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【medical-news】数学模型预测癌症病理过程

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http://www.medicalnewstoday.com/medicalnews.php?newsid=58076

Math Model Predicts Cancer Behavior

Vito Quaranta clicks on a small black dot on his computer screen. The dot - which represents about a thousand cancer cells - begins to "grow," morphing into a mass with finger-like projections that looks like an invasive tumor.

The Vanderbilt professor of cancer biology envisions a future when computer simulations like this will be used to predict a tumor's clinical progression and formulate individualized treatment plans. For the last two years, he has headed a major effort to develop the kind of mathematical model for cancer invasion powerful enough for this purpose. The result was published as an entirely theoretical paper in the journal Cell and, if he is right, it represents a "sea change" in how biology is done.

The new approach is not so different from forecasting the weather.

"Today we can know pretty well that for the next few days we're going to expect good weather or that there's a storm on the way," Quaranta said. "That's the kind of predictive power we want to generate with our model for cancer invasion."

Quaranta and colleagues at Vanderbilt University and the University of Dundee in Scotland developed a computational model for cancer invasion and described the model in the Dec. 1 issue of Cell. The model - a series of mathematical equations that drive computer simulations of tumor growth - suggests that the microenvironment around tumor cells determines the tumor's ultimate cellular makeup and invasive potential.

The investigators have focused on the events of invasion and metastasis (movement of a tumor to distant sites), Quaranta said, because these events mark "the critical transition of a tumor that in the end will be lethal for the patient." A tumor that does not penetrate the surrounding tissue can often be surgically removed with curative success.

"When a patient comes in with a tumor, we'd like to understand for that particular tumor, what are the chances that metastasis is going to occur," Quaranta said. "Does that patient need to be treated very aggressively, or not so aggressively""

Today, a tumor's size and shape are evaluated, but they can be poor indicators of invasive potential: a very small tumor can be highly invasive. Even "molecular signatures" - profiles of molecules that suggest how tumor cells will behave - are not entirely predictive, he added.

Quaranta and colleagues opted for a new approach - using the tools of mathematics to tackle the complex problem of cancer behavior.

"We have mathematics driving experimentation," Quaranta said. The team will tailor its biological experiments to test and validate the model. If the experimental data don't fit the predictions from the model, either the experiments or the model need to be corrected, he said.

"You go back and forth, and every time you get a new result, you correct the model, and you're a little bit closer to reality," Quaranta said. "This is a paradigm that is new to experimental biology."

"What is happening in biology is similar to trends seen in recent decades in the physical sciences," Cummings said. "Computational models like this, in which complex behavior emerges from computer simulations grounded in understanding phenomena at a smaller scale, have been a staple of chemistry, physics, and related engineering disciplines for a long time."

Quaranta and Cummings expect to see this new way of thinking sweep through biology.

"Particularly in cancer biology, we know so much about tumors, but we can do so little: why is that"" Quaranta said. "I think the reason is that we need additional tools, and those are the tools of mathematics."

The team's model is an initial effort. It is sophisticated enough to begin capturing tumor behavior, without being so complicated that computing power and running time for simulations become limiting. The current model simulates about four months of tumor growth in about eight hours, he said.

"The beauty of our model is that it really represents the cancer cells very well," Quaranta said. "Sandy (Anderson) was able to capture the random behavior of cells."

In the model, when cells divide they randomly choose from a set of 100 different "phenotypes" - behaviors that result from distinct genetic characteristics. For example, a cell might choose characteristics that allow it to divide more quickly or to detach from its neighbors. The investigators set the environmental conditions: these include the oxygen and nutrient concentrations and the landscape of connective tissue that surrounds the cells. They were surprised to find that the microenvironment around the tumor determines both the tumor's shape and its composition.

"What we get is a picture of cells that are evolving and growing within a microenvironment," Quaranta said. "The nice thing about computer simulations is you can create 'what if' scenarios: what if we make the oxygen very high, what if we turn oxygen off in the middle of tumor growth, what if we change the landscape of connective tissue"

"By doing this we discovered new things that we didn't know before. And that is the hallmark of a good mathematical model: it's not just a repository of data that is put together; it actually tells you which variables are the important ones and gives outcomes that you wouldn't have otherwise predicted."

The current model predicts that in mild environmental conditions - imagine a lush rainforest, Quaranta said - many cell types co-exist and the tumor shape is round with smooth edges, characteristic of a non-invasive tumor. Under harsh environmental conditions - imagine a desert - the most aggressive cell types dominate and the tumor shape has fingering, invasive projections.

By changing a single condition - oxygen concentration - the investigators can modulate the tumor's degree of invasiveness, Quaranta said.

The findings suggest that current chemotherapy approaches which create a harsh microenvironment in the tumor may leave behind the most aggressive and invasive tumor cells.

"In the immediate term we may be diminishing tumor burden, but the long term effect is to have a much nastier tumor than there was to begin with," Quaranta said. There is anecdotal evidence, he added, to support the idea that changes to the microenvironment result in a tumor with more or less invasive potential. Such manipulations of the microenvironment could offer new directions for cancer treatment, he said.

Next up for the group are in vitro and in vivo experiments designed to test, validate and refine the mathematical model.

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Math Model Predicts Cancer Behavior
数学模型预示癌症行为

Vito Quaranta clicks on a small black dot on his computer screen. The dot - which represents about a thousand cancer cells - begins to "grow," morphing into a mass with finger-like projections that looks like an invasive tumor.
Vito Quaranta点击他的计算机屏幕上的一个小黑点，这个黑点—象征着无数的癌细胞，开始“生长”，形成指状放散的团块，看起来像侵袭性的肿瘤。
The Vanderbilt professor of cancer biology envisions a future when computer simulations like this will be used to predict a tumor's clinical progression and formulate individualized treatment plans. For the last two years, he has headed a major effort to develop the kind of mathematical model for cancer invasion powerful enough for this purpose. The result was published as an entirely theoretical paper in the journal Cell and, if he is right, it represents a "sea change" in how biology is done.
肿瘤生物学的Vanderbilt教授预想了像这样的计算机模拟将被用来预测某种肿瘤的临床发展和阐明个体化的治疗计划的前景。近2年，为此目的他牵头完成一项主要成果，有力地发展了癌症侵袭的数学模型。
The new approach is not so different from forecasting the weather.
这项新技术与天气预报并没有太大的不同。
"Today we can know pretty well that for the next few days we're going to expect good weather or that there's a storm on the way," Quaranta said. "That's the kind of predictive power we want to generate with our model for cancer invasion."
“今天我们几乎能够知道我们期待的未来几天里是好天气或者暴风雪正在途中，” Quaranta说。“这就是我们想要通过我们的癌症侵袭模型产生的那种预言性的力量。”
Quaranta and colleagues at Vanderbilt University and the University of Dundee in Scotland developed a computational model for cancer invasion and described the model in the Dec. 1 issue of Cell. The model - a series of mathematical equations that drive computer simulations of tumor growth - suggests that the microenvironment around tumor cells determines the tumor's ultimate cellular makeup and invasive potential.
Quaranta和Vanderbilt大学、苏格兰敦提大学的同事们发展了癌症侵袭性的计算模型并在12月1日的细胞杂志中描述了该模型。模型—一连串的数学方程式驱动着癌症生长的计算机模拟—提示癌细胞周围的微环境决定肿瘤最终的细胞结构和侵袭潜能。
The investigators have focused on the events of invasion and metastasis (movement of a tumor to distant sites), Quaranta said, because these events mark "the critical transition of a tumor that in the end will be lethal for the patient." A tumor that does not penetrate the surrounding tissue can often be surgically removed with curative success.
研究人员已经集中于浸润和转移（肿瘤向远处位置的移动）事件，Quaranta说，因为这些事件标志着“肿瘤的临界转变对患者来说最终是致命的。”一个没有弥漫到周围组织的肿瘤在成功的医疗方面通常能够外科式的移除。
"When a patient comes in with a tumor, we'd like to understand for that particular tumor, what are the chances that metastasis is going to occur," Quaranta said. "Does that patient need to be treated very aggressively, or not so aggressively""
“当一个患者发生了肿瘤，我们愿意了解详细的肿瘤信息，即将发生的转移可能是什么，” Quaranta说，“确定患者需要损伤性的治疗或者不那么破坏。”
Today, a tumor's size and shape are evaluated, but they can be poor indicators of invasive potential: a very small tumor can be highly invasive. Even "molecular signatures" - profiles of molecules that suggest how tumor cells will behave - are not entirely predictive, he added.
今天，肿瘤的大小和形态被评价，但是他们对侵袭潜能的指示是贫乏的：一个小肿瘤也能具有高度侵袭性。甚至“分子信号”—分子的外形预示肿瘤细胞如何运转—也不能完全的预示，他补充说。
Quaranta and colleagues opted for a new approach - using the tools of mathematics to tackle the complex problem of cancer behavior.
Quarant和同事们选择了一些新方法—利用数学工具处理癌症行为复杂的难题。
"We have mathematics driving experimentation," Quaranta said. The team will tailor its biological experiments to test and validate the model. If the experimental data don't fit the predictions from the model, either the experiments or the model need to be corrected, he said.
“我们有数学演算实验室，” Quarant说。实验室欲开展生物学试验以测试和验证这个模型。如果试验数据与模型预测不能适应，那么试验或者模型就需要修正，他说。
"You go back and forth, and every time you get a new result, you correct the model, and you're a little bit closer to reality," Quaranta said. "This is a paradigm that is new to experimental biology."
“你反复的进行，每次得到一些结果，修正模型，你就会离真实更进一步，” Quarant说“这是一个范例，对于实验生物学来说是崭新的。”
"What is happening in biology is similar to trends seen in recent decades in the physical sciences," Cummings said. "Computational models like this, in which complex behavior emerges from computer simulations grounded in understanding phenomena at a smaller scale, have been a staple of chemistry, physics, and related engineering disciplines for a long time."
“生物学发生的近似自然科学领域近十年所看到的趋势，” Cummings说。“很长一段时间像这样的计算模型，以较小范围内的数值来理解现象的计算机模拟为基础而出现复杂的行为，为化学、物理学和相关工程学的来源。”
Quaranta and Cummings expect to see this new way of thinking sweep through biology.
Quaranta和Cummings期望理解这种扫遍生物学的思维新路子。
"Particularly in cancer biology, we know so much about tumors, but we can do so little: why is that"" Quaranta said. "I think the reason is that we need additional tools, and those are the tools of mathematics."
“在独特的癌症生物学领域，关于肿瘤我们知道的就只有那么多，但是我们能做的还有：为什么是那样，” Quaranta说。“我考虑原因是我们还需要额外的工具，那些就是数学的工具。”
The team's model is an initial effort. It is sophisticated enough to begin capturing tumor behavior, without being so complicated that computing power and running time for simulations become limiting. The current model simulates about four months of tumor growth in about eight hours, he said.
团队的模型是最初的结果。除了复杂难解的模拟计算能力和运行时间变成受限以外，对于开始捕获肿瘤的行为它是足够考验的。他说。
"The beauty of our model is that it really represents the cancer cells very well," Quaranta said. "Sandy (Anderson) was able to capture the random behavior of cells."
“我们模型的美丽前景在于它非常真实的描绘了癌细胞。” Quaranta说。“Sandy (Anderson)能够捕获细胞的随机行为。”
In the model, when cells divide they randomly choose from a set of 100 different "phenotypes" - behaviors that result from distinct genetic characteristics. For example, a cell might choose characteristics that allow it to divide more quickly or to detach from its neighbors. The investigators set the environmental conditions: these include the oxygen and nutrient concentrations and the landscape of connective tissue that surrounds the cells. They were surprised to find that the microenvironment around the tumor determines both the tumor's shape and its composition.
在这个模型中，当细胞分裂时，他们随机选择一套100个不同的“显型”—由清晰的遗传特征产生的行为。例如，细胞可以选择特征，允许它更快的分裂或者从邻近细胞分离。调查人员设定了环境条件：包括氧和营养浓度，以及包绕细胞的结缔组织构造。他们惊奇的发现肿瘤周围的微环境决定了肿瘤的形态和肿瘤合成物。
"What we get is a picture of cells that are evolving and growing within a microenvironment," Quaranta said. "The nice thing about computer simulations is you can create 'what if' scenarios: what if we make the oxygen very high, what if we turn oxygen off in the middle of tumor growth, what if we change the landscape of connective tissue"
“我们得到的是一张在微环境中展开生长的细胞的图片，” Quaranta说，“计算机模型带来的美好事情就是你能够创造‘什么，如果’场景：如果我们给予高浓度的氧会怎样，如果我们在肿瘤生长中中止氧的供应会怎样，如果我们改变结缔组织的构造会怎样。”
"By doing this we discovered new things that we didn't know before. And that is the hallmark of a good mathematical model: it's not just a repository of data that is put together; it actually tells you which variables are the important ones and gives outcomes that you wouldn't have otherwise predicted."
“这样做我们会发现以前不知道的新事物。并且这就是好的数学模型的特点：它不仅仅是整理在一起的数据的仓库，事实上它告诉你们哪个变量是重要的一方并且在没有其他预示的情况下给你结果。”
The current model predicts that in mild environmental conditions - imagine a lush rainforest, Quaranta said - many cell types co-exist and the tumor shape is round with smooth edges, characteristic of a non-invasive tumor. Under harsh environmental conditions - imagine a desert - the most aggressive cell types dominate and the tumor shape has fingering, invasive projections.
当前的模型预言, 在适合的环境条件- 想象一片茂盛的雨林，Quaranta说—许多细胞类型共存并且肿瘤形状是圆润的并有光滑的边缘, 典型的一个非侵入性的肿瘤。在苛刻荒芜的环境条件下—想象一片沙漠—最具侵袭力的细胞类型占据优势并且肿瘤形态呈指状, 蔓延性放散。
By changing a single condition - oxygen concentration - the investigators can modulate the tumor's degree of invasiveness, Quaranta said.
通过改变一个单一条件—氧浓度—调查人员能调整肿瘤的侵袭程度，Quaranta说。
The findings suggest that current chemotherapy approaches which create a harsh microenvironment in the tumor may leave behind the most aggressive and invasive tumor cells.
研究结果暗示, 给肿瘤创造一个苛刻微环境的当前的化疗方法也许会遗留最具侵略性和蔓延性的肿瘤细胞。
"In the immediate term we may be diminishing tumor burden, but the long term effect is to have a much nastier tumor than there was to begin with," Quaranta said. There is anecdotal evidence, he added, to support the idea that changes to the microenvironment result in a tumor with more or less invasive potential. Such manipulations of the microenvironment could offer new directions for cancer treatment, he said.
“短期内我们也许减少肿瘤负担，但长期影响则是有比开始更具威胁的肿瘤”Quaranta 认为。他补充说，有尚不可靠的证据支持在一个肿瘤中改变微环境的结果可以导致更高或较小的侵袭潜力的想法。微环境的这种操作能为癌症治疗提供新方向，他说。
Next up for the group are in vitro and in vivo experiments designed to test, validate and refine the mathematical model.
小组接着要做的就是有计划的进行测试体外和体内实验, 验证和提精炼此数学模型。

2006-12-14 20:17

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数学模型预示癌症行为

Vito Quaranta点击他的计算机屏幕上的一个小黑点，这个黑点—象征着无数的癌细胞，开始“生长”，形成指状放散的团块，看起来像侵袭性的肿瘤。

肿瘤生物学的Vanderbilt教授预想了像这样的计算机模拟将被用来预测某种肿瘤的临床发展和阐明个体化的治疗计划的前景。近2年，为此目的他牵头完成一项主要成果，有力地发展了癌症侵袭的数学模型。

这项新技术与天气预报并没有太大的不同。

“今天我们几乎能够知道我们期待的未来几天里是好天气或者暴风雪正在途中，” Quaranta说。“这就是我们想要通过我们的癌症侵袭模型产生的那种预言性的力量。”

Quaranta和Vanderbilt大学、苏格兰敦提大学的同事们发展了癌症侵袭性的计算模型并在12月1日的细胞杂志中描述了该模型。模型—一连串的数学方程式驱动着癌症生长的计算机模拟—提示癌细胞周围的微环境决定肿瘤最终的细胞结构和侵袭潜能。

研究人员已经集中于浸润和转移（肿瘤向远处位置的移动）事件，Quaranta说，因为这些事件标志着“肿瘤的临界转变对患者来说最终是致命的。”一个没有弥漫到周围组织的肿瘤在成功的医疗方面通常能够外科式的移除。

“当一个患者发生了肿瘤，我们愿意了解详细的肿瘤信息，即将发生的转移可能是什么，” Quaranta说，“确定患者需要损伤性的治疗或者不那么破坏。”
今天，肿瘤的大小和形态被评价，但是他们对侵袭潜能的指示是贫乏的：一个小肿瘤也能具有高度侵袭性。甚至“分子信号”—分子的外形预示肿瘤细胞如何运转—也不能完全的预示，他补充说。

Quarant和同事们选择了一些新方法—利用数学工具处理癌症行为复杂的难题。

“我们有数学演算实验室，” Quarant说。实验室欲开展生物学试验以测试和验证这个模型。如果试验数据与模型预测不能适应，那么试验或者模型就需要修正，他说。

“你反复的进行，每次得到一些结果，修正模型，你就会离真实更进一步，” Quarant说“这是一个范例，对于实验生物学来说是崭新的。”

“生物学发生的近似自然科学领域近十年所看到的趋势，” Cummings说。“很长一段时间像这样的计算模型，以较小范围内的数值来理解现象的计算机模拟为基础而出现复杂的行为，为化学、物理学和相关工程学的来源。”

Quaranta和Cummings期望理解这种扫遍生物学的思维新路子。

“在独特的癌症生物学领域，关于肿瘤我们知道的就只有那么多，但是我们能做的还有：为什么是那样，” Quaranta说。“我考虑原因是我们还需要额外的工具，那些就是数学的工具。”

团队的模型是最初的结果。除了复杂难解的模拟计算能力和运行时间变成受限以外，对于开始捕获肿瘤的行为它是足够考验的。他说。

“我们模型的美丽前景在于它非常真实的描绘了癌细胞。” Quaranta说。“Sandy (Anderson)能够捕获细胞的随机行为。”

在这个模型中，当细胞分裂时，他们随机选择一套100个不同的“显型”—由清晰的遗传特征产生的行为。例如，细胞可以选择特征，允许它更快的分裂或者从邻近细胞分离。调查人员设定了环境条件：包括氧和营养浓度，以及包绕细胞的结缔组织构造。他们惊奇的发现肿瘤周围的微环境决定了肿瘤的形态和肿瘤合成物。

“我们得到的是一张在微环境中展开生长的细胞的图片，” Quaranta说，“计算机模型带来的美好事情就是你能够创造‘什么，如果’场景：如果我们给予高浓度的氧会怎样，如果我们在肿瘤生长中中止氧的供应会怎样，如果我们改变结缔组织的构造会怎样。”

“这样做我们会发现以前不知道的新事物。并且这就是好的数学模型的特点：它不仅仅是整理在一起的数据的仓库，事实上它告诉你们哪个变量是重要的一方并且在没有其他预示的情况下给你结果。”

当前的模型预言, 在适合的环境条件- 想象一片茂盛的雨林，Quaranta说—许多细胞类型共存并且肿瘤形状是圆润的并有光滑的边缘, 典型的一个非侵入性的肿瘤。在苛刻荒芜的环境条件下—想象一片沙漠—最具侵袭力的细胞类型占据优势并且肿瘤形态呈指状, 蔓延性放散。

通过改变一个单一条件—氧浓度—调查人员能调整肿瘤的侵袭程度，Quaranta说。

研究结果暗示, 给肿瘤创造一个苛刻微环境的当前的化疗方法也许会遗留最具侵略性和蔓延性的肿瘤细胞。

“短期内我们也许减少肿瘤负担，但长期影响则是有比开始更具威胁的肿瘤”Quaranta 认为。他补充说，有尚不可靠的证据支持在一个肿瘤中改变微环境的结果可以导致更高或较小的侵袭潜力的想法。微环境的这种操作能为癌症治疗提供新方向，他说。

小组接着要做的就是有计划的进行测试体外和体内实验, 验证和提精炼此数学模型。

2006-12-14 20:21

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