Kargar Soudabeh, Borisch Eric A, Froemming Adam T, Kawashima Akira, Mynderse Lance A, Stinson Eric G, Trzasko Joshua D, Riederer Stephen J
Biomedical Engineering and Physiology Program, Mayo Graduate School, Rochester, MN, United States; Department of Radiology, Mayo Clinic, Rochester, MN, United States.
Department of Radiology, Mayo Clinic, Rochester, MN, United States.
Magn Reson Imaging. 2018 May;48:50-61. doi: 10.1016/j.mri.2017.12.021. Epub 2017 Dec 24.
To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer.
Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time.
The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%.
The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method.
描述一种高效的数值优化技术，该技术使用非线性最小二乘法从动态对比增强（DCE）MRI数据中估计Tofts模型和扩展Tofts模型的灌注参数，并将该技术应用于前列腺癌。
通过非线性最小二乘法将基于Tofts的两个灌注模型拟合到采集的数据来估计参数。我们应用变量投影（VP）将拟合问题从多维转换为一维线搜索，以提高计算效率和鲁棒性。在20例疑似前列腺癌患者中进行模拟和DCE-MRI研究，将基于VP的求解器与传统的Levenberg-Marquardt（LM）策略在准确性、噪声放大、收敛鲁棒性和计算时间方面进行比较。
模拟表明，VP和LM在准确性方面都表现良好，即对于两个Tofts模型，在典型信噪比（SNR）水平下，中位数与假设值紧密匹配。VP和LM表现出相似的噪声敏感性。使用患者数据的研究表明，对于标准（双参数）和扩展（三参数）Tofts模型，VP方法可靠收敛，并且与LM的结果匹配，计算时间分别减少了约3倍和2倍。虽然LM在14%的患者数据中未能收敛，但VP的收敛率达到了理想的100%。
基于VP的前列腺MRI灌注参数非线性最小二乘估计方法在准确性和对噪声的鲁棒性方面相当，同时比基于LM的方法更可靠（100%）收敛，计算速度快约3倍（TM）和2倍（ETM）。
