Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.
It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model the effects of immersing a tumor into a nutrient bath. Similarly, this model could represent the addition of nutrient to the tissue surrounding a spherical tumor.
In this paper, we model several problems associated with the clinical observations noted above, and draw conclusions based on the obtained results.
","abstract_html":"<p>Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.</p> <p>It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model the effects of immersing a tumor into a nutrient bath. Similarly, this model could represent the addition of nutrient to the tissue surrounding a spherical tumor.</p> <p>In this paper, we model several problems associated with the clinical observations noted above, and draw conclusions based on the obtained results.</p>","abstract_has_math":false,"creators":["Bellomo, Carryn"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["John Adam","D. Glenn Lasseigne","Richard Noren","Roger Perry"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1998,"date_issued":"1998-04-01T08:00:00Z","date_published":"1998-04-01T08:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Mathematical models","Tumors","Mathematics","Oncology"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model the effects of immersing a tumor into a nutrient bath. Similarly, this model could represent the addition of nutrient to the tissue surrounding a spherical tumor.
In this paper, we model several problems associated with the clinical observations noted above, and draw conclusions based on the obtained results.
"]},{"key":"dc:title","label":"Title","values":["Mathematical Models of Tumors and Their Remote Metastases"]}]}],"canonical_facts":{"dc:contributor":["John Adam","D. Glenn Lasseigne","Richard Noren","Roger Perry"],"dc:creator":["Bellomo, Carryn"],"dc:date.available":["2019-06-05T07:00:00Z"],"dc:description.abstract":["Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.
It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model the effects of immersing a tumor into a nutrient bath. Similarly, this model could represent the addition of nutrient to the tissue surrounding a spherical tumor.
In this paper, we model several problems associated with the clinical observations noted above, and draw conclusions based on the obtained results.
"],"dc:identifier":["9780591815719","https://digitalcommons.odu.edu/mathstat_etds/8"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Mathematical models","Tumors","Mathematics","Oncology"],"dc:title":["Mathematical Models of Tumors and Their Remote Metastases"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:53Z"}