Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions
Breast cancer remains a leading cause of mortality among women worldwide. While metastatic-stage cancer has no cure, understanding the spatiotemporal dynamics of tumor-immune interactions at the pre-synthetic stage is essential for developing effective immunotherapies. Recent advances in cancer mode...
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001275 |
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| author | Kennedy Mensah Joseph Abeiku Ackora-Prah Dominic Otoo Atta Kwame Gyamfi |
| author_facet | Kennedy Mensah Joseph Abeiku Ackora-Prah Dominic Otoo Atta Kwame Gyamfi |
| author_sort | Kennedy Mensah |
| collection | DOAJ |
| description | Breast cancer remains a leading cause of mortality among women worldwide. While metastatic-stage cancer has no cure, understanding the spatiotemporal dynamics of tumor-immune interactions at the pre-synthetic stage is essential for developing effective immunotherapies. Recent advances in cancer modeling emphasize the need to incorporate both spatial and temporal dynamics for accurate simulations. This study presents a continuum model that ensures biological well-posedness. The steady state of the spatially homogeneous model exhibits stability but becomes unstable when spatial effects are incorporated. We performed a parameter sweep analysis to identify stability regions, revealing a critical threshold near η1≈0.04 where the system transitions from instability to stability. Additionally, the boundaries near α1≈0.2 and η4≈0.3 show the most significant sensitivity to stability changes. By employing an explicit finite difference scheme, our simulations demonstrate spatially heterogeneous interactions among tumor cells, NK cells, and cytokines, with NK cells being most effective near the tumor. This suggests active immune recruitment in response to cancer progression. The spatiotemporal dynamics observed in our model are consistent with findings from existing studies, and the temporal behavior aligns with established patterns of immune-tumor interactions, further validating the robustness of our approach. Further analysis shows that higher per-capita growth rates (ω) of tumor cells correlate with rapid proliferation, aligning with their direct influence on tumor growth. This study provides valuable insights into spatial and temporal mechanisms of tumor-immune interactions, offering a foundation for optimizing immunotherapy strategies. |
| format | Article |
| id | doaj-art-5452ee1ea7494e3296d6bb6fde41e36e |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-5452ee1ea7494e3296d6bb6fde41e36e2025-08-20T02:18:47ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410120010.1016/j.padiff.2025.101200Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactionsKennedy Mensah0Joseph Abeiku Ackora-Prah1Dominic Otoo2Atta Kwame Gyamfi3Department of Mathematics Kwame Nkrumah University of Science and Technology, Kumasi, 00233, Ashanti, Ghana; Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, 00233, Bono Region, Ghana; Corresponding author at: Department of Mathematics Kwame Nkrumah University of Science and Technology, Kumasi, 00233, Ashanti, Ghana.Department of Mathematics Kwame Nkrumah University of Science and Technology, Kumasi, 00233, Ashanti, GhanaDepartment of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, 00233, Bono Region, GhanaDepartment of Mathematics Kwame Nkrumah University of Science and Technology, Kumasi, 00233, Ashanti, GhanaBreast cancer remains a leading cause of mortality among women worldwide. While metastatic-stage cancer has no cure, understanding the spatiotemporal dynamics of tumor-immune interactions at the pre-synthetic stage is essential for developing effective immunotherapies. Recent advances in cancer modeling emphasize the need to incorporate both spatial and temporal dynamics for accurate simulations. This study presents a continuum model that ensures biological well-posedness. The steady state of the spatially homogeneous model exhibits stability but becomes unstable when spatial effects are incorporated. We performed a parameter sweep analysis to identify stability regions, revealing a critical threshold near η1≈0.04 where the system transitions from instability to stability. Additionally, the boundaries near α1≈0.2 and η4≈0.3 show the most significant sensitivity to stability changes. By employing an explicit finite difference scheme, our simulations demonstrate spatially heterogeneous interactions among tumor cells, NK cells, and cytokines, with NK cells being most effective near the tumor. This suggests active immune recruitment in response to cancer progression. The spatiotemporal dynamics observed in our model are consistent with findings from existing studies, and the temporal behavior aligns with established patterns of immune-tumor interactions, further validating the robustness of our approach. Further analysis shows that higher per-capita growth rates (ω) of tumor cells correlate with rapid proliferation, aligning with their direct influence on tumor growth. This study provides valuable insights into spatial and temporal mechanisms of tumor-immune interactions, offering a foundation for optimizing immunotherapy strategies.http://www.sciencedirect.com/science/article/pii/S2666818125001275Continuum modelsPerturbation systemsParameter sweep analysisDispersion relationStability analysisNumerical simulations |
| spellingShingle | Kennedy Mensah Joseph Abeiku Ackora-Prah Dominic Otoo Atta Kwame Gyamfi Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions Partial Differential Equations in Applied Mathematics Continuum models Perturbation systems Parameter sweep analysis Dispersion relation Stability analysis Numerical simulations |
| title | Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions |
| title_full | Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions |
| title_fullStr | Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions |
| title_full_unstemmed | Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions |
| title_short | Modeling the spatiotemporal dynamic heterogeneity of pre-synthetic stage breast cancer tumor-immune interactions |
| title_sort | modeling the spatiotemporal dynamic heterogeneity of pre synthetic stage breast cancer tumor immune interactions |
| topic | Continuum models Perturbation systems Parameter sweep analysis Dispersion relation Stability analysis Numerical simulations |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001275 |
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