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腫瘤成長的單相模型 = A single phase model for...

國立高雄大學應用數學系碩士班

腫瘤成長的單相模型 = A single phase model for the growth of a solid tumour

Record Type:	Language materials, printed : monographic
Paralel Title:	A single phase model for the growth of a solid tumour
Author:	李威昀,
Secondary Intellectual Responsibility:	國立高雄大學
Place of Publication:	[高雄市]
Published:	撰者;
Year of Publication:	2012[民101]
Description:	34面圖，表格 : 30公分;
Subject:	應力
Subject:	stress
Online resource:	http://handle.ncl.edu.tw/11296/ndltd/82509021983873935629
Notes:	參考書目：面28
Summary:	本論文以數學模型來描繪腫瘤細胞的成長, 並假設腫瘤的外部有正常的組織, 分別討論血管瘤與無血管瘤兩種模型. 我們藉由 linear stress-strain relation 來建構模型的組成律, 以類似熱膨脹的過程, 用較合理的方式引入細胞的成長. 為了組成律在模型中得以適用, 我們延伸考慮應力率的方程式. 無血管瘤模型的結果顯示腫瘤細胞的成長集中於邊界, 且應力在邊界為推擠的狀態, 而無血管瘤的模型描繪腫瘤的內部為推擠的力, 此與實驗的結果更加符合. In this thesis we present two mathematical models to describe the growth of a solid tumour which is assumed to be imbedded in a surrounding medium. Both avascular tumour and vascularised tumour are considered. The linear stress-strain relation is used to construct a constitutive law with a growth term derived by analogy with thermal expansion. The constitutive law is then differentiated to derive a stress-rate equation to accommodate the continuous nature of the tumour growth. The numerical results show that the growth of the avascular tumour mainly occurs near the tumour boundary where the resulting stress indicates that the tumour is under compression. For the vascularised case, the force is compressive throughout the entire tumour, a result that is consistent with experimental observations.

腫瘤成長的單相模型 = A single phase model for the growth of a solid tumour
李, 威昀

腫瘤成長的單相模型 = A single phase model for the growth of a solid tumour / 李威昀撰 - [高雄市] : 撰者, 2012[民101]. - 34面 ; 圖，表格 ; 30公分.
參考書目：面28.
應力stress

腫瘤成長的單相模型 = A single phase model for the growth of a solid tumour
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328 $a 碩士論文--國立高雄大學應用數學系碩士班
330 $a 本論文以數學模型來描繪腫瘤細胞的成長, 並假設腫瘤的外部有正常的組織, 分別討論血管瘤與無血管瘤兩種模型. 我們藉由 linear stress-strain relation 來建構模型的組成律, 以類似熱膨脹的過程, 用較合理的方式引入細胞的成長. 為了組成律在模型中得以適用, 我們延伸考慮應力率的方程式. 無血管瘤模型的結果顯示腫瘤細胞的成長集中於邊界, 且應力在邊界為推擠的狀態, 而無血管瘤的模型描繪腫瘤的內部為推擠的力, 此與實驗的結果更加符合. In this thesis we present two mathematical models to describe the growth of a solid tumour which is assumed to be imbedded in a surrounding medium. Both avascular tumour and vascularised tumour are considered. The linear stress-strain relation is used to construct a constitutive law with a growth term derived by analogy with thermal expansion. The constitutive law is then differentiated to derive a stress-rate equation to accommodate the continuous nature of the tumour growth. The numerical results show that the growth of the avascular tumour mainly occurs near the tumour boundary where the resulting stress indicates that the tumour is under compression. For the vascularised case, the force is compressive throughout the entire tumour, a result that is consistent with experimental observations.
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