Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour
The concentration of glioblastomas multiforme (GBM) tumour equation is numerically solved in terms of net rates of proliferation and invasion. The GBM tumour cells concentration evolution is known as a reaction-diffusion process and the diffusion coefficients differ according to the brain’s white an...
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| Format: | Article |
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Asian Scholars Network
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/94238/ |
| _version_ | 1848861943899619328 |
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| author | Mohd, Fashareena Sulaiman, Hanifah Alias, Nor Azlina |
| author_facet | Mohd, Fashareena Sulaiman, Hanifah Alias, Nor Azlina |
| author_sort | Mohd, Fashareena |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The concentration of glioblastomas multiforme (GBM) tumour equation is numerically solved in terms of net rates of proliferation and invasion. The GBM tumour cells concentration evolution is known as a reaction-diffusion process and the diffusion coefficients differ according to the brain’s white and grey matter composition. An Integer order non-linear equation can produce significant errors as most of the method used to solve the equation require linearization, discretization and perturbation which involved more computational work. Hence, a non-linear diffusion logistic density model proposed by Özuğurlu (2015) is modified to non-linear fractional-order partial differential equation (FPDE) that described in the Caputo sense. This study presents another alternative to investigate the GBM tumour growth using the theory of fractional calculus (FC). Q-homotopy analysis transform method (q-HATM) and Laplace Adomian decomposition method (LADM) were applied to solve the proposed model. From the results obtained, the fractional order (α) has greater flexibility which allows more degree of freedom in design and analysis. Results derived are in more accurate manner. Q-HATM is more efficient as it proposes a modest way to adjust the stability and the convergence region of the solution using an auxiliary parameter (h) and asymptotic parameter (n≥1). |
| first_indexed | 2025-11-15T13:09:10Z |
| format | Article |
| id | upm-94238 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:09:10Z |
| publishDate | 2021 |
| publisher | Asian Scholars Network |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-942382023-05-09T01:51:38Z http://psasir.upm.edu.my/id/eprint/94238/ Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour Mohd, Fashareena Sulaiman, Hanifah Alias, Nor Azlina The concentration of glioblastomas multiforme (GBM) tumour equation is numerically solved in terms of net rates of proliferation and invasion. The GBM tumour cells concentration evolution is known as a reaction-diffusion process and the diffusion coefficients differ according to the brain’s white and grey matter composition. An Integer order non-linear equation can produce significant errors as most of the method used to solve the equation require linearization, discretization and perturbation which involved more computational work. Hence, a non-linear diffusion logistic density model proposed by Özuğurlu (2015) is modified to non-linear fractional-order partial differential equation (FPDE) that described in the Caputo sense. This study presents another alternative to investigate the GBM tumour growth using the theory of fractional calculus (FC). Q-homotopy analysis transform method (q-HATM) and Laplace Adomian decomposition method (LADM) were applied to solve the proposed model. From the results obtained, the fractional order (α) has greater flexibility which allows more degree of freedom in design and analysis. Results derived are in more accurate manner. Q-HATM is more efficient as it proposes a modest way to adjust the stability and the convergence region of the solution using an auxiliary parameter (h) and asymptotic parameter (n≥1). Asian Scholars Network 2021-03-01 Article PeerReviewed Mohd, Fashareena and Sulaiman, Hanifah and Alias, Nor Azlina (2021) Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour. International Journal of Advanced Research in Engineering Innovation, 3 (1). pp. 1-18. ISSN 2682-8499 https://myjms.mohe.gov.my/index.php/ijarei/article/view/12441 |
| spellingShingle | Mohd, Fashareena Sulaiman, Hanifah Alias, Nor Azlina Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour |
| title | Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour |
| title_full | Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour |
| title_fullStr | Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour |
| title_full_unstemmed | Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour |
| title_short | Modified Swanson’s equation to detect the growth of glioblastomas multiforme (GBM) tumour |
| title_sort | modified swanson’s equation to detect the growth of glioblastomas multiforme (gbm) tumour |
| url | http://psasir.upm.edu.my/id/eprint/94238/ http://psasir.upm.edu.my/id/eprint/94238/ |