Mathematical modelling of microtumour infiltration based on in vitro experiments
The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of th...
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paper:paper_17579694_v8_n8_p879_Lujan2023-06-08T16:28:58Z Mathematical modelling of microtumour infiltration based on in vitro experiments Guerra, Liliana Noemí Soba, Alejandro Calvo, Juan Carlos Suárez, Cecilia Ana animal cell animal experiment Article cell proliferation collagen degradation controlled study diffusion coefficient epithelium cell experimental neoplasm image processing in vitro study mathematical model Monte Carlo method mouse nonhuman phenotype priority journal surface property tumor cell tumor invasion tumor microenvironment tumor spheroid animal biological model biophysics brain tumor computer simulation epithelium glioma human metabolism microcirculation multicellular spheroid neoplasm pathology Animals Biophysical Phenomena Brain Neoplasms Cell Proliferation Computer Simulation Epithelium Glioma Humans Image Processing, Computer-Assisted In Vitro Techniques Mice Microcirculation Models, Biological Monte Carlo Method Neoplasm Invasiveness Neoplasms Spheroids, Cellular The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment. © 2016 The Royal Society of Chemistry. Fil:Guerra, L.N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Soba, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Calvo, J.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Suárez, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17579694_v8_n8_p879_Lujan http://hdl.handle.net/20.500.12110/paper_17579694_v8_n8_p879_Lujan |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
animal cell animal experiment Article cell proliferation collagen degradation controlled study diffusion coefficient epithelium cell experimental neoplasm image processing in vitro study mathematical model Monte Carlo method mouse nonhuman phenotype priority journal surface property tumor cell tumor invasion tumor microenvironment tumor spheroid animal biological model biophysics brain tumor computer simulation epithelium glioma human metabolism microcirculation multicellular spheroid neoplasm pathology Animals Biophysical Phenomena Brain Neoplasms Cell Proliferation Computer Simulation Epithelium Glioma Humans Image Processing, Computer-Assisted In Vitro Techniques Mice Microcirculation Models, Biological Monte Carlo Method Neoplasm Invasiveness Neoplasms Spheroids, Cellular |
spellingShingle |
animal cell animal experiment Article cell proliferation collagen degradation controlled study diffusion coefficient epithelium cell experimental neoplasm image processing in vitro study mathematical model Monte Carlo method mouse nonhuman phenotype priority journal surface property tumor cell tumor invasion tumor microenvironment tumor spheroid animal biological model biophysics brain tumor computer simulation epithelium glioma human metabolism microcirculation multicellular spheroid neoplasm pathology Animals Biophysical Phenomena Brain Neoplasms Cell Proliferation Computer Simulation Epithelium Glioma Humans Image Processing, Computer-Assisted In Vitro Techniques Mice Microcirculation Models, Biological Monte Carlo Method Neoplasm Invasiveness Neoplasms Spheroids, Cellular Guerra, Liliana Noemí Soba, Alejandro Calvo, Juan Carlos Suárez, Cecilia Ana Mathematical modelling of microtumour infiltration based on in vitro experiments |
topic_facet |
animal cell animal experiment Article cell proliferation collagen degradation controlled study diffusion coefficient epithelium cell experimental neoplasm image processing in vitro study mathematical model Monte Carlo method mouse nonhuman phenotype priority journal surface property tumor cell tumor invasion tumor microenvironment tumor spheroid animal biological model biophysics brain tumor computer simulation epithelium glioma human metabolism microcirculation multicellular spheroid neoplasm pathology Animals Biophysical Phenomena Brain Neoplasms Cell Proliferation Computer Simulation Epithelium Glioma Humans Image Processing, Computer-Assisted In Vitro Techniques Mice Microcirculation Models, Biological Monte Carlo Method Neoplasm Invasiveness Neoplasms Spheroids, Cellular |
description |
The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment. © 2016 The Royal Society of Chemistry. |
author |
Guerra, Liliana Noemí Soba, Alejandro Calvo, Juan Carlos Suárez, Cecilia Ana |
author_facet |
Guerra, Liliana Noemí Soba, Alejandro Calvo, Juan Carlos Suárez, Cecilia Ana |
author_sort |
Guerra, Liliana Noemí |
title |
Mathematical modelling of microtumour infiltration based on in vitro experiments |
title_short |
Mathematical modelling of microtumour infiltration based on in vitro experiments |
title_full |
Mathematical modelling of microtumour infiltration based on in vitro experiments |
title_fullStr |
Mathematical modelling of microtumour infiltration based on in vitro experiments |
title_full_unstemmed |
Mathematical modelling of microtumour infiltration based on in vitro experiments |
title_sort |
mathematical modelling of microtumour infiltration based on in vitro experiments |
publishDate |
2016 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17579694_v8_n8_p879_Lujan http://hdl.handle.net/20.500.12110/paper_17579694_v8_n8_p879_Lujan |
work_keys_str_mv |
AT guerraliliananoemi mathematicalmodellingofmicrotumourinfiltrationbasedoninvitroexperiments AT sobaalejandro mathematicalmodellingofmicrotumourinfiltrationbasedoninvitroexperiments AT calvojuancarlos mathematicalmodellingofmicrotumourinfiltrationbasedoninvitroexperiments AT suarezceciliaana mathematicalmodellingofmicrotumourinfiltrationbasedoninvitroexperiments |
_version_ |
1768545712631447552 |