[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-333202-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-333202-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","dynamics-of-a-diffusive-model-for-cancer-stem-cells-with-time-delay-in-microrna-differentiated-cancer-cell-interactions-and-radiotherapy-effects","Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects","","Understand the dynamics of cancer stem cells (CSCs) and the mechanisms behind recurrence requires integrating cell diffusion, the plasticity of differentiated cancer cells (DCs), and regulatory signaling. This study builds an analytical and numerical dynamical model that includes delayed microRNA interactions with DCs under radiotherapy effects. Stability is analyzed via Hopf bifurcation to identify a critical time delay for DC-to-CSC transformation. Parameterized simulations for prostate, lung, and breast cancers show spatiotemporal circular patterns and quantify radiation dose to reduce local recurrence.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/dynamics-of-a-diffusive-model-for-cancer-stem-cells-with-time-delay-in-microrna-differentiated-cancer-cell-interactions-and-radiotherapy-effects/333202/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/dynamics-of-a-diffusive-model-for-cancer-stem-cells-with-time-delay-in-microrna-differentiated-cancer-cell-interactions-and-radiotherapy-effects/333202.png","ImageObject",300,407,{"name":42,"@type":43},"Anda","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-06","2026-09-21",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What processes are included in the diffusive dynamical model?","Question",{"text":63,"@type":64},"The model includes diffusion of cells, a de-differentiation (plasticity) mechanism converting differentiated cancer cells into CSCs, and a time delay in the interaction between microRNAs and DCs.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is stability of the model studied?",{"text":68,"@type":64},"Stability is investigated using a Hopf bifurcation analysis, which is used to determine behavior changes as the parameters and time delay vary.",{"name":70,"@type":61,"acceptedAnswer":71},"What do the numerical simulations show under radiotherapy?",{"text":72,"@type":64},"Numerical simulations predict spatiotemporal circular patterns and identify scenarios where radiotherapy applied early can lead to complete eradication of these patterns, with microRNAs acting as suppressors in the prostate model.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},333202,1790291788,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":97,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145,"preview_page_count":4},962075006959,"https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297","[www. nature.com/scientificreports](www. nature.com/scientificreports)  \nOPEN  \nDynamics of a diffusive model for cancer stem cells with time delay in microRNA‑differentiated cancer cell interactions and radiotherapy effects  \nFrank Eric Essongo1, Alain Mvogo2* & Germain Hubert Ben‑Bolie1  \nUnderstand the dynamics of cancer stem cells (CSCs), prevent the non‑recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de‑differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay , that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time 􀀞􀀞. This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non‑recurrence of cancers.  \nKeywords Cancer cells, Cancer stem cells, MicroRNAs, Hopf bifurcation, Time delay, Circular patterns, Radiotherapy  \nCancer cells result of abnormal growth and uncontrolled division of normal cells1. Cancers grow from stem cells in the way that healthy organs do. The discovery of the existence of cancer stem cells (CSCs) in cancers has led to an understanding the mechanisms of cancer proliferation and development. The CSCs have been identified and isolated in many so-called solid tumors such as breast cancer, pancreatic cancer, glioblastoma (a type of brain cancer) and colon adenocarcinoma2. Recent reports, primarily for haematopoietic malignancies, have suggested that CSCs can be selectively targeted without ablating normal stem cell function. The CSCs can be more resistant to chemotherapy and radiotherapy3. Sometimes, after cancer treatment, the cancer comes back or recurs, this is called a cancer recurrence. The CSCs are a minor population of tumor cells that possess the stem cell property of self-renewal. Dysregulation of stem cell self-renewal is likely requirement for the development of cancer4. The CSCs are biologically unique cells within a tumor, possessing self renewal capacity and produce progeny with self proliferative capacity, similar to normal stem cells5. All these properties have led many researchers to believe that CSCs are responsible for the recurrence and spread of glioblastoma and other cancers, since they give rise to multiple other cancer cells and produce new tumors6.  \n1Laboratory of Nuclear Physics, Dosimetry and Radiation Protection, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon. 2Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812 Yaounde, Cameroon.*[email: mvogal_2009@yahoo.fr](email: mvogal_2009@yahoo.fr)  \n[www. nature.com/scientificreports/](www. nature.c","cbCaiuPDGim4nKHF","https://ap.wps.com/l/cbCaiuPDGim4nKHF","pdf",3041950,17,"English","# Model formulation and biological motivation\n## CSCs, recurrence, and microRNA regulation\n## Diffusion, de-differentiation, and delayed microRNA interactions\n# Mathematical analysis\n## Hopf bifurcation and stability of the system\n# Numerical simulations and radiotherapy outcomes\n## Spatiotemporal circular pattern formation\n## Optimal radiation dose and recurrence avoidance","[{\"question\":\"What processes are included in the diffusive dynamical model?\",\"answer\":\"The model includes diffusion of cells, a de-differentiation (plasticity) mechanism converting differentiated cancer cells into CSCs, and a time delay in the interaction between microRNAs and DCs.\"},{\"question\":\"How is stability of the model studied?\",\"answer\":\"Stability is investigated using a Hopf bifurcation analysis, which is used to determine behavior changes as the parameters and time delay vary.\"},{\"question\":\"What do the numerical simulations show under radiotherapy?\",\"answer\":\"Numerical simulations predict spatiotemporal circular patterns and identify scenarios where radiotherapy applied early can lead to complete eradication of these patterns, with microRNAs acting as suppressors in the prostate model.\"}]","Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects | PDF",1790001400,43]