Abstract A42: A mechanically coupled reaction-diffusion model for predicting in vivo C6 glioma growth in rats

2015 ◽  
Author(s):  
David A. Hormuth ◽  
Jared A. Weis ◽  
Michael I. Miga ◽  
Thomas E. Yankeelov
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
C6 Glioma ◽  
Reaction Diffusion Model ◽  
Glioma Growth ◽  
Coupled Reaction

scholarly journals Mechanically Coupled Reaction-Diffusion Model to Predict Glioma Growth: Methodological Details

2018 ◽  
pp. 225-241 ◽  
Author(s):  
David A. Hormuth ◽  
Stephanie L. Eldridge ◽  
Jared A. Weis ◽  
Michael I. Miga ◽  
Thomas E. Yankeelov
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Glioma Growth ◽  
Coupled Reaction

scholarly journals A mechanically coupled reaction–diffusion model for predicting the response of breast tumors to neoadjuvant chemotherapy

2013 ◽  
Vol 58 (17) ◽  
pp. 5851-5866 ◽  
Author(s):  
Jared A Weis ◽  
Michael I Miga ◽  
Lori R Arlinghaus ◽  
Xia Li ◽  
A Bapsi Chakravarthy ◽  
...  
Keyword(s):  
Neoadjuvant Chemotherapy ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Breast Tumors ◽  
Reaction Diffusion Model ◽  
Coupled Reaction

scholarly journals Numerical solution of a coupled reaction-diffusion model using barycentric interpolation collocation method

2020 ◽  
Vol 24 (4) ◽  
pp. 2561-2567
Author(s):  
Yu Zhang ◽  
Wei Zhang ◽  
Chenhui Zhao ◽  
Yulan Wang
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Collocation Method ◽  
Diffusion Model ◽  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Barycentric Interpolation ◽  
Reaction Diffusion Model ◽  
Linear Reaction ◽  
Coupled Reaction

In thermal science, chemical and mechanics, the non-linear reaction-diffusion model is very important, and an approximate solution with high precision is always needed. In this article, the barycentric interpolation collocation method is proposed for this purpose. Numerical experiments show that the proposed approach is highly reliable.

A mechanically coupled reaction diffusion model of breast tumor response during neoadjuvant chemotherapy

2013 ◽  
Author(s):  
Jared A. Weis ◽  
Michael I. Miga ◽  
Xia Li ◽  
Lori R. Arlinghaus ◽  
A. Bapsi Chakravarthy ◽  
...  
Keyword(s):  
Neoadjuvant Chemotherapy ◽  
Diffusion Model ◽  
Breast Tumor ◽  
Tumor Response ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Coupled Reaction

scholarly journals Predicting the Response of Breast Cancer to Neoadjuvant Therapy Using a Mechanically Coupled Reaction–Diffusion Model

2015 ◽  
Vol 75 (22) ◽  
pp. 4697-4707 ◽  
Author(s):  
Jared A. Weis ◽  
Michael I. Miga ◽  
Lori R. Arlinghaus ◽  
Xia Li ◽  
Vandana Abramson ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Neoadjuvant Therapy ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Coupled Reaction

scholarly journals Enhancement of combustion by drift in a coupled reaction-diffusion model

2006 ◽  
Vol 4 (1) ◽  
pp. 213-225
Author(s):  
David Andrzejewski ◽  
Erick Butzlaff ◽  
Alexander Kiselev ◽  
Lam Raga A. Markely
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Coupled Reaction

scholarly journals A mechanically coupled reaction–diffusion model that incorporates intra-tumoural heterogeneity to predict in vivo glioma growth

2017 ◽  
Vol 14 (128) ◽  
pp. 20161010 ◽  
Author(s):  
David A. Hormuth ◽  
Jared A. Weis ◽  
Stephanie L. Barnes ◽  
Michael I. Miga ◽  
Erin C. Rericha ◽  
...  
Keyword(s):  
Carrying Capacity ◽  
Biological Effects ◽  
Reaction Diffusion ◽  
Model Parameters ◽  
Tumour Heterogeneity ◽  
Time Points ◽  
Tissue Tumour ◽  
Reaction Diffusion Model ◽  
Glioma Growth

While gliomas have been extensively modelled with a reaction–diffusion (RD) type equation it is most likely an oversimplification. In this study, three mathematical models of glioma growth are developed and systematically investigated to establish a framework for accurate prediction of changes in tumour volume as well as intra-tumoural heterogeneity. Tumour cell movement was described by coupling movement to tissue stress, leading to a mechanically coupled (MC) RD model. Intra-tumour heterogeneity was described by including a voxel-specific carrying capacity (CC) to the RD model. The MC and CC models were also combined in a third model. To evaluate these models, rats ( n = 14) with C6 gliomas were imaged with diffusion-weighted magnetic resonance imaging over 10 days to estimate tumour cellularity. Model parameters were estimated from the first three imaging time points and then used to predict tumour growth at the remaining time points which were then directly compared to experimental data. The results in this work demonstrate that mechanical–biological effects are a necessary component of brain tissue tumour modelling efforts. The results are suggestive that a variable tissue carrying capacity is a needed model component to capture tumour heterogeneity. Lastly, the results advocate the need for additional effort towards capturing tumour-to-tissue infiltration.

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