A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup

Paul M. Darbyshire

doi:doi:10.11648/j.cbb.20150305.11

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A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup

Paul M. Darbyshire

Published in Computational Biology and Bioinformatics (Volume 3, Issue 5)

Received: 3 August 2015 Accepted: 13 August 2015 Published: 26 August 2015

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Abstract

The challenging issues of cancer prevention and cure lie in the need for a more detailed knowledge of the internal processes and mechanisms of tumour growth. We present a mathematical model of avascular tumour growth formulated in a system of coupled nonlinear PDEs. The interaction between the surrounding tissue and cell motility of the developing tumour are also included to more realistic replicate an in-vivo environment. The mathematical model is solved using finite difference methods and implemented in the C programming language. The CUDA programming framework is then introduced to allow a parallelisation of the sequential C implementation. Results show a dramatic Speedup of around 26x that of conventional implementations in C. Such increased computational efficiency clearly highlights the possibility of improvements in the numerical simulation of more complex mathematical models of 2D and 3D tumour growth, such as angiogenesis and vascularisation. Parallelisation of such models can greatly facilitate researchers, clinicians and oncologists by performing time-saving in-silico experiments that have the potential to highlight new cancer treatments and therapies without the need for the use of valuable resources associated with excessive pre-clinical trials.

Published in	Computational Biology and Bioinformatics (Volume 3, Issue 5)
DOI	10.11648/j.cbb.20150305.11
Page(s)	65-73
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Avascular Tumour Growth, Multicellular Spheroids (MCS), Parallel Programming, Compute Unified Device Architecture (CUDA), Graphical Processing Unit (GPU)

References

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[2]	Sutherland, R.M. and Durand, R. E. Growth and cellular characteristics of multicell spheroids. Recent Results in Cancer Research 95, 24-49. 1984.
[3]	Sutherland, R. M., Sordat, B., Bamat, J., Gabbert, H., Bourrat, B., Mueller-Klieser,W. Oxygenation and differentiation in multicellular spheroids of human colon carcinoma. Cancer Research, Vol. 46, 5320–5329. 1986.
[4]	Sutherland, R. M. Cell and environment interaction in tumour microregions: the multicell spheroid model. Science, Vol. 240, 177-184. 1988.
[5]	Freyer, J. P. and Schor, P. L. Regrowth of cells from multicell tumour spheroids. Cell and Tissue Kinetics, 20, 249. 1987.
[6]	Orme, M. and Chaplain M.A.J. A mathematical model of vascular tumor growth and invasion. Mathematical and Computational Modelling, 23. 1996.
[7]	Sherratt, J. A. Wave front propagation in a competition equation with a new motility term modelling contact inhibition between cell populations. Proceedings of the Royal Society of London, A456, 2365–2386. 2000.
[8]	Sherratt, J. A and Chaplain M.A.J. A new mathematical model for avascular tumour growth. Journal of Mathematical Biology, Vol. 43, pp291–312. 2001.
[9]	Huttenlocher, A., Lakonishok, M., Kinder, M., Wu, S., Truong, T., Knudsen, K. A. and Horwitz, A. F. Integrin and cadherin synergy regulates contact inhibition of migration and motile activity. Journal of Cell Biology 141, 515-526. 1998.
[10]	McElwain, D. L. S. and Pettet, G. J. Cell migration in multicell spheroids: swimming against the tide. Bulletin of Mathematical Biology, 55, 655–674. 1993.
[11]	Nvidia Corporation. CUDA C programming guide. Version 6.0. 2014.
[12]	Amdahl, G. M. Validity of the Single Processor Approach to Achieving Large-Scale Computing Capabilities. AFIPS Conference Proceedings (30): 483–485. 1967.

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APA Style

Paul M. Darbyshire. (2015). A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Computational Biology and Bioinformatics, 3(5), 65-73. https://doi.org/10.11648/j.cbb.20150305.11

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ACS Style

Paul M. Darbyshire. A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Comput. Biol. Bioinform. 2015, 3(5), 65-73. doi: 10.11648/j.cbb.20150305.11

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AMA Style

Paul M. Darbyshire. A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Comput Biol Bioinform. 2015;3(5):65-73. doi: 10.11648/j.cbb.20150305.11

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@article{10.11648/j.cbb.20150305.11,
  author = {Paul M. Darbyshire},
  title = {A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup},
  journal = {Computational Biology and Bioinformatics},
  volume = {3},
  number = {5},
  pages = {65-73},
  doi = {10.11648/j.cbb.20150305.11},
  url = {https://doi.org/10.11648/j.cbb.20150305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20150305.11},
  abstract = {The challenging issues of cancer prevention and cure lie in the need for a more detailed knowledge of the internal processes and mechanisms of tumour growth. We present a mathematical model of avascular tumour growth formulated in a system of coupled nonlinear PDEs. The interaction between the surrounding tissue and cell motility of the developing tumour are also included to more realistic replicate an in-vivo environment. The mathematical model is solved using finite difference methods and implemented in the C programming language. The CUDA programming framework is then introduced to allow a parallelisation of the sequential C implementation. Results show a dramatic Speedup of around 26x that of conventional implementations in C. Such increased computational efficiency clearly highlights the possibility of improvements in the numerical simulation of more complex mathematical models of 2D and 3D tumour growth, such as angiogenesis and vascularisation. Parallelisation of such models can greatly facilitate researchers, clinicians and oncologists by performing time-saving in-silico experiments that have the potential to highlight new cancer treatments and therapies without the need for the use of valuable resources associated with excessive pre-clinical trials.},
 year = {2015}
}

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TY  - JOUR
T1  - A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup
AU  - Paul M. Darbyshire
Y1  - 2015/08/26
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N1  - https://doi.org/10.11648/j.cbb.20150305.11
DO  - 10.11648/j.cbb.20150305.11
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JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
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PB  - Science Publishing Group
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AB  - The challenging issues of cancer prevention and cure lie in the need for a more detailed knowledge of the internal processes and mechanisms of tumour growth. We present a mathematical model of avascular tumour growth formulated in a system of coupled nonlinear PDEs. The interaction between the surrounding tissue and cell motility of the developing tumour are also included to more realistic replicate an in-vivo environment. The mathematical model is solved using finite difference methods and implemented in the C programming language. The CUDA programming framework is then introduced to allow a parallelisation of the sequential C implementation. Results show a dramatic Speedup of around 26x that of conventional implementations in C. Such increased computational efficiency clearly highlights the possibility of improvements in the numerical simulation of more complex mathematical models of 2D and 3D tumour growth, such as angiogenesis and vascularisation. Parallelisation of such models can greatly facilitate researchers, clinicians and oncologists by performing time-saving in-silico experiments that have the potential to highlight new cancer treatments and therapies without the need for the use of valuable resources associated with excessive pre-clinical trials.
VL  - 3
IS  - 5
ER  -

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Author Information

Paul M. Darbyshire

Department of Computational Biophysics, Algenet Cancer Research, Nottingham, UK

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Plain Text BibTeX RIS

APA Style

Paul M. Darbyshire. (2015). A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Computational Biology and Bioinformatics, 3(5), 65-73. https://doi.org/10.11648/j.cbb.20150305.11

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ACS Style

Paul M. Darbyshire. A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Comput. Biol. Bioinform. 2015, 3(5), 65-73. doi: 10.11648/j.cbb.20150305.11

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AMA Style

Paul M. Darbyshire. A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup. Comput Biol Bioinform. 2015;3(5):65-73. doi: 10.11648/j.cbb.20150305.11

Copy | Download

@article{10.11648/j.cbb.20150305.11,
  author = {Paul M. Darbyshire},
  title = {A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup},
  journal = {Computational Biology and Bioinformatics},
  volume = {3},
  number = {5},
  pages = {65-73},
  doi = {10.11648/j.cbb.20150305.11},
  url = {https://doi.org/10.11648/j.cbb.20150305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20150305.11},
  abstract = {The challenging issues of cancer prevention and cure lie in the need for a more detailed knowledge of the internal processes and mechanisms of tumour growth. We present a mathematical model of avascular tumour growth formulated in a system of coupled nonlinear PDEs. The interaction between the surrounding tissue and cell motility of the developing tumour are also included to more realistic replicate an in-vivo environment. The mathematical model is solved using finite difference methods and implemented in the C programming language. The CUDA programming framework is then introduced to allow a parallelisation of the sequential C implementation. Results show a dramatic Speedup of around 26x that of conventional implementations in C. Such increased computational efficiency clearly highlights the possibility of improvements in the numerical simulation of more complex mathematical models of 2D and 3D tumour growth, such as angiogenesis and vascularisation. Parallelisation of such models can greatly facilitate researchers, clinicians and oncologists by performing time-saving in-silico experiments that have the potential to highlight new cancer treatments and therapies without the need for the use of valuable resources associated with excessive pre-clinical trials.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A System of Coupled Nonlinear Partial Differential Equations Describing Avascular Tumour Growth Are Solved Numerically Using Parallel Programming to Assess Computational Speedup
AU  - Paul M. Darbyshire
Y1  - 2015/08/26
PY  - 2015
N1  - https://doi.org/10.11648/j.cbb.20150305.11
DO  - 10.11648/j.cbb.20150305.11
T2  - Computational Biology and Bioinformatics
JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
SP  - 65
EP  - 73
PB  - Science Publishing Group
SN  - 2330-8281
UR  - https://doi.org/10.11648/j.cbb.20150305.11
AB  - The challenging issues of cancer prevention and cure lie in the need for a more detailed knowledge of the internal processes and mechanisms of tumour growth. We present a mathematical model of avascular tumour growth formulated in a system of coupled nonlinear PDEs. The interaction between the surrounding tissue and cell motility of the developing tumour are also included to more realistic replicate an in-vivo environment. The mathematical model is solved using finite difference methods and implemented in the C programming language. The CUDA programming framework is then introduced to allow a parallelisation of the sequential C implementation. Results show a dramatic Speedup of around 26x that of conventional implementations in C. Such increased computational efficiency clearly highlights the possibility of improvements in the numerical simulation of more complex mathematical models of 2D and 3D tumour growth, such as angiogenesis and vascularisation. Parallelisation of such models can greatly facilitate researchers, clinicians and oncologists by performing time-saving in-silico experiments that have the potential to highlight new cancer treatments and therapies without the need for the use of valuable resources associated with excessive pre-clinical trials.
VL  - 3
IS  - 5
ER  -

Copy | Download