Department of Medical Physics, University of Wisconsin-Madison, 1111 Highland Avenue, Madison, WI, 53705, USA.
Department of Radiology, University of Wisconsin-Madison, 600 Highland Avenue, Madison, WI, 53792, USA.
Med Phys. 2019 Nov;46(11):4881-4897. doi: 10.1002/mp.13805. Epub 2019 Sep 23.
The purpose of this work was to develop a theoretical framework to pinpoint the quantitative relationship between input parameters of deconvolution-based cerebral computed tomography perfusion (CTP) imaging systems and statistical properties of the output perfusion maps.
Deconvolution-based CTP systems assume that the arterial input function, tissue enhancement curve, and flow-scaled residue function k(t) are related to each other through a convolution model, and thus by reversing the convolution operation, k(t) and the associated perfusion parameters can be estimated. The theoretical analysis started by deriving analytical formulas for the expected value and autocovariance of the residue function estimated using the singular value decomposition-based deconvolution method. Next, it analyzed statistical properties of the "max" and "arg max" operators, based on which the signal and noise properties of cerebral blood flow (CBF) and time-to-max ( ) are quantitatively related to the statistical model of the estimated residue function [ ] and system parameters. To validate the theory, CTP images of a digital head phantom were simulated, from which signal and noise of each perfusion parameter were measured and compared with values calculated using the theoretical model. In addition, an in vivo canine experiment was performed to validate the noise model of cerebral blood volume (CBV).
For the numerical study, the relative root mean squared error between the measured and theoretically calculated value is ≤0.21% for the autocovariance matrix of , and is ≤0.13% for the expected form of . A Bland-Altman analysis demonstrated no significant difference between measured and theoretical values for the mean or noise of each perfusion parameter. For the animal study, the theoretical CBV noise fell within the 25th and 75th percentiles of the experimental values. To provide an example of the theory's utility, an expansion of the CBV noise formula was performed to unveil the dominant role of the baseline image noise in deconvolution-based CBV. Correspondingly, data of the three canine subjects used in the Part I paper were retrospectively processed to confirm that preferentially partitioning dose to the baseline frames benefits both nondeconvolution- and deconvolution-based CBV maps.
Quantitative relationships between the statistical properties of deconvolution-based CTP maps, source image acquisition and reconstruction parameters, contrast injection protocol, and deconvolution parameters are established.
本研究旨在建立一个理论框架，以确定基于去卷积的脑计算机断层灌注（CTP）成像系统的输入参数与输出灌注图的统计特性之间的定量关系。
基于去卷积的 CTP 系统假设动脉输入函数、组织增强曲线和流量标度残差函数 k(t) 之间存在卷积模型的关系，因此通过反转卷积运算，可以估计 k(t) 和相关的灌注参数。理论分析首先从基于奇异值分解的去卷积方法估计的残差函数的期望值和自协方差的解析公式开始。接下来，分析了“max”和“arg max”运算符的统计特性，在此基础上，脑血流量（CBF）和达峰时间（ ）的信号和噪声特性与估计的残差函数的统计模型[ ]和系统参数定量相关。为了验证理论，对数字头颅体模的 CTP 图像进行了模拟，从中测量了每个灌注参数的信号和噪声，并与使用理论模型计算的值进行了比较。此外，还进行了犬体内实验以验证脑血容量（CBV）的噪声模型。
在数值研究中，对于 的自协方差矩阵，测量值与理论计算值的相对均方根误差≤0.21%，对于 的期望形式，相对均方根误差≤0.13%。Bland-Altman 分析表明，对于每个灌注参数的均值或噪声，测量值与理论值之间无显著差异。对于动物研究，理论上的 CBV 噪声落在实验值的 25%和 75%百分位数范围内。为了说明该理论的实用性，对 CBV 噪声公式进行了扩展，揭示了基线图像噪声在基于去卷积的 CBV 中的主导作用。相应地，对第一部分论文中使用的三只犬科动物的数据进行了回顾性处理，以证实优先将剂量分配给基线帧有利于非去卷积和基于去卷积的 CBV 图。
建立了基于去卷积的 CTP 图的统计特性、源图像采集和重建参数、对比剂注射方案以及去卷积参数之间的定量关系。
