An adjoint-based method for a linear mechanically-coupled tumor model: application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging

Feng, Xinzeng; Hormuth, David A.; Yankeelov, Thomas E.

doi:10.1007/s00466-018-1589-2

Cited by 13 publications

(8 citation statements)

References 68 publications

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“…Feng et al . [60] recently used a linearized growth model to map the spatial variation of volumetric growth across a murine model of glioma using MRI data to quantify spatial heterogeneity of in vivo tumor proliferation. Conversely, Hormuth et al .…”

Section: Mathematical Modeling Of Proliferation and Therapy Across Scmentioning

confidence: 99%

Mathematical models of tumor cell proliferation: A review of the literature

Jarrett

Lima

Hormuth

et al. 2018

Expert Review of Anticancer Therapy

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107

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Introduction: A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways, to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. Areas Covered: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. Expert Commentary: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.

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Section: Mathematical Modeling Of Proliferation and Therapy Across Scmentioning

confidence: 99%

Mathematical models of tumor cell proliferation: A review of the literature

Jarrett

Lima

Hormuth

et al. 2018

Expert Review of Anticancer Therapy

Self Cite

107

View full text Add to dashboard Cite

show abstract

“…There exist multiple options for evaluating the gradient (and higher order derivatives) of the objective function, such as automatic differentiation, numerical approximation through finite differences, and adjoint-based methods. For oncology models, several groups have employed adjoints for inversion [19,27,29,35,57,104]. Some efforts also employ Hessian information to accelerate convergence [29,97].…”

Section: Inverse Problems For Oncology Modelsmentioning

confidence: 99%

Quantitative in vivo imaging to enable tumor forecasting and treatment optimization

Lorenzo,

Hormuth,

Jarrett

et al. 2021

Preprint

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Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inherent evolving heterogeneity that requires an individual approach based on rigorous and precise predictions of cancer growth and treatment response. To this end, we advocate the use of quantitative in vivo imaging data to calibrate mathematical models for the personalized forecasting of tumor development. In this chapter, we summarize the main data types available from both common and emerging in vivo medical imaging technologies, and how these data can be used to obtain patient-specific parameters for common mathematical models of cancer. We then outline computational methods designed to solve these models, thereby enabling their use for producing personalized tumor forecasts in silico, which, ultimately, can be used to not only predict response, but also optimize treatment. Finally, we discuss the main barriers to making the above paradigm a clinical reality.

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“…However, they lead to sub-optimal algorithms with slow convergence, typically resulting in an excessive number of iterations and high computational costs (perhaps run times of days on medium size clusters). This renders these methods impractical, especially for problems parameterized by a large number of unknowns p. The works in [36,47,54,71,88,89,101,139] use adjoint information, i.e., methods that exploit analytical derivatives. These methods are preferable to derivative-free approaches as they offer better convergence guarantees, are founded on rigorous mathematical principles, can reveal structure (sensitivities) that can be rigorously analyzed, and can be exploited for further integration with imaging (e.g., construction of priors for Bayesian inference).…”

Section: Deterministic Formulationsmentioning

confidence: 99%

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

Mang,

Bakas,

Subramanian

et al. 2020

Preprint

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Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular and radiographic landscape, 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 (i) detection/segmentation of tumor sub-regions, and (ii) computer-aided diagnostic/prognostic/predictive modeling. This paper presents a summary of (i) biophysical growth modeling and simulation, (ii) inverse problems for model calibration, (iii) their integration with imaging workflows, and (iv) their application on 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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An adjoint-based method for a linear mechanically-coupled tumor model: application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging

Cited by 13 publications

References 68 publications

Mathematical models of tumor cell proliferation: A review of the literature

Mathematical models of tumor cell proliferation: A review of the literature

Quantitative in vivo imaging to enable tumor forecasting and treatment optimization

Integrated Biophysical Modeling and Image Analysis: Application to Neuro-Oncology

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