization task for a cohort of glioma patients. Bayesian inference using the proposed surrogate yields estimates analogous to those obtained by solving the forward model with a regular numerical solver. The near real-time computation cost renders the proposed method suitable for clinical settings. The code is available at https://github.com/IvanEz/tumor-surrogate. Index Terms-Bayesian inference, physics-based deep learning, glioma, model personalization, tumor modeling, MRI, FET-PET I. INTRODUCTION S IMULATION of brain tumor progression can provide complementary information to medical imaging for radiotherapy planning. As shown in [1]-[13], tumor modeling can be employed to define a personalized radio-treatment area using biophysical models to estimate the most likely directions of tumor cell infiltration instead of solely targeting tumor area The first two authors contributed equally.
Learn-Morph-Infer: A new way of solving the inverse problem for brain tumor modeling
Medical Image Analysis
Current treatment planning of patients diagnosed with brain tumor could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, such as magnetic-resonance imaging (MRI), contrast sufficiently well areas of high cell density. However, they do not portray areas of low concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. 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 that prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a methodology for inferring patient-specific spatial distribution of brain tumor 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.
Real-time Bayesian personalization via a learnable brain tumor growth model
ArXiv, 2020
Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using highly-efficient numerical solvers, a single forward simulation takes up to a few minutes of compute. At the same time, clinical applications of the tumor modeling often imply solving an inverse problem, requiring up to tens of thousands forward model evaluations when used for a Bayesian model personalization via sampling. This results in a total inference time prohibitively expensive for clinical translation. Moreover, while recent data-driven approaches become capable of emulating physics simulation, they tend to fail in generalizing over the variability of the boundary conditions imposed by the patient-specific anatomy. In this paper, we propose a learnable surrogate with anatomy encoder for simulating tumor growth which maps the biophysical model parameters...
Learning a Classification-based Glioma Growth Model Using MRI Data
Journal of Computers, 2006
Gliomas are malignant brain tumors that grow by invading adjacent tissue. We propose and evaluate a 3D classification-based growth model, CDM, that predicts how a glioma will grow at a voxel-level, on the basis of features specific to the patient, properties of the tumor, and attributes of that voxel. We use Supervised Learning algorithms to learn this general model, by observing the growth patterns of gliomas from other patients. Our empirical results on clinical data demonstrate that our learned CDM model can, in most cases, predict glioma growth more effectively than two standard models: uniform radial growth across all tissue types, and another that assumes faster diffusion in white matter. We thoroughly study CDM results numerically and analytically in light of the training data we used, and we also discuss the current limitations of the model. We finally conclude the paper with a discussion of promising future research directions.
Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth
Cornell University - arXiv, 2022
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. This work introduces a Bayesian framework to calibrate the spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient > 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model predicted tumor shape.
Glioblastoma multiforme is an aggressive brain tumor with the lowest survival rate of any human cancer due to its invasive growth dynamics. These dynamics result in recurrent tumor pockets hidden from medical imaging, which standard radio-treatment and surgical margins fail to cover. Mathematical modeling of tumor growth via partial differential equations (PDE) is well-known; however, it remains unincorporated in clinical practice due to prolonged run-times, inter-patient anatomical variation, and initial conditions that ignore a patient’s current tumor. This study proposes a glioblastoma multiforme tumor evolution model, GlioMod, that aims to learn spatiotemporal features of tumor concentration and brain geometry for personalized therapeutic planning. A dataset of 6,000 synthetic tumors is generated from real patient anatomies using PDE-based modeling. Our model employs image-to-image regression using a novel encoder-decoder architecture to predict tumor concentration at future sta...
Communications Medicine
Background In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient’s pathology producing a variety of clinical data. However, investigation of these data faces two major challenges. Firstly, we lack the knowledge of the mechanisms involved in regulating these data variables, and secondly, data collection is sparse in time since it relies on patient’s clinical presentation. The former limits the predictive accuracy of clinical outcomes for any mechanistic model. The latter restrains any machine learning algorithm to accurately infer the corresponding disease dynamics. Methods Here, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning, aiming at improving individualized predictions by addressing the aforementioned challenges. Results We evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two relevant clinical outputs. The m...
Data Assimilation in Brain Tumor Models
Lecture Notes on Mathematical Modelling in the Life Sciences, 2012
A typical problem in applied mathematics and science is to estimate the future state of a dynamical system given its current state. One approach aimed at understanding one or more aspects determining the behavior of the system is mathematical modeling. This method frequently entails formulation of a set of equations, usually a system of partial or ordinary differential equations. Model parameters are then measured from experimental data or estimated from computer simulation or other methods, for example chi-squared parameter optimization as done in [26] or genetic algorithms which are frequently used in neuroscience [33]. Solutions to the model are then studied through mathematical analysis and numerical simulation usually for qualitative fit to the dynamical system of interest and any relative time-series data that is available. While mathematical modeling can provide meaningful insight, it may have limited predictive value due to idealized assumptions underlying the model, measurement error in experimental data and parameters, and chaotic behavior in the system. In this chapter we explore a different approach focused on optimal state estimation given a model and observational data of a biological process, while accounting for the relative uncertainty in both. The case explored
Macroscopic Cerebral Tumor Growth Modeling From Medical Images: A Review
IEEE Access, 2018
Mathematical models have been ubiquitously employed in various applications. One of these applications that arose in the past few decades is cerebral tumor growth modeling. Simultaneously, medical imaging techniques, such as magnetic resonance imaging, computed tomography, and positron emission tomography, have witnessed great developments and become the primary clinical procedure in tumors diagnosis and detection. Studying tumor growth via mathematical models from medical images is an important application that is believed to play significant role in cancer treatment by predicting tumor evolution, quantifying the response to therapy, and the effective treatment planning of chemotherapy and/or radiotherapy. In this paper, we focus on the macroscopic growth modeling of brain tumors, mainly glioma, and highlight the current achievements in the state-of-the-art methods. In addition, we discuss some challenges and perspectives on this research that can further promote the research of this field. INDEX TERMS Mathematical modeling, cerebral tumors, glioma growth, macroscopic models, diffusive model, biomechanical model, chemotherapy, radiotherapy.
Background The diffuse growth pattern of glioblastoma is one of the main challenges for improving patient survival. Computational tumor growth modeling has emerged as a promising tool to guide personalized therapy. Here, we performed clinical and biological validation of a novel, deep learning - based growth model, aiming to close the gap between the experimental state and clinical implementation. Methods 124 patients from The Cancer Genome Archive network and 397 patients from the UCSF Glioma MRI Dataset were assessed for correlations between clinical data, genetic pathway activation maps (generated with PARADIGM; TCGA only), and infiltration (Dw) as well as proliferation (r) parameters stemming from a Fisher-Kolmogorov growth model adjusted to the patients’ preoperative images using deep learning. Cox multivariable regression and Spearman correlation were performed to test for statistical significance. To further evaluate clinical potential, we performed the same growth modeling o...