Division of Medical Physics, University of Leeds, Leeds, United Kingdom.
Magn Reson Med. 2011 Sep;66(3):735-45. doi: 10.1002/mrm.22861. Epub 2011 Mar 7.
The Tofts model (TM) and extended Tofts model (ETM) have become a standard for the analysis of dynamic contrast-enhanced MRI. In this study, a mathematical analysis is used to identify exactly in which tissue types the Tofts models may be applied. The results show that the TM is accurate if and only if the tissue is weakly vascularised (small blood volume). The ETM is additionally accurate in highly perfused tissues (high blood flow). In tissues that are highly vascularised, or where tracer exchange is very fast or very slow, TM and ETM accurately fit the data but lead to a misinterpretation of the parameters. In tissue types with intermediate vascularity, perfusion and tracer exchange, neither model offers a good fit to the tissue concentrations. A good fit can be obtained with a measured input function by reducing the temporal resolution, but this does not improve the accuracy of the parameters. In conclusion, the Tofts models only produce reliable parameter values if the tissue is weakly vascularized (TM or ETM) or highly perfused (ETM). Without prior knowledge that at least one of these constraints is fulfilled, the physiological interpretation of the values produced by the Tofts models is unclear.
Tofts 模型（TM）和扩展 Tofts 模型（ETM）已成为分析动态对比增强 MRI 的标准方法。在这项研究中，我们使用数学分析来确定 Tofts 模型可以应用于哪些组织类型。结果表明，只有当组织为弱血管化（小血容量）时，TM 才是准确的。ETM 另外在高灌注组织（高血流）中是准确的。在高血管化的组织中，或者示踪剂交换非常快或非常慢的情况下，TM 和 ETM 可以准确拟合数据，但会导致参数的错误解释。在具有中等血管化、灌注和示踪剂交换的组织类型中，两种模型都不能很好地拟合组织浓度。通过降低时间分辨率，可以用测量的输入函数获得良好的拟合，但这并不能提高参数的准确性。总之，如果组织为弱血管化（TM 或 ETM）或高灌注（ETM），Tofts 模型才能产生可靠的参数值。如果没有事先知道至少满足其中一个约束条件，那么由 Tofts 模型产生的参数值的生理解释就不清楚。
