A fully coupled space–time multiscale modeling framework for predicting tumor growth

Mohammad Mamunur Rahman, Yusheng Feng, Thomas E. Yankeelov, J. Tinsley Oden

Research output: Research - peer-reviewArticle

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Abstract

Most biological systems encountered in living organisms involve highly complex heterogeneous multi-component structures that exhibit different physical, chemical, and biological behavior at different spatial and temporal scales. The development of predictive mathematical and computational models of multiscale events in such systems is a major challenge in contemporary computational biomechanics, particularly the development of models of growing tumors in humans. The aim of this study is to develop a general framework for tumor growth prediction by considering major biological events at tissue, cellular, and subcellular scales. The key to developing such multiscale models is how to bridge spatial and temporal scales that range from 10−3 to 103 mm in space and from 10−6 to 107 s in time. In this paper, a fully coupled space–time multiscale framework for modeling tumor growth is developed. The framework consists of a tissue scale model, a model of cellular activities, and a subcellular transduction signaling pathway model. The tissue, cellular, and subcellular models in this framework are solved using partial differential equations for tissue growth, agent-based model for cellular events, and ordinary differential equations for signaling transduction pathway as a network at subcellular scale. The model is calibrated using experimental observations. Moreover, this model is biologically-driven from a signaling pathway, volumetrically-consistent between cellular and tissue scale in terms of tumor volume evolution in time, and a biophysically-sound tissue model that satisfies all conservation laws. The results show that the model is capable of predicting major characteristics of tumor growth such as the morphological instability, growth patterns of different cell phenotypes, compact regions of the higher cell density at the tumor region, and the reduction of growth rate due to drug delivery. The predicted treatment outcomes show a reduction in proliferation at different rates in response to different drug dosages. Moreover, the results of several 3D applications to tumor growth and the evolution of cellular and subcellular events are presented.

LanguageEnglish (US)
Pages261-286
Number of pages26
JournalComputer Methods in Applied Mechanics and Engineering
Volume320
DOIs
StatePublished - Jun 15 2017

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tumors
Tumors
Tissue
drugs
cells
biodynamics
multiscale models
phenotype
scale models
conservation laws
organisms
partial differential equations
mathematical models
delivery
differential equations
dosage
acoustics
predictions
Drug dosage
Biomechanics

Keywords

  • Bridging scale algorithm
  • Cancer modeling
  • Continuum mixture theory
  • Network modeling
  • Signaling transduction pathway
  • Treatment outcome prediction

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

A fully coupled space–time multiscale modeling framework for predicting tumor growth. / Rahman, Mohammad Mamunur; Feng, Yusheng; Yankeelov, Thomas E.; Oden, J. Tinsley.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 320, 15.06.2017, p. 261-286.

Research output: Research - peer-reviewArticle

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