German Cancer Consortium (DKTK), Heidelberg, Germany. Translational Radiation Oncology, Heidelberg Institute of Radiation Oncology (HIRO), German Cancer Research Center (DKFZ), Heidelberg, Germany. Department of Radiation Oncology, Heidelberg Ion-Beam Therapy Center (HIT), Heidelberg University Hospital, Heidelberg, Germany. National Center for Tumor Diseases (NCT), Heidelberg, Germany.
Phys Med Biol. 2017 Nov 21;62(24):9322-9340. doi: 10.1088/1361-6560/aa8989.
Parameter estimation in dynamic contrast-enhanced MRI (DCE MRI) is usually performed by non-linear least square (NLLS) fitting of a pharmacokinetic model to a measured concentration-time curve. The two-compartment exchange model (2CXM) describes the compartments 'plasma' and 'interstitial volume' and their exchange in terms of plasma flow and capillary permeability. The model function can be defined by either a system of two coupled differential equations or a closed-form analytical solution. The aim of this study was to compare these two representations in terms of accuracy, robustness and computation speed, depending on parameter combination and temporal sampling. The impact on parameter estimation errors was investigated by fitting the 2CXM to simulated concentration-time curves. Parameter combinations representing five tissue types were used, together with two arterial input functions, a measured and a theoretical population based one, to generate 4D concentration images at three different temporal resolutions. Images were fitted by NLLS techniques, where the sum of squared residuals was calculated by either numeric integration with the Runge-Kutta method or convolution. Furthermore two example cases, a prostate carcinoma and a glioblastoma multiforme patient, were analyzed in order to investigate the validity of our findings in real patient data. The convolution approach yields improved results in precision and robustness of determined parameters. Precision and stability are limited in curves with low blood flow. The model parameter v shows great instability and little reliability in all cases. Decreased temporal resolution results in significant errors for the differential equation approach in several curve types. The convolution excelled in computational speed by three orders of magnitude. Uncertainties in parameter estimation at low temporal resolution cannot be compensated by usage of the differential equations. Fitting with the convolution approach is superior in computational time, with better stability and accuracy at the same time.
动态对比增强磁共振成像（DCE MRI）中的参数估计通常通过将药代动力学模型非线性最小二乘（NLLS）拟合到测量的浓度-时间曲线来进行。两室交换模型（2CXM）根据血浆流动和毛细血管通透性来描述“血浆”和“间质体积”这两个腔室及其交换。模型函数可以通过两个耦合微分方程系统或封闭形式的解析解来定义。本研究的目的是根据参数组合和时间采样，比较这两种表示形式在准确性、稳健性和计算速度方面的差异。通过将 2CXM 拟合到模拟的浓度-时间曲线，研究了参数估计误差的影响。使用了代表五种组织类型的参数组合，以及两种动脉输入函数，一种是实测的，一种是基于群体的理论的，以在三个不同的时间分辨率下生成 4D 浓度图像。通过 NLLS 技术对图像进行拟合，其中残差平方和通过使用龙格-库塔方法进行数值积分或卷积来计算。此外，还对前列腺癌和胶质母细胞瘤多形性患者的两个示例病例进行了分析，以调查我们在真实患者数据中的发现的有效性。卷积方法在确定参数的精度和稳健性方面产生了改进的结果。在血流低的曲线中，精度和稳定性受到限制。在所有情况下，参数 v 都表现出很大的不稳定性和可靠性。时间分辨率降低会导致微分方程方法在几种曲线类型中产生显著误差。卷积在计算速度方面具有三个数量级的优势。在低时间分辨率下，参数估计的不确定性无法通过使用微分方程来补偿。卷积方法在计算时间上具有优势，同时具有更好的稳定性和准确性。
