A dynamic model of CT scans for quantifying doubling time of ground glass opacities using histogram analysis

József Z. Farkas; Gary T. Smith; Glenn F. Webb; József Z. Farkas; Gary T. Smith; Glenn F. Webb

doi:10.3934/mbe.2018055

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1203-1224. doi: 10.3934/mbe.2018055

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A dynamic model of CT scans for quantifying doubling time of ground glass opacities using histogram analysis

1.
Division of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK
2.
Department of Medical Imaging, Department of Veterans Affairs Hospital, Tennessee Valley Healthcare System, Nashville, Tennessee, 37212, USA
3.
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

Received: 09 October 2017 Revised: 20 January 2018 Published: 01 October 2018
MSC : Primary: 92C50, 92C55; Secondary: 35K58

We quantify a recent five-category CT histogram based classification of ground glass opacities using a dynamic mathematical model for the spatial-temporal evolution of malignant nodules. Our mathematical model takes the form of a spatially structured partial differential equation with a logistic crowding term. We present the results of extensive simulations and validate our model using patient data obtained from clinical CT images from patients with benign and malignant lesions.
- Medical imaging,
- CT scan,
- logistic partial differential equation
Citation: József Z. Farkas, Gary T. Smith, Glenn F. Webb. A dynamic model of CT scans for quantifying doubling time of ground glass opacities using histogram analysis[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1203-1224. doi: 10.3934/mbe.2018055

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Abstract

We quantify a recent five-category CT histogram based classification of ground glass opacities using a dynamic mathematical model for the spatial-temporal evolution of malignant nodules. Our mathematical model takes the form of a spatially structured partial differential equation with a logistic crowding term. We present the results of extensive simulations and validate our model using patient data obtained from clinical CT images from patients with benign and malignant lesions.

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