A mechanically coupled reaction-diffusion model that incorporates intra-tumoural heterogeneity to predictin vivoglioma 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.
Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, TX, USA david.hormuth@utexas.edu.
David A
0000-0002-9643-1694
DA
Hormuth
Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, USA.
Jared A
JA
Weis
Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, TX, USA.
Stephanie L
SL
Barnes
Department of Biomedical Engineering, Vanderbilt University, Nashville, TN, USA.|Department of Radiology and Radiological Sciences, Vanderbilt University, Nashville, TN, USA.|Department of Neurological Surgery, Vanderbilt University, Nashville, TN, USA.
Michael I
MI
Miga
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, USA.
Erin C
EC
Rericha
Department of Cancer Biology, Vanderbilt University, Nashville, TN, USA.
Vito
V
Quaranta
Institute for Computational and Engineering Sciences, The University of Texas at Austin, Austin, TX, USA thomas.yankeelov@utexas.edu.|Biomedical Engineering, The University of Texas at Austin, Austin, TX, USA.|Internal Medicine, The University of Texas at Austin, Austin, TX, USA.
Thomas E
TE
Yankeelov
D000818:Animals; D001932:Brain Neoplasms / Q000000981:diagnostic imaging / Q000503:physiopathology; D005260:Female; D005910:Glioma / Q000000981:diagnostic imaging / Q000503:physiopathology; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D009374:Neoplasms, Experimental / Q000000981:diagnostic imaging / Q000503:physiopathology; D051381:Rats; D017208:Rats, Wistar
brain; cancer; forecast; glioma; mathematical model