mcm1991B The Steiner Tree Problem 最小费用极小生成树美国数学建模 - matlab数学建模

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标题：mcm1991B The Steiner Tree Problem 最小费用极小生成树美国数学建模
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所属分类: 数学建模资源类型：文档文件大小: 8.52 KB 上传时间: 2019-08-19 21:23:09 下载次数: 981 资源积分：1分提供者: jiqiren 20190819092408203

内容：
(MCM 1990A)

Researches on brain disorders test the effects of the new medical drugs -- for example, dopamine against Parkinson's disease -- with intracerebral injections. To this end, they must estimate the size and the shape of the spatial distribution of the drug after the injection, in order to estimate accurately the region of the brain that the drug has affected.

The research data consist of the measurements of the amounts of drug in each of 50 cylindrical tissue samples (see Figure 1 and Table 1). Each cylinder has length 0.76 mm and diameter 0.66 mm. The centers of the parallel cylinders lie on a grid with mesh 1mm X 0.76mm X 1mm, so that the sylinders touch one another on their circular bases but not along their sides, as shown in the accompanying figure. The injection was made near the center of the cylinder with the highest scintillation count. Naturally, one expects that there is a drug also between the cylinders and outside the region covered by the samples.

Estimate the distribution in the region affected by the drug.

One unit represents a scintillation count, or 4.753e-13 mole of dopamine. For example, the table shows that the middle rear sylinder contails 28353 units.

Table 1. amounts of drug in each of 50 cylindrical tissue samples.

rear vertical section 164 442 1320 414 188

480 7022 14411 5158 352

2091 23027 28353 13138 681

789 21260 20921 11731 727

213 1303 3765 1715 453

front vertical section 163 324 432 243 166

712 4055 6098 1048 232

2137 15531 19742 4785 335

444 11431 14960 3182 301

294 2061 1036 258 188

药物在脑内的分布(美国竞赛1990年A题)

研究脑功能失调的人员欲测试新的药物的效果，例如治疗帕金森症往脑部注射多巴胺(Dopamine)的效果，为了精确估计药物影响到的脑部区域，他们必须估计注射后药物在脑内空间分布区域的大小和形状。

研究数据包括50个圆柱体组织样本的每个样本药物含量的测定值(如图90A-1)，每个圆柱体长0.76mm，直径0.66mm，这些互相平行的圆柱体样本的中心位于网络距为1mm×0.76mm×1mm的格点上，所以圆柱体互相向在底面上接触，侧面互不接触。注射是在最高计数的那个圆柱体的中心附近进行的。自然在圆柱体之间以及由圆柱体样本覆盖的区域外也有药物。

试估计受到药物影响的区域个药物的分布。

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